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TECHNICAL EFFICIENCY AND PRODUCTIVITY GROWTH OF RURAL AND COMMUNITY BANKS (RCBs) IN GHANA Thesis · November 2015 DOI: 10.13140/RG.2.2.11294.74567
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KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY, GHANA DEPARTMENT OF ECONOMICS
TECHNICAL EFFICIENCY AND PRODUCTIVITY GROWTH OF RURAL AND COMMUNITY BANKS (RCBs) IN GHANA
By OTENG-ABAYIE, Eric Fosu MA Economics, BA (Hons) Economics & Law
A THESIS SUBMITTED TO THE SCHOOL OF GRADUATE STUDIES IN FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF THE DEGREE OF DOCTOR OF PHILOSOPHY (PHD) IN ECONOMICS
NOVEMBER 2014
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DECLARATION I declare that I have personally, under supervision, undertaken the study herein submitted towards the PhD. Economics, and to the best of my knowledge, it contains no material previously published by another person or material which has been accepted for the award of any other degree of the University, except where due acknowledgement has been made in the text.
ERIC FOSU OTENG-ABAYIE (PG6959111)
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CERTIFIED BY: DR. DAVID OUATTARA (1ST SUPERVISOR)
CERTIFIED BY: DR. EMMANUEL CLEEVE (2ND SUPERVISOR)
CERTIFIED BY: DR. SR. EUGENIA AMPORFU (HEAD OF DEPARTMENT)
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ACKNOWLEDGEMENTS I am grateful to my supervisors Dr. Osman Ouattara (Manchester University, UK) and Dr. Emmanuel Cleeve (Manchester Metropolitan University, UK) for their professional approach in advising and supervising this thesis. We have become more of friends than a student and supervisors. Thanks to Professor Yaw Aboagye Debrah (Swansea, UK and the International Coordinator for VC’s PhD Initiative) and Professor I. K. Dontwi (Dean, IDL) for their fatherly advice during the research process. Many thanks also to Professor W. O. Ellis (Vice Chancellor, KNUST) for the opportunity and confidence reposed in me to be part of the Staff Phd Initiative and for his encouragement during the research. I wish to acknowledge the immense help I received from the staff of the Research Department of ARB Apex Bank in Accra and all the regional branches. I also acknowledge the assistance with data received from all the sample of 107 Rural and Community Banks (RCBs) for making their annual reports available to complete the research work. Thanks to all other persons who helped make this thesis become a reality. I can mention Prof. Arnge Hennisten (University of Copehengen, Denmark) for his note on production analysis, Dr. Nana Kwame Anokye (HERG, Brunel University, UK), Prof. J.M. Frimpong (KNUST School of Business), Maame Esi Eshun (Research Assistant, ACET), Kofi Amanor, and Dr. Daniel Sakyi. Thanks to my bestfriend Henry Kofi Mensah (Phd), for the times we shared home and away, advising and encouraging each other on our respective theses.
Finally, I am grateful to my entire family for their encouragement and for allowing me space, which enabled me to undertake this study. To God is the Glory!
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DEDICATION To my entire family!
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ABSTRACT The study sought to fill in the gaps in research concerning knowledge about the technical efficiency and productivity growth of Rural and Community Banks (RCBs) in Ghana. To be able to improve the efficiency and productivity of RCBs, there is also the need to investigate the potential factors that determine the productivity of RCBs. Several factors were identified through the review of relevant literature on efficiency and productivity in financial institutions, particularly banks. Research on productivity was found to concentrate on the formal universal banks as there were no known studies on RCBs. This thesis, thus, aimed mainly to estimate the level of technical efficiency and productivity growth of RCBs and to also estimate the determinants of productivity growth of RCBs in Ghana. We estimated the technical efficiency and productivity changes, using both parametric SFA and non-parametric DEA frontier methods. For the determinants of productivity changes, efficiency changes, and technical changes, both static and dynamic panel models (POLS, RE, FE, and GMM-System) were fitted, using available data sourced from the ARB-Apex Bank for a sample of 107 out of 137 RCBs in Ghana. The findings suggest that RCBs have room to improve on their technical efficiency and productivity levels. For the determinants of productivity growth, the study revealed that bank-specific factors and the macroeconomic factors were responsive to productivity changes, efficiency changes, and technical changes in diverse ways. On the basis of the findings, the implications are that the RCBs and the Apex Bank must use staff productivity
and
bank
technology-enhancing
measures
to
achieve
efficiency
improvements and productivity growth of RCBs in Ghana. Also, the strengthening of the research capacity of the RCBs and the Apex body concerning the impact of the macroeconomy on the industry is considered.
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TABLE OF CONTENTS DECLARATION................................................................................................................ii ACKNOWLEDGEMENTS .............................................................................................iii DEDICATION................................................................................................................... iv ABSTRACT ........................................................................................................................ v TABLE OF CONTENTS ................................................................................................. vi LIST OF TABLES ............................................................................................................. x LIST OF FIGURES .........................................................................................................xii CHAPTER ONE ................................................................................................................ 1 INTRODUCTION.............................................................................................................. 1 1.1 Background to the Study ......................................................................................... 1 1.2 Statement of Research Problem .............................................................................. 3 1.3 Research Objectives ................................................................................................. 5 1.4 Significance of the Study.......................................................................................... 5 1.5 Contribution to Knowledge ..................................................................................... 6 1.6 Scope of the study ..................................................................................................... 7 1.7 Organisation of the Study ........................................................................................ 8 CHAPTER TWO ............................................................................................................... 9 LITERATURE REVIEW ................................................................................................. 9 2.0 Introduction .............................................................................................................. 9 2.1 Production Theory ................................................................................................ 9 2.2 The Concepts of Efficiency and Productivity ...................................................... 10 2.2.1 Efficiency in Production ..................................................................................... 11 2.3 Types of Efficiency ................................................................................................. 15 2.3.1 Economic (Cost) Efficiency ................................................................................ 15 2.3.2 Technical Efficiency ............................................................................................ 16 2.3.3 Allocative Efficiency ............................................................................................ 18 2.4 Measurement of Efficiency in Banks ................................................................. 20 2.4.1 Classical (Accounting Ratios) Approach ....................................................... 20 2.4.2 Econometric Regression Analysis ...................................................................... 23 2.4.3 Frontier Approach ........................................................................................... 25 2.5 Approaches to Efficiency Modelling Banks Production .................................. 33 2.6 Productivity Concept .......................................................................................... 36 2.6.1 Measuring Productivity (Partial and Total Factor Productivity) ............... 38 2.6.2 Determinants of Bank Efficiency and Productivity ...................................... 40 2.7 Empirical Literature on Bank Efficiency and Productivity in Sub-Saharan African (SSA) Countries .............................................................................................. 42 2.8 Review of Empirical Literature on Rural Banking Efficiency and Productivity ........................................................................................................................................ 48 vi
2.9 Extant Evidence on Bank Efficiency and Productivity in Ghana ...................... 51 2.10 Chapter Summary ................................................................................................ 53 CHAPTER THREE ......................................................................................................... 55 A REVIEW OF THE RURAL BANKING SECTOR IN GHANA ............................. 55 3.0 Introduction ............................................................................................................ 55 3.1 Structure of the Banking Sector in Ghana........................................................... 55 3.2 Developments and the Structure of Rural Banking in Ghana ........................... 60 3.3 Rural Banking Reforms in Ghana ........................................................................ 65 3.3.1 Regulatory and Legal Reforms .......................................................................... 65 3.3.2 Financial Restructuring ...................................................................................... 66 3.3.3 Institutional Reforms .......................................................................................... 67 3.4 A Review of the Financial Performance of the Rural Banking Sector in Ghana ........................................................................................................................................ 68 3.5 Chapter Summary .................................................................................................. 71 CHAPTER FOUR ............................................................................................................ 73 RESEARCH METHODOLOGY ................................................................................... 73 4.0 Introduction ............................................................................................................ 73 4.1 Non-Parametric Method ........................................................................................ 74 4.1.1 Data Envelopment Analysis (DEA) ................................................................... 75 4.1.2 Returns to Scale ................................................................................................... 77 4.1.3 DEA Malmquist Productivity Index .................................................................. 79 4.2 Parametric Methodology ....................................................................................... 81 4.2.1 Stochastic Frontier Approach ............................................................................ 83 4.2.2 Stochastic Frontier Production Function .......................................................... 84 4.2.3 Time Varying Efficiency Models ....................................................................... 86 4.2.4 Model Choice ....................................................................................................... 90 4.2.5 Empirical Specification ....................................................................................... 91 4.2.6 SFA Productivity Analysis.................................................................................. 94 4.3 Determinants of Productivity ................................................................................ 95 4.4 Data Sources ........................................................................................................... 95 4.5 Concluding Remarks.............................................................................................. 96 CHAPTER FIVE ............................................................................................................. 98 TECHNICAL EFFICIENCY ANALYSIS OF RURAL BANKS IN GHANA .......... 98 5.1 Introduction ............................................................................................................ 98 5.2 Description of the Data .......................................................................................... 99 5.3 Results Based on the DEA Approach ................................................................. 101 5.2.1 DEA Technical Efficiency Results for Individual RCBs ............................... 104 5.2.2 Quarterly Mean Overall Technical Efficiency (CRSTE) .............................. 109 5.2.3 Pure Technical Efficiency (VRSTE) ................................................................ 111 5.2.4 Scale Efficiency (SCALE) ................................................................................. 111 5.3 Results Based on the SFA Approach .................................................................. 113 vii
5.3.1 Parameter Estimates of SFA Models ............................................................... 113 5.4 Results Derived from SFA Approach ................................................................. 117 5.4.1 Quarterly Mean Technical Efficiency ............................................................. 117 5.4.2. SFA Technical Efficiency Results for Individual RCBs ............................... 118 5.3.3 Comparing DEA and SFA Technical Efficiency Results ............................... 122 5.3.4 Technical Efficiency and Accounting-Based Efficiency Measure................. 128 5.4 Chapter Summary ................................................................................................ 129 CHAPTER SIX .............................................................................................................. 132 EMPIRICAL ANALYSIS OF PRODUCTIVITY CHANGES OF RURAL AND COMMUNITY BANKS (RCBs) IN GHANA ............................................................. 132 6.1 Introduction .......................................................................................................... 132 6.2 Estimates of Productivity: DEA approach......................................................... 133 6.2.1 DEA TFP Changes - Summary of Bank Means ............................................. 133 6.2.2 DEA Total Factor Productivity (TFP) Changes – Summary of Quarterly Means........................................................................................................................... 138 6.2.3 DEA Technical Efficiency Change (Catching-up).......................................... 142 6.2.4 DEA Technical Change (Technological Innovation)...................................... 147 6.3 Estimates of Productivity: SFA approach ......................................................... 150 6.3.1 SFA TFP Changes - Summary of Bank Means .............................................. 150 6.3.2 SFA Total Factor Productivity (SFA-TFP) Changes – Quarterly Means ... 154 6.3.3 Cumulative Change of TFP and Its Components .......................................... 157 6.4 Consistency of DEA and SFA Productivity Estimates ...................................... 159 6.5 Chapter Summary ................................................................................................ 163 CHAPTER SEVEN ........................................................................................................ 164 DETERMINANTS OF PRODUCTIVITY CHANGE OF RURAL AND COMMUNITY BANKS (RCBs) IN GHANA ............................................................. 164 7.1 Introduction .......................................................................................................... 164 7.2 Econometric Methods, Empirical Model, and Data Description ..................... 165 7.2.1 Econometric Methods ....................................................................................... 165 7.2.2 Empirical Model ................................................................................................ 169 7.2.3 Data Description ................................................................................................ 171 7.3 Empirical Results ................................................................................................. 176 7.3.1 Determinants of Productivity Changes (TFP) ................................................ 178 7.3.2 Determinants of Efficiency Change (EFFCH) ................................................ 182 7.3.3 Determinants of Technical Change (TECH) .................................................. 185 7.4 Chapter Summary ................................................................................................ 189 CHAPTER EIGHT ........................................................................................................ 192 SUMMARY OF FINDINGS AND IMPLICATIONS ................................................ 192 8.0 Introduction .......................................................................................................... 192 8.1 Summary of Key Findings ................................................................................... 194 8.1.1 Technical Efficiency Estimates ........................................................................ 194 viii
8.1.3 Determinants of Productivity Changes ........................................................... 197 8.2Policy Implications ................................................................................................ 199 8.4Limitations and Suggestions for Future Research ............................................. 203 REFERENCES ............................................................................................................... 205 APPENDIX ..................................................................................................................... 226
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LIST OF TABLES Table 2.1: A Summary of Definitions of Efficiency in Extant Literature................... 14 Table 3.1: Selected Reforms and Projects in the Ghanaian Banking Sector ............. 59 Table 3.1: Cont’d ............................................................................................................. 60 Table 3.2: RCBs Performance Classification (BoG) ..................................................... 69 Table 3.3: Selected Performance of the Rural Banking Sector in Ghana and the Economy 2010-2013 .................................................................................................. 72 Table 4.1: Selected Best Fit Models ................................................................................ 91 Table 5.1: Summary Statistics for Input and Output Variables ............................... 100 Table 5.2: Summary Statistics for Input-Oriented DEA Technical Efficiency ........ 102 Table 5.3: Mean DEA Technical Efficiency of RCBs, 2009q1-2012q3 ..................... 106 Table 5.4: Quarterly Average Overall Technical Efficiency Scores (CRSTE) ........ 110 Table 5.5: Quarterly Average Pure Technical Efficiency Scores (VRSTE) ............. 111 Table 5.6: Quarterly Average Scale Efficiency Scores (SCALE) .............................. 112 Table 5.7: Likelihood-Ratio Test of Models ................................................................ 114 Table 5.8: Parameter Estimates for the Stochastic Frontier Models ........................ 115 Table 5.8: Cont’d ........................................................................................................... 116 Table 5.9: Quarterly Technical Efficiency, 2009q1 – 2012q3 .................................... 117 Table 5.10: Mean Technical Efficiency of Firms for 2009 - 2012 – SFA Analysis ... 119 Table 5.11: Technical Efficiency Bounds ..................................................................... 122 Table 5.12: Summary Statistics for SFA and DEA Efficiency Estimates ................. 123 Table 5.13: Frequency Distribution of Efficiency Estimates from the SFA and DEA .................................................................................................................................. 124 Table 5.14: Comparing SFA and DEA Technical Efficiency by Quarters ............... 124 Table 5.15: Spearman’s and Kendall’s Rank Correlations for SFA and DEA ........ 126 Table 5.16: RCBs in Top and Bottom Deciles ............................................................. 127 Table 5.17: Correlations between Frontier Efficiencies and Accounting-Based Efficiency Ratio ....................................................................................................... 128 Table 6.1: DEA TFP Changes and Components - RCBs Means (2009Q1-2012Q3) 134 Table 6.2: Frequency Distribution of TFP, TECH, and EFFCH .............................. 137 x
Table 6.3: Quarterly Mean TFP Changes (2009Q1 - 2012Q3) .................................. 138 Table 6.4: Cumulative Change of TFP and Components .......................................... 141 Table 6.5: Sources of DEA Technical Efficiency Change .......................................... 142 Table 6.6: Cumulative Change of Technical Efficiency and Components ............... 146 Table 6.7: Technical Change and Cumulative Technical Change ............................ 149 Table 6.8: SFA TFP Changes and Components - Bank Means (2009Q1-2012Q3) .. 151 Table 6.9: Quarterly Mean SFA-TFP Changes (2009Q1 - 2012Q3) ......................... 154 Table 6.10: Cumulative Change of TFP and Components ........................................ 158 Table 6.12: TFP Change, EFFCH and TECH of DEA and SFA, 2009Q1-2012Q3 . 159 Table 6.13: Rank Correlation Tests between DEA and SFA Estimates ................... 162 Table 7.1 Expected Signs of Explanatory Variables ................................................... 175 Table 7.2: Summary Statistics for Dependent and Independent Variables ............. 175 Table 7.3: Determinants of Total Factor Productivity (TFP) - Static Analysis (POLS, RE, and FE Estimators) ......................................................................................... 177 Table 7.4: Determinants of Total Factor Productivity (TFP) Two-Step GMM-System .................................................................................................................................. 179 Table 7.5: Determinants of Efficiency Change - Static Analysis (POLS, RE, and FE) .................................................................................................................................. 181 Table 7.6: Determinants of Efficiency Change - Two-Step GMM-System............... 183 Table 7.7: Determinants of Technical Change – Static Analysis (POLS, RE, and FE) .................................................................................................................................. 186 Table 7.8: Determinants of Technical Change - Two-Step Sys-GMM ..................... 187
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LIST OF FIGURES
Figure 2.1 Efficiency Concepts ....................................................................................... 16 Figure 2.2: Measurement of Efficiency .......................................................................... 20 Figure 2.3: Regression Analysis for Production Function ........................................... 24 Figure 2.4: Modeling Approaches .................................................................................. 33 Figure 3.1: Structure of the Banking Sector in Ghana................................................. 56 Figure 3.2: A Typical Organization of RCBs ................................................................ 64 Figure 3.3: Capital Requirement .................................................................................... 66 Figure 5.1 Quarterly Mean Technical Efficiency Score ............................................. 103 Figure 5.2: Kernel Density Function for CRSTE, VRSTE, and SCALE ................. 103 Figure 5.3: Quarterly Mean Technical Efficiency ...................................................... 118 Figure 5.4: Comparison of Technical Efficiency Scores, DEA and SFA .................. 125 Figure 6.1: Quarterly Changes in Productivity Index (MPI) .................................... 139 Figure 6.2: Cumulative TFP Change and Components ............................................. 141 Figure 6.3: Sources of Technical Efficiency Change (Quarterly) .............................. 145 Figure 6.4: Cumulative Changes in Technical Efficiency and Components ............ 146 Figure 6.5: Quarterly Changes in Productivity - SFA Analysis ................................ 156 Figure 6.6: Cummulative TFP Change and Component - SFA Analysis ................. 158 Figure 6.7a: Cumulative TFP Change – DEA and SFA Trend ................................. 160 Figure 6.7b: Cumulative EFFCH – DEA and SFA Trend ......................................... 161 Figure 6.7c: Cumulative TECH – DEA and SFA Trend ............................................ 161
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CHAPTER ONE INTRODUCTION 1.1 Background to the Study Financial institutions play a fundamental role in economic development (World Bank, 1989), as their operations are crucial in determining who uses society’s resources and how such resources are used. King and Levine (1993) account the significant role an efficient financial system plays in accelerating economic development and output, through prudent management of risks, efficient allocation of credit, and funding of feasible investments. This exerts huge impact on total factor productivity, which leads to higher long-term growth rates.
Ghana embraced formal financial system intermediation in 1896, and since then, Ghana has never looked back after moving away from the traditional barter system of trade prior to 1896. Indeed, the country has supervised critical transformations in its financial system, especially in the banking sector, from the early days of a command market to a more competitive and market-driven system. The massive transformations in the banking sector especially have been driven mostly, in part, by technological, financial, and economic factors (see Amidu and Hinson, 2006; Nabieu, 2013); and also by the motivation to remove wastes and inefficiencies in the system.
The concept of rural banking was introduced in Ghana in 1976 by the central bank of Ghana with the motive of mobilizing rural capital resources to finance viable rural-based economic ventures whilst promoting rural development. This was against the bedrock that existing financial institutions in the country were reluctant, incapable, or slow in expanding financial services to rural communities. As a result, Rural and Community 1
Banks (RCBs) were established as unit banks to perform such functions as serving small and micro enterprises, agricultural activities, and households within the demarcated rural polity. The Year 2000 IFAD Country’s Report shows that, on the average, a unit rural bank serves within a range of 53 000 km2; however, recent developments show that most of the RCBs are operating outside their allotted demarcation and, more or less, duplicating the functions and structure of commercial banks. From the initial one RCB, the number of RCBs in the country has increased tremendously. By 2010, the number of RCBs totaled about 137 RCBs, with a total asset size exceeding GH₵800 million; a percentage rise of 39.82% from 2009 (Ghana Business News, 2011). It is also estimated that the RCBs network in Ghana has reached about 2.8 million depositors and 680,000 borrowers. According to an Economic Value Added (EVA) performance report for 2009, RCBs created the highest value for their shareholders than the universal banks by 2009. Market statistics show that RCBs have a market share of slightly over 65 percent of depositors and 48 percent of borrowers in rural areas (Ampah, 2010).
Yet, aside all these contributions that rural banking makes to the economy of Ghana, there are concerns of limited capacity and liquidation threats, amidst fierce competition from the commercial banks and the proliferation of other players, including the savings and loans companies, finance houses and microfinance institutions. Until now, many of these RCBs have been shut down, for a variety of reasons. RCBs are also unequally distributed, with the fewest in the Upper East, Upper West and Northern regions. Reports suggest that, out of the 137 RCBs currently operating in the country, approximately 70 have been classified by the Central Bank as operating satisfactorily. The performances of 50 of the RCBs have been described as mediocre, and the rest will need close monitoring and nurturing to avoid being closed down by the Central Bank. It is, therefore, recognized 2
that, in order to consolidate the benefits of Rural and Community banks, frequent assessment of their performance must be conducted so as to remove wastes and improve on efficiency. In other words, RCBs must be constantly monitored and placed on par with international standards in respect of rural banking services and other prudential financial norms, as required by all the universal banks in Ghana.
If the operational rigidities in the rural financial intermediation system are to be removed, an attempt has to be made to frequently monitor and measure the efficiency and productivity of the associated institutions (especially RCBs and MFIs) that focus on rural banking and financial services. Unfortunately, studies on the efficiency and productivity growth of RCBs, not only in Ghana but also across the financial globe, are largely unexplored, in spite of the importance of rural banking in the mobilization of rural savings, poverty-reduction, and rural-development. It is for this cause that the thrust of this study is placed.
1.2 Statement of Research Problem The above discussion reveals several gaps in empirical rural banking efficiency and productivity studies that are critical to this study. Firstly, it is observed that, though the implementation of the rural banking concept has been successful across the globe and even in Ghana, continuous operational wastes confront optimal performance. To know the source of such wastes in order to tackle them requires accurate assessment of the state of inefficiency in the sector. However, though researchers recognise the importance of efficiency studies in all aspects of the banking system, majority of these works have concentrated on conventional banks to the neglect of RCBs (see, among others, Allen and Rai, 1996; Pastor, Perex and Quesada, 1997; Resti, 1997; Mukherjee et al, 2001; Altunbaş 3
et al, 2001; Chen, 2009). It is also seen that these studies tend to focus on advance countries; little has been contextualized on transitional economies (see Christopoulos, Lolos and Tsionas, 2002; Bonin et al, 2005; Nghiem et al, 2006; Semih-Yildirim et al, 2007).
The gap is even wider when a search is conducted on Sub-Saharan African economies (SSA). The evidence shows that, though there is a steady growth in the number of studies on banking efficiency and productivity for SSAs, the focus has been to assess the level of achievement, after different reforms have been implemented (see Musonda, 2008; Ncube, 2009; Kiyota, 2011; Kamau, 2011). In Ghana, the bank efficiency and productivity literature have mostly focused on the mainstream universal banks, mostly examining small sample sizes (see Akoena et al (2009); Frimpong (2010); Isshag and Bokpin (2011); and Adjei-Frimpong et al (2013), (2014)). There are limited works with regard to RCBs. Danquah et al (2013) appeared to be the only study that has tackle the technical efficiency of RCBs in Ghana. Other studies such as Obeng (2008); Gatsi and Akoto (2010); and EtuMensah and Enyamful (2010) that concentrated on RCBs were however targeted at assessing their capital structures, profit ratios, and contributions to agricultural and rural development activities. No study has focused simultaneously on the efficiency and productivity change of RCBs in Ghana from the accessible literature to the best of the author’s knowledge.
Secondly, productivity analysis of financial institutions in literature also focused largely on advanced economies. A known study on an African setting, which was conducted in Botswana, was absorbed with only the commercial banks (see Moffat, 2008). It is upon this reason that the motivation for this study is set; to make a significant and original 4
contribution to existing literature by identifying the levels of wastes and sources of productivity (technical efficiency change and technical change), including the determinants of total factor-productivity growth in the rural banking sector in Ghana, particularly what influences technical efficiency and technical change. This work will, therefore, add to the existing literature on RCBs in Ghana by considering a larger sample of 107 out of 137 RCBs to monitor their performances in terms of technical efficiency and productivity growth.
1.3 Research Objectives Following from the research problem, the general objective of this study is to derive a measure of technical efficiency and productivity growth of Rural and Community Banks (RCBs) in Ghana. The study is guided by the following specific objectives: 1. To derive a measure of technical efficiency scores of RCBs in Ghana. 2. To rate the RCBs in terms of their technical efficiency scores. 3. To evaluate the level and sources of productivity growth of the RCBs in Ghana. 4. To examine the determinants of productivity growth of RCBs in Ghana.
1.4 Significance of the Study The study’s significance is dual. First, from a management policy perspective, the calculation of relative efficiency and productivity scores will provide a benchmarking analysis to stimulate efficiency of RCBs towards the direction of best practices. Indeed, empirical studies have totally neglected this area of the financial system. The study focuses on both productivity and technical efficiency to assist bankers to identify areas of improvement so that rural banking operations can improve in tandem with the conventional counterparts. Moreover, the decomposition of efficiency and productivity 5
components would draw immediate attention to the sources of inefficiencies and, thus, management may find solutions to correct these operational wastes. Secondly, the study presents conclusions and recommendations that will impinge on policy modeling and discourse in the rural banking sector in Ghana and the sub-region as a whole.
1.5 Contribution to Knowledge This section describes the study’s contribution to the body of literature and management practice. Empirical reviews on rural banking efficiency and productivity are laboriously few, particularly because no published studies exist on Ghana. Since RCBs have to compete with the universal banks, on even grounds, for clients, more studies are needed to find out ways to improve their efficiency. More specifically, early studies, have both theoretically and empirically established a direct relationship between financial-institution technical efficiency, financial development, and economic growth (see Mckinnon, 1973; Levine, 1997). A study to find out the RCBs’ technical efficiency and productivity and, consequently, their sources in order to oversee progress in the financial sector is, therefore, not misplaced, especially given the operational rigidities found in the sector. The study’s contribution to knowledge is in four folds. First, unlike most banking efficiency studies using the Cross-Sectional Stochastic Frontier approach, this thesis adopts Panel Data Stochastic Frontier approaches and systematically compares and analyzes four time-varying models, selects the best model for analysis and compares results with DEA estimation. Second, it reviews separate literature on the technical efficiency and productivity of financial institutions and adopts empirical approaches to an area that has been unattended in research on efficiency that is rural banking. Third, the study further attempts to find out the sources and determinants of efficiency and productivity, using rigorous inferential analysis, and checks the consistency of results 6
through varied approaches; a step beyond the simplistic efficiency empirical studies that usually uses one approach. Fourth, the study closes the gap in the existing literature by focusing on Ghana. This presents empirical evidence on a Sub-Saharan African economy. It also presents more knowledge on efficiency analysis in a transitional economy context. This is even more significant considering the rural banking outlook the study presents. The study shows how RCBs can improve upon efficiency and achieve growth in productivity, given that little attention is given to them and little knowledge is presented in this area in literature.
1.6 Scope of the study This thesis is focused on the technical efficiency and productivity growth and their determinants with respect to rural banking in Ghana for the period 2009 - 2012. The study attempts to measure the efficiency levels and, consequently, the productivity of the RCBs for the period. The research covers the intermediation activities of the RCBs, especially the distribution of loanable funds collected from rural savers to respective borrowers for them to engage in economic ventures; and how such functions are performed efficiently or otherwise, although there were many other functions upon which the performance of these RCBs could have been assessed, especially production functions, value-added functions, creation of assets, and so on, excluding forestry and fishery components. The study expands the analysis to consider quarterly performance but not restricted to yearly performance in order to tell an in-depth story. Analyses are conducted with a nonparametric DEA and parametric SFA on a panel dataset of 107 RCBs across the 10 regions of Ghana.
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1.7 Organisation of the Study The study is divided into eight main chapters. Chapter One, the introduction, looks at the background of the study, the research problem, objectives of the study and the significance of the study. In Chapter Two, an extensive literature focusing on all the relevant objectives and sections of the work have been reviewed. The chapter covers the two main theoretical frameworks used for the study, namely, the concept and measurement of efficiency and productivity. The chapter closes by looking at empirical studies conducted in the area of financial institutions’ efficiency and productivity across the globe. Chapter Three reviews the rural banking system in Ghana by providing a historical account, organizational structure and performance review. Chapter Four covers the applied methodology and the estimation procedure used. Under this chapter, detailed explanation is given to the choice of variables, methods and models used in the estimation of productivity and technical efficiencies. Chapter Five focuses on presenting and discussing the empirical results of the technical efficiency scores and rankings of the technical efficiency of the RCBs in Ghana over the operational period 2009q1 to 2012q3, after varied frontier methods are applied on the available data. The empirical results pertaining to productivity change and productivity ranking of the RCBs are then presented in Chapter Six. In Chapter Seven, the study presents the findings of the determinants of the technical efficiency and productivity change of the RCBs in Ghana over the study period. The final chapter, Chapter Eight, presents a summary of the findings, conclusions, and limitations of the study. Implications for further studies are also provided.
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CHAPTER TWO LITERATURE REVIEW 2.0 Introduction This chapter is aimed at reviewing the relevant theoretical concepts of production, efficiency and productivity, and their measurement in financial institutions. Section 2.1 deals with the theory of production and is followed by a review of the concepts of efficiency and production, which are presented in Section 2.2. In Section 2.3 and Section 2.4, the types of efficiency and the measurement methods are presented respectively. Section 2.5 then deals with the approaches to modeling bank production. Section 2.6 presents a detailed review of the concept of productivity and the measurements of it, such as partial and total-factor productivity. A review of empirical studies in Sub-Saharan Africa and Ghana in particular are also presented in sections 2.7and 2.8 while finally a review of Rural banking efficiency and productivity studies are reviewed in section 2.9. section 2.10 concludes the chapter.
2.1
Production Theory
Under Production Theory, production is defined as any process that converts a set of inputs into a set of outputs. Given available or existing technology, all the feasible mixtures of minimum input set used to produce the outputs defines the production function of an economic decision-making unit (DMU) or firm. According to Battese and Coelli (1992), a production function could be alternatively defined in terms of the maximum output that can be produced from a specified set of inputs, given the existing technology available to the firms involved. The production function is used to express the transformation of inputs into outputs, which shows the maximum output obtainable from various input vectors (Forsund et al, 1980). According Ashton (1997), a production
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function assumes that the level of output of an individual firm is dependent on the amount of inputs employed in production, plus random error and any other variables that account for the environment or the particular circumstances of the particular firm.
A production function, in theory, is depicted by a production (possibility) frontier, which shows the maximum output attainable from each input set or, alternatively, the minimum input set used to produce the given level of output (Coelli et al, 2005). The concept of a production possibilities frontier is consistent with the typical representation of technology, specifically a production function (Poudel et al, 2011).
2.2 The Concepts of Efficiency and Productivity Measuring the performance of a firm is one of the critical issues that managers of firms are always faced with. It is one of the key aims of any business operations and includes different connotations of efficiency and effectiveness. According to Lin et al (2011), fundamentally, even without considering the level of resource consumed, the higher the level of output value derived from using inputs in production, the higher is the indication of the efficiency level. The efficient use of economic resources is central to assessing the success of any firm in both the short run and the long run. To this extent, productivity and efficiency have emerged as two very key economic concepts in assessing the performance of firms as economic decision-making units (Wang et al, 2002). Albeit being used interchangeably, the two concepts do not stand for exactly the same things (Coelli et al, 2005). Efficiency and productivity are, however, two cooperating concepts; productivity incorporates efficiency. By the meaning of the productivity of a firm, it would be realized that the focus is on how well inputs are churned out for a given level of output. However, by the efficiency of same firm, reference is given to how the actual outputs or inputs 10
compare to the optimal levels of outputs or inputs. Here, the optimum is defined by the behavioural goals of the decision-making firm, which include cost minimization, revenue maximization, and profit maximization objectives (Koopmans, 1951 and Fried et al, 2008). Efficiency does not include a time component, that is, it is static, whilst productivity can change through time. Change in productivity can be due to differences in production technology and/or change in the efficiency of the production process. Therefore, productivity measurement incorporates efficiency measurement. The following sections review the concepts in turn, in the contexts of banks and non-bank financial institutions.
2.2.1 Efficiency in Production The concept of efficiency in production has been dealt with in a plethora of theoretical and empirical studies. The theoretical literature on economic efficiency originated with the work of Koopmans (1951) and Debreu (1951), while the first attempt to estimate or measure efficiency was found in Farrell’s (1957) seminal work. There is a mix of perspectives to the definition and explanation of what constitutes efficiency in production because of the diverse units, contexts, or sectors of the economy in which it could be looked at. The fundamental idea underlying all efficiency measurements is the quantity of goods and services produced per unit of input (Ajibefun and Daramola, 2003). This idea is limited in the consideration of the input quantity that may be used to produce a specified quantity of output.
Lin et al (2011) argued that efficiency is a concept that originates from physics or engineering and refers to the optimization of resource allocation to maximize output levels, using minimum resource costs in order to achieve stated business operational
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goals. Efficiency is measured by the concept of relative investment and production, and can be divided into two major components: economic and productive efficiency.
According to Chukwuji et al (2006), economic efficiency is achieved when the producer combines resources in the least combination to generate maximum output (technical) as well as ensuring least cost to obtain maximum revenue (allocative). Productive efficiency, on the other hand, is achieved when a producer uses the least amount of resources to produce goods or services relative to others. The producer might achieve this by exploiting economies of scale or by having the advantage of the most efficient production technology, the cheapest labor, or minimal production waste (Elle Greco, 2008). In the opinion of Parkin et al (2003), production efficiency is achieved when it is not possible to produce more of one good without producing less of some other good.
The production frontier can be used to measure the efficiency of a firm. The frontier measure of efficiency implies that efficient firms are those operating on the production frontier (the boundary between those combinations of goods and services that can be produced with the available resource and the state of technology). The rate at which a firm lies below its production frontier is regarded as the measure of inefficiency, from a technical perspective (Farrell, 1957 and Poudel et al, 2011). Production points inside the frontier are points at which resources are either wasted or misallocated. Resources are wasted when they are idle when they could be working. Resources are misallocated when they are assigned to inappropriate tasks. Accordingly, in the process of transforming inputs into some output value, a change that increases output value is an efficient change and one that decreases value is an inefficient change.
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Van Peursem et al (1995) and Kokkinou (2012) suggest that efficiency is related to a wide range of controllable activities. According to them, efficiency is a measure of the relationship between the outputs or outcomes converted and the resources used to produce them. That is the relationship between what an economic decision-making unit actually produces and what it could potentially produce. Precisely, a comparison between a firm’s observed values and optimal values of output and input where the optimum is defined by the production possibilities. The comparison is made either by looking at the ratio of observed output to maximum potential output, or given the input mix, the ratio of minimum potential to observed input required to produce the given output.
In summary, efficient firms, such as banks, are those that use their inputs (e.g. assets and deposits) to produce maximum output (e.g. loans and other services) possible for consumers, with the aim of making maximum profit for its stockholders. Following from the reviewed definitions, there is a limit to the volume of output (commodities or services) that an efficient firm can produce using available inputs and given state of technology.
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Table 2.1: A Summary of Definitions of Efficiency in Extant Literature Authors Definitions Koopman (1951)
A decision-making unit (DMU) or firm is efficient if and only if it is possible to improve some of its inputs (or outputs) without the worsening of some its other inputs (or outputs).
Forsund et al (1980)
Productive efficiency represents the efficient resource input mix for any given output that minimizes the cost of producing that level of output or, equivalently, the combination of inputs that, for a given monetary outlay, maximizes the level of production.
Kumbhakar and Lovell (2000)
Production efficiency is the extent of success that firms achieve in allocating their inputs to produce their required outputs, subject to an initial stated goal or objective.
Coelli et al (2005)
Efficiency refers to how a firm allocates scarce resources to meet production targets. The primary principle underlying the concept of efficiency (in production) is that output can only be produced with resources (inputs) and that these resources are scarce.
Cooper, Seiford and Tone (2006)
Efficiency is simply defined as the ratio of output to input
Al-Jarrah (2007)
Efficiency is the relationship between production and the specific desirable objective function (such as cost minimization, revenue maximization and profit maximization) of the firm, given the state of technology
Fried, Lovell, and Schmidt (2008)
Efficiency is defined by comparing some observed and optimal values of a producer’s output and input
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2.3 Types of Efficiency Different concepts of efficiency can be found in the financial market literature, depending on the focus of the particular study. In the financial systems literature, productive efficiency, from the Farrell school of thought (see Farrell, 1957), and x-efficiency, from the Leibenstein School (see Leibenstein, 1966), are the two main efficiency concepts used in measuring performance in financial institutions. The studies recognize that banks are production units. While productive efficiency theory focuses on measuring optimal efficiency, x-efficiency theory, on the other hand, focuses on explaining why firms may not achieve the optimal level of efficiency in their productive decisions and behavior (Kamaruddin, 2007). Though x-efficiency theory makes use of productive efficiency, it relaxes the restrictive assumptions made by Farrell (1957) on the nature of market structure. The following section discusses some concepts of efficiency commonly used in bank efficiency studies, such as economic efficiency, technical efficiency, and allocative efficiency.
2.3.1 Economic (Cost) Efficiency According to Colman and Young (1995), the concept of economic efficiency provides a theoretical basis for the measurement of the performance of firms. Farrell’s (1957) seminal work on the empirical measurement of economic efficiency argued that the economic efficiency of a production unit is better seen as relative to deviation from the best practice of an average peer group of production units.
Economic efficiency is also commonly referred to as Cost Efficiency. A cost-efficient firm will choose its input mixes according to their prices so as to minimize total cost. Economic efficiency may arise from two different sources. One is efficiency in applying
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the technology (Technical Efficiency), and the other one is the optimal allocation of resources (Allocative Efficiency). Farrell (1957) described economic efficiency as Product or Global Efficiency. It is the simultaneous achievement of both technical efficiency and allocative efficiency (Farrell, 1957; Coelli, 1996; Paxton, 2003). Thus, overall economic efficiency can be presented as the product of technical efficiency and allocative efficiency (see Figure 2.1). Figure 2.1 Efficiency Concepts
resources
allocative efficiency
economic efficiency
production
output
technical efficiency
Source: Author’s construct
2.3.2 Technical Efficiency Technical Efficiency is the effectiveness with which a given set of inputs is used to produce an output. If a firm is producing the maximum output attainable, given the resources it employs, such as labor and capital, and the best technology available, it is technically efficient (Leibenstein, 1966). Technical Efficiency has also been defined as the distance, in terms of output produced, between an individual firm and the ‘optimal’ or ‘best-practice’ firm. Technical Efficiency (TE), thus, measures the firm’s ability to use
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the best available practices and technology in the most effective way (Olson and Vu, 2007).
Thus, a bank will be considered as technically efficient if it produces optimal quantities of output given the amount of inputs or, alternatively, if it produces given amounts of output with minimum quantities of inputs (Guerrero and Negrin, 2005; Sun, 2006). In other words, a technically efficient financial institution is one that can best transfer physical inputs, such as labor and capital, into outputs at the best level of performance. Hence, there is no waste in using inputs to produce a specific quantity of output (Al-Delaimi and Al-Ani, 2006). In this respect, when a firm’s expected output (frontier) is equal to its actual output, then technical efficiency is attained.
Greene (1993) made the point that the level of technical efficiency of a particular firm is characterized by the relationship between observed production and some ideal or potential production. In basic terms, technical efficiency is concerned with achieving maximum outputs with the least cost. The measurement of firm-specific technical efficiency is based upon deviations of observed output from the best production or efficient production frontier. If a firm’s actual production point lies on the frontier, it is perfectly efficient. If it lies below the frontier, then it is technically inefficient, with the ratio of the actual to the potential production defining the level of efficiency of the individual firm (Okoruwa and Ogundele, 2008). A unit that operates on its production frontier can then be referred to as a “best-practice” firm. This hypothesized ‘best practice’ firm is defined with reference to all the firms in the sample set. The distance of a sample firm from this ‘optimal’ firm or the production function is viewed as productive inefficiency (Farrell, 1957). For Farrell (1957), the appropriate measure of technical
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efficiency is input-saving, which gives the maximum rate at which the use of all the inputs can be reduced, without reducing the output. According to Koopmans (1951), a producer is technically efficient if an increase in any output requires a reduction in, at least, one other output or an increase in, at least, one input, and if reduction in any input requires an increase in, at least, one other input or a reduction in, at least, one output. Thus, a technically-efficient producer could produce the same outputs with less of, at least, one input, or could use the same inputs to produce more of, at least, one output.
Rahman and Rahman (2009) posit, then, that a firm’s level of efficiency in the technical sense could be considered, given locational and environmental constraints. That is, they consider a firm to be technically efficient if it produces the maximum attainable output from inputs used, or it minimizes resources used for any given level of output, with respect to specific locational and environmental factors. According to Greco (2008), as a precondition for allocative efficiency, technical efficiency describes production that has the lowest possible opportunity cost. Material and labor resources are not wasted in the production of goods or services in technically-efficient production. When it is achieved, technical efficiency allows for but does not guarantee allocative efficiency. According to Färe et al (1985), a producer is said to be technically-efficient if production occurs on the boundary of the producer’s production-possibilities set, and technically inefficient, if production occurs on the interior of the production-possibilities set.
2.3.3 Allocative Efficiency From Farrell (1957), Allocative Efficiency is the extent to which DMUs equate the marginal value product of a factor of production to its price. In other words, it deals with the extent to which firms make efficient decisions by using inputs up to the level at which 18
their marginal contribution to production value is equal to the factor cost. Allocative efficiency broadly matches society’s value (or price) for a product to the costs of production inputs in equilibrium (Greco, 2008). It is usually achieved when a decisionmaking unit allocates its resources to the production of what society values most. In Harvey and Leibenstein (1966), it refers to the efficient distribution of productive resources among alternative uses so as to produce the optimal mix of output. Allocative efficiency involves an interaction between the productive capacity and the consumption activity of society.
Olson and Vu (2007) explain that Allocative Efficiency is conditional on input prices and measures the firm’s ability to make optimal decisions on product mix and resource allocation. According to Coelli (1996), Allocative Efficiency refers to how different resource inputs are combined to produce a mix of different outputs. In other words, Allocative Efficiency is concerned with the choice that best compares to the budget constraint among different possible combinations of input that yield the same amount of the desired output. It is, therefore, the ability of economic agents to equate marginal cost with marginal benefit (Guerrero and Negrin, 2005; Manjunatha et al, 2013).
In contrast to allocative efficiency is allocative inefficiency, which is about the use of an uneconomical combination of resources to produce goods and services (Kumbahkar, 1987). It is also referred to as the use of resources to produce goods that are not intensely desired relative to their opportunity cost. Thus, allocative inefficiency occurs when firms do not equalize marginal returns with true factor market prices (Fan, 1999). Therefore, allocative inefficiency arises when the input mix is not consistent with the cost minimization objective of the firm. 19
2.4
Measurement of Efficiency in Banks
In the extant literature, three main approaches have been used to measure bank efficiency – the classical (accounting) approach, the econometric approach, and the frontier approach. Numerous comprehensive methodological surveys on all approaches exist (Banker et al (1989); Bauer (1990); Seiford and Thrall (1990); Ali and Seiford (1993); Greene (1993); Grosskopf (1993); Lovell (1993), and Charnes et al (1994)). See Figure 2.2. Figure 2.2: Measurement of Efficiency Measurement of Efficiency
Traditional (accounting) approach
Econometric approach
Accounting ratios
Regression approach
Nonparametric
Efficiency ratios
average efficiency
Data Envelope Analysis (DEA)
Frontier approach
Parametric
Stochastic Frontier Analysis (SFA)
Source: Author’s Construct
2.4.1
Classical (Accounting Ratios) Approach
The measurement of efficiency as an indicator of firm performance was formalized in the early works of Edgeworth (1881) and Pareto (1927), and empirically operationalized in Shephard (1953). There are several traditional methods that literature identifies. These include Accounting Ratios, Productivity per Employee Indicators, Reserve Requirements, Monetary Indicators, and Interest Rate Spreads (Moffat, 2008). The most popularly-used in bank-efficiency studies is the Accounting and Efficiency Ratios, which is briefly
20
discussed below.
Sherman (1984) and Ehreth (1994) consider ratio analysis as one of the simplest and most frequently used methods for assessing performance and efficiency. Generally, the ratio approach is based on basic profit-cost analysis that is considered a very simple and most naïve measure of efficiency. The method defines efficiency, using the ratio of a single output to a single input. In the banking system, the types of ratios most widely used are Capital Adequacy Ratios, Asset Quality Ratios, Management Soundness Indicators, Earnings and Profitability Indicators, Liquidity Ratios, and Sensitivity to Market Risk Indicators. Some specific ratios include Return on Assets (ROA), Return on Equity (ROE), Capital Asset Ratio, Growth Rate of Total Revenue, and Cost Income Ratio, among others, which are used by industry. These ratios are gleaned from financial statements and annual reports of banks. The approach is commonly used among regulators, managers of financial institutions, and industry consultants to evaluate bank performance. In general, simple ratios can be used to compare the performance of a unit to other units and the performance of a single unit over time. The appeal of ratio analysis as a means for efficiency assessment is the simplicity of its calculation. In addition, ratio analysis seems to be useful in identifying which aspects of an organization’s operations are out of line with the norm (Pham, 2008).
Each simple ratio is limited to a comparison of two variables, one measuring an input quantity and another measuring an output quantity. Accordingly, it examines only a part of the unit’s activity. To get around this limitation, the performance evaluation is generally based on the calculation of several ratios simultaneously. These ratios, however, tend to present a set of numbers that give no clear indication of true efficiency.
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For example, if a bank opens a new branch and hires more labor and installs new technology, it can increase productivity per employee, but the cost per employee may be increased. In such a case, the former ratio suggests that the bank is relatively more efficient, but the latter ratio implies that the bank is less-efficient. Therefore, there is no comprehensive picture of how the bank is operating, and ratio analysis becomes ineffective in efficiency evaluations.
Daley and Matthews (2009) point out that the traditional efficiency ratio (ER), for instance, is generally regarded as a critical tool for analysis and decision-making. It has also been used as a basis for measuring bank efficiency in empirical analyses. Smaller values of this ratio are more desirable as they suggest greater efficiency in producing a given output with fewer inputs or utilizing a given set of inputs to produce greater output. The efficiency ratios have also been challenged by a strand appearing in the empirical literature on the grounds that while efficiency ratios are useful and give some indication of the level and changes in efficiency over time, they represent a final outcome and do not allow for identification of the sources of inefficiency and where improvements are necessary.
Moreover, the classical view of bank efficiency measurement in accounting ratio analysis is considered misleading as the cross-sectional differences in input and output mixes and their prices are not properly accounted for, and besides, the analysis requires great caution and in-depth knowledge of the indigenous conditions of the bank (Berger et al, 2009). Conventional performance ratios fail to control for the influences of input price, output price and other exogenous market factors, which constrain the standard performance ratios from reaching closer estimations of the true performance.
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In an attempt to overcome some of the limitations of the use of ratio methods for performance measurement, some modern and powerful approaches, such as frontier methods, have been developed. A comparison of the ratio analysis to other methods is given in more detail in the studies of Sherman (1984); Thanassoulis et al (1996); and Nyhan and Martin (1999).
2.4.2 Econometric Regression Analysis According to Greene (1997), estimation of production functions is standard exercise in the field of econometrics. Greene (1997), however, points out that a frontier production is an extension of the basic microeconomic-based regression model representing some sort of ideal, the maximum output attainable, given a set of inputs. The estimation of the frontier production function is premised on the theoretical foundation that all observed units cannot exceed the maximum attainable output, with the given set of inputs.
An alternative method to ratio analysis, when measuring efficiency, is to use multiple regression techniques (Nyhan and Martin, 1999; Smith et al, 2006). These techniques involve the modeling of the production function and estimate the relationship between a predicted output and various inputs of individual units. A simple form of this relationship (production line) with given inputs is illustrated in Figure 2.3.
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Figure 2.3: Regression Analysis for Production Function
Sources: Jacobs (2001), pg. 104
The primary advantage of regression techniques over ratio analysis is that they can handle multiple inputs measured against a single output. However, there are a number of shortcomings of using regression analysis as a way of measuring efficiency. Firstly, regression analysis suffers from the same major limitation as ratio analysis – the inability to incorporate multiple outputs in the model. Single-equation regression analysis assumes that there is only one output in the model, therefore, multiple outputs need to be combined into a single indicator of production. Multiple equation regression models can be used, but there is no explicit way to interpret performance by the multiple set of residuals. Secondly, regression analysis measures efficiency based on estimates of average production functions. Therefore, it provides little direct information concerning the potential extent of efficiency gains for individual units in the sample. Finally, regression analysis requires the parametric specification of a production function, which is unlikely to be known for many units. For example, it is difficult to say, on average, how hospitals combine and should combine their inputs to produce outputs.
24
In summary, “traditional ratio and regression analyses, the most often used techniques in performance measurement, provide only limited information about efficiency” (DeLancer, 1996, p.16).
2.4.3 Frontier Approach On the basis of the weaknesses and criticisms of the classical methods of measuring efficiency, most contemporary research has increasingly focused on frontier efficiency methods based on the Neoclassical Production Theory to measure the performance of financial institutions. Frontier Efficiency measures deviations in performance from that of ideal “best-practice firms” on the efficient frontier, controlling for the effect of a number of exogenous factors, such as the prices faced in local markets.
In other words, the Frontier Efficiency method measures how well the financial institution performs relative to the predicted performance of the best firms facing the same market conditions in the industry. It represents the ability of management to control costs and use resources to produce output. Frontier Efficiency scores summarize firm performance in a single statistic that can control differences among firms in a sophisticated multidimensional framework that has its roots in economic theory (Cummins and Weiss, 2000). Therefore, Frontier Efficiency appears to be superior to classical performance ratios and obtains better estimates of the underlying efficiencies of firms. In the Frontier approach, bank efficiency performance is evaluated by economic (cost), technical, or allocative efficiency under the assumption that they are economic units or firms converting inputs into outputs.
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Efficiency measurement in banks, based on existing literature (e.g. Mester, 1992, Berger and Humphrey, 1997, Paxton, 2002, among others), varies, depending on the underlying assumptions and methods used to build the efficient frontier, the treatment of the random error, the distributions assumed for inefficiency and the random error (Bauer et al, 1998).
There are basically two main frontier methods of measuring efficiency in banks (see Figure 2.2), which are classified into parametric (Stochastic Frontier Approach (SFA), Distribution-Free Approach (DFA), Thick Frontier Approach (TFA)) methods, and nonparametric (Data Envelopment Analysis (DEA), Free Disposal Hull (FDH)) methods. The parametric methods estimate the frontier with statistical methods and the non-parametric methods rely on the mathematical linear programming to calculate piecewise linear segments of the efficient frontier. Parametric methods impose an explicit functional form for both the frontier and deviations from it, which is inefficiency. Non-parametric methods, in contrast, do neither impose any assumptions about the functional form of the frontier nor any distributional assumptions about inefficiency. This entirely-deterministic construction of the frontier attributes the entire difference between an inefficient observed DMU and an efficient referenced DMU on the frontier exclusively to inefficiency. Estimation of the frontier, in turn, allows for random noise in the analysis. This involves the estimation of a stochastic frontier. Thus, in the context of a production function, the output of a firm is a function of inputs, subject to a production technology and inefficiency arising from the employment of that technology. Non-parametric methods, in turn, also allow random error in observed input-output combinations (Fiorentino, Karmann, and Koetter, 2006).
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The classification into parametric and nonparametric can further be divided into their deterministic and stochastic approaches. The deterministic approach uses the mathematical programming technique to estimate the frontier. It assumes that all deviations of observed production from the estimated efficiency frontier are due to inefficiency. No random factors, such as random noise or measurement errors in data, are assumed to affect the frontier, and, therefore, all observations must lie on or beneath the frontier. The stochastic approach uses the statistical technique to estimate the frontier. It allows for random noise and errors in the data. Therefore, it separates the inefficiency and random factors from the possible deviations of observed production from the efficiency frontier. As a result, the observations can lie on, above, or beneath the frontier (Pham, 2011). Thus, four major divisions of frontier methodologies can be derived as follows: deterministic parametric technique (Aigner and Chu, 1968), parametric stochastic frontier technique (Aigner et al, 1977; Meeusen and Van den Broeck, 1977), nonparametric deterministic DEA and DEA based Malmquist Productivity Index techniques (Charnes et al, 1978; Caves et al, 1982), and nonparametric stochastic Bootstrapping DEA method (Simar and Wilson, 1998; Sengupta, 1987).
On the empirical front, both parametric and non-parametric frontier techniques have been used to construct the best-practice production frontier for samples of firms and then measure the efficiency of each firm in the sample relative to the determined frontier (Coelli et al, 1998). According to Berger and Humphrey (1997), the choice of a method is decided at the researcher’s own prerogative and not theory determined. However, due to the difficulty in operationalizing some of the methods principally based on data requirement problems, the bank efficiency literature is dominated by the parametric (stochastic) SFA and the non-parametric (deterministic) DEA approaches. The two are
27
reviewed below. More detailed reviews of the frontier methods can be found in Seiford and Thrall (1990), Kalirajan and Shand (1999), Murillo-Zmorano (2004), among others.
2.4.3.1 Stochastic Frontier Approach (SFA) Analysis of economic efficiency has a long pedigree dating back to Knight (1933), Debreu (1951), Farrell (1957), Koopmans (1951), and others. An efficiency measure emerges naturally from the frontier production model as the distance between an observation and the empirical estimate of the theoretical ideal.
Aigner and Chu (1968) developed the deterministic parametric frontier method to measure efficiency. This approach requires a prior specification of the functional form for the production frontier. The parameters of the econometric production function are estimated from empirical data, with the application of mathematical programming techniques. The production function is modeled as a function of efficiency to determine the variations in output. Therefore, the residual of the production function (the nonnegative random variable) is defined as the technical inefficiency in production (Smith and Street, 2005). As a deterministic model, it requires that the functional form of the production function be assumed, though no distributional function of the inefficiency score is required. The approach is, however, criticized for the possibility of it ignoring random shocks and measurement errors, and for its dependence on the position of the single most efficient unit in the sample to estimate its efficiency scores.
The stochastic frontier production function model suggested independently by Aigner et al (1977) and Meeusen and Van den Broeck (1977) has been used in several empirical studies, such as Battese and Corra (1977), Lee and Tyler (1978) and Pitt and Lee (1981).
28
The basic model separates the residual into two independent components, a random error and the inefficiency term random variable. The random error follows asymmetric standard normal distribution and the inefficiency term follows a one-sided distribution. The inefficiency term is non-negative, therefore, they must have a truncated distribution such as half-normal, or truncated normal or gamma. The parameters of these two distributions are estimated using maximum likelihood techniques and then used to obtain estimates of bank-specific efficiency.
The requirement for the specification of the functional form for the parametric stochastic frontier is criticized as restrictive, even though it can handle the random errors. Misspecification of the form of function could lead to inefficiency scores that are confused with the random errors instead of the functional specification helping to separate the two components distinctly. Furthermore, different estimates of efficiencies can result from the different distributional assumptions.
In the empirical literature, the most widely-used functional forms are the Cobb-Douglas and the Translog functions. The two are used to specify production, cost and profit functions to measure inefficiencies. There are several developments in the SFA since 1977. First, Pitt and Lee (1981) extended the SFA model, which was originally defined for analysis of cross-sectional data to also account for panel data. Later, the model was further extended to allow the use of unbalanced panel data. Other developments include Schmidt and Sickles (1984) extending the original work of Hoch (1955, 1962) and Mundlak (1961) by applying fixed-effects and random-effects methods to the efficiency measurement problem (Kumbhakar and Lovell, 2003). Finally, if efficiency varied across producers or through time, it is necessary to seek determinants of efficiency variation. 29
Early studies adopted a two-stage approach for this purpose. However, more recent studies have adopted a single-stage approach, so called the technical inefficiency effects model (Battese and Coelli (1995) and Baek and Pagan (2002)).
2.4.3.2 Data Envelopment Analysis (DEA) The most widely used nonparametric technique is Data Envelopment Analysis (DEA) developed by Charnes, Cooper and Rhodes (1978) and is called CCR model, named after the authors. This method does not require the pre-specified form of the underlying production technology. The non-parametric DEA technique concentrates on technological optimization. In DEA, the frontier is generated from the actual data by connecting linear segments of efficient observations, yielding a convex production possibility set. The efficiency score for the specific unit is not defined by an absolute standard, but is defined relative to other units. The efficient observations are those for which no other units have more of, at least, one output with given inputs or less of, at least, one input with given outputs. The efficiency measure is obtained with the application of mathematical programming techniques. The CCR model used constant returns to scale (CRS) concept to assess relative productive efficiencies of decision-making units (DMUs) with multiple inputs and outputs.
Since its conception by Charnes et al (1978), the original DEA model has undergone many modifications and developments. Most of these developments occurred when some of the deficiencies of the original model were exposed during its application to solving real-life problems. This section focuses on the most basic models of DEA rather than its modifications.
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Cooper et al (2004) considered Constant Returns to Scale (CRS) and Variable Returns to Scale (VRS) models as the basic models in DEA literature. The Constant Returns to Scale (CRS) model developed by Charnes et al (1978) implies that DMU size does not matter for efficiency. The CRS assumption is only appropriate when all DMUs are operating at an optimal scale and yield an objective evaluation of the overall technical efficiency and identify the sources of inefficiency. Imperfect competition or constraints on finance, among others, may cause a DMU not to operate optimally. However, factors like imperfect competition and constraints on finance may cause a DMU not to be operating at optimal scale. As a result, the use of the CRS specification, when some DMUs are not operating at optimal scale, will result in measures of technical efficiency (TE), which are confounded by scale efficiencies (SE).
The Variable Returns to Scale (VRS) model, introduced by Banker et al (1984), is similar to the CRS model, since it is based on radial minimization (or maximization) of all inputs (or outputs). However, the VRS model ensures that an efficient DMU is only benchmarked against DMUs of similar size, while in the CRS model, a DMU may be benchmarked against DMUs which are substantially larger (or smaller) than it.
A key weakness of DEA is that it assumes that there is no random noise or measurement error in the data. In order to get around this limitation, a stochastic version of DEA, which provides a statistical foundation for DEA methods, has been pursued (Sengupta, 1987; Simar and Wilson, 1998). Using a resampling technique, such as bootstrapping, is one way to empirically obtain the true distribution underlying the DEA efficiency estimates. The bootstrap, in its simplest form, involves randomly selecting thousands of ‘pseudo samples’ from the observed set of sample data. These thousands of pseudo estimates form 31
an empirical distribution for the estimator of interest, which is used as the approximation of the true underlying distribution. Once the underlying distribution is approximated, statistical inference and hypothesis tests can be conducted.
The strength of the DEA methodology is that it can be applied to firms that produce multiple outputs from multiple inputs. The multiple inputs and outputs of each DMU can be combined into an overall single measure of technical efficiency. In addition, DEA does not require input prices or output prices in order for a best practice production frontier to be identified. Therefore, if a researcher chose to apply the DEA technique, he or she can elect to concentrate on measures of technical, pure technical, and scale efficiency of each bank, apart from concentrating on measures of cost or profit efficiency alone.
Additionally, DEA not only determines the degree of scale efficiency, but also gives the source of scale inefficiency. In this context, DEA generates a best practice frontier under the four different assumptions of constant returns to scale (CRS), variable returns to scale (VRS), non-increasing returns to scale (NIRS) and non-decreasing returns to scale (NDRS). The benefits of VRS assumption are that, it separates scale efficiency from technical efficiency, and that, it provides information about the returns to scale in the production of firms on the efficient frontier, as mentioned earlier. An efficient firm’s production exhibits increasing returns to scale if a small proportionate increase in all inputs produces a greater proportionate increase in outputs, and it exhibits decreasing returns to scale vice-versa. Otherwise, an efficient firm’s production exhibits CRS when it achieves the most productive scale size, where a small increase (or decrease) in all inputs equals the proportionate increase (or decrease) in outputs, keeping the mix of inputs and that of outputs constant. 32
2.5
Approaches to Efficiency Modelling Banks Production
The determination of input and output within financial institutions is a controversial issue in efficiency studies in the financial sector of an economy. There have been varying views with regard to what constitute inputs and outputs in a financial set up, but there is always the need to specify the output and input of a financial institution before efficiency can be measured.
Figure 2.4: Modeling Approaches
Modelling Approaches
Intermediation
Operating
Value-added
Source: Author’s Construct
A variety of inputs and outputs are used to estimate the efficiency of banks. In many industries, physical measures of inputs and outputs are readily available. Berger and Humphrey (1991) point out that physical measures are, however, not readily available for bank services. Differences on the definition and measurement of inputs and outputs related to financial services are yet to be resolved in the literature (Paxton, 2003). According to Paxton (2003), there is no consensus within the banking literature with regard to the specification of inputs and outputs. Though the selection of input-output variables in efficiency analysis of banks remains vital, nonetheless, there is still the lack
33
of a theoretical basis for the selection of input and output variables (Jayamaha and Mula, 2011).
For modeling purposes and definition of input-output variables, banks could be classified into three categories, depending on their perceived role (see Moffat, 2008; Camanho and Dyson, 2005; and Athanassoupoulos, 1997). The classifications determine the nature of the input and output variables that will be used for modeling and measuring bank efficiency. Sealey and Lindley (1977); Colwell and Davis (1992); Berger and Humphrey (1997) provide detailed discussions of problems involved in the selection of inputs and outputs to be used for evaluating the efficiency of financial institutions. They suggested two main approaches, namely the production and intermediation approaches that can be used to identify appropriate inputs and outputs in efficiency analysis. Additionally, they suggest that the asset approach, the user-cost approach and the value-added approach are also important in the measurement of efficiency. Similarly, Favero and Papi (1995) emphasize that the intermediation approach, the production approach, and the asset approach produce better input-output combinations than the other approaches in efficiency analysis. The intermediation approach, the production approach, and the asset approach have dominated the selection of inputs and outputs in the measurement of efficiency in the banking literature (Berger and Humphrey, 1997).
The intermediation approach is appropriate for institutions where deposits are converted into loans. Funds are intermediated between savers and borrowers (Avkiran, 1999). Yue (1992) also emphasizes that the intermediation approach views banks as intermediaries whose core business is to borrow funds from depositors and lend for profit. Thus, deposits and loans are considered as outputs with loanable funds, interest expense, and 34
labor cost as inputs. This approach is used frequently in the literature for measuring efficiency in the banking industry (Avkiran, 1999; Drake and Hall, 2003; Sathye, 2002; Kao and Liu, 2004, among others). With the frontier analysis of efficiency, the intermediation approach is more suitable for the minimization of all costs to enable the maximization of profits. In addition, this approach is important to banking institutions because the interest expense is used as a key input, as it often comprises two-thirds of the total costs of financial institutions (Berger and Humphrey, 1997).
The production approach views deposit-taking institutions as producers of services for account holders. This approach assumes that these services are produced by utilizing capital and labor inputs (Berger and Humphrey, 1997). Further, the production approach considers that financial institutions provide transactions on deposit accounts and also provide loans and advances. Thus, the number of accounts in different loans and deposit categories are generally taken to be the appropriate measures of outputs under this approach (Drake and Weyman-Jones, 1992). Berger and Humphrey (1997) also stress this argument and suggest that the best measure of output is number and type of transactions for the period. However, this approach is inconvenient because not all such data are readily available. Hence, the production approach is more suitable for the evaluation of the relative efficiency of single branches within the institution. Further, the production approach places less emphasis on the transfer of funds as a bank’s main role as a financial intermediary. In contrast, the intermediation approach evaluates the entire institution (Berger and Humphrey, 1997).
The assets approach, the value-added approach and the user-cost approach provide guidelines on how to identify variables in different ways. According to Favero and Papi 35
(1995), in the assets approach, outputs are strictly defined by assets and mainly by the production of loans in which firms have advantages over other institutions in the industry. Under the asset approach, loans and other assets are considered as outputs, while deposits, other liabilities, labor and physical capital are considered as inputs (Drake and Weyman-Jones, 1992).
Generally, the adoption of a particular approach to modeling and measuring efficiency depends on the available data in the industry. However, neither of the two main approaches is perfect, because they cannot fully capture the dual role of financial institutions as providers of transactions or document processing services and also being financial intermediaries (Berger and Humphrey, 1997). Therefore, we could argue that the production approach may be somewhat better for evaluating the efficiencies of bank branches, whereas the intermediation approach may be more appropriate for evaluating financial institutions as a whole. The extant literature indicates that the intermediation approach is the most favored approach between researchers. A few studies, such as (Kao and Liu, 2009; Asaftei, 2008; Suhaimi, 2008; among others), used a combination of more than one approach; we call this a mixed approach and it represents 19% of the total applications.
2.6
Productivity Concept
Productivity refers to the technical efficiency of production relative to the allocation of resources of enterprises (Ahmed, 2014). Productivity is a firm’s effectiveness in using all its resources (Monga, 1992). According to Syverson (2011), productivity is efficiency in production. That is, how much output is obtained from a given set of inputs. In the view of Forfas (2009), productivity is a measure of a firm’s return on investment and is a basic
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indicator of how efficiently inputs are converted to outputs. Productivity is typically expressed as a ratio of overall inputs (labor, raw materials or other resources) to output (products or value added) (Syverson, 2011 and Forfas, 2009). Fulginti et al (2004) and Ahuja (2006) also defined productivity as output per unit of input. Ahmed (2003), described productivity is an efficiency index that measures the rate of output per unit of input used.
Productivity is seen as a very important indicator in firm performance. According to Drucker (1980), a firm’s productivity objectives provide the sense of direction and control over resources used. Productivity therefore explains the effciency with which factors of production employed are used by a firm.
Productivity growth, as measured by either partial productivity or total factor productivity indices (an index of output divided by an index of total input usage), is synonymous with technical change (or shifts in the technology boundary), assuming that observed output is best practice or frontier output. However, in a world in which inefficiency exists, total factor productivity can no longer be interpreted as technical progress, unless there is either no technical inefficiency or unless technical inefficiency does not change over time. If these conditions do not hold, then total factor productivity is redefined as the net effect of changes in efficiency (or movements relative to the existing frontier) and shifts in the production frontier (or technical change). This distinction is important from a policy viewpoint, since changes in productivity growth due to inefficiency suggest different policies to those concerning technical change (Grosskopf, 1993). For example, slow productivity growth due to inefficiency may be due to institutional barriers to the
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diffusion of innovations. In this case, policies to remove these barriers may be more effective in improving productivity than those aimed at innovation per se.
In this study, however, the three terms above have different meanings, since technical efficiency change and technical change are components of productivity change. In order to understand clearly the meanings of technical efficiency change and technical change, mathematical expressions are needed. These derivations are deferred to and further discussed in Chapter 4 (the Methodology).
2.6.1 Measuring Productivity (Partial and Total Factor Productivity) The two basic methods of measuring productivity are Partial and Total Factor Productivity (TFP). Partial Factor Productivity (PFP), also known as Single-Factor Productivity, measures the relationship between one or more outputs relative to a single input, such as land or labor. PFP measures reflect units of output produced per unit of a particular input. Thus, PFP focuses on the output achieved relative to one type of input. Labor productivity (person-hours worked) is the most common measure of this type, though occasionally, capital or even materials productivity measures are used (Syverson, 2011). Some application of partial productivity is found in Craig et al (1997), which shows the direction of technical change in a group of developed and developing countries, using the famous graphical techniques developed by Hayami and Ruttan (1985).
PFP has a number of weaknesses. Firstly, it has a number of measures that embrace a wide range of influencers, based on the different inputs. PFP is, therefore, believed to be
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misleading as it considers one input (such as labor) at a time, thereby, ignoring all other possible relevant inputs (such as material and capital) of production. This is a reflection of the complex nature of the concept of productivity. Secondly, PFP levels are affected by the intensity of use of the excluded inputs. For instance, two producers may have quite different labor productivity levels, even though they have the same production technology, if one is relatively capital-intensive, say because they face different factor prices.
Due to the weaknesses in PFP, contemporary researchers often use a productivity concept that is invariant to the intensity of use of observable factor inputs. This measure is called Total Factor Productivity (TFP). (It is also sometimes called Multifactor Productivity). Trueblood (1996) argues that TFP is more complex than Partial Factor Productivity but theoretically appealing, as it accounts for elasticities of substitution among all inputs.
Grosskopf (1993) defined Total Factor Productivity growth as the net effect of changes in efficiency and shifts in the production frontier, the latter being technical change. TFP can be broken down into two components, namely efficiency change and technical change, according to Grosskopf (1993). The term, Technical Change, is synonymous with technological change or technological or technical progress. It is also often referred to as innovation.
Total factor productivity (TFP) combines all inputs and outputs involved in the production process. It is the ratio of an index of aggregate outputs to an index of aggregate inputs. If the ratio increases, it can be interpreted to mean that more outputs can
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be obtained for a given level of input. As a result, TFP tends to be a more useful measure, but it can also be more difficult to calculate. Conceptually, TFP changes reflect shifts in the isoquants of a production function: a change in output produced from a fixed set of inputs. Higher-TFP producers will produce greater amounts of output with the same set of observable inputs than lower-TFP producers and, hence, have isoquants that are shifted up and to the right. Factor price variation that drives factor intensity differences does not affect TFP, because it induces movements along isoquants rather than shifts in isoquants (Monika, 2013). In this thesis, Total Factor Productivity measurement is used. The measurement of TFP is discussed further in the chapter on methodology.
2.6.2 Determinants of Bank Efficiency and Productivity Some unique factors based on the type and the operating environment of the firm may influence the efficiency of any firm. As Lovell (1993) indicates, “The identification of the factors that explain differences in efficiency is essential for improving the results of firms, although, unfortunately, economic theory does not supply a theoretical model of the determinants of efficiency”.
A plethora of studies has itemized the global determinants of bank efficiency and productivity. The existing literature identified two main broad determinants of efficiency and productivity treated as environmental factors: the internal (bank-specific factors) and external (environmental) factors. Commonly found bank-specific factors are size, profitability, capitalization, ownership type, loans to assets, age, location, risk profile, return on assets and return on equity. External factors include market concentration, presence of foreign banks, ratios of private investments to GDP, fiscal deficits to GDP, GDP growth, capital adequacy regulations, private monitoring, banks’ activities, deposit
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insurance schemes, supervisory power, and bank entry into the industry. These variables are used to explain the differences in efficiency according to the selected variables. Although there are conflicts in the results, using such variables could help banks or any industry players to take their decisions.
Hughes and Mester (2008) observed that banks’ ability to perform efficiently – to obtain accurate information concerning its customers’ financial prospects and to write effective contracts and to enforce them – depends, in part, on the property rights, legal, regulatory, and contracting environments in which they operate. Such an environment includes accounting practices, chartering rules, government regulations, and the market conditions (for example, market power) under which banks operate. Differences in these features across political jurisdictions can lead to differences in the efficiency of banks across jurisdictions. This means that the efficiency of a bank cannot be determined in isolation, but both endogenous and exogenous factors are very crucial in bank efficiency analysis.
Based on a review of studies by Allen and Rai (1996), Berger and Mester (1997), Casu and Molyneux (2003), Fries and Taci (2005), and Bonin et al (2005), Kosak and Zajc (2009) formed three groups of variables that are assumed to be associated with changes in efficiency and productivity across banks. These variables included country level variables (macroeconomic conditions), structure of banking industry variables (intermediation ratios, demand density, deposit per capita and concentration ratios), and bank specific variables (ownership status, return on average assets, net interest margins, etc.). Kamaruddin et al (2008) grouped the determinants of efficiency under six categories including (i) ownership structure, (ii) market structure, (iii) bank profitability, (iv) risk structure, (v) asset quality structure, and (vi) corporate social responsibility. 41
Moreover, studies have established that bank efficiency is also affected by the institutional settings under which they operate (Haselmann and Wachtel, 2010). For instance, in most transitional economies, economic reform programs led to the development of key institutional frameworks in the banking sector, leading to cost reductions in the initial stages of the reforms and over time increments in costs of implementation of reforms (Fries and Taci, 2005).
Griogorian and Manola (2002) argue that different regulatory measures affect cost efficiencies differently. For example, higher minimum capital requirement for banks improved cost efficiency, but limits on exposure to a single borrower had no significant impact. In contrast, Asafteri and Kumbhakar (2008) and Tockhov and Nenovsky (2009) found a negative impact of banking regulatory changes on bank cost efficiency.
2.7
Empirical Literature on Bank Efficiency and Productivity in Sub-Saharan
African (SSA) Countries There is a steady growth in the number of studies on banking efficiency and productivity for Sub-Saharan African (SSA) countries. This is because most countries want to assess the level of achievement, after implementing different reforms. Before the reforms, developing countries’ financial institutions were experiencing a number of problems, such as poor service delivery, high-level of credit risk, poor quality of loans, limited and inadequate capitalization and operational inefficiencies. Others were high incidence of non-performing loans as well as high liquidity risks. The study of commercial banks in SSA is very important because most of these countries have similar regulatory conditions and other contingency factors.
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Generally, for Sub-Saharan African (SSA) countries, studies of banking efficiency and productivity are limited and include, among others, Ikhide (2000) and Adongo et al (2005a; 2005b) for Namibia; Hauner and Peiris (2008) and Beck and Hesse (2009) for Uganda, and Čihák and Podpiera (2005) for Kenya, Tanzania and Uganda. The extant literature on bank efficiency and performance in Sub-Saharan Africa have mainly focused on cost and profit efficiency, comparison of foreign banks and domestic banks’ efficiency, foreign banks’ penetration and the economies of scale, etc.
Ikhide (2000) and Adongo et al (2005a; 2005b) reached contrasting conclusions on the efficiency of Namibian banks, with the former positing that banks in Namibia were characterized by inefficiency, while Adongo et al (2005a; 2005b) indicated that Namibian banks compared relatively well with international evidence. The contrasting evidence is attributed to differences in the approaches used to estimate bank efficiency and the variables included in the specified models.
On the other hand, Čihák and Podpiera (2005) and Hauner and Peiris (2008) reported similar results for East African countries, noting that an increase in bank competition was associated with a rise in efficiency. Cihak and Podpiera (2005) independently found that the banking systems of Kenya, Tanzania and Uganda were inefficient and had only a limited intermediation role, despite recent reforms and even with the presence of international banks. In contrast, Beck and Hesse (2009) observed that banking spreads have been significantly high in Uganda, indicating inadequate efficiency in the banking industry. It is important, however, to point out that Beck and Hesse (2009) inferred efficiency from high spreads rather than rely on more robust techniques to estimate 43
efficiency. It is well acknowledged that an efficiency analysis based on ratios and spreads suffers from a number of shortcomings and may not provide reliable estimates of banking efficiency.
Kablan (2007) and Kirkipatrick et al (2008) estimated banking efficiency for countries in the West African Monetary Union (WAEMEU) and SSA, respectively. Kablan (2007) observed that banking efficiency was generally higher in the majority of WAEMU states except for Burkina Faso and Cote d’Ivoire, while Kirkipatrick et al (2008) found lower profit X-inefficiency than cost X-inefficiency for SSA countries. Both studies observed that inefficiency was sensitive to the quality of loans and bank soundness. Interestingly, Kirkipatrick et al (2008) also found a negative effect of financial liberalization but found that foreign bank penetration helped dampen cost X-inefficiency. Although many countries were already implementing financial reforms during this period, it is important to note that the banking industry in majority of these countries also experienced significant instability. It is not surprising, therefore, that cost-efficiency was susceptive to risk and solvency factors and the turbulent economic environment.
Tefula and Murinde (2002), using translog stochastic cost and profit frontier approach study measurement and determinants of X-inefficiency in commercial banks in SubSaharan Africa, found that the degree of cost inefficiency was exacerbated by bad loans, high capital ratio and financial liberalization. Moreover, it was shown that the large banks were more efficient, and the level of foreign bank penetration reduces X- inefficiency.
Kiyota (2011) provides a comprehensive banking sector efficiency analysis of Sub-
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Saharan African countries (SSA). He employs two stage analyses in the examination of profit efficiency and cost efficiency of commercial banks: the Stochastic Frontier approach and the Tobit Regression. The Stochastic Frontier approach was utilized to estimate profit efficiency and cost efficiency, whereas the Tobit Regression was employed to provide cross-country evidence of the influence of environmental factors on efficiency in Sub-Saharan African commercial banks. In a similar vein, Kiyota (2011) examined whether foreign banks are more efficient than domestic banks. The empirical results of the study indicated that foreign banks outperform domestic banks, which are consistent with the Agency Theory postulates, that is, banks with higher leverage or lower equity are associated with higher profit efficiency. In terms of bank size, smaller banks were more profit-efficient, whereas medium-size and larger banks are cost-efficient. On another hand, the findings of the study suggested that non-SSA foreign banks were more cost-efficient than Sub-Saharan foreign as well as domestic banks, for the period of 20002003.
Using Econometrics such as the Cost Frontier approach and the Operating Ratios, Ikhide (2008) examined the efficiency of commercial banks in Namibia. Different from other studies, Ikhide (2008) integrated the Operating Ratio and the Stochastic Frontier approach. In the study, he used interest margin, interest income, gross margin, operating costs, loan-loss provision, total cost pre-tax income and after-tax income. Similar to Musonda (2008), Ikhide (2008) employed the trans logarithmic cost function with labor, capital, and deposits as inputs, while price of labor, capital and deposit, respectively, were the outputs. The empirical findings from the translog cost function established the existence of economies of scale of banking operations in Namibia, which can be exploited through banks expanding their scale of operation. The study also established
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that more banks could still join the industry without compromising the industry profitability since most of the existing commercial banks were operating under the falling portion of their average cost curve.
Musonda (2008) analyzed the advantages and disadvantages of the different approaches and applied the Stochastic Frontier Approach (SFA), using a single stage maximum likelihood estimation procedure applied to a stochastic frontier cost function. The study applied the intermediation approach, where three inputs were selected, namely labor, funds and capital, with corresponding price defined by labor cost, funding cost as well as capital cost, on the other hand. The outputs were defined by net loans overdraft and interbank placement (loans). The empirical findings observed that Zambian banks are, on average, inefficient in order of 11.4%. Furthermore, it was also found that foreign banks are more efficient than domestic banks, and the main cause of inefficiency was attributed significantly to regulatory framework.
Kamau (2011), using the non-parametric Data Envelopment Analysis (DEA), investigated intermediation efficiency and productivity in Kenyan commercial banks, in the banking sector, in the post-liberalization period.. The results showed that, though the banks were not fully efficient in all aspects, they performed fairly well during the period under study. Moreover, the commercial banks’ efficiency score was not less than 40% at any point. In terms of ownership and size, foreign banks were found to be more efficient than local banks, and in the local category, local private banks were more efficient than local public banks, while large-size banks were more efficient than medium and small-size banks.
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Using Data Envelopment Analysis (DEA), Soboddu and Akiedo (1998) investigated bank performance and supervision in Nigeria during the transition and deregulated economy. The study assessed whether the policy package resulted in an improvement in the technical efficiency of the banking industry. They found that banking industry intermediation efficiency declined significantly during the years immediately following the adoption of the deregulation, with slight improvements noticed only in recent times. The study concluded that inconsistent policies to which the sector was subjected during this period might have been the cause. Furthermore, the study revealed that private and government banks differ in their technical efficiency; the average efficiency measures were higher for private banks than for the government banks.
Ncube (2009) examined the South African banking sector efficiency. The main focus of the study was on the cost and profit efficiency of banks in South Africa. Applying the stochastic frontier model, the study examined cost and profit efficiency of small and four large banks. The results indicated that, over the period of study (2000-2005), South African banks significantly improved their cost efficiencies but no significant gains in profitability fronts. The results also indicated that there was a weak positive correlation between the cost and profit efficiencies of South African banks. In addition, most costefficient banks were also most profit efficient. A regression analysis of cost efficiency in bank size suggested a negative relationship, with cost efficiency declining with the increasing bank size.
Aikaeli (2008) investigated efficiency of commercial banks in Tanzania, utilizing secondary time series of the Tanzania banking sector (1998-2004). Aikaeli examined technical, scale and cost efficiency of banks. The Data Envelopment Analysis (DEA) 47
model was applied to derive efficiency estimates of the banks. The results of the study suggested that the overall bank efficiency was fair, and there was room for marked improvements on all the three aspects of efficiency examined. Foreign banks ranked highest in terms of technical efficiency, followed by small banks and then large domestic banks.
Hauner and Peiris (2008) investigated whether the banking sector reforms undertaken in Uganda to improve competition and efficiency have been effective. Using the model of Panzar and Rosse (1987) to assess competitiveness and the Data Envelopment Analysis (DEA) to assess efficiency, they found that competition has increased significantly and has been associated with a rise in efficiency.
2.8 Review of Empirical Literature on Rural Banking Efficiency and Productivity There are several empirical studies focusing directly on rural banking efficiency and productivity in developing countries such India, Philippines, Ghana, and Indonesia.
Gordo (2013) used DEA (window analysis) to estimate technical efficiencies and producutvity of Philippine banks, including rural banks for the period 1999-2009. The results showed a general decline in technical efficiency over the period of the study. The results also indicated that Philipine banks experienced decline in productivity, which was mainly due to declines technical efficiency changes with weak technological progress over the study period. The study was however not conclusive as the differences in efficiencies and changes in total factor productivity are not supported statistically.
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Ahmed (2014) assessed the productivity performance of rural banks in India using accounting based methods. Productivity was estimated in terms of labour, branch, return on asset (ROA) and investment (ROI), profit per cent of business volume, etc. for a case study rural bank (Meghalaya Rural Bank) and compared to trends of rural banks in the national context. The study found the case bank relative to the national context utilised its resources efficiently and also that productivity changes are higly affected by the nonprofit activities and low payment of loans by rural clients.
Khankhoje and Sathye (2008) investigated the effect of restructuring on the production efficiency of regional rural banks for the period 1990 to 2002. The study applied nonparametric data envelopment analysis (DEA). Using interest and non-interest income as outputs and interest and non-interest expeses as inputs, they found that restructuring significantly improved the production efficiency of the RRBs in India.
Amarender (2006) also examined total factor productivity technical and scale efficiency changes in India regional rural banks by using data from 192 banks for the period 1996 to 2002. Based on the assets and number of branches under each bank, the regional rural banks exhibited significant economies of scale. The study therefore recommended bank enlargement and mergers to take advantage of the scale economies. On the total factor productivity growth of rural banks, it was revealed that rural banks situated in all regions (both economically developed and low banking density regions) showed significant
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growth in productivity. Generally the study concluded that there was a convergence of efficiency of rural banks during the study period.
In the only known study on Ghana rural banks by Danquah et al. (2013) an attempt was made to estimate the technical efficiency. They estimated a “true” random effect and random parameter stochastic frontier models in a panel data framework using loans as output and deposits and fixed assets (physical capital) as inputs. The study applied the two models using annual data of rural and community banks in Ghana from 2006 to 2011. They found that the two models address the issue of unobserved heterogeneity, and therefore omitted unobserved heterogeneity in the production model may always show up in the estimated inefficiency. The results also indicated that average technical effi-ciency of RCBs in Ghana, as a whole is 66% for the true random effects model, and 63% for the random parame-ter model. Both models indicate increases in efficiency levels from the 2006-2008 period, followed by a decrease in the 2008-2010 period, and a marginal increase from 2010 to 2011. The period of increasing efficiency levels is associated with a positive growth trend for deposits and loan balances, but loan balances grew at a faster rate, showing RCBs were successful in increasing lending during the study period.
Mongid et al. (2010) estimated the technical and scale efficiency of rural banks in Indonesia during the period of 2006 and 2007 by using the non-parametric approach – Data Envelopment Analysis (DEA). The study used the intermediation approach defining bank total earning assets as outputs and total deposits and total overhead expenses as inputs. The results revealed that the estimates of technical efficiency was lower than scale efficiency, which indicates that portion of overall inefficiency, is due to producing below 50
the production frontier rather than producing at an inefficient scale. The study also found that majority of the rural banks explored showed below optimal scale efficiency implying that output could be expanded to reach the optimal scale.
2.9 Extant Evidence on Bank Efficiency and Productivity in Ghana The following section presents the related literature on efficiency in the financial sector in Ghana. This is to provide a contextual view of the existing gap in research in relation to this study. The bank efficiency literature on Ghana is also limited, especially with regard to Rural and Community Banks (RCBs). The accessible studies have all focused on the mainstream commercial banks (Adjei-Frimpong et al, 2013; Frimpong, 2010; Ziorklui, 2001) and microfinance institutions (Oteng-Abayie et al, 2012). In a recent study, AdjeiFrimpong et al (2013a) analyzed the efficiency of the banking industry in Ghana over the period of 2001–2010, using the data envelopment analysis. The study investigated the impact of size, capitalization, loan loss provision, inflation rate and GDP growth rate on Ghana’s bank efficiency, using both static and dynamic panel data models. The FixedEffects Estimator was used to estimate the static model, whereas the Dynamic model was estimated by the two-step system GMM estimator. The results suggested that banks in Ghana are inefficient. The study also revealed that well-capitalized banks in Ghana are less cost-efficient. In addition, it was found that bank size has no influence on bank cost efficiency, suggesting that larger banks in Ghana have no cost advantages over their smaller counterparts. The findings also exhibited that loan loss provision ratio has no effect on bank efficiency in Ghana. This study finds that the GDP growth rate negatively influences bank cost efficiency and that, lagged cost efficiency tends to persist from year to year.
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In another study, Adjei-Frimpong et al (2013b) also examined the causal link between bank efficiency and bank competition. The study estimated bank competition with the Lerner index and bank cost efficiency with the Data Envelopment analysis, using annual data over the period of 2001–2010. Using the system generalized method of moments (system GMM) estimator, the results suggest that bank cost efficiency positively Granger-causes market power and, hence, causality negatively runs from bank cost efficiency to bank competition, indicating that bank cost efficiency precedes bank competition. However, the reverse causality running from bank competition to bank cost efficiency was not supported.
Frimpong (2010) investigated the relative efficiency of Ghanaian banks for the year 2007, using DEA approach. The study, among other things, found that the average technical efficiency of the banking sector, as at 2007, was 74%. The study also showed 18 banks in a sample of 22 banks were efficient; only 4 banks were inefficient in 2007. In terms of group efficiency, the study found that private domestic banks were the most technically efficient group, followed by the foreign banks and the state-owned banks, in that order.
Akoena et al (2009) studied technical efficiency and economies of a scale of categories of Ghanaian banks. Using the non-parametric approach of the data envelopment analysis, the study revealed that the technical efficiencies of large banks, on one side, and small banks, on the other side, are similar. Further, they established that small banks have larger scale efficiencies than the big banks. This implies that (on the average, at least) the large banks in Ghana are more removed from the point of their lowest average costs than the small banks. Thus, bank consolidation, mergers, and the recapitalization drive initiated by
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the Central Bank must be cautiously implemented. Using the same model, Buchs and Mathiesen (2005) found that bank size is a determining factor of bank revenue in Ghana, and foreign banks are more efficient in generating revenue (interest, commissions, and fees).
The existing surveys in the literature on Ghana indicate an absence of studies on Rural and Community Banks, possibly, due to the difficulty in obtaining reliable and comprehensive data. The present study fills the literature gap in a unique way through primary data collection on Ghanaian banks.
2.10 Chapter Summary The chapter dealt with a review of efficiency and productivity concepts and their measurement, without detailed mathematical or statistical derivations. It found that estimating the efficiency of decision-making units is vital in ensuring that scarce economic resources are put into good use to attain maximum satisfaction (utility). The literature suggests that, especially in the financial sector, classical methods of accounting, though simplistic, do not convey in-depth information on efficiency, hence, the recent development of parametric and non-parametric methods. Unfortunately, though many empirical studies have been conducted elsewhere, only a few of such works have focused on Sub-Saharan African countries. Even the few that focused on SSA countries have largely focused on cross-country differences, the effects of reforms and the comparison of foreign and local banks. Whilst much focus has been given to cost and profit efficiencies; little attention has been given to the technical efficiency of financial institutions and to rural and community banks. Even in Ghana, not much work has been conducted on rural and community banks. Most empirical studies have focused on mainstream commercial
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banks and microfinance. It is for this purpose that the significance of this study lies: to close the existing gap and contribute to literature.
The relevant research methods will be reviewed in the methodology sections of the various empirical chapters that will follow from Chapter Five to Chapter Seven. The next chapter will deal with the banking sector and the development of the Rural and Community Banks in Ghana.
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CHAPTER THREE A REVIEW OF THE RURAL BANKING SECTOR IN GHANA 3.0 Introduction The aim of this chapter is to provide an overview of the developments in the rural banking sector in Ghana since its inception. Specifically, the chapter provides the settings compulsory for understanding the productivity and efficiency analysis of RCBs in Ghana, as presented in subsequent chapters of this study. As unit banks, RCBs, as earlier stated, play an important role in organizing rural finance and stimulate economic activities. Though they are hooked by lots of operational challenges in meeting their goals and mission, Rural and Community Banks (RCBs), in general, play a key role in ensuring a complete structure of the banking sector. The chapter is organized as follows: Section 1 reviews the structure of the banking sector in Ghana and exposes the unique role RCBs play in ensuring a dense banking economy. Section 2 illustrates the developments and structure of the rural banking sector in Ghana. The reforms that have been implemented and their associated impacts on rural banking are then presented in Section 3, followed by Section 4, which presents a review of the financial performance of the rural banking sector in Ghana. The final part of the chapter, Section 5, then presents the summary and concluding remarks.
3.1 Structure of the Banking Sector in Ghana The banking sector in Ghana has experienced critical transformations in its structure, from a highly public-owned market to its current laissez-faire structure, with the influx of more domestic and foreign private ownerships. These transformations were driven by “technological innovation, government regulation, economic and financial deregulation, information and communication technology; and opening-up to international competition;
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corporate behavior, such as growing disintermediation and increased emphasis on shareholder value that are changing incessantly” (Amidu and Hinson, 2006; Nabieu, 2013). The change has been key to sustaining economic growth and capital investments in the economy of Ghana. It is estimated that, overall, the banking sector currently carries up to about 50% of the services sector contribution of the Gross Domestic Product (GDP) (ISSER, 2011). Supervised by the Bank of Ghana (BoG), the financial sector in Ghana is made up of three main tiers: the formal banking sector, the non-banking sector and the informal sector.
Figure 3.1: Structure of the Banking Sector in Ghana BANK OF GHANA (BoG)
NON BANK FINANCIAL INSTITUTIONS (NBFIs)
FORMAL BANKS
UNIVERSAL BANKS (COMMERCI AL BANKS)
RURAL AND COMMUNITY BANKS
SAVINGS AND LOANS COMPANIES (SLCs)
INFORMAL SECTOR
MICRO CREDIT BUREAUX
FINANCE AND LEASING
MORTGAGE FINANCE
FINANCE
ROSCAS (SUSU) MONEY LENDERS
COMPANIES
Source: Author’s Construct (2014)
From the structure presented in Figure 3.1, the BoG is the apex institution obligated to provide the sound and efficient financial system necessary for wealth creation, economic growth and development. Authorized by Act 612 and Act 673, the BoG is concerned with such broad activities as monetary management, regulation of the financial system and direct involvement in the development of the economy in order to serve the interest of financial institutions and their clients as well as other users of financial services and the
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economy at large. Among the many reforms that the BoG has facilitated for the efficient running of the financial wheel in Ghana, a major policy initiative has been the enactment of the Financial Institutions (Non-Banking) Law in 1993, which saw the proliferation of Non-Bank Financial Institutions (NBFIs) in Ghana, including Savings and Loans Companies (SandLs), Cooperative Unions (CUs), finance houses, mortgage companies, among others, consequently opening up the financial sector for enhanced financial intermediation. Currently, it is estimated that 145 NBFIs, including 90 microfinance companies, 28 finance houses, and 21 savings and loans companies operate in Ghana (Bank of Ghana).
The informal sector, on the other hand, is basically made up of the Rotatory Savings Companies (ROSCAS), which are locally referred to as the susu companies and moneylenders. The informal sector is a potent subsector with an estimated value of more than £75-million untapped savings. Estimates also show that the average ROSCA has the potential of engaging over 10,000 depositors (Microfinance Insider, 2008; Steel and Andah, 2003).
The formal financial institutions are those incorporated under the Companies Code 1963 and licensed by the Bank of Ghana (BOG) under either the Banking Law 1989 or the Financial Institutions (Non-Banking) Law 1993 (NBFI Law) to provide financial services under the Bank of Ghana regulation (Steel and Andah, 2003). As shown on Figure 3.1, the formal banking sector comprises the Universal Banks and the Rural and Community Banks (RCBs). These institutions operate as licensed and statutory financial institutions engaged in the business of banking under the banking laws of Ghana and are required to 57
have a large capital base with good liquidity reserve. It must be stated, however, that, until 2003, banks were not allowed to operate as universal banks. Until the adoption of the universal banking policy in 2003, banks were constrained separately to the traditional activities of commercial (retail) banking, investment banking, development banking, and merchant banking. According to Bank of Ghana (2013), as at December 2013, there were 26 Class-1 licensed universal banks operating in Ghana. These comprised 15 foreignowned and 11 Ghanaian-owned. The top five universal banks with large market share as at 2012 included Ghana Commercial Bank (GCB - 12.6%); Ecobank Ghana (EBG 11.80%); Standard Chartered Bank (SCB - 10.00%); and Barclays Bank Ghana Limited (BBGL - 9.80%).
The RCBs, on the other hand, operate under the apex body of ARB Apex Bank, which has its delegated authority from the BoG to supervise and streamline rural banking services in Ghana. “The ARB Apex Bank was granted a banking license in 2001 and commenced commercial operations in 2002 with significant financial support from the Rural Financial Services Project (RFSP), which was funded by the World Bank, the International Fund for Agricultural Development (IFAD), and the African Development Bank (AfDB)” (Nair and Fissha, 2010). Current statistics show that 137 RCBs exist in Ghana, with Ashanti (25) and Eastern (22) regions being the most concentrated (Bank of Ghana, 2013).
The banking sector has seen tremendous growth and improvements in performance over the past few years partly due to reforms, mergers and acquisitions, privatizations and competition. Recent acquisitions include Access Bank’s acquisition of Intercontinental 58
Bank of Ghana (ICB) and Ecobank acquiring The Trust Bank Limited (TTL) in 2012; and Fortiz Private Equity Fund acquisition of 90% shares of Merchant Bank Ghana Ltd in 2013. Moreover, key laws and reforms have characterized the banking industry for improvement and efficient financial delivery. Major infrastructural projects essential for improving the electronic payment systems environment have been consistently pursued by the Bank of Ghana (see Table 3.1).
Table 3.1: Selected Reforms and Projects in the Ghanaian Banking Sector 1963 The Companies Act (Act 179) This Act governs the operations of all companies in Ghana, including banks 1989 The Banking Law 1989 1993 The Financial Institutions (Non-Banking) Law 1993 (NBFI Law) 2003 Universal Banking Law By this law, all banks with 70 billion cedis in capital were granted permission to operate in various banking activities. The purpose was to open up the system for healthy competition and facilitate efficiency. 2003 2004
Rural and Financial Services Project (RFSP) The Bank of Ghana Act (Act 612) The Banking Act 2004 replaced the Banking Law 1989 to enable the BoG to strengthen prudential supervision policies.
2006 2006
ARB Apex Bank Ltd. Regulations, 2006 (L.I. 1825) The Foreign Exchange Act (Act 723) The Foreign Exchange Act (Act 723) sanctioned the foreigners the ability to hold local securities. The Insurance Act (Act 724) The Insurance Act was passed to streamline insurance operations with a comprehensive provision for vigorous regulation of the insurance industry and for related matters. The Credit Reporting Act (Act 726) The Credit Reporting Act was enacted to register and regulate credit bureaus, data providers and credit information recipients and their agents. It establishes the conditions for credit reporting in Ghana, with the aim of reducing the risks of lending and sharing data on the debt profile and repayment history of borrowers while protecting borrowers’ rights as far as possible. The Banking Act (Amendment) Act (Act 738) The Banking Act was amended to enable the establishment of international financial services in Ghana. The Anti-Money Laundering Act (Act 749) Anti-Money Laundering Act prohibits money laundering, establishes a Financial Intelligence Center, and provides for matters related to anti-money laundering in Ghana
2006
2007
2007
2008
59
Table 3.1: Cont’d 2008
2008
2009
2010 2011
The Borrowers and Lenders Act (Act 773) The Borrowers and Lenders Act addresses the legal framework for credit; standards of disclosure of information by borrowers and lenders; prohibiting credit practices; and promoting a consistent credit enforcement framework and related matters in the credit market. The Non-Bank Financial Institutions Act (Act 774) The Non-Bank Financial Institutions Act provides a framework to promote effective prudential regulation and supervision for the wide range of nonbank financial institutions. It puts all financial institutions, essentially, on a level regulatory playing field, reduces the scope for regulatory arbitrage, and improves the efficiency of the credit system as a whole. Cheque Code Line Clearing This framework was established to ensure efficiency, reliability and timeliness in the clearing of cheques Ghana Rural Banks Computerization and Interconnectivity Project (GRBCIP) The project was sponsored as part of the Millennium Challenge Fund. The Anti-Money Laundering (Amendments)
Source: Author’s Construct (2014), Based on IMF Country Report (2011).
3.2 Developments and the Structure of Rural Banking in Ghana The rest of the discussion focuses on the activities and the structure of rural banking in Ghana. As cited in Obeng (2008), Ghana, like other Sub-Saharan African countries, has traditionally experienced low productivity, low-income levels, low domestic savings, unemployment, and malnutrition. In 1976, the Ghanaian government, through the Bank of Ghana, established RCBs to channel credit to productive rural ventures and promote rural development.
Rural enterprise finance was extremely limited in Ghana before the First Rural Bank was established in the Central Region as a locally-owned unit bank in 1976. The initial success of the rural banking compelled the BoG to establish guidelines for streamlining operations and the setting up of new RCBs, by 1985. In order to foster collaboration and
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information transfer, the network of RCBs formed the Association of Rural Banks (ARB) in 1980. By 1988, the number of RCBs operating across the country had grown to 122, with growth in deposits and consolidated loans. This growth was driven by a number of factors, including the Akuafo Check Operations, the policy to use RCBs to transmit pension and salary accounts, and the rising interest of rural folks in accessing financial services. Unfortunately, by the turn of the same year, the performance of RCBs had hit a trough, with 98 out of the 122 banks being distressed with nonperforming loans (NPLs) amounting to over 70%. Through a combination of rapid inflation, currency depreciation, economic decline, mismanagement of funds and natural disasters combined with weak supervision, many of the RCBs faced problems, including poor financial intermediation, weak management and staff capacity, and low capitalization. There was a lack of public confidence in RCBs. They had difficulty linking to the financial system (e.g., to obtain specie, purchase Treasury Bills, clear cheques) through correspondent commercial banks, which were also their competitors. These difficulties led the BoG to close as many as 23 distressed RCBs. Only 23 of the 123 RCBs qualified as “satisfactory” in 1992. This forced the BoG to also institute a number of structural reforms to restore confidence in the financial market. The obvious need for re-capitalization and capacity-building was addressed during 1990-94, under the World Bank’s Rural Finance Project, with half of the RCBs achieving “satisfactory” status by 1996.
The Rural Finance Project (RFP), which provided outsourcing and capacity building to the RCBs in terms of financial auditing, loan recovery programs and credit administration systems, was established in 1988. The RFP restructured rural banking operations and streamlined activities of the RCBs, though the achievements were minimal. The
61
combination of very high (62%) primary and secondary reserve requirements imposed by the BoG in 1996 and the high Treasury Bill rates helped to reduce the risk assets and increase net worth, further improving the financial performance of the banks. The number of banks increased to 125 with 55 banks achieving satisfactory performance according to the RFP criteria, with the loan recovery rate of 60% (Osei- Bonsu, 1998). By 1999, the total number of banks had moved up to 134, yet with most RCBs being financially distressed. Twenty-three banks were consequently closed, while 56 of those that remained operational were classified mediocre with a capital adequacy ratio of between 1% - 6% (Steel and Andah, 2003).
The Rural Finance Service Project I (RFSP I) was subsequently designed to address these weaknesses that still plagued the rural bank system by strengthening the capacities of the RCBs individually and as a system, including the creation of the Apex Bank, which was owned by the RCBs themselves. Apex Bank was granted a banking license in 2001 and commenced business in July 2002. The ARB Apex Bank was set up by the BoG to help supervise the network of RCBs in the country. Its mission included transforming RCBs into efficient financial institutions serving their communities. Though the Bank of Ghana performed both on-site and off-site supervisions through its Banking Supervision Department (BSD), effective supervision was made arduous considering the growing number of RCBs springing up across the country. Capital and human resource constraints also made this task very challenging to perform. As a result, poorly-performing banks were starved from the regular on-site inspection they needed (Nair and Fissha, 2010). The setting up of the ARB Apex bank was vital to the progress of the rural banking sector. Key services that the ARB Apex Bank offers to RCBs include cheque clearing; account maintenance services; investment services; funds transfer among RCBs; credit facilities
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to meet liquidity needs; supply of cash (bank notes); guarantee support for RCBs’ own cheques; special assistance to distressed or marginal RCBs; training of staff and directors; computerization; and bank operation inspection. A move away from the manual system of reporting was also initiated through the electronic Financial Analysis and Surveillance System (e-FASS). By the e-FASS, RCBs were required to send periodic returns electronically to both the ARB Apex and the BoG (Asiedu-Mante, 2011).
By 2008, the number of RCBs has risen to 127, with most of the RCBs located in the southern sector of Ghana, since only 11% of banks were located in the northern sector (Asiedu-Mante, 2011). The main reason being that the Ghanaian population is skewed towards the southern sector (about 82%). As at the end of 2012, the growth of RCBs has reached a total of 136 banks, with controlled assets amounting to 4.8 per cent of total assets of banks and NBFIs, compared with 4.6 per cent in 2011. Currently, there are 137 RCBs with about 651 branches (agencies) in Ghana (Bank of Ghana, 2012).
The structure of rural and community banks is uniquely set. Unlike the universal banks, RCBs are required to function within 53 000 km2 radius and to operate as unit banks with shareholders typically from the local community. Each shareholder is limited by law on the amount of shares it can control within the group. The current practice is that, for corporate organizations, shares must not exceed 50% of total floated shares, whilst individuals and other groups are capped to hold a maximum of 30% and 40% respectively (Nair and Fissha, 2010). The interests of the shareholders are then carried by a board of directors who are elected by the shareholders within the community. The board of directors then functions as the internal supervisors and audits the decisions of the management staff, headed by the general manager (see Figure 3.2). 63
Figure 3.2: A Typical Organization of RCBs
Board of Directors
Internal Controls
Bank Manager
Finance Department
Credit Department
Microfinance Department
Information and Communication Department
Human Resource Department
Source: Author’s Construct Based on Nair and Fissha (2010)
“The core management staffs of RCBs include an internal auditor supported by assistant accountants; a finance officer; a credit head supported by credit officers and project officers in charge of the microfinance portfolio; and a system administrator, if a bank is computerized. Some larger banks have additional departments, such as research and business development support units. At the branch level, the structure typically includes a branch manager, an accountant, credit officers, clerks and cashiers, and support staffs. Rural banks that provide susu products have susu supervisors and susu collectors at the branch levels” (Nair and Fissha, 2010).
One of the challenges to the growth and success of rural banking in Ghana has been the seeming lack of qualified personnel, as compared to the universal banks. Nair and Fissha (2010) attribute this to the high opportunity cost of recruiting professionals and limited rural resources. As a result, recruitment is based on other social indicators, aside individual competencies. This has, generally, led to the huge chunk of wastes experienced in the services and management of RCBs.
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3.3 Rural Banking Reforms in Ghana The supreme purpose for the introduction of the rural banking scheme was to bring desired financial services and products to the doors of the rural folks in a sustainable approach, such that the quantity and quality of rural financial intermediation can be fostered for rural growth and development. To this day, various formalized guidelines and reforms have been facilitated to ensure the smooth implementation of rural banking. These reforms can be grouped under three main categories: regulatory and legal reforms, financial restructuring, and institutional restructuring.
3.3.1 Regulatory and Legal Reforms The primary policy to reforming activities in the rural banking sector has been through the legal and regulatory measures. Indeed, several changes have been made in the reserve requirement in order to streamline activities. The first minimum paid up increased the required minimal capital of RCBs from GH 5 in 1976 through GH 25 to GH 150 in 1987 (Asiedu-Mante, 2011). Since then, the BoG has cited several reasons for consequent increases in capital requirement, the major one being to strengthen the operational capital of the banks in order to reduce dependency on the Central Bank and customers.
Major attempts have, therefore, been made to reduce the level of risks in the operational, liquidity and credit facilities of RCBs, whilst deepening the financial sector, and support Ghana’s drive for accelerated growth. Unfortunately, for most parts, the RCBs have been struggling to meet these requirements. In 2011, only 106 out of 136 RCBs were able to comply. Indeed the BoG directs that non-complying banks are not permitted to open new branches or to pay dividends until they have met this compliance criterion. Other regulatory reforms that have affected the rural banking sector in the country include the
65
Bank of Ghana Act 2002 (Act 612), the Banking Act 2004 (Act 673), Companies Code 1963 (Act 179), and the Banking Act 2007.
Figure 3.3: Capital Requirement
2004 2008 2013
Source: Author’s Construct Based on Nair and Fissha (2010)
3.3.2 Financial Restructuring To help sustain and enhance good corporate governance in the RCBs, some reforms were also detailed to ensure management and financial restructuring. This included the setting up of new boards. It also involved recruitment standards in terms of qualification of staff and directors as well as the tenure limits to board members. Financial restructuring measures were directed towards the recapitalization of financially-distressed banks, whilst some which performed poorly were closed down. For instance, RCBs are required to hold 30% of their deposits in BoG bonds and government treasury bills. Through the Rural Finance Project (1989), RCBs were assisted to recover all non-performing loans through an outsourced agent. A recapitalization fund equivalent to the value of the nonperforming loans was set up to supplement the loan collection effort (Nair and Fissha,
66
2010). Also, internal control, internal audit and compliance systems were instituted to ensure efficient financial management. Other prudential requirements to ensure a robust financial stance include a capital adequacy ratio of 10 percent with a liquidity reserve ratio of 43 percent. Concerning credit, RCBs reforms shifted away from the sectorspecific credit to a market-based credit. However, the RCBs were authorized to keep overall exposure limit to 25 percent for secured loans, and 10 percent for unsecured loans.
3.3.3 Institutional Reforms Institutional reforms involved the ARB Apex Bank Ltd. Regulations 2006 (L.I. 1825) grant the ARB Apex Bank more legal flexibilities to conduct its role as the supervisory body to “provide banking and non-banking support services to the RCBs with the aim of improving their operational efficiency and thereby transforming them into efficient financial institutions which could effectively address the banking needs of the communities in which they operate” (Asiedu-Mante, 2011). Institutional restructuring was also to provide capacity building in terms of staff training, computerization, donor support, monitoring and supervision and other technical support systems. Imminent projects undertaken to strengthen the institutions include the Rural Financial Services Project (RFSP, 2000 - 2007), Support Program for Enterprise Empowerment and Development (SPEED, 2004), Ghana Rural Banks Computerization and Interconnectivity Project (GRBCIP) and the Rural and Agricultural Finance Program (RAFiP). These projects embedded capacity-building programs, which were directed at enhancing access to financial services through an improved outreach, operational efficiency and technical networks through staff training and investments in technologies. Technical supports were also given to BoG and ARB Apex Bank in the areas of supervision and monitoring,
67
whilst management staffs of RCBs were taken through rudimentary management training and given assistance.
3.4 A Review of the Financial Performance of the Rural Banking Sector in Ghana The financial and non-financial services that RCBs offer to their customers can be seen as vital to the development of rural communities and their livelihoods. Literature accounts that the relative contribution of RCBs to the mobilization of rural savings and loans and, thus, the promotion of economic activities and the enhancing of the socioeconomic lives of rural dwellers (Steel and Andah, 2003; Afrane, 2007; Chowdhury, 2009; Okukpara, 2009).
The evidence shows the increasing performance of RCBs in terms of savings mobilization and consolidated loans. For 2012, RCBs mobilized about GH¢1.27 billion in savings deposits, and total loans advances of GH¢670 million and a total investment of GH¢0.5 billion. Pre-tax profit stood at GH¢62.42 million; an increase of GH¢26.03 million or 71.5 percent, compared to the 2011 pre-tax earnings of GH¢36.39 million. Total assets also went up by 29.2% to GH¢386.2 million. In 2013, the total assets of RCBs went up by 44.5 per cent to GH¢1,524.0 million, with growth funded mainly by loans and advances, investments, cash, and balances with other banks, which grew by 37.5 percent, 31.2 percent and 15.9 percent, compared to the previous year.
However, a comparison of RCBs performance to the universal institutions indicates a very sluggish performance. Aboagye and Otieku (2010) account that the percentage of RCBs total deposits to overall bank savings averaged only 7%, 4% for loans and 6% for
68
total asset. Bashin and Akpalu (2001) suggest that RCBs must elevate their scope of outreach. Reports indicate that a total of 23 distressed RCBs have been closed down by the BoG since 2007.
Table 3.2: RCBs Performance Classification (BoG) Classification 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2006 2008 2012
Satisfactory 23 43 57 53 61 59 52 53 64 87 82 n/a 85
Mediocre 82 61 51 54 50 55 58 56 47 27 23 n/a 19
Distressed 18 19 19 18 17 17 23 n/a n/a n/a 16 6 15
Sources: Steel and Andah, 2003. BOG Annual Reports (Various).
As shown in Table 3.2, the number of satisfactory RCBs (based on the BOG criterion) has been increasing over the years. The worst performing years were the years between 1992 and 1995, where the number of mediocre banks was significantly more than the number of satisfactory banks. In 1992 and 1993, for instance, the number of distressed banks was close to 78% and 44% of the total number of satisfactory banks. However, from 1996 to date, a greater number of RCBs have been passed as satisfactory banks, although the Bank of Ghana needs to put in place stringent measures to help increase the overall industrial efficiency, as the mediocre banks are still more. Between 1999 and 2001, there was a 64% increase in the number of satisfactory banks.
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It is also observed that, though there has been a persistent increase in the mobilization of rural finance and credit by the RCBs, performance has not been consistent. It is shown, for instance, in Table 3.3 that mobilization of resources contracts for every fourth to first quarter, meanwhile, activities pick up by the third quarter. This is portrayed by the loans or deposit ratio during the periods of analysis. This occurrence is in spite of the growing number of RCBs operating in the country. However, banks appear to be experiencing a surge in total assets, which is exemplified by the presence of shareholder funds, bank credit and total deposits. The increasing amount of shareholder funds is indicative of the progressive acceptance the rural banking sector has enjoyed from the Ghanaian population. It also shows the commitment of the communities to building up their own banking institutions to, consequently, reap some economic benefits.
The developments in the rural sector are reflective of the overall monetary expansion. One development in the monetary sector that has expanded the operations of RCBs has been the advancement in payment systems introduced by the Bank of Ghana: e-zwich, Akuafo checks, internal monetary transfers, etc. Currently, the rural banking sector has been operating the open system, where high performing RCBs have been allowed to open branches at the urban sectors as well, with headquarters situated at the rural communities where they initiated their operations. This has, consequently, resulted in an increase in the branches of units within the sector. Distressed banks and non-compliant RCBs (until they meet the reserve requirements) are, however, not permitted to open new branches or pay dividends to shareholders. It is observed that the general growth in monetary development has been fuelled by developments in the oil sector, which assumed full-scale operations by 2010 (see Table 3.3 for details). The hikes in inflation is attributed to the upward
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adjustments in domestic petroleum prices, the energy crisis and pressures resulting from the effects of the expansionary fiscal stance during the last quarter of 2012 (BoG, 2014).
3.5 Chapter Summary The year 1976 saw a major shift to the efforts of bringing financial services to the doorsteps of the rural people. Since then, rural and community banks have acted as real agents of change in rural communities; with an overlap effect on the whole economy. RCBs have contributed immensely to the mobilization of rural resources and facilitated economic activities within catchment localities. Unfortunately, such benefits were shortlived, following the national wide, structural cracks that slowed down economic growth by the early 1980s: decline in real output coupled with persistent balance of payment deficits.
Structural maladies in the economy transformed into negative growth in the entire financial sector, including the rural banking sector. Additionally, weak internal management controls and inefficiencies saw the erosion of gains made in the sector. This called for financial and banking reforms to instill confidence and mitigate the foreseen breakdown in the rural banking sector. Reforms introduced by the Bank of Ghana to bring regulatory, institutional and financial restructuring saw much advancement in the operations of RCBs, though performance is still not optimal. Unfortunately, the Bank of Ghana has relied mainly on accounting measures to evaluate the performance of RCBs. Such measures have been found not to bring out much information concerning performances for policy-modeling, for instance, whether available resources have been combined optimally to bring out the real outputs. It is upon this shortfall that the premise of this study is set.
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Table 3.3: Selected Performance of the Rural Banking Sector in Ghana and the Economy 2010-2013 RCBs Performance Indicators
2010 Q4 136.46
2011 Q4 na
Q1 188.18
2012 Q2 Q3 196.24 186.85
Q1 204.47
2013 Q2 Q3 234.07 216.55
Q4 202.47
Q4 266.71
289.37
na
384.7
380.22
372.66
461.2
502.96
485.93
449.02
537.67
Loans and Advances
311.06
na
507.64
555.09
611.55
648.52
637.96
674.06
683.46
716.81
Other Assets
122.23
na
200.06
206.36
208.96
211.84
258.17
304.62
298.76
Total Assets
859.13
na
1,280.58
1,337.90
1,380.01
1,524.03
1,603.57
1,697.66
1,647.78
1,852.86
Liabilities (Millions of Ghana Cedis) Total Deposits 667.31 Shareholders’ Funds 104.47
na na
991.88 147.7
1,029.90 160.39
1,053.31 175.85
1,185.57 188.65
1,229.41 231.64
1,272.25 229.35
1,210.34 237.33
1,372.48 246.8
Other Liabilities
87.34
na
141
147.61
150.86
149.81
142.52
196.6
199.71
233.58
Total Liabilities
859.13
na
1,280.58
1,337.90
1,380.01
1,524.03
1,603.57
1,697.66
1,647.78
1,852.86
Financial Indicators Loans/Deposits Ratios
0.46614
na
0.5117957
0.53897
0.580598
0.547011
0.518915
0.529817
0.564684
0.52227
Number of Reporting Banks
135
na
132
133
134
134
134
137
140
140
Monetary Development M2
10273.2
13555.91
10763.776
11407.8
11778.35
13555.91
10763.77
11407.82
11778.35
13555.9
M2+
12949.1
17505.76
13899.76
14886.2
15531.25
17505.76
13899.76
14886.29
15531.25
17505.7
Reserve Money
4445.09
5467.453
3745.3233
4220.83
4394.566
5467.453
3745.323
4220.833
4394.566
5467.45
Treasury Bill - 91 Days
12.3266
9.81
12.126666
11.0366
9.66
9.81
12.12666
11.03666
9.66
9.81
Economic Indicators Cocoa Exports (Vol, metric tons)
705,610
296,481
207,037
503,517
127,620
253,983
196,180
50,341
na
Gold Exports (Vol, ounces)
117,739
1,057,749
880,137
546,272
825,179
900,356
868,959
763,836
na
Crude Oil Exports (Vol, barrels)
7,166,177
5,871,464
5,873,700 6,816,863
7,868,898
9,941,523
8,812,157
8,827,903
na 8.56333
Cash Holdings & Balances with Banks (Millions Ghana Cedis) Bills and Bonds
Inflation (Year on Year)
9.01333
8.563333
9.1233333
8.83666
8.4
8.563333
9.123333
8.836666
8.4
Overall Balance
1,432.92
2,328.79
-1,256.50
-708.05
-302.17
1,055.82
-132.2
-545.55
-991.96
Source: Bank of Ghana, Statistical Bulletins 2012, 2013, 2014
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CHAPTER FOUR RESEARCH METHODOLOGY 4.0 Introduction This chapter explains the methodology that was applied to the study as well as the estimation procedures that were employed. It is noted, however, that, in recent years, the financial institutions efficiency literature has been primarily dominated by the simultaneous application of parametric and non-parametric approaches in evaluating financial institutions’ performance. As Delis et al (2009) explain, imposing more than one technique on the same dataset captures how consistent the efficiency results are, as no technique can suffice for mutual exclusivity or universality. Bauer et al (1998) also confer that once the results obtained from the two methodologies satisfy mutual consistency and believability conditions (consistency with reality), then exploiting a single best frontier technique is empirically tangential. To elucidate their argument, they highlighted that in terms of ranking, time and magnitude of ratios, results from the different approaches should not vary significantly. Hence, the means, standard deviations and other distributional properties should be statistically comparable. For believability, they requested that results should correspond with competitive market conditions and standard non-frontier measures of performance.
Based on the above, the study exploits both the parametric and non-parametric methodologies to estimate the technical efficiency scores of the sample of RCBs in Ghana. The significance of using the two methodologies is established in the comparison dimension it gives to the analysis, owing to the given limitations of each methodology. The parametric methodology involved the use of the Stochastic Frontier models capturing for the basic Battese and Coelli (1995) model, fixed effects, random effect, true fixed
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effect and true random effects estimation procedures. The non-parametric methodology, on the other hand, involved the use of Data Envelopment Approach, with an inputoriented procedure under both constant returns and variable returns to scale. The DEAMalmquist Productivity Index and the SFA divisia index were also employed to capture for productivity changes and their sources.
The section 4.1 of this chapter will, therefore, involve highlighting the non-parametric methods and their variants. Their strengths, weaknesses and significance were dealt with. Section 4.2 throws light on the parametric methods and their variants, also considering strengths, weaknesses, and significance. Section 4.3 focused on the determinants of productivity, and section 4.4 provides a description of the data set and source. The final part, section 4.5 then concludes on the chapter.
4.1 Non-Parametric Method The non-parametric method, which is also known in literature as the mathematical approach, involves the construction of a frontier space, using the input and output information of homogeneous sampled units. The relative deviation of each unit from the estimated frontier curve is then measured as the technical efficiency ratio. “Regularity assumptions are imposed on the empirical production set so that its elements can be characterized as efficient or inefficient” (Caceres, 2002). The most widely used nonparametric approach in efficiency estimation is the Data Envelopment Analysis (DEA) technique.
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4.1.1 Data Envelopment Analysis (DEA) The DEA involves linear programming estimation of the observed data sets to construct a convex, piece wise, and quasi envelop of data points to create a best fit isoquant. This is then used to evaluate the relative efficiency of firms by comparing output and input ratios relative to the surface. The underpinning premise is that there exists an idealized production point that all decision-making entities aspire to reach. The approach, therefore, grants the opportunity to conduct intra and inter comparisons of units within a sector. The advantage of using the DEA is that its usage is relatively flexible, as it does not impose a functional form on the observed data, and, hence, relaxes on the structure and shape in which the best practice curve should assume. The snag of using the DEA is the difficulty of model specification. Though DEA does not restrict the number of variables, results will tend to be bias if too many variables are selected in the modeling. As a result, it is acknowledged that the total number of banks observed, N, should be thrice the sum of inputs and outputs (N> 3(p + q)), whilst their product should be lesser than N (N>pq) (Abdelkader, 2012).
Mathematically, DEA measures technical efficiency as the ratio of the vector of outputs to discretionary inputs. This ratio (4.1a and b) ensures that efficiency scores are bounded between zero (0) and one (1).
Maximize 𝑇𝐸0 =
∑𝑤 𝑟=1 𝑢𝑟 𝑦𝑟0
∑𝑤 𝑟=1 𝑢𝑟 𝑦𝑟
subject to
(4.1a)
∑𝑐𝑖=1 𝑣𝑖 𝑥𝑖0
𝑗 𝑐 ∑𝑖=1 𝑣𝑖 𝑥𝑖 𝑗
≤ 1; 𝑗 = 1, … 𝑛
(4.1b)
𝑢𝑟 , 𝑣𝑖 ≥ 0𝑟 = 1 … 𝑤; 𝑖 = 1 … 𝑐
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where TE0 = relative efficiency score; w and c are number of outputs and inputs observed; xi and yr are levels of the observed ith input and the observed rth output; v = variable weight of input; and u = variable weight of output.
Intuitively, DEA captures the possible number of inputs that can be transformed to obtain the maximum weight of output. Hence, computations can be conducted from either an input-oriented or output-oriented perspective, depending on the nature of operations of observed units. From an input-oriented perspective, research attempts to measure the proportional reduction of input usage possible to maintain the same level of output. Alternatively, output-oriented measures capture the maximum percentage of output that can be obtained with the same amount of input. This gap of potential improvement in either output or input usage will then represent technical inefficiency.
Indeed, empirical studies do not congregate on the choice of orientation for model specification. According to Delis et al (2009), whilst input orientation is commonly applied due to the discretionary properties of input quantities in the production cycle, other researchers insist on the use of both orientations on the logic that focusing on a single strand will ultimately overlook other sources of inefficiency in the alternative orientation. Murillo-Zamorano (2004) also concludes that the choice of either the inputoriented or output-oriented model must, essentially, be dependent on the nature of datasets.
In this study, the task was set to compute input-oriented measures of DEA efficiency scores, owing to the assumption that the RCBs’ primary focus is financial intermediation.
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Hence, they are involved in receiving of deposits (inputs) from clients and turning them out as loans or credits (output) to borrowers, who might need them. As a result, the level of loans they can give is dependent on the level of inputs they have. Buttressing this point, unlike the commercial banks, which are endowed with huge capital base (inputs) and can, therefore, afford to set output targets to achieve, the RCBs, on the other hand, tend to be inward-looking in terms of setting up of targets or financial goals. That is due to the relatively small resource base of RCBs. They tend to consider how much output they can churn out of the limited input available. Hence, efficient input usage is prioritized rather than maximum output acquisition. Moreover, the characteristics of the data-set obtained only allowed for the usage of the input-oriented model, as, mostly, input variables were gathered.
4.1.2 Returns to Scale Imperatively, DEA efficiency scores are calculated assuming either constant or variable returns to scale. Constant Returns to Scale (CRS) is evoked on the premise that all the units are operating under optimal scalability. Literature converges on the fact that efficiency results obtained under constant returns are similar for both the input-oriented and output-oriented models. This, therefore, suggests that prioritization has no effect on performance, so long as units are operating in optimal scale. Typically, the Charnes, Cooper and Rhodes (CCR) model (1978) is used to measure DEA efficiency ratios based on constant return to scale. Under the input-oriented approach, the CCR model becomes: 𝑇𝐸𝐶𝑅𝑆 = 𝑀𝑖𝑛𝜌 𝜇 0 s. t.
(4.2a)
0 ∑𝑚 𝑗=1 𝜕𝑗 𝑥𝑖𝑗 ≤ 𝜃𝑥𝑖 ; 𝑖 = 1 … 𝑐
(4.2b)
0 ∑𝑚 𝑗=1 𝜕𝑗 𝑦𝑟𝑗 ≥ 𝑦𝑟 ; 𝑟 = 1 … 𝑤
(4.2c)
𝜕𝑗 ≥ 0; 𝑗 = 1 … 𝑚
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where x = observed inputs; y = observed output
Hence, the feasible solution for the above problem requires that each unit of RCB will generate, at least, the same level of output (second constraint) whilst expending just a proportion (𝜃) of each of the inputs used (first constraint). The objective then is to determine the optimum combination of x and y that minimizes the value of 𝜇. The technical efficiency scores will be measured relative to the optimal 𝜇 (𝜇 ∗ ), (MurilloZamorano, 2004).
It must, however, be stated that because, in real world, optimal operations are difficult to achieve due to such bottlenecks as imperfect competition, market power, economic constraints, government controls and externalities, CRS hypothesis does not reflect reality. CCR efficiency results may, therefore, be bias, as they do not discriminate between scale efficiencies. For this reason, the Variable Returns to Scale (VRS) is widely harnessed in DEA efficiency literature (Delis et al, 2009). The Banker, Charnes and Copper (BCC) model (1984) is an extension of the CCR model that facilitates expertise on VRS to DEA efficiency measure, in terms of decreasing, constant and increasing returns to scale. The input option under VRS is given by: 𝑇𝐸𝑉𝑅𝑆 = 𝑀𝑖𝑛𝜌 𝜇 0 s. t.
(4.3a)
0 ∑𝑚 𝑗=1 𝜕𝑗 𝑥𝑖𝑗 ≤ 𝜃𝑥𝑖 ; 𝑖 = 1 … 𝑐
(4.3b)
0 ∑𝑚 𝑗=1 𝜕𝑗 𝑦𝑟𝑗 ≥ 𝑦𝑟 ; 𝑟 = 1 … 𝑤
(4.3c)
𝜕𝑗 ≥ 0; 𝑗 = 1 … 𝑚 ; ∑𝑚 𝑗 𝜕𝑗 = 1
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Mathematically, the linear programming specifications for efficiency measures under constant returns to scale have fewer constrictions than the VRS formulation of the same problem. As a result, the calculi of lower efficiency rates are possible with VRS, hence, more units can be recognized as efficient for a VRS than in a CRS envelope surface.
Characteristically, this present work adopts both constant and variable returns to scale specifications to explore the input measurement of DEA efficiency scores, as frequently implemented in empirical studies. Conducting such an analysis helps to decompose technical efficiency results in terms of scale and other technical efficiency elements.
4.1.3 DEA Malmquist Productivity Index The vector of efficiency ratios, by itself, does not provide adequate information on the level of productivity, productivity growth and its source. To do this, the Malmquist Productivity Index (MPI), among the group of productivity indices, is regularly used. MPI measures the productivity growth of units between two periods (T and T+1 periods), whilst splitting productivity growth into efficiency changes and technological changes. The premise is that the best practice curve can either move downward or upward, caused by such changes in the state of factors such as available technology, knowledge, experience, strategic management, etc. Hence, change in the total factor productivity (productivity growth) is the resultant effect of a combination of technical change resulting in shifts in frontier and efficiency change (movements of firms towards the frontier).
Efficiency Change, also known as Catch-up, captures the extent to which efficiency improves or degrades over the period t and t+1. Efficiency change is further broken into pure technical efficiency change (PECH) and scale efficiency change (SECH). The scale 79
efficiency change index captures whether or not the movements within the frontier follow a constant return to scale, whilst pure efficiency change rate measures the deviation between an observed unit’s efficiency from the best practice frontier, devoid of scale effects. Meanwhile, technical change dimension shows the distance between the best practice frontiers of the two time periods. MPI does not only allow for a comparison of productivity between units of an industry, but also for the tracing of the source of such changes. The period upon which analysis is referenced usually affects the way in which indices are interpreted. According to Mathews and Ismail (2006), if the period, T+1, is used as a reference point, then, MPI greater than unity implies a slack in productivity over the studied periods. Otherwise, an MPI greater than 1 is interpreted as a positive production growth when the reference technology is based on period, T. The basic Malmquist index for measuring productivity is then given as: 1
𝐷1 (𝑦1 , 𝑥1 )𝐷2 (𝑦1 , 𝑥1 ) 2 𝑀𝑃𝐼 = [ ] 𝐷1 (𝑦2 , 𝑥2 )𝐷1 (𝑦1 , 𝑥1 ) Rewriting, 1
𝑀𝑃𝐼 =
𝐷1 (𝑦1 ,𝑥1 ) 𝐷 (𝑦 ,𝑥 )𝐷 (𝑦 ,𝑥 ) 2 × [𝐷2 (𝑦2 ,𝑥2 )𝐷2(𝑦1 ,𝑥1 )] 𝐷2 (𝑦2 ,𝑥2 ) 1 2 2 1 1 1
(4.4)
In this study, following five DEA Malmquist indices for period T relative to period T+1, the total factor productivity change for the RCBs is computed as follows:
a. Total Factor Productivity Change:
𝑇𝐹𝑃𝐶𝐻 =
𝐷 𝑡+1 (𝐶𝑅𝑆)(𝑋 ,𝑌 ) ( 0 𝐷𝑡 (𝐶𝑅𝑆)(𝑋𝑡+1,𝑌 )𝑡+1 ) ⏟ 0 𝑡 𝑡
1
×
𝐷0𝑡 (𝐶𝑅𝑆)(𝑋𝑡+1 ,𝑌𝑡+1 ) 𝐷0𝑡 (𝐶𝑅𝑆)(𝑋𝑡 ,𝑌𝑡 ) 2 [𝐷𝑡+1 ] ⏟0 (𝐶𝑅𝑆)(𝑋𝑡+1 ,𝑌𝑡+1 ) 𝐷0𝑡+1 (𝐶𝑅𝑆)(𝑋𝑡,𝑌𝑡)
𝐸𝐹𝐹𝐶𝐻 (𝑐𝑎𝑡𝑐ℎ𝑖𝑛𝑔−𝑢𝑝)
𝑇𝐸𝐶𝐻𝐶𝐻 (𝑖𝑛𝑛𝑜𝑣𝑎𝑡𝑖𝑜𝑛)
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(4.5)
b. Technology Change Index
𝑇𝐸𝐶𝐻𝐶𝐻 =
𝐷0𝑡 (𝐶𝑅𝑆)(𝑋𝑡+1 ,𝑌𝑡+1 ) (𝐷𝑡+1 ) 0 (𝐶𝑅𝑆)(𝑋𝑡+1 ,𝑌𝑡+1 )
1
×
𝐷0𝑡 (𝐶𝑅𝑆)(𝑋𝑡 ,𝑌𝑡 ) 2 [𝐷𝑡+1 ] 0 (𝐶𝑅𝑆)(𝑋𝑡 ,𝑌𝑡 )
(4.6)
c. Efficiency Change Index 𝐸𝐹𝐹𝐶𝐻 = (
𝐷0𝑡+1 (𝐶𝑅𝑆)(𝑋𝑡+1 ,𝑌𝑡+1 ) ) 𝐷0𝑡 (𝐶𝑅𝑆)(𝑋𝑡 ,𝑌𝑡 )
(4.7)
d. Pure Technical Efficiency Change 𝐷0𝑡+1 (𝑉𝑅𝑆)(𝑋𝑡+1 ,𝑌𝑡+1 ) ) 𝐷0𝑡 (𝑉𝑅𝑆)(𝑋𝑡 ,𝑌𝑡 )
𝑃𝐸𝐶𝐻 = (
(4.8)
e. Scale Efficiency Change: 𝐸𝐹𝐹𝐶𝐻 𝑆𝐸𝐶𝐻 = 𝑃𝐸𝐶𝐻
(4.9)
The application of Malmquist productivity indices enables the study to infer on the banks’ static efficiency level and dynamic productivity change. The rule of thumb for MPI estimates is that higher values of MPI greater than 1 show higher productivity, whilst lower values below unity show lower productivity.
4.2 Parametric Methodology The parametric methodology exploits either a Cobb-Douglas, a Translog, a Fourier Flexible or an Ordinary Least Squares (OLS) functional form to detail its production function. The specified functional form represents the best technology available (best practice frontier). Two broad forms of the parametric approach are highlighted in literature in terms of how random variations across firms are considered (MurrilloZamorano, 2004): the deterministic parametric models and the stochastic parametric
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models. The deterministic models (OLS functions) construe all regression residuals as inefficiency. This is a major weakness as this does fail to capture the effects of exogenous factors on decision-making. Hence, it is difficult to analyse random shocks with a deterministic parametric model. This major drawback led to the development of stochastic parametric models, which account for exogenous heterogeneity when approximating real world efficiency. Under the stochastic models, deviations from the frontier are split into an econometric error and a random error. The econometric error assumed to be independently identically distributed (iid) captures functional form misspecification, measurement errors, and omission of variables, influential values plus all other factors outside the control of the firm. The one-sided random error term measures management inefficiency. The challenge, therefore, remains the most efficient way to divide the observed heterogeneous variations into the two error terms.
The two popular stochastic models are the Thick Frontier Approach (TFA) and the Stochastic Frontier Approach (SFA). These approaches are separated based on how the residuals are divorced to unravel the inefficiency component: whilst some assume a distributional form for the inefficiency term (SFA), others do not. Parametric models have been generally criticized for imposing a more restrictive structure on the shape of the frontier (Bauer et al, 1998). A detailed exposition is given on the SFA in the subsequent section, since it was the main parametric technique used in the study. The task will then be to highlight its theoretical and methodological underpinnings and how it was used in this present study.
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4.2.1 Stochastic Frontier Approach The SFA is widely applied among the group parametric methodologies. It employs a number of statistically distributive forms in estimating the inefficiency error, with half normal, truncated normal and exponential distributions frequently used. Here, efficiency is measured as the conditional mean of the inefficiency term in reference to the econometric error, which is expected to follow a symmetric distribution. However, both the inefficiency and econometric error terms are expected to be orthogonal to the independent variables specified (Bauer et al, 1998). In empirical estimation, SFA is commended for its consistent results irrespective of the distributional assumption formed. The basic SFA model proposed by Pitt and Lee (1981) with a normal-half normal assumption is specified as follows: 𝑦𝑖𝑡 = 𝑓(𝑥𝑖𝑡 , 𝑐𝑖 ) + 𝑒𝑖
𝑖 = 1 … … 𝑁,
𝑡 = 1…….𝑇
𝑒𝑖 = 𝑢𝑖𝑡 ± 𝑣𝑖𝑡
(4.10a) (4.10b)
𝑣𝑖𝑡 ~ 𝑖𝑖𝑑𝑁[0, 𝜎𝑣2 ] and 𝑢𝑖𝑡 ~𝑁 + [0, 𝜎𝑢2 ] where 𝑦𝑖𝑡 represents the output of firm i in period t; 𝑥𝑖𝑡 represents the vector of input, whilst 𝑐𝑖 is the vector of firm attributes. 𝑢𝑖𝑡 is the asymmetric inefficiency term with 𝑣𝑖𝑡 representing the stochastic error term.
The asymmetric inefficiency term can be separated using either a Jondrow et al (1982) specification (JLMS estimator) or Battese and Coelli (1995) function (BC estimator). According to Jondrow et al (1982), the expected value of the ui’s conditional on the composed error term under half normal assumption is measured as follows:
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U E i i 1 2
i f s i Fc i
(4.11)
where fs (.) is the density of the standard normal distribution and Fc (.) is the cumulative
density function u2 v2
1
2
; u v
2 2 where = total variation, u = variation due to inefficiency, v = variation due to noise,
and = the ratio of the standard deviation of the inefficiency component to that of the noise component.
Once conditional estimates have been found, Jondrow et al (1982) measure each unit’s 𝑢 technical efficiency as 𝑇𝐸𝑖 = 1 − 𝐸[ 𝑖⁄𝑒𝑖 ]. Battese and Coelli (1988) then fit a conditional mean model in which the stochastic inefficiency term is also expressed as a time decaying model with a truncated normal distribution defined as: 𝐸[exp(−𝑢𝑖 )⁄𝑒𝑖 ] = where 𝛿 =
𝜎𝑢 𝜎𝑣 𝜎
1−𝐹𝑐 (𝛿+(𝛾𝑒𝑖 ⁄𝛿)) 1−𝐹𝑐 (𝛾𝑒𝑖 ⁄𝛿)
∗ exp(𝛾𝑒𝑖 (𝛿 2 ⁄2))
(4.12)
𝜎2
and 𝛾 = 𝜎𝑢2
4.2.2 Stochastic Frontier Production Function SFA commonly employs Cobb-Douglas or Translog functional forms applied to both cross-sectional and panel data to predict efficiency scores that can be subjected to statistical inference. Panel data stochastic frontier models are normally preferred over cross-sectional data, due to the fact that the latter, although produces unbiased estimates, is noted for inconsistent results requiring strong distributional assumptions on the form of inefficiency. Panel data, on the other hand, yields consistent results without requiring any robust assumptions about inefficiency effect, which makes it possible to develop time-
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varying and time invariant characteristics in an SFA model. This study uses both the Cobb-Douglas and the Translog functions for panel data to estimate production efficiency.
Greene (2005) suggests that the choice of functional form brings a series of implications, with respect to the shape of the implied isoquant and the values of elasticities of factor demand and factor substitution. The Cobb-Douglas function uses a strong assumption concerning the elasticities to be estimated. It requires that the factor shares are constant with the Allen elasticities of factor substitution also –1 (Greene, 2005). A time trend variable can be introduced in the Cobb Douglas function to observe for Hicksian neutral technological change.
The general Cobb-Douglas function used in the study is specified as: 𝑙𝑛𝑌𝑖 = 𝛽0 + 𝛽𝑖 𝑙𝑛𝑋𝑖 + 𝜗𝑜 𝑇 − 𝑒𝑖
𝑖 = 1, 2 … … 𝑁
(4.13)
where 𝑌𝑖 represents the output of the ith bank, 𝑋𝑖 represents the vector of the logarithm of input variables, 𝛽, 𝜗 denote the parameters to be estimated and 𝑒𝑖 is the composed error term, whilst T represents time trend.
The Translog form, which brings more flexibility in terms of assumption of the shape of factor shares, is useful when the researcher is interested in interactive or integration effects. The Translog model is commended for its advantage of relaxing the restrictions on demand elasticities and elasticities of substitution, as expressed in Cobb-Douglas functions. A Translog specification of a production function is often found to fit data better than the Cobb-Douglas specification (Headey et al, 2010). According to Diewert 85
(1976), productivity indices are shown to be superlative in the sense that they are exact for translog function, which provides a second-order approximation to the function under consideration.
Similarly, with the same notations of output and input, as in the Cobb-Douglas form, the translog function1 assuming a time trend includes the interactive terms and is represented as follows: 1
𝑀 𝑀 𝑀 ln𝑌𝑖 = 𝛼 + ∑𝐾 𝑘=1 𝛽𝑘 𝑙𝑛𝑋𝑖𝑘 + ∑𝑚=1 𝛽𝑚 𝑙𝑛𝑋𝑖𝑚 + 𝜗𝑜 𝑇 + 2 (∑𝑚=1 ∑𝑚=1 𝛾𝑚 𝑙𝑛𝑋𝑚 𝑙𝑛𝑋𝑚 + 𝐾 𝐾 𝑀 2 ∑𝐾 𝑘=1 ∑𝑘=1 𝛾𝑘 𝑙𝑛𝑋𝑘 𝑙𝑛𝑋𝑘 + 𝜗01 𝑇 ) + ∑𝑘=1 𝜃𝑘 𝑙𝑛𝑋𝑖𝑘 ∗ 𝑇 + ∑𝑚=1 𝜃𝑚 𝑙𝑛𝑋𝑖𝑚 ∗ 𝑀 𝑇 + ∑𝐾 𝑘=1 ∑𝑚=1 𝜃𝑘𝑚 𝑙𝑛𝑋𝑖𝑘 ∗ 𝑙𝑛𝑋𝑖𝑚 + 𝑒
(4.14)
where 𝑌𝑖 represents the output of the ith bank, 𝑋𝑘 represents the vector of the logarithm of input, k,𝑋𝑚 represents the vector of the logarithm of input, m. 𝛽𝑚 , 𝛽𝑘 , 𝛾𝑚 , 𝛾𝑘 , 𝜃𝑚 , 𝜃𝑘 𝜃𝑘𝑚 denote the parameters to be estimated, and 𝑒𝑖 is the composed error term.
4.2.3 Time Varying Efficiency Models The SFA models can be classified as time invariant and time-varying models. The time invariant models are distinguished from time-varying models on the grounds that they allow for the estimation of producer effects, excluding time effects. By using conventional panel model techniques, such as a fixed effect, random effect, and/or maximum likelihood approach, inefficiency scores are predicted with the basic assumption that inefficiency cannot vary over time, hence, no technical change among the observed units.
1
Preestimation analysis showed that the preferred functional form for our data is the translog function.
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However, there are instances when an observation of technical change is warranted, especially with longer panels. This makes it desirable to include time as a regressor to proxy for technical change. This practice is even more common, currently, in an empirical research that uses panel model techniques (Kumbhakar and Lovell, 2000). This, therefore, precipitates the use of time-varying technical efficiency models in current efficiency literature. Particularly, if the operating environment is competitive, like the banking industry, it will be hard to assume that technical inefficiency remains constant over various time periods. To observe for changes in technology and efficiency, this study deems it fit to focus on the time-varying models, as typified in recent efficiency studies.
Time varying models specify the production function and related efficiency measurements based on the assumption of time. Cornwell, Schmidt and Sickles (1990) modified the Schmidt and Sickles (1984) model to comprise time-varying inefficiency effects for an SFA framework for panel data. The intercept parameters are expressed as a quadratic function of time: 𝛽𝑖𝑡 = 𝛽0𝑡 − 𝑢𝑖𝑡 . The time variables, here, are couples to producers’ specific parameters. The technical inefficiency error term is, therefore, detail as: 𝑢𝑖𝑡 = 𝜑1𝑖 + 𝜑2𝑖 𝑡 + 𝜑3𝑖 𝑡 2 , where the 𝜑s represent individual producer specific parameters. Kumbhakar (1990) adds a time factor to the fixed-effect model and expresses 𝑢𝑖 as: 𝑢𝑖𝑡 = 𝑔(𝑡). 𝑢𝑖 𝑔(𝑡) = [1 + 𝑒(𝛾𝑡 + 𝛿𝑡 2 )]−1
(4.15)
where 𝛾 𝑎𝑛𝑑 𝛿 are the parameters to be estimated. By setting 𝛾 = 𝛿 = 0, time invariant hypothesis could be tested. Empiricists apply the Battese and Coelli (1992, 1995) model,
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which adopts an additional term by resting the assumption of time-invariant inefficiency 𝑈𝑖𝑡 = exp(−𝑛(𝑡 − 𝑇)) ∗ 𝑈𝑖 into Pitt and Lee (1981) RE model. Battese and Coelli (1992) also proposed that 𝑔(𝑡) can be set to assume the following series: 𝑔(𝑡) = 𝑒[−𝛾(𝑡 − 𝑇𝑖 )
(4.16)
Greene (2005), however, suggests that all these models are limited on the grounds of excluding the time-invariant heterogeneities in those models. This may result in overestimated parameters, if time invariant heterogeneities are present and yet excluded. According to Greene (2005), following the principle of orthogonality between the error term and the independent variables, if there is any variable, 𝑧𝑖𝑡, whose characteristics also explain the variations in the inefficiency error, 𝑢𝑖𝑡 , then such an influential variable should enter the model, otherwise, this will lead to bias inefficiency parameters. That is, so far as 𝑢𝑖𝑡 is expected to be uncorrelated with 𝑥𝑖𝑡 with a population mean of zero and constant variance, true estimate of 𝑢𝑖𝑡 will not suffice if the model cannot encapsulate a vector of variables (𝑧𝑖𝑡 ) whose variation has a strong effect on 𝑢𝑖𝑡 . The challenge is identifying whether such a variable exists, and if so, how to factor such influential effects in the initial stage of the modelling.
Greene (2005) proposes the true fixed effect and true random effect models, which are estimated by maximum likelihood techniques. In both these cases, all the time invariant effects are reflected as unobserved heterogeneity, with inefficiency term allowed to decay freely with time.
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The true FEM, firm specific constant terms, are introduced in the stochastic frontier models, written as: 𝑙𝑛𝑦𝑖𝑡 = 𝛼𝑖 + 𝛽 𝑇 𝑥𝑖𝑡 + 𝑣𝑖𝑡 − 𝑢𝑖𝑡 𝑢𝑖𝑡 ~|𝑁(0, 𝜎 2 )| 𝑣𝑖𝑡 ~𝑁(0, 𝜎𝑣2 )
(4.17)
where α encompasses all the time-invariant produce-specific heterogeneities. It also allows the inefficiency term, 𝑢𝑖𝑡 , to be uncorrelated with the random errors, and regressors. The inefficiency term is not limited to be time-invariant.
The true REM, on the other hand, exploits the random constant term to represent the individual producer time-invariant heterogeneities in the production function: 𝑙𝑛𝑦𝑖𝑡 = (𝛼 + 𝑤𝑖 ) + 𝛽 𝑇 𝑥𝑖𝑡 + 𝑣𝑖𝑡 − 𝑢𝑖𝑡 𝑢𝑖𝑡 ~|𝑁(0, 𝜎𝑢2 )| 𝑣𝑖𝑡 ~𝑁(0, 𝜎𝑣2 )
(4.18)
𝑤𝑖 ~ 𝑤𝑖𝑡ℎ 𝑚𝑒𝑎𝑛 0 𝑎𝑛𝑑 𝑓𝑖𝑛𝑖𝑡𝑒 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒
As Greene (2005b) pointed out, neither formulation is a priori completely satisfactory and the choice should be driven by the features of the data at hand (Belotti et al, 2012).
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4.2.4 Model Choice For the purposes of validity of results and consistency checks, different sets of SFA models were specified in this study, to observe which model(s) will best fit the data. Indeed, no convincing theoretical argument is found in literature on the relative efficacy of the sets of SFA models used in empirical research which can serve as the basis of the model selection in this study. Hence, the choice of the Frontier models is “frequently a judgment call” (Kumbhakar and Lovell, 2000: 266). Hence, the choice of the estimated Frontier models is usually ad hoc and is based on tractability rather than on any optimal theoretical criteria for assessing efficiency (Kumbhakar et al, 1997). Consequently, this study plumps for the efficiency models, based on similarities of results in terms of scores and ranking. Where the ranking or scores deviated significantly from the observed patterns, such a particular SFA Frontier model was dropped accordingly on the basis of reliability and robustness of the results.
In the initial stages, a total of 11 models, both time varying and invariant SFA models were estimated and patterns observed. The next step was to reduce the number of models useful for further analysis, based on judgment call. Due to the objective of observing for productivity growth and efficiency change, it was necessary that all the time invariant models were dropped since using time invariant models to predict efficiency and productivity changes did not yield the required periodic changes in efficiency and productivity. Consequently, four best-fit models were “called” for further analysis, all being time-varying models. The chosen Frontier models used for this study are briefly summarised in Table 4.1 below:
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Table 4.1: Selected Best Fit Models Models
Functional Form
1. Greene (2005), True fixed-
Status
𝑙𝑛𝑦𝑖𝑡 = 𝛼𝑖 + 𝛽 𝑇 𝑥𝑖𝑡 + 𝑣𝑖𝑡 − 𝑢𝑖𝑡
Selected
𝑙𝑛𝑦𝑖𝑡 = (𝛼 + 𝑤𝑖 ) + 𝛽 𝑇 𝑥𝑖𝑡 + 𝑣𝑖𝑡 − 𝑢𝑖𝑡
Selected
effects model 2. Greene (2005), True randomeffects model 3.
ML random-effects (RE) time-
𝑦𝑖𝑡 = 𝛼0 + 𝑓(𝑥𝑖𝑡, 𝑡; 𝛽) + 𝑣𝑖𝑡 − 𝑢𝑖𝑡 ;
varying efficiency decay model
𝑢𝑖𝑡 = [𝑒(−𝛾(𝑡 − 𝑇𝑖 )] 𝑢𝑖
Selected
(Battese and Coelli, 1992) yit = xit + (vit - uit)
4. ML random-effects (RE) timevarying inefficiency effects model
𝑢𝑖 ~𝑁 + (𝛾 ′ 𝑧, 𝜎𝑢2 )
(Battese and Coelli, 1995)
𝑣𝑖𝑡 ~𝑁 (0, 𝜎𝑢2 )
Selected
Source: Author compilation (2014)
These models use different assumptions for the distribution of inefficiency terms. However, for the purposes of consistency, all the models were estimated, using a truncated normal distribution about the inefficiency. Again, for each of the models, conditional estimates were based on both the Battese and Coelli (1995) and Jondrow et al (1982) measures.
4.2.5 Empirical Specification The model used in the study is based on the Intermediation approach of technological specification, as proposed by Sealey and Lindley (1977) and typified in efficiency research, including Barry et al, 2011 and Hermes et al, 2009. Berger and Humphrey (1997) describe the appropriateness of the Intermediation approach as a superior for evaluating the importance of frontier efficiency, since it best illustrates the characteristics of the unit rural bank. The Intermediation approach illustrates a rural bank as a unit that
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accepts deposits backed by their capital assets and invests them, and also lends them when required and gains profits in the process. Inputs and outputs selected for the empirical analysis of the technical efficiency of the sampled RCBs in Ghana was based on existing literature, data availability and theoretical strands. For instance, deposits which represent all group, commercial, and individual voluntary savings (time and demand deposits) that are harnessed by the banks, were used as one of the input variables in the production function. Deposits have the characteristics of an input, in that, the funds raised through deposits enable banks to advance more loans. Again, RCBs pay for the cost of attaining the deposit funds through the interest on deposits received by customers. Among the studies that used deposits as a technological input are Elyasiani and Mehdian (1990), Casu and Molyneux, (2003), Isik and Hassan (2003), and Danquah et al., (2013).
The output variables include net loans and fixed assets. Net loans are defined as the difference between Gross Loan Portfolio and Loan Losses. The conventional definition of fixed assets describes them as tangible (capital and physical) assets that are in operational use and have a useful recurrent economic life of more than a year.
Specifically, the production frontier assuming a time-trend representation of technical change was specified of the following form:
Model 1: Cobb Douglas Function lnLoani,t = β0 + β1 lnDepositsi,t + β2 lnFxAssetsi,t + β3 Time i,t + vi,t − u i,t
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(4.19a)
Model 2: Translog Function 1
2 lnnLoani,t = 𝛽0 + 𝛽1 𝑙𝑛𝐷𝑒𝑝𝑜𝑠𝑖𝑡𝑠𝑖,𝑡 + 𝛽2 𝑙𝑛𝐹𝑥𝐴𝑠𝑠𝑒𝑡𝑠 𝑖,𝑡 + 𝛽3 𝑇𝑖𝑚𝑒 𝑖,𝑡 + 2 (+𝛽4 𝑇𝑖𝑚𝑒𝑖,𝑡 + 2 2 𝛽5 𝑙𝑛𝐷𝑒𝑝𝑜𝑠𝑖𝑡𝑖,𝑡 + 𝛽6 𝑙𝑛𝐹𝑥𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 ) + 𝛽7 (𝑙𝑛𝐷𝑒𝑝𝑜𝑠𝑖𝑡𝑠𝑖,𝑡 ∗ 𝑙𝑛𝐹𝑥𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 ) + 𝛽8 (𝑙𝑛𝐷𝑒𝑝𝑜𝑠𝑖𝑡𝑠𝑖,𝑡 ∗
𝑇𝑖𝑚𝑒𝑖,𝑡 ) + 𝛽9 (𝑙𝑛𝐹𝑥𝐴𝑠𝑠𝑒𝑡𝑠𝑖,𝑡 ∗ 𝑇𝑖𝑚𝑒𝑖,𝑡 ) + 𝑣𝑖,𝑡 − 𝑢𝑖,𝑡
(4.19b)
where v = statistical noise, u = the error due to inefficiency, and betas represent coefficients or factor shares of the production function.
As shown earlier, four SFA models were eventually selected for the analysis. The models were then estimated, using both the Cobb-Douglas (CD) and the Translog (TL) functional formations. The estimates of the CD and TL functions are then compared and the TL functions were selected for further analysis, based on test statistics, extant literature, and economic underpinnings of the rural banking sector in Ghana. Indeed, one basic reason for utilising the TL functions for further analysis was that the CD specifications are also nested in the TL models. Meanwhile, the Translog models also presented more information on interactive effects useful for policy-making, including performance, exhibiting all the attributes of the CD. Hence, because TL is useful in practice, although the results of the two models (CD and TL) were found not to be significantly different, the equation 4.19b was used as the main production function.
Ultimately, the choice was made on one of the four best-fit models useful for further analysis. The correlation matrix was used to determine the consistency of the estimated SFA models and, subsequently, settle on the most reasonable model for further analysis. The best-fit SFA model was then compared with the technical efficiency results from the non-parametric DEA approach. The application of the non-parametric Spearman’s and
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Kendall’s rank correlation test and the Wilcoxon signed-rank test of differences was necessitated for efficiency comparisons and to check for consistencies. Moreover, to check for the consistency of the estimates from both DEA and SFA methods, the estimates were also ranked and correlated with standard industry managerial efficiency and cost-related indicators.
4.2.6 SFA Productivity Analysis The next department of the SFA analysis, after estimating the vector of technical efficiency ratios, was to conduct a productivity analysis. The focus is to estimate the technical change (TECH), efficiency change (EFFCH) and then total factor productivity change (TFP). Based on estimates of equations (4.19b), TECH, EFFCH and TFPCH for the RCBs in 2009q1-2012q3 could be captured. The TEC is the ratio between TE score from the period to the previous period. 𝑇𝐸𝑖(𝑡)
Mathematically, 𝐸𝐹𝐹𝐶𝐻 = 𝑇𝐸 𝑖(𝑡−1)
(4.21)
To estimate for the technical change (TECH), the partial derivative of the estimated translog function (4.19b) is calculated, with respect to time (T). The TECH index then becomes the geometric mean between each two periods (Coelli et al, 2005). 1 𝜕𝑙𝑛𝑦
𝜕𝑙𝑛𝑦
𝑇𝐶 = 𝑒𝑥𝑝 {2 [ 𝜕𝑠 𝑖𝑡 + 𝜕𝑡 𝑖𝑡 ]}
(4.22)
Following the multiplicative Malmquist TFP concept, the TFP index is estimated by taking the product of EFFCH and TECH. 𝑇𝐹𝑃𝐶𝐻 = 𝐸𝐹𝐹𝐶𝐻 ∗ 𝑇𝐸𝐶𝐻
(4.23)
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4.3 Determinants of Productivity Among the main objectives of this study, the study focuses to estimate the determinants of productivity of RCBs in Ghana. Indeed, there is a substantial dearth of information regarding the factors that affect productivity on both across firms within the financial industry and across branches within a single firm (Berger and Humphrey, 1997). “In the context of policy implications, it is more important to determine what influences inefficiency (or to which variables it is related) than simply to measure it” (PadillaFernandez and Nuthall, 2009). The study uses regression analysis to examine the drivers of productivity within the RCBs industry.
Literature converge that exogenous variables or factors can be grouped into three main constructs: (1) bank specific factors, (2) macroeconomic variables and (3) regulatory variables. Most common, bank-specific factors are size, market share, bank’s profitability, and capital adequacy. Macroeconomic variables used in efficiency studies also include GDP, GDP per capita, GDP growth, inflation, inflation ratio, fiscal deficit, and stock market capitalization. On the other hand, regulatory specific variables included in empirical research are ownership structure, age, financial reforms, and ethics. Regulatory variables are entered usually as dummy variables (see Sharma et al, 2013). Chapter Seven (7) deals with the determinants of productivity and its components.
4.4 Data Sources A balanced cross-sectional and panel data analysis was used in the estimation of the technical efficiency and productivity levels of the RCBs. Data for the study was obtained from annual reports and from the Association of Rural Bank (ARB), Apex Bank. ARB Apex Bank is the regulator of all RCBs in Ghana. The study considered 107 RCBs in
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Ghana who have been operating consistently over the period 2009q1 to 2012q3. Sample units are distributed over the 10 regions of Ghana.
Table 4.3: Regional Distribution of RCBs in Ghana Region Total number Ashanti 25 Brong Ahafo 20 Central 21 Eastern 22 Greater Accra 7 Northern 7 Upper East 5 Upper West 4 Volta 12 Western 14 Total 137 Source: Bank of Ghana Bank, January 2013
No. of RCBs selected 20 13 20 18 5 5 4 3 8 11 107
4.5 Concluding Remarks The study described both the parametric and nonparametric methodologies used to estimate the technical efficiency scores of the sampled RCBs in Ghana for reasons of comparing estimates and also validating the results. The parametric methodology involved the use of the Stochastic Frontier models. Four SFA models were selected for the analysis, which were, eventually, reduced to only one for further analysis. Panel data model forms were used, as typified in various works, using both the Cobb-Douglas and the Translog production functions. However, due to its relative advantage, the Translog functions were employed for the analysis, although parameter estimates were comparable to the Cobb-Douglas production function estimates. Technical efficiency estimates were obtained utilizing the Jondrow Estimator (Jondrow et al, 1982). The selected best-fit translog function was then compared with the estimates of the non-parametric model, DEA, to check for consistency.
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Indeed, the Data Envelopment Approach with an input-oriented procedure under both constant returns and variable returns to scale was exploited for the non-parametric efficiency analysis, which preceded the SFA analysis. The DEA approach allowed scalability to be estimated and observed. This was then followed by the DEA-Malmquist Productivity Index, which was used to examine the productivity changes. The final part of the analysis proceeded with the determination of the drivers of productivity of the sample of RCBs in Ghana, using the scores of both the DEA and the SFA models. Panel regression analysis was utilized to estimate the effect of the determinants of productivity among the sampled units. Quarterly data for the sample periods between 2009q1 to 2012q3 will be used for the estimation.
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CHAPTER FIVE TECHNICAL EFFICIENCY ANALYSIS OF RURAL BANKS IN GHANA 5.1 Introduction The main objective of this chapter is to estimate and rank the technical efficiency of the rural banks (RCBs) in Ghana over the operational period 2009q1 to 2012q3, using different frontier methods. The rural banking sector in Ghana has received numerous interventions aimed at improving the service operations of the banks and, ultimately, their efficiency. More details are found in Chapter Two of the thesis. From the existing literature on RCBs, there is a conspicuous lack of empirical research concerning the efficiency of RCBs in Ghana. Research into RCBs in Ghana is in its developing stage as most authors of existing studies state the lack of comprehensive data as the main reason for the situation. From the literature review, Danquah et al. (2013) is the only known study estimating the technical efficiency of RCBs in Ghana. A couple of studies were found relating to the efficiency of the formal universal banks in Ghana. The general findings from those studies are that the universal banks were not fully efficient (Frimpong, 2010, etc.). Clearly, there is the need to contribute to the body of knowledge and policy by studying the technical efficiency of RCBs in Ghana. This background inspires this chapter.
The specific objectives of the chapter are: (a) to estimate and analyse the technical efficiency of the RCBs, using both the DEA and the SFA approaches; (b) to rank the RCBs based on the technical efficiency estimates from the DEA and SFA methods; and (c) to evaluate the consistency of the technical efficiency estimates based on comparison with standard industry performance indicators. The rest of the chapter is structured as follows. Section 5.2 describes the data and defines the specific variables used in the
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estimations. Sections 5.3 and 5.4 contain the empirical results and discussions on the DEA and the SFA technical efficiency respectively while Section 5.5 provides the comparison between the DEA, SFA efficiency estimates, and standard industry performance indicators. Conclusions are offered in section 5.6.
5.2 Description of the Data The data used for the analysis is the quarterly panel dataset obtained from the prudential returns of RCBs submitted to the Efficiency Monitoring Unit (EMU) in the Audit Department of the ARB Apex Bank and to the Bank Supervision Division (BSD) of the Bank of Ghana. The data covered 15 quarters, from 2009q1 to 2012q3. The data was based on the financial statements (Assets and Liabilities, BSD R2) of the RCBs. The original dataset included all the 137 RCBs, as at the end of the financial year, 2012. However, data was not consistently available for some RCBs for the study period, for which reason they were removed from the sample. The data, therefore, excludes 26 RCBs with less than 15 quarters of data points. The RCBs with missing values on inputs, outputs, and environmental variables within the study period were also excluded. Therefore, the total sample data for the study is a strong, balanced panel data of 107 RCBs by 15 quarters, yielding 1,605 panel observations, which make up about 81% of all 137 RCBs during the study period.
Net-loan (Lnnloan) is specified in this study as the output variable from the financial intermediation approach. This was reviewed extensively in Chapter Two. Net loans are defined as Gross Loans and Advances less provisions for Loan Losses. Natural log values were used. The input variables included both net fixed assets and total deposits. The conventional definition of fixed assets describes them as tangible (capital and physical)
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assets that are in operational use and have a useful recurrent economic life of more than a year. In this study, net fixed asset (LnFxasst) of RCBs is measured as total assets (property and equipment) less accumulated depreciation. Deposits (LnDep) are defined in this study as current deposits, savings deposits, and time deposits from customers and other banks. The descriptive summary of the dataset is reported in Table 5.1.
Table 5.1: Summary Statistics for Input and Output Variables Netloans
Deposits
Fixed Assets
Stats mean sd min max mean sd min max mean sd min max
2009 2015.02 1967.85 40.22 11000.00 3474.86 3128.62 136.67 20250.00 727.01 685.78 45.54 4000.00
2010 2431.23 2122.01 88.88 10025.00 4756.15 4233.90 164.11 25500.00 894.55 802.65 46.06 4725.00
2011 3411.65 2887.51 84.69 14750.00 6834.66 5997.91 236.46 33500.00 1337.21 1166.10 55.73 5675.00
2012 4618.43 3856.54 132.08 19333.33 8872.20 7765.51 277.82 41000.00 2016.79 1782.96 68.07 8966.67
Source: Author’s Calculations Based on Apex Data (in million Ghana cedis)
It is evident from Table 5.1 that net loans, total deposits, and fixed assets of the sample RCBs have increased steadily during the study period. The respective average annual growth rates are 24%, 27%, and 29% over the period 2009 to 2012. This implies that the industry is very vibrant and keeps expanding annually. The growth in fixed assets might point to the increased outreach drive of RCBs through the acquisition of property and equipment (e.g. the establishment of new agencies and acquisition of computers and ICT equipment, among others). This growth in fixed assets is supported by the corresponding increase in both total deposits mobilized and the total loans disbursed over the same period.
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5.3 Results Based on the DEA Approach This section presents the results and discussions on the input-oriented DEA technical efficiency model. The results were presented by quarters and by category of bank size and Apex efficiency rating. DEA was performed for 107 RCBs using the intermediation approach due to the nature of the available data. The overall technical efficiency (CRSTE) of the RCBs is decomposed into two parts: pure technical efficiency (VRSTE) and scale efficiency (SCALE). First, the pure technical efficiency (VRSTE), deals with managers’ ability to generate the maximum level of outputs, given the inputs. That is, VRSTE measures managerial efficiency devoid of any scale effects and, hence, implies managers’ ability to avoid waste. The second, scale efficiency (SCALE), gives information about exploiting economies of scale by operating at the “most productive scale size” (Banker, 1984; Ohene-Asare, 2011).
Running the input-oriented DEA method, the technical efficiency scores of individual RCBs in the sample (107 RCBs) were relatively calculated on the basis of individual frontiers constructed from ‘best practice’ banks, for each quarter of the period (15 quarters) considered, yielding a total of 1,605 observations. The input-oriented DEA means that efficiency is interpreted relative to the amount of input needed to produce a given amount of output, as opposed to the amount of output that can be produced with a given amount of inputs2. Efficient RCBs have efficiency scores of 1, whilst inefficient RCBs, relative to the rest of the sample banks during a particular quarter, have scores less than 1. The mean efficiency (CRSTE, VRSTE, and SCALE) scores of the RCBs are
2
Note that output-oriented DEA was also estimated and compared to the input-oriented DEA model. The results were significantly the same.
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presented in tables with trend graphs across all RCBs categorizations (banksize and Apex efficiency rating).
Table 5.2 (also plotted as Figure 5.1) reports the results of the input-oriented technical efficiency scores and components for the study period (2009q1 to 2012q3). The results reveal that the overall technical efficiency (CRSTE) score is 0.959 (95.9%), revealing that, from the input-oriented approach, about 4.1% of inputs of production can be saved to achieve a full level of efficiency without affecting RCBs’ outputs. The pure technical efficiency (VRSTE) component is averaged at 0.975 (97.5%), also indicating that 2.5% of input is lost in the process of generating output by management, devoid of any scale effects. The average scale efficiency for the period is 0.984 (98.4%), showing that the difference between the constant and variable returns to scale is only 1.6%, which is close to the CRS parts of the technology RCBs operate.
Table 5.2: Summary Statistics for Input-Oriented DEA Technical Efficiency Variable CRSTE VRSTE SCALE
Mean 0.959 0.975 0.984
Std. Dev. 0.032 0.023 0.024
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Min 0.826 0.876 0.838
Max 1 1 1
Figure 5.1 Quarterly Mean Technical Efficiency Score 1.02
CRSTE
VRSTE
SCALE
Efficiency Scores
1 0.98 0.96 0.94 0.92 0.9 0.88 Quarters
An examination of the kernel density plots (Figure 5.2) shows that the technical efficiency and scale efficiency of the RCBs are clustered at the high level around their mean. The overall technical, pure technical and scale efficiency of RCBs, generally, lies between 83% and 100%. From the density function, it is observed that majority of RCBs have scale efficiency, the mean of 98%.
Figure 5.2: Kernel Density Function for CRSTE, VRSTE, and SCALE
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5.2.1 DEA Technical Efficiency Results for Individual RCBs In this section, we provide and discuss the contents of CRSTE, VSRTE and SCALE scores that are obtained by executing the two most generic DEA models, namely, CRS and VRS models. As stated in Chapter Four, the variable returns to scale (VRS) model is preferred, because we assume that there is a strong disposability of inputs and outputs in the period under study. According to Färe et al (1994), the VRS assumption isolates overall technical efficiency into the two components: pure technical efficiency and scale efficiency. Table 5.3 shows the average efficiency scores of the individual RCBs over the study period 2009q1 to 2012q3. The nature of RTS and input slacks for individual banks in the sample, over the study period, is also presented in Table A5.1 in the Appendix.
A number of comments can be made from Table 5.3. First, the RCBs with an efficiency score equal to one are the most efficient, therefore, from the CRS model, there were only two (2) out of the 107 RCBs (RCBs 65 and 66) that were fully overall technicallyefficient. These two RCBs were also fully efficient under the VRS model, signifying that the dominant source of efficiency is scale inefficiency. Interestingly, both banks (RCBs 65 and 66) were ranked among the Ghana Club 100 companies between 2009 and 2011, which is based on their profitability (GIPC, 2011). During the period, the VRS model
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shows that eight (8) out of 107 RCBs were fully pure technical-efficient due to management skills. The pure technical efficiency frontier banks were RCBs 45, 51, 61, 65, 66, 76, 78, and 79. These fully efficient RCBs together define the technical efficiency frontier of the rural banking industry and, thus, form the reference set for the relatively inefficient banks. The results show that RCB61, for instance, served as a reference point for 78 other relatively less-efficient RCBs, followed by RCB66 with 59 RCBs serving as its reference point. This means that the relatively less-efficient RCBs would have to emulate their peer banks in the quest to become fully efficient. For instance, RCB1 has as its peers, RCBs 79 (6%), 76 (25.8%), and 61 (68.2%) and, by the peer weights, would have to mostly understudy RCB61 to become fully efficient3. The scale efficiency (SCALE), coupled with the nature of the returns to scale (RTS) results, revealed that majority of the RCBs in the industry operated at increasing returns to scale (irs). Only two (2%) of the RCBs in our sample exhibited the ideal constant returns to scale (crs). About 93 (87%) exhibited increasing returns to scale (irs), while 12 (11%) banks exhibited diminishing returns to scale (drs). With increasing returns to scale, RCBs may be small in size and, therefore, may have to increase their size in relation to input mix if increasing returns persist over time. From the observed data, most of the RCBs that exhibited irs are classified as medium and small. It is, therefore, probable that the sector may be in need of bank consolidations, as has been proposed by industry experts. The 2012 proposed merger of the three RCBs (Gomoa Ajumako Rural Bank limited at Gomoa Afransi, Gomoa Rural Bank Limited at Apam and Eastern Gomoa Assin Rural Bank at Gomoa Dominase) in the Central Region is a case in point (Ghana News Agency, October 2012). Also, the ARB Apex Bank, through DANIDA, has seeded a Merger
3
The peers represent the frontier rural banks, which are efficient, with which a particular rural bank under study is to be compared as reference for the other banks, which are inefficient. Summary of peers and peer weights are found in the Appendix Table A5.2.
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Fund4 to help all RCBs interested in consolidating pay for the consultancy services (ARB Apex Bank, 2011). Similarly, RCBs with decreasing returns to scale may be too large in scale size and require reduction in scale in terms of input mix. The implication, here, is that some RCBs, due to their large size, are wasting resources5.
Observing from the results presented here, it is interesting to note that most of the popular and large RCBs such as RCBs 31, 48, 54, and 57, are not ranked here among the top 10 in terms of overall technical and scale efficiency. This might go to explain that large size does not imply high technical efficiency, all things being equal (Nakamura, 1993 and Mester et al, 1998).
Table 5.3: Mean DEA Technical Efficiency of RCBs, 2009q1-2012q3 CRSTE VRSTE SCALE_ RCB CRSTE VRSTE SCALE _Rank _Rank Rank 1 0.923 62 0.979 0.943 34 75 2 0.92 68 0.982 0.937 32 80 3 0.918 74 0.981 0.936 33 85 4 0.92 68 0.975 0.944 43 74 5 0.926 55 0.971 0.954 52 63 6 0.928 49 0.969 0.957 57 60 7 0.928 49 0.969 0.957 57 60 8 0.931 42 0.968 0.962 59 56 9 0.931 42 0.964 0.966 64 53
Nature of RTS irs irs irs irs irs irs irs irs irs
4
The Merger Fund was to be established by the Danida project to assists RCBs which intend to merge to procure consultancy services and enable them carry out their intentions by paying for the cost of such services. The Merger Fund is a very important component of the DANIDA project as it seeks financial inclusion for RCBs, which are unable to meet the minimum capital requirements (Source: http://www.arbapexbank.com/danida.php). 5
The slack estimation results reported in Table A5.1 indicate that very few RCBs had non-zero slacks in their input usage. None of these banks had slacks in both inputs simultaneously. Six RCBs have slack in input1 and 27 RCBs had significantly high input2 slacks. With these banks, it means that there are potentially major technical efficiency improvement prospects.
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Table 5.3 cont’d RCB
CRSTE
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
0.93 0.934 0.923 0.925 0.928 0.935 0.941 0.931 0.92 0.913 0.912 0.911 0.902 0.903 0.914 0.911 0.91 0.915 0.93 0.934 0.942 0.937 0.941 0.939 0.935 0.928 0.925 0.924 0.919 0.919 0.921 0.929 0.921 0.921 0.924 0.931 0.96 0.956 0.96 0.953 0.95 0.977
CRSTE _Rank 46 38 62 57 49 36 31 44 68 80 82 83 88 86 78 83 85 75 46 38 30 35 31 34 36 49 57 60 71 71 64 48 64 64 60 44 19 21 19 22 24 8
VRSTE 0.959 0.959 0.947 0.944 0.942 0.944 0.989 0.984 0.978 0.973 0.974 0.972 0.962 0.961 0.964 0.95 0.941 0.945 0.949 0.946 0.946 0.944 0.945 0.944 0.938 0.932 0.929 0.926 0.929 0.937 0.949 0.97 0.966 0.988 0.986 1 0.995 0.985 0.992 0.984 0.979 1
VRSTE _Rank 73 73 80 88 94 88 18 27 37 47 44 50 69 70 64 77 96 85 78 81 81 88 85 88 98 101 105 107 105 99 78 55 61 20 24 1 11 25 13 27 34 1
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SCALE 0.969 0.974 0.975 0.98 0.985 0.99 0.952 0.947 0.941 0.939 0.937 0.937 0.938 0.939 0.948 0.959 0.967 0.967 0.979 0.987 0.995 0.993 0.995 0.995 0.996 0.995 0.995 0.999 0.989 0.981 0.97 0.958 0.953 0.932 0.937 0.931 0.965 0.97 0.968 0.968 0.97 0.977
SCALE_ Rank 47 42 40 32 30 22 66 70 76 77 80 80 79 77 68 58 51 51 34 28 11 21 11 11 10 11 11 3 25 31 44 59 65 87 80 88 55 44 49 49 44 39
Nature of RTS irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs drs drs drs drs drs drs drs drs irs irs irs irs irs irs
Table 5.3 cont’d RCB
CRSTE
52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
0.971 0.97 0.962 0.944 0.949 0.933 0.932 0.928 0.944 0.966 0.948 0.98 0.986 1 1 0.993 0.988 0.983 0.974 0.969 0.971 0.966 0.963 0.967 0.887 0.893 0.9 0.915 0.921 0.919 0.913 0.914 0.925 0.915 0.926 0.94 0.946 0.952 0.927 0.898 0.903 0.901
CRSTE _Rank 10 12 18 28 25 40 41 49 28 15 26 7 5 1 1 3 4 6 9 13 10 15 17 14 99 95 92 75 64 71 80 78 57 75 55 33 27 23 54 94 86 90
VRSTE 0.992 0.99 0.983 0.963 0.96 0.945 0.943 0.937 0.946 1 0.985 0.99 0.987 1 1 0.995 0.991 0.989 0.979 0.974 0.973 0.971 0.964 0.973 1 0.998 1 1 0.998 0.988 0.984 0.977 0.977 0.965 0.968 0.97 0.971 0.974 0.951 0.977 0.976 0.976
VRSTE _Rank 13 16 31 67 71 85 92 99 81 1 25 16 22 1 1 11 15 18 34 44 47 52 64 47 1 9 1 1 9 20 29 38 38 62 59 55 52 44 75 38 41 41
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SCALE 0.979 0.979 0.979 0.98 0.989 0.987 0.988 0.99 0.998 0.966 0.962 0.99 0.999 1 1 0.998 0.997 0.994 0.995 0.995 0.998 0.995 0.998 0.994 0.887 0.894 0.9 0.915 0.923 0.93 0.928 0.935 0.947 0.948 0.956 0.969 0.974 0.978 0.975 0.919 0.925 0.923
SCALE_ Rank 34 34 34 32 25 28 27 22 5 53 56 22 3 1 1 5 9 19 11 11 5 11 5 19 107 106 105 101 93 89 90 86 70 68 62 47 42 38 40 99 91 93
Nature of RTS irs irs irs irs irs irs irs irs drs irs irs irs drs crs crs irs irs irs irs irs irs irs drs drs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs irs
Table 5.3 cont’d RCB
CRSTE
94 95 96 97 98 99 100 101 102 103 104 105 106 107
0.899 0.89 0.877 0.883 0.877 0.873 0.869 0.882 0.891 0.884 0.888 0.884 0.901 0.902
CRSTE _Rank 93 97 104 102 104 106 107 103 96 100 98 100 90 88
VRSTE 0.972 0.965 0.96 0.963 0.951 0.946 0.943 0.942 0.941 0.932 0.93 0.933 0.984 0.987
VRSTE _Rank 50 62 71 67 75 81 92 94 96 101 104 101 29 22
SCALE 0.925 0.922 0.914 0.917 0.922 0.923 0.921 0.937 0.947 0.949 0.954 0.947 0.915 0.914
SCALE_ Rank 91 96 103 100 96 93 98 80 70 67 63 70 101 103
Nature of RTS irs irs irs irs irs irs irs irs irs irs irs irs irs irs
5.2.2 Quarterly Mean Overall Technical Efficiency (CRSTE) Table 5.4 reports the results of the overall technical efficiency (assuming constantreturns-to-scale) during the study period for all RCBs in the study sample. The average overall technical efficiency is 95.9%, indicating that, with scale effect taken into consideration, RCBs can improve technical efficiency by reducing the amount of inputs by about 4.1%, if they adopted the best practice technology. The highest level of technical efficiency of 97.4% was experienced in 2011q2 and the lowest level of 92.9% in 2009q1. There is no particular pattern in the trends. It can be observed that there was an upward trend over the first three quarters (92.9% to 96.9%) after which it dropped to 95.6% in the 4th quarter of 2009 and rises for the next two quarters up to 96% in 2010q2. After this period, there were down and up swings to the end of the period under consideration. The last two quarters in 2012 saw a drop in overall technical efficiency from 97.4% in 2012q1 down to 94.7% in 2012q3. Also, comparing the endpoint of the period under study,
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2009q1 to 2012q3, the overall technical efficiency increased from 92.9% to 94.7% over the period.
The second quarter of 2011 was a period of strong growth in economic activities. Developments in the real sector indicated that overall business confidence index, which is used to gauge the sentiments of businesses, increased in the second quarter (Bank of Ghana, 2011). This was likely to affect loan efficiency of RCBs in Ghana as financial intermediation of banks picks up. The period also saw the highest ever level of Banks’ loans to deposit-takers and other financial companies as a proportion to total banking loans in Ghana’s financial sector (Bank of Ghana, 2011). The increase in the commercial banks’ efficiency ratios appears to reflect the technical efficiency of RCBs.
Table 5.4: Quarterly Average Overall Technical Efficiency Scores (CRSTE) Quarter 2009q1 2009q2 2009q3 2009q4 2010q1 2010q2 2010q3 2010q4 2011q1 2011q2 2011q3 2011q4 2012q1 2012q2 2012q3 Mean
Mean 0.929 0.963 0.969 0.956 0.959 0.960 0.945 0.974 0.940 0.979 0.967 0.953 0.974 0.973 0.947 0.959
Sd 0.029 0.024 0.024 0.034 0.019 0.027 0.041 0.016 0.041 0.020 0.028 0.036 0.015 0.021 0.041 0.032
Min 0.869 0.916 0.870 0.867 0.918 0.896 0.828 0.926 0.855 0.894 0.882 0.831 0.945 0.890 0.826 0.826
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Max 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Efficient RCBs 2 3 4 5 2 3 3 5 4 6 2 2 4 3 1
5.2.3 Pure Technical Efficiency (VRSTE) Pure technical efficiency, a component of overall technical efficiency, was also estimated for the sample period. Table 5.5 presents a summary of the quarterly mean pure technical efficiency (VRSTE) scores with standard deviations, minimum and maximum efficiency scores and the numbers of efficient RCBs identified for each quarter. The quarterly mean pure technical efficiency for the period is 97.5%, indicating that, devoid of any scale effects, managers could reduce inputs usage by about 3.5% to achieve the same level of outputs.
Table 5.5: Quarterly Average Pure Technical Efficiency Scores (VRSTE) Quarter 2009q1 2009q2 2009q3 2009q4 2010q1 2010q2 2010q3 2010q4 2011q1 2011q2 2011q3 2011q4 2012q1 2012q2 2012q3 Mean
Mean 0.968 0.973 0.979 0.966 0.976 0.971 0.967 0.982 0.960 0.987 0.980 0.978 0.983 0.978 0.980 0.975
Sd 0.021 0.023 0.016 0.027 0.017 0.028 0.027 0.015 0.038 0.011 0.020 0.018 0.013 0.022 0.018 0.023
Min 0.926 0.927 0.925 0.887 0.920 0.903 0.895 0.927 0.876 0.959 0.927 0.926 0.951 0.890 0.925 0.876
Max 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Efficient RCBs 8 10 11 11 7 10 9 13 16 20 13 11 10 13 15
5.2.4 Scale Efficiency (SCALE) Scale efficiency scores for the sample RCBs in each quarter under consideration is presented as follows in Table 5.6. It is worth noting that scale efficiency measures the extent to which a bank can take advantage of returns to scale by changing its size towards optimal scale. Scale efficiency is estimated by the ratio of overall technical efficiency
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(CRSTE) to pure technical efficiency (VRSTE). Scale efficiency implies how close the production size of a rural bank is to the most productive scale size. Scale efficient RCBs have a score of one (or 100%), whilst the relatively inefficient RCBs have a score less than one (or less than 100%).
The average scale efficiency over the study period was 98.4% (standard deviation = 0.024), meaning that, on average, the scale inefficient RCBs could reduce their size by 1.6% without affecting their current output levels. Thus, about 1.6% of inefficiency is accounted for by unsuitable bank size (inefficiently large, medium, or small). The average quarterly scale efficiency scores are quite high and range from a minimum score of 96.1% in 2009q1 to a maximum of 99.5% in 2012q2. Over the period under study, scale efficiency marginally increased from 96.1% in 2009q1 to 96.6% in 2012q3 with some variations in between the end periods.
Table 5.6: Quarterly Average Scale Efficiency Scores (SCALE) Quarter 2009q1 2009q2 2009q3 2009q4 2010q1 2010q2 2010q3 2010q4 2011q1 2011q2 2011q3 2011q4 2012q1 2012q2 2012q3 Mean
Mean 0.961 0.989 0.990 0.990 0.983 0.988 0.977 0.993 0.978 0.992 0.987 0.974 0.990 0.995 0.966 0.984
Sd 0.029 0.009 0.018 0.018 0.016 0.012 0.031 0.009 0.025 0.019 0.024 0.031 0.011 0.006 0.042 0.024
Min 0.887 0.963 0.908 0.901 0.921 0.950 0.853 0.962 0.906 0.900 0.900 0.852 0.949 0.953 0.838 0.838
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Max 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Efficient RCBs 2 8 15 26 3 9 8 12 14 30 10 2 12 15 4
5.3 Results Based on the SFA Approach In Chapter Four of this thesis, four SFA models were described using the Translog (TL) production functions6. We considered only time-varying specifications, that is the Battasse and Coelli (1992) model (BC92), the Battese and Coelli (1995) model (BC95), the Greene (2005a) true random effects model (TRE), and the Greene (2005a) true fixed effects model (TFE). All models were estimated using the Maximum Likelihood methods (ML). The analysis was done using the Stata sfpanel command (Belotti et al, 2013).
5.3.1 Parameter Estimates of SFA Models The maximum likelihood estimates of the parameters of the selected translog stochastic frontier production functions (equation 4.19b) are presented in Table 5.7 to enable a comparison of the models. From the results, the parameter estimates appear reasonably consistent in magnitudes across the various models. All the time, parameters are statistically significant and negatively signed, indicating some technical regress. Moreover, the estimates of variance parameters, sigma_u, sigma_v, and lambda (λ) are mostly statistically significant for all the models, suggesting evidence of technical inefficiency in the data as expected (Wadud and White, 2000, Sharma et al, 1997, Hjalmarsson et al, 1996). For instance, lambda ( ), which is significant at 1% in all models shows that null hypothesis of no technical inefficiency effects is rejected. Thus, it can be concluded that a significant amount of the variation in the composite error term (vu) is due to the inefficiency component.
6
See chapter 4 for selection criterion.
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According to Jung and Pyo (2009), using different models with different assumptions underlying might lead to different rankings of estimated efficiency. It is, therefore, important to choose the model that is suitable, considering the available data for the purposes of further analysis. The SFA estimates in Table 5.8 were subjected to the Likelihood Ratio Test (lrtest) with the null hypothesis to find the stochastic production frontier model that best fits the data. The Chi-Square statistic (LR chi2(66) = 2499.36) rejects the null hypothesis of no difference among the models at 1% significance level, and judging from the minimized AIC and BIC information criterion, the true fixed effect model (Model 2) is selected for the subsequent prediction of technical efficiency, technical change and total factor productivity (see Table 5.7).
Table 5.7: Likelihood-Ratio Test of Models LR chi2(66) = 2499.36 Prob > chi2 = 0.0000 Assumption: Model (1, 3, 4) nested in Model (2) Model Obs ll(model) df 1 1605 71.57 13 2 1605 481.50 106 3 1605 -878.94 13 4 1605 39.19 14
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AIC -117.14 -751.00 1783.87 -50.38
BIC -47.18 -180.63 1853.82 24.96
Table 5.8: Parameter Estimates for the Stochastic Frontier Models True Random Effects – True Fixed Effects – TL(Model 1) TL(Model 2) Variables Parameter Coefficients (SE) Coefficients (SE)
Battese and Coelli, 1995 (Model 3) Coefficients (SE)
Battese and Coelli, 1992, (Model 4) Coefficients (SE)
0.3920277*** (0.0393667)
1.11547*** (0.1512757)
𝛼
0.1346*** (0.0277)
𝛽𝑘 𝑙𝑛𝑋𝑖𝑘
𝛽𝑘
0.5743*** (0.0279)
0.306469*** (0.0235816)
0.943394*** (0.0429067)
0.3398275*** (0.0649175)
𝑙𝑛𝑋𝑘 𝑙𝑛𝑋𝑘
𝛾𝑘
𝛽𝑚 𝑙𝑛𝑋𝑖𝑚
𝛽𝑚
-0.1779*** (0.0221) 0.0816*** (0.0248)
-0.295488*** (0.0142839) 0.0997017*** (0.0275298)
-0.1106878** (0.0439942) 0.0620984** (0.0376022)
-0.1925852*** (0.0425417) 0.1070805*** (0.0297762)
𝑙𝑛𝑋𝑚 𝑙𝑛𝑋𝑚
𝛾𝑚
-0.0333431 (0.0203591)
-0.0124859 (0.0146196)
-0.16143*** (0.0361148)
-0.0663874*** (0.0234502)
𝑙𝑛𝑋𝑖𝑘 ∗ 𝑙𝑛𝑋𝑖𝑚
𝜃𝑘𝑚
0.0246776 (0.0196668)
0.039451** (0.0120153)
0.1218232*** (0.0403513)
0.0346072 (0.0250325)
𝑇
𝜗𝑜
-0.031137*** (0.005073)
-0.0215269** (0.006448)
-0.0365967*** (0.0106055)
-0.0236757*** (0.0071893)
𝑙𝑛𝑋𝑖𝑘 ∗ 𝑇
𝜃𝑘
0.0060612** (0.002449)
0.0151953*** (0.0024917)
-0.0067523 (0.0045402)
0.0217775*** (0.004248)
𝑙𝑛𝑋𝑖𝑚 ∗ 𝑇
𝜃𝑚
-0.0014073 (0.0022137)
-0.0061332** (0.0021337)
0.0021232 (0.0039688)
-0.0028017 (0.0025016)
𝑇2
𝜗01
0.0034177*** (0.000318)
0.0039219*** (0.0004174)
0.0021394*** (0.0006426)
0.0013896*** (0.0003485)
Cons
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Table 5.8: Cont’d True Random Effects – TL(Model 1)
True Fixed Effects – TL(Model 2)
Battese and Coelli, 1995 (Model 3)
Battese and Coelli, 1992, (Model 4)
Sigma_u
0.3486148*** (0.0093811)
0.3585125*** (0.0063301)
1.914539* (1.010039)
0.2070355*** (0.0426973)
Sigma_v
0.0593132*** (0.0074448)
3.28E-10 (1.17E-07)
0.3071226*** (0.0120558)
0.041066**** (0.0015328)
Lambda
5.877521*** (0.0151057)
1.09E+09*** (0.0063301)
6.233792*** (1.008654)
Variance Parameters
Note: Significance Level at 10%: *, 5%:**, 1%: ***.
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5.4 Results Derived from SFA Approach This section presents the results for the SFA technical efficiencies predicted from the selected TFE Translog Model 2 for the RCBs. The results are presented in Tables 5.9 to 5.19 by firms and quarterly averages, followed with discussions.
5.4.1 Quarterly Mean Technical Efficiency Table 5.9: Quarterly Technical Efficiency, 2009q1 – 2012q3 Quarter 2009q1 2009q2 2009q3 2009q4 2010q1 2010q2 2010q3 2010q4 2011q1 2011q2 2011q3 2011q4 2012q1 2012q2 2012q3 Mean
Mean 0.7512 0.7943 0.8147 0.8103 0.8031 0.8087 0.8417 0.8029 0.8076 0.8126 0.8587 0.8075 0.7825 0.7654 0.7563 0.8012
Sd 0.1955 0.1834 0.1664 0.1683 0.1603 0.1408 0.1407 0.1671 0.1597 0.1413 0.1400 0.1642 0.1578 0.1633 0.1739 0.1639
Min 0.2259 0.2203 0.2330 0.2236 0.2953 0.2871 0.2915 0.2722 0.2872 0.2130 0.1770 0.2380 0.2549 0.2670 0.2435 0.1770
Max 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
The quarterly results presented in Table 5.9 show that, over the period under study, RCBs’ technical efficiency fluctuated. It can be observed that the quarterly measure of overall technical efficiency was highest in the third quarters of each year, followed by lower efficiency levels in the fourth quarter. The trends show that the technical efficiency level rises from the first quarter and peaks during the 3rd quarter of each year and falls by the 4th, as shown on Figure 5.3 below. This is interesting to note, because the third quarter is known
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to be the time when RCBs actively lend to businesses to finance trade activities in preparation for the Christmas season and offer individual loans to finance schooling, and other consumption expenditure by working and salaried workers. The trend, therefore, could be explained, once again, by the seasonal shifts in economic activities, which affect banking operations. The third quarter is the peak of business activities in the economy of Ghana. The mean technical efficiency for the period is 80.12%, indicating that RCBs could improve on inputs (fixed assets and deposits) used to achieve the same level of outputs (loans).
Figure 5.3: Quarterly Mean Technical Efficiency mean
min
max
Technical Efficiency
1.2000 1.0000 0.8000 0.6000 0.4000 0.2000 0.0000
Quarters
5.4.2. SFA Technical Efficiency Results for Individual RCBs In this section, we present the SFA mean technical efficiency scores of the individual RCBs over the study period, 2009q1 to 2012q3. A couple of comments can be made from Table 5.10. First, it is observed on average that no RCB was fully technical efficient over the study
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period7. Second, the variability in the efficiency estimates among the RCBs is low, as indicated by the low standard deviations relative to the mean values. This is indicative of the homogeneous characteristics of the RCBs in the industry. From the mean results, RCB 34 is the most efficient, and RCB 44 was the least efficient, from the SFA analysis. The ranking for RCB 44 is not surprising, as it currently ceased to operate, after the APEX rated it as nonsatisfactory. The SFA ranking of the RCBs also appears to include about 9 banks that are rated among the top Ghana Club 100 companies. These include RCBs 65, 3, 58, 63, 73, 86, 98, 23, and 90.
Table 5.10: Mean Technical Efficiency of Firms for 2009 - 2012 – SFA Analysis RCB 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Ranking 13 83 3 41 92 77 69 39 71 61 80 74 19 105 44 60 88 85 30 40 38
Mean 0.8956 0.7466 0.9165 0.8554 0.6888 0.7709 0.7856 0.8563 0.7825 0.8142 0.7569 0.7749 0.8855 0.5686 0.8519 0.8157 0.7247 0.7341 0.8681 0.8556 0.8564
Sd 0.0656 0.1259 0.0499 0.1348 0.1970 0.1385 0.1346 0.0986 0.1480 0.0959 0.1845 0.1228 0.0888 0.2275 0.0805 0.1112 0.1334 0.1559 0.1232 0.0874 0.1113
7
Min 0.8061 0.5936 0.8279 0.6129 0.4306 0.4965 0.5783 0.6869 0.5299 0.6825 0.4536 0.5886 0.7437 0.3479 0.7252 0.6407 0.5109 0.4928 0.6330 0.7167 0.6225
Max 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Note however that at some point within the study period, the RCBs achieved full technical efficiency. See maximum values of efficiency scores for each individual RCB in Table 5.10.
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Table 5.10 cont’d RCB 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
Ranking 106 11 63 99 57 14 98 70 84 94 33 73 1 64 49 78 101 59 100 24 9 17 107 97 58 36 43 75 82 37 15 68 76 35 32 81 4 90 103 89
Mean 0.5627 0.8960 0.8098 0.6303 0.8195 0.8956 0.6344 0.7828 0.7454 0.6719 0.8661 0.7776 0.9481 0.8019 0.8362 0.7675 0.5779 0.8160 0.6104 0.8774 0.9005 0.8877 0.5517 0.6550 0.8179 0.8610 0.8537 0.7747 0.7485 0.8596 0.8953 0.7926 0.7714 0.8636 0.8670 0.7554 0.9076 0.7077 0.5737 0.7204
Sd 0.2843 0.0516 0.0902 0.1715 0.1134 0.0527 0.2042 0.1059 0.1570 0.1758 0.0845 0.1159 0.0554 0.1142 0.1076 0.1280 0.2822 0.0873 0.2064 0.0697 0.0589 0.1067 0.3262 0.2123 0.1466 0.1131 0.0954 0.1347 0.1172 0.0866 0.0833 0.1299 0.1354 0.0880 0.0737 0.1300 0.0589 0.2211 0.2788 0.1883
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Min 0.2871 0.7974 0.6889 0.3521 0.6874 0.7973 0.2951 0.6197 0.4481 0.4510 0.7216 0.5768 0.8113 0.6191 0.6521 0.6179 0.2236 0.6746 0.2868 0.8024 0.8191 0.7036 0.1770 0.3026 0.5557 0.6094 0.6401 0.5663 0.5947 0.7376 0.7688 0.5359 0.6058 0.7270 0.7028 0.5502 0.8192 0.2259 0.2330 0.4452
Max 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Table 5.10 cont’d RCB 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
Ranking 56 5 50 2 47 55 72 34 66 23 93 6 21 27 20 29 8 96 104 102 87 65 62 26 7 48 79 45 18 28 22 46 25 54 86 53 10 67 51 95
Mean 0.8212 0.9065 0.8321 0.9267 0.8441 0.8242 0.7804 0.8642 0.8012 0.8799 0.6764 0.9038 0.8823 0.8721 0.8845 0.8682 0.9024 0.6574 0.5723 0.5769 0.7303 0.8014 0.8128 0.8734 0.9030 0.8434 0.7579 0.8469 0.8874 0.8715 0.8822 0.8452 0.8749 0.8249 0.7327 0.8265 0.9000 0.7970 0.8296 0.6702
Sd 0.1095 0.0586 0.0950 0.0946 0.0945 0.1272 0.1160 0.0879 0.1096 0.0615 0.1829 0.0749 0.0782 0.1137 0.1012 0.0731 0.0635 0.2054 0.2423 0.2294 0.1276 0.1464 0.1561 0.0760 0.0482 0.1293 0.1503 0.1204 0.0727 0.0710 0.0832 0.1102 0.0662 0.1169 0.1612 0.1074 0.0565 0.2333 0.1137 0.2186
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Min 0.6185 0.8247 0.6569 0.7184 0.6770 0.6030 0.5900 0.7244 0.6675 0.7899 0.3144 0.7855 0.6858 0.6648 0.6589 0.7194 0.7846 0.3901 0.2203 0.2722 0.5663 0.5671 0.5328 0.7456 0.8389 0.6257 0.5375 0.5984 0.7628 0.7499 0.7415 0.6636 0.7714 0.6707 0.4408 0.5487 0.8308 0.2380 0.6708 0.4124
Max 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Table 5.10 cont’d RCB 102 103 104 105 106 107 Mean
Ranking 91 12 16 42 31 52
Mean 0.6987 0.8957 0.8930 0.8548 0.8679 0.8296 0.8012
Sd 0.2479 0.0572 0.0642 0.1016 0.0808 0.1065 0.1639
Min 0.2624 0.7839 0.7595 0.6751 0.7124 0.6665 0.1770
Max 1 1 1 1 1 1 1
Again, it is observed that most of the RCBs (53) fell within the middle bounds with technical efficiency ranging from 75.54% - 87.21%. A fairly equal number of RCBs was, however, found at the upper and lower bounds, as shown on Table 5.11.
Table 5.11: Technical Efficiency Bounds Bounds8 Mean Technical Efficiency Ranges High/ upper quartile >/0.8721 Middle quartile 0.7554 - 0.8721 Lower quartile /< 0.7554 Total
Number of Firms 29 53 25 107
5.3.3 Comparing DEA and SFA Technical Efficiency Results In order to further explore the link between the SFA and the DEA estimators, the efficiency scores and rankings are compared. Tables 5.3 and 5.10 are used in this exercise to compare the efficiency estimates computed by DEA under both constant (CRS) and variable (VRS) returns to scale, which are compared with the SFA estimates. The summary statistics and the
8
Bounds were calculated based on Quartiles
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frequency distribution of the efficiency estimates obtained from the DEA and the SFA model are presented in Tables 5.12 and 5.13, respectively. The following observations can be made.
First, from Table 5.12, the RCBs have high technical efficiency estimates under the DEA methods than the SFA method. The average technical efficiency estimated by SFA (80.12%) is lower than the ones estimated by DEA (92.94% and 96.76%). Second, the standard deviations given by the two main methods are quite different but similar for the two DEA variants. The SFA exhibits greater variability in technical efficiency than in the DEA frontier. The standard deviation for the SFA is high due to the relatively low mean estimates of the SFA-TE. Also, from the skewness and kurtosis statistics, the estimates are highly skewed (SFA and DEA-VRSTE to the left and DEA-CRSTE to the right), while the kurtosis statistics suggest that the SFA is more single-peaked and the DEA methods have a relatively flat distribution. Third, none of the RCBs is fully efficient under the SFA, while 2 and 8 banks were fully efficient under the DEA-CRS and VRS, respectively (see Tables 5.3, 5.10 and 5.13).
Table 5.12: Summary Statistics for SFA and DEA Efficiency Estimates Statistics SFA-TE DEA-CRSTE DEA-VRSTE Mean 0.8012 0.9294 0.9676 Standard Deviation 0.1639 0.0291 0.0207 Kurtosis 4.2953 -0.1557 -1.0351 Skewness -1.1894 0.3162 -0.1992 Minimum 0.1770 0.869 0.926 Maximum 0.9481 1 1 Range 0.8230 0.131 0.074 No. Efficient 0 2 8 No. of Banks 107 107 107
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Table 5.13: Frequency Distribution of Efficiency Estimates from the SFA and DEA Efficiency Range 0.5 - 0.6 0.6 - 0.7 0.7 - 0.8 0.8 - 0.9 0.9 - 1.0 =1 Total
SFA-TE No. of Banks 7 10 24 56 10 0 107
% of Banks 7% 16% 22% 52% 9% 0% 100%
DEA-CRSTE No. of % of Banks Banks 0 0% 0 0% 0 0% 15 14% 90 84% 2 2% 107 100%
DEA-VRSTE No. of Banks % of Banks 0 0% 0 0% 0 0% 0 0% 99 93% 8 7% 107 100%
Table 5.14: Comparing SFA and DEA Technical Efficiency by Quarters Quarter 2009q1 2009q2 2009q3 2009q4 2010q1 2010q2 2010q3 2010q4 2011q1 2011q2 2011q3 2011q4 2012q1 2012q2 2012q3 Mean
DEA-CRSTE 0.9294 0.9627 0.9688 0.9560 0.9589 0.9602 0.9449 0.9742 0.9396 0.9790 0.9670 0.9527 0.9739 0.9733 0.9467 0.9592
DEA-VRSTE 0.9676 0.9731 0.9786 0.9659 0.9757 0.9715 0.9672 0.9816 0.9605 0.9875 0.9803 0.9777 0.9834 0.9780 0.9800 0.9752
SFA-TE 0.7512 0.7943 0.8147 0.8103 0.8031 0.8087 0.8417 0.8029 0.8076 0.8126 0.8587 0.8075 0.7825 0.7654 0.7563 0.8012
Moreover, from Table 5.14, the quarterly trends show that, for all methods, technical efficiency increased by the end of the period under study. This, therefore, confirms the operational behaviour of RCBs in Ghana. As it can also be seen on Figure 5.4 below, the DEA efficiencies are very close and differ significantly in terms of estimates from the SFA
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estimates. However, in terms of pattern, it is observed that the two models may not be highly different. Figure 5.4: Comparison of Technical Efficiency Scores, DEA and SFA Quarterly Average Technical Efficiency Scores (DEA and SFA) DEA-TE (CRS)
DEA-TE (VRS)
1
SFA-TE 0.9752 0.9592
0.95 0.9 0.85
0.8012
0.8 0.75 0.7
From the above observations, the SFA and DEA have different distributions, thus, the correlation of rankings offers a way of directly comparing efficiency estimates. To do this comparison, RCBs were ranked such that the highest ranked (Rank 1) was assigned as the most efficient RCB under each method9. Table 5.15 displays both the Spearman’s and Kendall’s rank correlations. The results of the Spearman and Kendall tests show that all correlation coefficients indicated very low but significant, positive correlation between the SFA and the DEA methods. In other words, there is a very minimal significant dependency between the rankings of efficiency measured by SFA and DEA, and both frontier methods show little significant concordance on the evaluation of the efficiencies of the RCBs. The Wilcoxon test also showed that both efficiency rankings are significantly different10.
9
See Tables 5.3 and 5.10 for the rankings. See Appendix Table A5.3 for Wilcoxon test results.
10
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Table 5.15: Spearman’s and Kendall’s Rank Correlations for SFA and DEA Spearman’s Rank Correlation DEA-VRSTE VRSTE 1 CRSTE 0.5794* SFA-TE 0.0957* Kendall’s Rank Correlation VRSTE 0.9127 CRSTE 0.4391* SFA-TE 0.0646*
DEA-CRSTE
SFA-TE
1 0.1239*
1
0.9203 0.0832*
0.9953
Finally, following the rationale of Chirikos and Sear (2000)11, the top (high) and bottom (low) deciles (10%) of the rankings were observed and compared. Table 5.16 displays RCBs in the top and bottom deciles rankings. From Table 5.16, the identification of the high and low rank RCBs leads again to very weak matches between SFA and DEA rankings. Table 5.16 reveals that top deciles of CRSTE and VRSTE contain more identical RCBs, specifically 63, 64, 65, 68, 69, 53, 52 and 51. The bottom deciles have RCBs 100, 101, 102, 103, 105, and 104 being identical. When the SFA-TE and CRSTE deciles are compared, only RCBs 63 and 65 are identified for the top deciles, and they are non-identical for the bottom deciles. Interestingly, RCBs 63, 65, and 73, which rank high in both SFA-TE and CRSTE, are also ranked among the Ghana Club 100 companies.
With regards to the SFA and VRSTE, three RCB’s were identically ranked including 78, 63, and 65 for the top decile; whilst 14 and 38 is identical for the bottom decile. RCBs 44, 45 and 81 which are classified in the bottom decile of the SFA move to the top decile of the VRSTE. 11
Chirikos and Sear (2000) discovered that various methods tend to classify observations in the top and bottom quantile of the efficiency distribution similarly.
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It is also identified that RCB 76 and 77, which were ranked in the top decile of the CRSTE, were also mixed up in the VRSTE. These observations suggest that most of the RCBs do not have comparable observations under the different methods. The instability of rankings over time supports the inconsistencies in the DEA and SFA comparisons.12 Thus the SFA ranking is not directly linked to the DEA rankings. Observing between these three rankings, the SFA tend to rank high more of the Ghana club 100 companies compared than the DEA. In conclusion, the weak correspondence between the two methods is not a surprise and is consistent with earlier research (Ferrier and Lovell, 1990; Bauer et al., 1998; Weill, 2004).
Table 5.16: RCBs in Top and Bottom Deciles SFA-TE Top Deciles 3
Bottom Deciles 25
23
DEA-CRSTE Top Deciles 52
Bottom Deciles 101
44
66
91
34 42
45 14
71 67, 68
58 63
40 38
65 73
DEA-VRSTE Top Deciles 64
Bottom Deciles 36, 38 33, 31, 15, 13
98 102, 95
66, 65, 51, 61, 45, 79, 78, 76 47 67, 46
72 70
97 103
43, 81 69, 16
104 35, 105, 103
28 81
53 63, 51
96 105
107, 44 63, 53
37 59, 39
78 86
80 60
64 69
104 76
52 48, 68
26, 102 34
98
22
65
77
80, 77
58, 100
14, 101
99, 100
12
Individual mean efficiency scores and rankings for all banks are found in the Appendix in Tables A5.4 and A5.5. It can be observed that rankings of rural banks are not stable over the study period as the rankings tend to differ among the SFA over the study period.
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5.3.4 Technical Efficiency and Accounting-Based Efficiency Measure Non-frontier standard measures of performance are widely used by industry regulators, bank managers and consultants. As observed by Bauer et al (1997), if the efficiency scores are related to standard financial ratio measures of performance, then authorities could be more confident that these scores are accurate indicators of performance and not just some artificial measures resulting of specific assumptions. In a way, this step can help to determine the “best” frontier technique, as we have observed above that the results of the various approaches were not robust. We analysed, here, the correlations between frontier efficiency scores and a standard performance indicator in order to evaluate their consistency. The chosen measure of performance is the efficiency ratio (ER, defined as the ratio of expense to income).
The bank efficiency ratio (ER) indicates what it costs a bank to generate its revenue. This ratio is often considered as the most popular non-frontier bank performance (efficiency) measure, in part, because it reflects operations both on and off the balance sheet (Forster and Shaffer, 2005). Smaller values of these cost-related performance ratios denote better-cost management and are more desirable. Thus, they are expected to be negatively correlated to the technical efficiency scores.
Table 5.17: Correlations between Frontier Efficiencies and Accounting-Based Efficiency Ratio SFA-TE DEA-CRSTE DEA-VRSTE ER
-0.2828**
0.0181
Notes: ** denote 5% significance level. ER = efficiency ratio.
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0.1284
Table 5.17 displays the correlations between efficiency scores obtained for each technique and an accounting measure of bank efficiency (efficiency ratio). A few interesting comments can be made from the Table. First, the correlation with the ER indicator is positive and insignificant for all the DEA technical efficiency scores, however, it correlates negatively and significantly with the SFA technical efficiency scores, as expected. The low magnitude of the correlation coefficients, ranging from 1.81% to 28.28%, may arise because the standard performance ratios do not consider the effects of differences in input and output mix (Berger and Humphrey, 1991). Secondly, the SFA measures have relatively higher correlations to the bank efficiency ratio than the DEA. This observation roughly suggests that the technical efficiency scores estimated with the SFA approaches are marginally consistent with the standard accounting measures of bank efficiency relative to the DEA technical efficiency scores.
5.4 Chapter Summary In this chapter, we have estimated the technical efficiency of the 107 RCBs, using both the non-parametric DEA and the parametric SFA methods. The main objectives of the chapter were to estimate and rank the technical efficiency of the RCBs in Ghana, over the period, 2009q1 to 2012q3. The consistency in the estimates derived from the two alternative methods was also explored. Using a still unexplored database for this purpose, a number of important findings emerged from the analysis.
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We, first, estimated an input-oriented DEA assuming variable return to scale. The mean overall technical efficiency (CRSTE) of the RCBs was about 95.9% and pure technical efficiency (VRSTE) was 97.5%. This implies that inputs can be reduced by 4%, on average, relative to the best-practice banks, during the sample period. The mean technical efficiency from the SFA is 80.12%. These average efficiency scores suggest there is still significant potential for further efficiency improvement among the RCBs.
Generally, the SFA estimates were found to be lower, compared to the DEA estimates. Overall, efficiency estimates showed positive trends over the study period, under both the DEA and the SFA and appeared to follow the general seasonal variations in economic activities in Ghana. High technical efficiency tends to be achieved with periods of high economic activities.
To examine the robustness of estimated efficiency ratings, we tested the consistency conditions for DEA and SFA techniques in three aspects. Firstly, we tested for the correlation between the DEA (CRSTE and VRSTE) and SFA technical efficiency levels, compared their rank-order correlations, and, finally, compared the frontier results with the standard accounting efficiency ratio indicator (ER) used by the banking industry. These findings were consistent with Thanassoulis et al. (1996). The ranking of the RCBs, using the two alternative methods, was found to be generally inconsistent. Efficiency rankings produced from the DEA and the SFA techniques were not directly comparable. The rank correlations produced very low and insignificant coefficients. The Wilcoxon sign-rank test supported the
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inconsistencies in the DEA and SFA rankings. This inconsistency makes it difficult to predict the efficiency performance of RCBs with a particular method. Also, it was found out that RCBs have different levels of technical efficiency, depending on the approach. However, RCBs 63, 65, and 73, which belong to the Ghana Club 100 companies and are known to be high performing banks, were consistently ranked high among all methods. Another clear finding is that most of the industry’s large banks, by assets and profits, were not ranked among the top 10 percent in both the DEA and the SFA, although the SFA ranks more of these RCBs among the top 20%. The implication is that large banks could be relatively inefficient, as they become wasteful as a result of agency problems. This is consistent with Mester et al (1996) Information Advantage Hypothesis. The SFA rankings also ranked RCB 44 as the least efficient over the period, and it is interesting to note that the bank has currently folded up due to managerial inefficiency13.
From the findings, one important conclusion is that policy conclusions resulting from technical efficiency estimates seem to be sensitive to the selection of the frontier efficiency estimation methods used. Overall, the point of convergence is that there are considerable capacities for RCBs to improve their efficiency in the industry.
13
Note that DEA –CRSTE and VRSTE ranked RCB 44 as 60 and 24, respectively.
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CHAPTER SIX EMPIRICAL ANALYSIS OF PRODUCTIVITY CHANGES OF RURAL AND COMMUNITY BANKS (RCBs) IN GHANA 6.1 Introduction This chapter evaluates the level and sources of productivity changes of RCBs in Ghana. The study applied the non-parametric frontier approach (DEA) and the parametric frontier approach (SFA). Several studies exist in the extant literature on productivity analysis on banks, as reviewed in Chapter Two. However, there are no studies investigating and comparing RCBs’ productivity performance in Ghana. The main reasons for this literature gap have been addressed in the Chapter One of this thesis.
The specific objectives of the chapter are: (a) to estimate the levels of total factor productivity (TFP) changes of the RCBs, using both DEA and SFA approaches, (b) to identify the sources of the TFP changes of the RCBs, by decomposing it into technical change and efficiency changes and (c) to examine the consistency of the DEA and SFA methods in measuring and ranking the TFP changes of the RCBs..
The same data used in Chapter 5, which is described in Table 5.1, is also used here. The productivity changes and components were estimated using the Variable Returns to Scale (VRS) assumptions14 in an input-oriented DEA model for a balanced panel of 107 RCBs over 15 quarters, from 2009q1 to 2012q3. For the SFA, the time-varying translog true fixed effect
14
Constant returns to scale assumption tends to under estimate efficiency and productivity scores. It assumes that the producers are able to linearly scale the inputs and outputs without increasing and decreasing the efficiency. In reality firms may not be able to scale their inputs and outputs linearly. Variable return to scale is generally manipulated to address this issue. (See Coelli et al, 2005 and Gee, 2008).
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model was used to measure the productivity changes and their components. Coelli’s (1996) DEAP 2.1 and STATA 12 software were used to estimate all the productivity indices. Further statistical analyses were done to generate geometric means and charts using STATA 12 and MS Excel.
The rest of the chapter is organized as follows. Section 6.2 presents the empirical results of DEA TFP change (the Malmquist productivity indices) and its decomposition for the RCBs. Section 6.3 presents the empirical results of SFA TFP change (the multiplicative Divisia indices) and its decomposition for the RCBs. Section 6.4 presents the comparison between the DEA and SFA productivity change estimates. Section 6.5 provides a summary and a conclusion for the chapter.
6.2 Estimates of Productivity: DEA approach In this section, the DEA productivity results for the RCBs are presented and discussed. The individual RCBs’ productivity estimates are presented first, followed by the estimates of the components. A quarterly summary of the results is also presented to show the trends over the study period.
6.2.1 DEA TFP Changes - Summary of Bank Means Table 6.1 reports the summary of the estimates of productivity changes and components for individual RCBs in the sample over the 15 pairs of quarters between 2009Q1 and 2012Q3. The frequency distribution is also reported in Table 6.2. A number of observations can be made from Table 6.1. 133
Firstly, with the exception of about 17 RCBs, 90 out of the 107 RCBs under study suffered technological regress over the study period. Secondly, 56 (52.34%) of the RCBs experienced productivity declines ranging from -0.1% to -0.9%. The sources of productivity declines for these banks could be attributed mainly to the technological regress. There was growth in productivity (ranging from 0.1% to 0.6%) for 35 (32.71%) RCBs, while 16 (14.95%) of them remained unchanged. Thirdly, all 41 RCBs that were scale inefficient tend to experience decline in productivity. The sources of the poor productivity performance were largely both technical inefficiency and technological regress (with the exception of a few of the banks). When the RCBs were ranked in terms of mean productivity change over the period, RCBs 76, 96, 92, and 91 came tops, with a productivity growth of 0.6%. Evidently, it is interesting to note that RCBs 76, 96, and 91 are classified as small banks by the size of total assets. RCB 92 is classified as medium. Bank 32, which is a medium bank, had the least productivity score of 0.991, indicating a productivity decline of -0.9%.
Table 6.1: DEA TFP Changes and Components - RCBs Means (2009Q1-2012Q3) RCB 1 2 3 4 5 6 7 8
EFFCH 1.002 1.003 0.995 0.996 0.995 0.995 0.997 0.995
TECH 0.999 0.999 0.999 0.998 0.998 0.998 0.998 0.997
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TFP 1.001 1.001 0.994 0.994 0.992 0.993 0.995 0.993
Table 6.1 cont’d RCB 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
EFFCH 0.996 0.995 0.997 0.999 1 0.998 1 1 1.001 0.993 0.993 0.996 0.997 0.997 0.998 0.999 0.998 1 0.999 0.998 0.998 0.998 0.998 0.998 1.002 1.003 1.003 1.003 1.003 1.004 1.003 1.002 1.002 1.002 1.003 1.002 1.002 1
TECH 0.997 0.998 0.998 0.996 0.999 0.999 0.998 1 1 1 1 1.001 0.998 0.997 0.999 0.996 0.995 0.997 0.999 0.998 0.999 0.996 0.995 0.993 0.994 0.994 0.994 0.994 0.994 0.994 0.997 0.997 0.997 0.997 0.997 0.996 0.997 0.997
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TFP 0.993 0.993 0.995 0.995 0.998 0.997 0.999 1 1.001 0.993 0.993 0.996 0.995 0.994 0.997 0.996 0.993 0.997 0.998 0.996 0.997 0.995 0.994 0.991 0.996 0.997 0.997 0.997 0.997 0.998 1 0.999 0.998 1 1 0.999 0.998 0.997
Table 6.1 cont’d RCB 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
EFFCH 1 1.001 1.002 1.002 1 1 1 1.001 1.003 1.002 1.003 1.004 1.004 1.003 1.002 1.002 1 0.999 0.999 0.999 0.999 1 1.001 1.001 1.001 1.001 1.002 1.003 1.002 1.008 1.007 1.004 1.004 1.003 1.002 1.003 1.004 1.003
TECH 1 0.999 0.998 0.998 0.998 0.998 0.997 0.998 0.997 0.997 0.999 1.001 1 1 1.001 0.999 0.999 0.999 0.998 0.998 0.997 0.998 0.996 0.999 0.999 0.997 0.997 0.998 0.999 0.998 0.995 0.996 0.999 0.999 0.999 1 1 0.999
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TFP 1 1 1 1 0.998 0.998 0.998 0.998 1 0.999 1.002 1.005 1.004 1.003 1.003 1.001 0.999 0.999 0.997 0.997 0.996 0.998 0.997 1 1 0.998 0.998 1 1 1.006 1.002 1 1.002 1.003 1 1.003 1.003 1.002
Table 6.1 cont’d RCB 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 mean
EFFCH 1 1.001 1 1 0.998 1.001 1.005 1.005 1.006 1.005 1.006 1.007 1.006 1.006 1.007 1.008 1.006 1.006 1.007 1.007 1.007 1.006 1.005 1.001
TECH 0.998 0.999 0.998 1.002 1.001 1 1.001 1.001 0.999 0.999 0.998 0.999 0.999 0.999 0.997 0.997 0.999 0.998 0.997 0.998 0.998 0.998 0.998 0.998
TFP 0.999 1 0.998 1.002 0.999 1.002 1.006 1.006 1.005 1.004 1.004 1.006 1.004 1.005 1.004 1.004 1.005 1.004 1.004 1.005 1.005 1.004 1.003 0.999
Table 6.2: Frequency Distribution of TFP, TECH, and EFFCH EFFCH
Freq.
%
TECH
Freq.
%
TFP
Freq.
%
1
35
32.71
Total
107
100
Total
107
100
Total
107
100
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6.2.2 DEA Total Factor Productivity (TFP) Changes – Summary of Quarterly Means This section presents the results of the total factor productivity changes (TFP), which is the product of efficiency change (EFFCH) and technical change (TECH). The quarterly average estimates of total factor productivity changes and their components for the RCBs are presented in Table 6.3 and graphed in Figure 6.1. Several observations can be made from the table. First, it is worth noting that TFP appeared to swing from regress to progress inbetween quarters. From Table 6.3, it can be observed that the RCBs experienced deterioration in TFP, mostly, every 1st to 2nd and 3rd to 4th quarters of the year (except the 3rd to the 4th quarter of 2010). In between these quarters, TFP also improved every 2nd to 3rd and 4th to 1st quarters of the year respectively (except the 2nd to 3rd quarter of 2010).
Table 6.3: Quarterly Mean TFP Changes (2009Q1 - 2012Q3) Quarter 2009Q1/2009Q2 2009Q2/2009Q3 2009Q3/2009Q4 2009Q4/2010Q1 2010Q1/2010Q2 2010Q2/2010Q3 2010Q3/2010Q4 2010Q4/2011Q1 2011Q1/2011Q2 2011Q2/2011Q3 2011Q3/2011Q4 2011Q4/2012Q1 2012Q1/2012Q2 2012Q2/2012Q3 Mean
EFFCH 1.036 1.006 0.987 1.003 1.001 0.984 1.032 0.964 1.043 0.988 0.985 1.023 0.999 0.972 1.001
TECH 0.96 1.004 0.997 1.02 0.997 1.004 0.974 1.046 0.936 1.026 1.004* 0.991 0.982 1.036 0.998
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TFP 0.995 1.01 0.984 1.024 0.998 0.988* 1.005* 1.008 0.976 1.013 0.989 1.014 0.981 1.007 0.999
Figure 6.1: Quarterly Changes in Productivity Index (MPI)
The overall mean TFP index for all the RCBs deteriorated by -0.1% for the period. The observed deterioration in TFP is mainly attributable to technical regress (frontier shifts) of 0.02% per quarter and a compensation of 0.1% per quarter improvement in technical efficiency. This is not surprising, as it can be observed from Table 6.3 that the patterns in the changes in the TFP are strongly influenced by similar patterns in technical change. It appears that the patterns could be attributed to the seasonal changes in rural banking activities in the banking system in Ghana, where banks change their operating technology with the change in seasons. The first to second quarters of every year are known to be low key for business activities and, therefore, banks experience lower levels of loan applications and loan disbursements. In the first quarter, banks focus on chasing (mobilization of) deposits in the presence of depleted loan portfolios (loanable funds) resulting from heavy withdrawals from all categories of customers during the previous 3rd to 4th quarters to finance school fees, cocoa production, and SMEs’ trade financing towards the end of the year. Figure 6.1 presents
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the graphical impression of the trends in the productivity change and its components over the study period. As displayed, all the indices show no particular trend in terms of direction. Over the period, there were upward and downward swings in productivity in alternating quarters. The trends in the frontier shift line follow closely with the productivity line. These changes, as previously mentioned, may be due to the adoption of new technologies by management over the period.
Further analysis, using the cumulative change of TFP for the period, is presented in Table 6.4 and Figure 6.2 to compare the endpoints quarters from the beginning period, 2009Q1. As shown, the results support the initial finding that productivity deteriorated during the period. Cumulatively, there was a -0.8% deterioration in total factor productivity over the entire period for the RCBs. The RCBs, thus, used 0.8% more inputs in 2012Q3, compared to 2009Q1. The cumulative trends for technological change indicate a regress (inward shift of the frontier) of -2.3% between 2009Q1 and 2012Q3, while the cumulative technical efficiency shows a progress (efficiency catch-up) of 2.3%. The implication is that while relatively less technically-efficient RCBs did catch-up with more technically-efficient ones in recent quarters, they were still wasteful, using relatively more inputs in production (unable to provide the same level of efficient services).
Figure 6.2 shows that, at the end of the period under study, the deterioration in productivity was influenced by the technological regression (inward shift of the efficiency frontier). Generally, for all periods, there was technology regress (except for the period 2009Q12011Q1). Also, for the entire period, there was technical efficiency improvement.
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Table 6.4: Cumulative Change of TFP and Components Quarter 2009Q1-2009Q2 2009Q1-2009Q3 2009Q1-2009Q4 2009Q1-2010Q1 2009Q1-2010Q2 2009Q1-2010Q3 2009Q1-2010Q4 2009Q1-2011Q1 2009Q1-2011Q2 2009Q1-2011Q3 2009Q1-2011Q4 2009Q1-2012Q1 2009Q1-2012Q2 2009Q1-2012Q3
CEFFCH 1.036 1.042 1.029 1.032 1.033 1.017 1.049 1.013 1.056 1.044 1.029 1.052 1.051 1.023
CTECH 0.960 0.964 0.961 0.981 0.978 0.982 0.956 1.002 0.938 0.964 0.968 0.959 0.941 0.977
Figure 6.2: Cumulative TFP Change and Components
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CTFP 0.995 1.005 0.989 1.013 1.011 0.999 1.004 1.012 0.988 1.001 0.990 1.004 0.985 0.992
6.2.3 DEA Technical Efficiency Change (Catching-up) This section deals with the DEA technical efficiency change (EFFCH) component of the total factor productivity change. The results for the EFFCH component of the total factor productivity change, which indicate the catch-up of the RCBs to their efficient frontier, are presented subsequently. The performances of the RCBs inside their production frontier relative to those on the best frontier were analyzed and discussed here. Table 6.5 provides a presentation of the technical efficiency change and its components for the period under study. These components are classified as the sources of the technical efficiency change.
Table 6.5: Sources of DEA Technical Efficiency Change Quarter 2009Q1/2009Q2 2009Q2/2009Q3 2009Q3/2009Q4 2009Q4/2010Q1 2010Q1/2010Q2 2010Q2/2010Q3 2010Q3/2010Q4 2010Q4/2011Q1 2011Q1/2011Q2 2011Q2/2011Q3 2011Q3/2011Q4 2011Q4/2012Q1 2012Q1/2012Q2 2012Q2/2012Q3 Mean
EFFCH 1.036 1.006 0.987 1.003 1.001 0.984 1.032 0.964 1.043 0.988 0.985 1.023 0.999 0.972 1.001
PECH 1.006 1.006 0.987 1.010 0.995 0.996 1.015 0.978 1.029 0.993 0.997 1.006 0.994 1.002 1.001
SECH 1.030 1.000 1.000 0.993 1.006 0.988 1.017 0.985 1.013 0.995 0.987 1.017 1.005 0.970 1.000
From Table 6.5, it can be observed that, overall, RCBs, on average, experienced progress in technical efficiency of 0.01%. There were periodic improvements (3.6%, 0.1%, and 4.3%, respectively) in technical efficiency every first to second quarter of the year, from 2009 to 2011 (2009Q1/Q2, 2010Q1/2010Q2, and 2011Q1/2011Q2), with the exception of the
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2012Q1/Q2 period, which saw a regression of -0.1%. The year 2012 being an election year, coupled with the difficult and uncertain economic environment that businesses experienced that same year, could, perhaps, explain this exception.
Another observation worth noting is that, with the exception of the period 2009Q2/Q3, which posted improvement in technical efficiency change of 0.6%, there were regressions in technical efficiency (-1.6%, -1.2%, and -2.8%) every second to third quarter (2010Q2/Q3, 2011Q2/Q3, and 2012Q2/Q3) of the financial year for the RCBs. Table 6.5 further shows the breakdown of the technical efficiency change into pure technical efficiency change (PECH) and scale efficiency change (SECH). As stated in Chapter Four, technical efficiency change (EFFCH) is the product of both pure technical efficiency change (PECH) and scale efficiency change (SECH). Therefore, we are able to attribute or source the changes in technical efficiency (EFFCH) to either PECH or SECH or both. It is also clear from the Table that technical efficiency changes (EFFCH) were mostly influenced by pure technical efficiency (see Table 6.5).
Interestingly, there were improvements in scale efficiency every 1st to 2nd quarter, followed by a decline in the subsequent 2nd to 3rd quarters. Relating this observation to EFFCH in the previous analysis above, it is possible to notice that, for all the 1st to 2nd quarter progresses posted by technical efficiency change, there was a corresponding increase in scale efficiency. It is also observed that the seasonal 2nd to 3rd quarter declines in scale efficiency influenced EFFCH. For instance, for all the 2nd to 3rd quarters of the periods from 2010 to 2012, SECH
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or both SECH and PECH mainly influenced technical efficiency declines. The year 2009 was an exception, where EFFCH progressed but SECH remained unchanged.
Considering quarter-by-quarter changes, however, it appears that, overall, pure technical efficiency (PECH) was the main source of technical efficiency changes. For all the periods where there were technical efficiency improvements, PECH also improved. The overall mean of EFFCH improvement (0.1%) for the whole sample period from 2009 to 2012 is attributed to the 0.1% improvement in PECH and no change in SECH. Thus, the sampled RCBs under study seem to have incurred little “wasted expenditure” due to their scale size, as opposed to relapse in management performance over the study period.
Figure 6.3 complements the preceding discussion on the sources of technical efficiency change, by providing a graphical impression of the trends. The results, as observed from Figure 6.3, showed fluctuations in the technical efficiency trends. For the period under consideration, there were seven periods of improvement in technical efficiency change and, equally, seven other periods of decline in technical efficiency change. From the figure, the trends show that technical efficiency grew in the first three quarters and dropped in the last two quarters under consideration.
Overall, Figure 6.3 depicts that both pure technical efficiency changes and scale efficiency changes tend to move with technical efficiency changes over the period under consideration. The trends in the above observations could be explained by the seasonal nature of the rural banking industry. This seasonality is justified by the fact that the deposit and savings 144
mobilization drives of the RCBs increases in the first to second quarters of each year, following the brisk business activities in the fourth quarter of the previous year, which is normally characterized by heavy withdrawals from the banks. The first to second quarters are known for the savings and deposit-mobilization drives of all banks and non-bank financial institutions in Ghana. Most banks decrease their size by operating lean.
Figure 6.3: Sources of Technical Efficiency Change (Quarterly)
So far, the results on the decomposed technical efficiency changes are only useful in highlighting the quarterly changes and not cumulative effects of the efficiency changes over the period. Therefore, the efficiency measures (reported in Table 6.5) were converted into cumulative percentage change measures, which are reported in Table 6.6 and plotted in Figure 6.4. This conversion is a useful way of estimating the cumulative value of the effect of efficiency changes for the entire period.
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Table 6.6: Cumulative Change of Technical Efficiency and Components Quarter 2009Q1-2009Q2 2009Q1-2009Q3 2009Q1-2009Q4 2009Q1-2010Q1 2009Q1-2010Q2 2009Q1-2010Q3 2009Q1-2010Q4 2009Q1-2011Q1 2009Q1-2011Q2 2009Q1-2011Q3 2009Q1-2011Q4 2009Q1-2012Q1 2009Q1-2012Q2 2009Q1-2012Q3
PECH 1.006 1.012 0.999 1.009 1.004 1.000 1.015 0.993 1.022 1.015 1.012 1.018 1.012 1.014
SECH 1.030 1.030 1.030 1.023 1.029 1.017 1.034 1.019 1.032 1.027 1.014 1.031 1.036 1.006
EFFCH 1.036 1.042 1.029 1.032 1.033 1.017 1.049 1.013 1.056 1.044 1.029 1.052 1.051 1.023
Figure 6.4: Cumulative Changes in Technical Efficiency and Components
A number of points can be made, with respect to the results in Table 6.6 and Figure 6.4. Firstly, it can be noted that between 2009Q1 to 2012Q3 endpoints, technical efficiency was 1.023. This indicates that, cumulatively, for the entire period under consideration, RCBs’ 146
technical efficiency improved by 2.3%. This was, primarily, due to the effect of both pure technical efficiency and scale efficiency, which is, most likely, a consequence of the ability of the management to choose the scale of production that will attain the expected production level and managerial performance to organize the inputs in the banking operations. This result is quite different from the impression given initially by the estimate of the level of technical efficiency change at the end of the period 2012Q3, which was a technical efficiency regression.
Similarly, the overall average technical efficiency, which is estimated at 0.01%, differs from the cumulative growth in technical efficiency, which is 2.3% over the period for the RCBs. Thus, from the cumulative point of view, RCBs appear to have improved on their technical efficiency. In summary, it can be said that RCBs moved closer to their best practice frontier.
6.2.4 DEA Technical Change (Technological Innovation) In this section, the technical change (TECHCH) component of the total factor productivity change (TFPCH) is presented. According to Berger (2003), technical change in banks can be linked with growth in organization size (new services and products), new bank production technologies (IT-driven innovations such as newer e-payments, ATMs, internet banking, etc.), reductions in managerial and operational inefficiencies and diseconomies of scale (IT advances may improve monitoring and control within large banks), and substitution effects (adoption of new risk management systems to control risk) as a result of increased economies of scale. The reverse is the case.
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Technical change shows the ‘frontier shift’ effect from quarter to quarter for all the RCBs in the sample and, hence, is an indicator to compare the performance of efficient RCBs operating on their frontier and relatively less-efficient RCBs operating within their production frontier. Technical or technological progress is indicated by a value greater than 1 and technical or technological regress by an index value less than 1. An index value of 1 indicates no technological change from the previous quarter.
The results for the technical change (TECH) and the cumulative technical change index are presented in Table 6.7. Table 6.1 reported average technical-change estimates for individual RCBs in the sample for the study period. From Table 6.7, the estimates show interesting patterns, considering the fact that technology change of the RCBs appeared to regress (-4%, 0.3%, -0.3%, -2.6%, -6.4%, and -1.8%) every 1st to 2nd quarter and 3rd to 4th quarter over the sample period, with the exception of 2011Q3-2011Q4, which had a progress (0.4%), although it was a decline from the previous quarter.
Interestingly, as mentioned above, all the technical regressions were followed by technical progressions (0.4%, 2%, 0.4%, 4.6%, 2.6%, and 3.6%) in the next periods, that is, the 2nd to 3rd quarters and the 4th to 1st quarters every year. This is explained by the seasonal nature of the banking industry’s activities. RCBs will remain productive, if they adopt appropriate production technology to suit the banking season.
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Table 6.7: Technical Change and Cumulative Technical Change Quarter 2009Q1/2009Q2 2009Q2/2009Q3 2009Q3/2009Q4 2009Q4/2010Q1 2010Q1/2010Q2 2010Q2/2010Q3 2010Q3/2010Q4 2010Q4/2011Q1 2011Q1/2011Q2 2011Q2/2011Q3 2011Q3/2011Q4 2011Q4/2012Q1 2012Q1/2012Q2 2012Q2/2012Q3 Mean
TECH 0.960 1.004 0.997 1.020 0.997 1.004 0.974 1.046 0.936 1.026 1.004 0.991 0.982 1.036 0.998
Quarter 2009Q1-2009Q2 2009Q1-2009Q3 2009Q1-2009Q4 2009Q1-2010Q1 2009Q1-2010Q2 2009Q1-2010Q3 2009Q1-2010Q4 2009Q1-2011Q1 2009Q1-2011Q2 2009Q1-2011Q3 2009Q1-2011Q4 2009Q1-2012Q1 2009Q1-2012Q2 2009Q1-2012Q3
Cum. TECH 0.960 0.964 0.961 0.981 0.978 0.982 0.956 1.002 0.938 0.964 0.968 0.959 0.941 0.977
On average, the rate of technical change is a regression of -0.2% per quarter. This is supported by the cumulative index of technical change for the entire period, 2009Q12012Q3. It shows that, from 2009Q1 to 2012Q3, RCBs’ cumulative technology change was 0.977, indicating an overall decline of -2.3%. Thus, over the period under consideration, RCBs operated inside their production frontier or function. From the rural banking industry perspective, this is likely to happen in the face of the expanding size of the RCBs, adoption of new services which were hitherto in the domain of commercial banks, implementation of IT innovations, and so on, which prompts banks to constantly change the mix of inputs aimed at producing their expected outputs. In terms of the output distance function, this decline in the rate of technical change means that the growth rate of the ratio of actual output to potential output declines as time passes (holding all other things constant).
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Compared with the estimates of technical efficiency, which also showed overall patterns of progress (as described in Section 6.2.3), the estimates of the rate of technical change rather declined over the period. In particular, while the cumulative rate of technical change for the entire period was -2.3%, that of technical efficiency change was 2.3%. These observations can also be linked to the continuous restructuring of rural banking services over this period, which might lead to technical declines but improved overall technical efficiency.
6.3 Estimates of Productivity: SFA approach For the purposes of checking the consistency of DEA results for productivity growth and components, SFA methods using the multiplicative procedure were also used to estimate the productivity indices.
6.3.1 SFA TFP Changes - Summary of Bank Means Table 6.8 reports the summary of the estimates of productivity changes and components for the individual RCBs between 2009Q1 and 2012Q3. Several observations can be made from the individual reports.
Firstly, on technical efficiency change, 48 out of the 107 RCBs under study suffered a regression over the study period, whilst 2 RCBs had a stable efficiency change. The rest of the RCBs achieved an improvement in efficiency over the period. Secondly, on technological growth, it is revealed that 10 (9.3%) of the RCBs experienced productivity declines ranging from -2.4% to -0.02%. Also, 95 RCBs (representing 88.8%) attained growth in technical progress (ranging from 0.087% to 3.44%). Two RCBs, however, had no change in their 150
technical growth. Thirdly, 75 (70%) RCBs obtained an improvement in productivity (TFP) ranging from 0.03% to 21.358%. Furthermore, 30 out of the 107 RCBs had a regression in productivity change over the period. The productivity of two RCBs remained unchanged. As identified earlier, the sources of poor productivity performance within the sector were largely due to technical efficiency declines (with the exception of a few banks).
Table 6.8: SFA TFP Changes and Components - Bank Means (2009Q1-2012Q3) Firm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
SFA-EFFCH 1.005 0.998 1.000 0.981 1.012 1.034 0.974 1.011 1.064 1.018 0.961 0.984 1.015 0.935 1.004 0.987 0.975 1.059 0.970 1.015 1.020 1.106 1.012 1.012 1.104 1.012 0.998 0.959
SFA-TECH 1.006 1.006 1.018 1.011 1.005 1.007 1.009 1.004 1.007 1.024 1.004 1.009 1.011 1.012 1.017 1.002 1.007 1.012 1.023 1.010 1.022 1.002 1.014 1.014 1.010 1.012 1.012 1.007
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SFA-TFP 1.011 1.005 1.018 0.991 1.015 1.040 0.982 1.015 1.071 1.042 0.964 0.994 1.026 0.946 1.021 0.989 0.982 1.072 0.991 1.025 1.041 1.110 1.026 1.027 1.115 1.024 1.009 0.965
Table 6.8 cont’d Firm 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
SFA -EFFCH 0.992 0.948 0.945 1.014 0.973 0.988 0.999 0.987 1.055 1.193 1.021 1.068 0.986 1.002 0.982 0.966 1.071 1.024 1.027 0.989 1.025 1.035 1.014 0.992 0.973 0.980 1.001 0.993 1.045 1.012 1.161 1.114 0.964 0.988 0.997 1.034 0.980 0.995 1.041 0.999 1.020
SFA –TECH 1.011 1.017 1.034 1.020 1.008 1.007 1.009 1.016 1.006 1.018 1.004 0.998 1.026 1.005 1.008 0.976 0.979 1.015 0.993 1.015 1.012 1.000 1.005 1.006 1.006 0.991 1.000 1.011 1.019 1.020 0.991 1.007 0.998 1.010 1.026 1.022 1.012 1.015 1.018 1.010 1.013
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SFA -TFP 1.004 0.964 0.978 1.033 0.981 0.995 1.007 1.002 1.063 1.214 1.025 1.062 1.012 1.007 0.989 0.943 1.049 1.038 1.019 1.003 1.037 1.034 1.018 0.998 0.978 0.971 1.000 1.004 1.065 1.032 1.144 1.121 0.962 0.997 1.023 1.056 0.991 1.010 1.060 1.008 1.033
Table 6.8 cont’d Firm 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 Mean
SFA -EFFCH 0.997 0.995 0.964 1.005 0.990 0.990 1.034 1.014 1.009 1.096 1.104 1.075 0.972 1.030 0.979 0.980 0.996 0.981 1.013 1.034 0.991 1.009 1.015 0.983 0.990 0.974 0.974 1.049 1.004 1.134 0.996 1.088 1.098 0.994 1.000 1.013 1.027 1.011 1.013
SFA –TECH 1.003 1.018 0.992 1.026 1.018 1.003 1.010 1.019 1.015 1.005 1.005 1.006 1.009 1.007 1.008 1.009 1.028 1.016 1.002 1.014 1.023 1.005 1.018 1.021 1.017 1.025 1.001 0.992 1.026 1.014 1.008 0.997 1.006 1.008 1.008 1.014 1.018 1.013 1.010
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SFA -TFP 0.999 1.013 0.954 1.031 1.008 0.992 1.044 1.032 1.024 1.102 1.108 1.082 0.981 1.036 0.986 0.989 1.023 0.996 1.015 1.048 1.014 1.013 1.033 1.003 1.007 0.999 0.974 1.040 1.030 1.154 1.003 1.085 1.103 1.001 1.007 1.026 1.045 1.025 1.023
6.3.2 SFA Total Factor Productivity (SFA-TFP) Changes – Quarterly Means Table 6.9 provides a presentation of the productivity growth and its components for the period, 2009 – 2012. These components are classified as the sources of the total factor productivity (TFP) growth.
Table 6.9: Quarterly Mean SFA-TFP Changes (2009Q1 - 2012Q3) Quarter 2009Q1/2009Q2 2009Q2/2009Q3 2009Q3/2009Q4 2009Q4/2010Q1 2010Q1/2010Q2 2010Q2/2010Q3 2010Q3/2010Q4 2010Q4/2011Q1 2011Q1/2011Q2 2011Q2/2011Q3 2011Q3/2011Q4 2011Q4/2012Q1 2012Q1/2012Q2 2012Q2/2012Q3 Mean
SFA-EFFCH 1.090 1.045 1.004 1.001 1.022 1.048 0.960 1.018 1.022 1.069 0.951 0.975 0.994 0.987 1.013
SFA-TECH 0.979 0.984 0.989 0.994 0.998 1.003 1.008 1.013 1.018 1.022 1.026 1.031 1.036 1.040 1.010
SFA-TFP 1.067 1.028 0.993 0.994 1.020 1.051 0.968 1.031 1.041 1.093 0.976 1.006 1.029 1.026 1.023
From Table 6.9, it can be observed that, overall, RCBs, on average, experienced progress in total factor productivity of 2.3%, consistent with the DEA results. There were also observed improvements in TFP for all the quarters within the study period, except for the 2009Q3/2009Q4, 2009Q4/2010Q1, 2010Q3/2010Q4, and 2011Q3/2011Q4 periods. Again, the analysis showed that TFP decreased for every third to fourth quarter of the year and rose at every first to second quarters, from 2009 to 2012. Banking experience showed that,
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usually, banks intensify their marketing and operational activities from the third to fourth quarter. As a result, the falls in total factor productivity could be due to either managerial inefficiencies and/or intensified competition.
A further breakdown of the TFP into its components: technical efficiency change (EFFCH) and technical change (TECH) results, showed that, overall, an improvement was observed for all the quarters of the years in technical efficiency change, averaging 1.3% from 2009Q1 to 2012Q1. Again, it is shown that, except for the 2009Q3/2009Q4, 2009Q4/2010Q1, 2010Q3/2010Q4, and 2011Q3/2011Q4 periods, there was efficiency improvement in all the periods. Just as was explained under TFP, decreases in efficiency changes were observed for every third to fourth quarter of the year, and increase for every second to third quarter, from 2009 to 2012. The fall in efficiency changes in the third to fourth quarter confirms the assertion that, on most occasions, the resultant decrease in productivity growth is largely due to managerial inefficiencies.
For TECH, the evidence showed that there was technological growth consistently for all the quarters of the years. Overall, an average percentage of 1% was estimated technical change for 2009 – 2012. The improvement in both efficiency change and technological growth of 1.3% and 1% respectively indicates that both significantly contributed to the growth in total factor productivity for the periods. Figure 6.5 complements the discussion on the sources of technical efficiency change by providing a graphical impression of the trends.
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It can also be seen in Figure 6.5 that both TECH and EFFCH have powered the movement of TFP for the periods. Considering quarter-by-quarter trends, it appears that, overall, changes in TFP for the periods 2009Q3/2009Q4, 2009Q4/2010Q1 and from the last quarter of 2011, through to the third quarter of 2012, were powered solely by technical change. Technical efficiency change was also identified as the major source of total factor productivity movements from the first quarter of 2009 through to the third quarter of the same year. However, for the periods between 2010Q4/2011Q1 and 2011Q1/2011Q2, TECH and EFFCH contributed simultaneously to significantly power the movement in total factor productivity, as can be observed in Table 6.9.
Figure 6.5: Quarterly Changes in Productivity - SFA Analysis 1.15
Productivity Indices
1.1 1.05 1
0.95 0.9 0.85
Quarters SFA - TFP
SFA - EFFCH
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SFA - TECH
6.3.3 Cumulative Change of TFP and Its Components A further analysis, using the cumulative change of TFP for the period, is presented in Table 6.10 and Figure 6.6 to compare the endpoints quarters from the beginning period, 2009Q1. Interestingly, the results seem to confirm the initial finding that productivity improved during the period. Cumulatively, there was a 32.3% growth in total factor productivity over the entire period for the RCBs. The RCBs, thus, expanded 32.3% of output in 2012Q3, compared to 2009Q1. The cumulative trends for technological change also indicated an improvement (outward shift of the frontier) of 14.1% between 2009Q1 and 2012Q3, while the cumulative technical efficiency showed a progress (efficiency catch-up) of 18.6%. The implication is that, while relatively less technically-efficient RCBs did catch-up with more technicallyefficient ones in recent quarters, these evident economies of scale ensured overall improvement in the rural banking sector.
Figure 6.6 shows that, at the end of the period under study, with the movement in productivity, though influenced by both EFFCH and TECH from the first quarter of 2009 through to the second quarter of 2011, TFP changes have been propelled by EFFCH. This observation confirms the conclusions drawn from Figure 6.6 that improvements in TFP during the period, 2009-2012, were caused by the shifting of rural banking production frontiers and efforts to close the gaps between actual and optimal output, represented by EFFCH. As a result, any effort which helped to close the gaps or even just maintain TE scores, will push up TFP growth further.
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Table 6.10: Cumulative Change of TFP and Components QUARTER 2009Q1-2009Q2 2009Q1-2009Q3 2009Q1-2009Q4 2009Q1-2010Q1 2009Q1-2010Q2 2009Q1-2010Q3 2009Q1-2010Q4 2009Q1-2011Q1 2009Q1-2011Q2 2009Q1-2011Q3 2009Q1-2011Q4 2009Q1-2012Q1 2009Q1-2012Q2 2009Q1-2012Q3
SFA- CEFFCH 1.090 1.135 1.139 1.140 1.162 1.210 1.130 1.188 1.210 1.279 1.230 1.205 1.199 1.186
SFA- CTECH 0.979 0.963 0.952 0.946 0.944 0.947 0.963 0.968 0.986 1.008 1.034 1.065 1.101 1.141
SFA-CTFP 1.067 1.095 1.088 1.082 1.102 1.153 1.089 1.152 1.193 1.286 1.262 1.268 1.297 1.323
Figure 6.6: Cummulative TFP Change and Component - SFA Analysis 1.4
Productivity Indices
1.2 1 0.8 0.6 0.4 0.2 0
Quarters SFA - TFP
SFA - EFFCH
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SFA - TECH
6.4 Consistency of DEA and SFA Productivity Estimates The previous Sections 6.2 and 6.3 presented empirical estimations of EFFCH, TECH, and TFP changes for RCBs for 2009-2012Q3 by both DEA and SFA methods. This section considers the consistency between those two estimations.
The estimated results (see Table 6.11) from the two methods are fairly consistent to each other, although there are some differences between them in terms of estimated values and trends. Both methods suggest that RCBs’ TFP change was positive for the study period (0.02% in DEA and 2.31% in SFA). This is an indication of overall growth in productivity for the RCBs. TFP component estimates in the two methods consistently show improvements in EFFCH (0.24% in DEA and 1.33% in SFA estimations) but a regress (-0.15% in DEA) and improvement (1.01% in SFA) in TECH. EFFCH, on average, was the main source of productivity growth during the period in both the DEA and SFA methods.
Table 6.12: TFP Change, EFFCH and TECH of DEA and SFA, 2009Q1-2012Q3 Quarter 2009Q1-2009Q2 2009Q1-2009Q3 2009Q1-2009Q4 2009Q1-2010Q1 2009Q1-2010Q2 2009Q1-2010Q3 2009Q1-2010Q4 2009Q1-2011Q1 2009Q1-2011Q2 2009Q1-2011Q3 2009Q1-2011Q4 2009Q1-2012Q1 2009Q1-2012Q2 2009Q1-2012Q3
DEACTFP 0.995 1.005 0.989 1.013 1.011 0.999 1.004 1.012 0.988 1.001 0.99 1.004 0.985 0.992
SFA CTFP 1.067 1.048 1.029 1.021 1.020 1.026 1.017 1.019 1.022 1.029 1.024 1.022 1.023 1.023
DEA CTECH 0.96 0.964 0.961 0.981 0.978 0.982 0.956 1.002 0.938 0.964 0.968 0.959 0.941 0.977
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SFA CTECH 0.979 0.982 0.984 0.986 0.989 0.991 0.994 0.996 0.998 1.001 1.003 1.005 1.008 1.010
DEA – CEFFCH 1.036 1.042 1.029 1.032 1.033 1.017 1.049 1.013 1.056 1.044 1.029 1.052 1.051 1.023
SFA CEFFCH 1.090 1.068 1.047 1.035 1.032 1.035 1.024 1.024 1.023 1.028 1.021 1.017 1.015 1.013
Figures 6.7a, b, and c, which give a snapshot of the cumulative trend as demonstrated by DEA and SFA, shows that the two approaches produced fairly dissimilar trends in productivity indices. As shown by Table 6.12 and supported by Figure 6.7, the DEA cumulative results for technical change (DEA-CTECH) showed that technical changes were below unit, signifying a condition of technical regress. This, however, was not consistent with the SFA result for the same component, technical change (SFA-CTECH). The SFACTECH cumulative trend showed that a technical regress (0.2%) was experienced in the earlier periods from 2009Q1 to 2011Q2. From 2011Q3, TECH improved and ended in 2012Q3 with an improvement of 1%. With respect to EFFCH, both methods showed that, cumulatively, the period under study saw a continuous improvement in technical efficiency, as the CEFFCH index was above unit.
Figure 6.7a: Cumulative TFP Change – DEA and SFA Trend Cummulative Productivity Indices
1.4 1.2 1 0.8 0.6 0.4 0.2 0
Quarters SFA - CUTFP
DEA- CUTFP
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Figure 6.7b: Cumulative EFFCH – DEA and SFA Trend Cummulative Productivity Indices
1.4 1.2 1 0.8 0.6 0.4 0.2 0
Quarters SFA - CUEFFCH
DEA - CUEFFCH
Figure 6.7c: Cumulative TECH – DEA and SFA Trend Cummulative Productivity Indices
1.2 1 0.8
0.6 0.4 0.2 0
Quarters SFA - CUTECH
DEA - CUTECH
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In order to test statistically the similarity between the DEA and SFA estimates of EFFCH, TECH, and TFP growth, the research conducted two non-parametric rank correlation tests, namely, Spearman’s and Kendall’s rank tests. The null hypothesis needed to be tested was that the estimations of the two methods were independent. Those tests’ results are reported in Table 6.13. Both the Spearman’s and Kendall’s rank tests show that the null hypothesis is rejected for technical change estimation at the 1% significance level. They also show that rankings for TFP and EFFCH are not statistically consistent. Hence, the null hypothesis was accepted. Table 6.13 also depicted that rho and tau values were highest for TECH (0.1241 and 0.087). TFP and efficiency change correlation coefficients were also very low, insignificant, and similar for both non-parametric rank tests, supporting the conclusion of results inconsistency in DEA and SFA for TFP and efficiency change. This conclusion is also suggested in Figure 6.7 above.
Table 6.13: Rank Correlation Tests between DEA and SFA Estimates
DEA - EFFCH DEA - TECH DEA - TFP
SFA - EFFCH Rho Sig 0.0119 0.467 0.021 0.425 0.026 0.323
Tau Sig 0.013 0.462 DEA - EFFCH 0.014 0.417 DEA - TECH 0.017 0.325 DEA - TFP Significance levels: *: 10%, **: 5%, ***: 1%
Spearman's Rank Test SFA - TECH Rho Sig -0.1214*** 0.000 0.1241*** 0.000 -0.034 0.191 Kendall's Rank Test Tau Sig -0.081*** 0.000 0.087*** 0.000 -0.024 0.169
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SFA - TFP Rho Sig -0.009 0.741 0.051** 0.049 0.019 0.465 Tau -0.005 0.033* 0.013
Sig 0.755 0.053 0.462
6.5 Chapter Summary The study sets out to measure the bank productivity and its components – technical change and efficiency changes of RCBs in Ghana during the period, 2009Q1 to 2012Q3. Both DEA and SFA methods were applied on panel dataset for 107 RCBs. Several interesting conclusions were drawn from the results of the two approaches. First, the results of the productivity indices demonstrate that the RCBs have, on average, experienced technical efficiency improvements during the study period with a quarterly change of 0.24% in DEA and 1.33% in SFA estimations. This suggests that, on average, the RCBs got closer to the frontier. However, whilst the DEA showed that RCBs have, on average, experienced technological regress, SFA results showed that, though there were periods of technical regress, especially before the third quarter of 2011, such reductions were overturned afterwards. Both DEA and SFA, however, converged on the grounds that technical efficiency, on average, was the main source of productivity growth during the period, though SFA also suggested that the shifting of the production frontier also caused improvement in the TFP.
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CHAPTER SEVEN DETERMINANTS OF PRODUCTIVITY CHANGE OF RURAL AND COMMUNITY BANKS (RCBs) IN GHANA 7.1 Introduction In Chapter Six, we presented and analyzed the total factor productivity changes (TFP) of the RCBs, using the DEA and SFA methods. In this chapter, we estimate the determinants of the total factor productivity change of the RCBs, based on the estimates derived from both the DEA and the SFA methods in Chapter 6. This is to address the third main objective of the study. In order to formulate appropriate industry policy, it is important to determine the potential factors that influence productivity change of the RCBs. In line with Mester (1996), the findings from the post-DEA and SFA regression analysis are intended, primarily, to point out areas for improving the efficiency of banks. In this chapter, we consider the impact of factors such as asset size, profit, and macroeconomic factors on RCBs’ productivity. This assessment will provide valuable regulatory and managerial information to trace the sources of productivity. From the extant literature, there are no empirical studies that have considered the determinants of the productivity change of RCBs in Ghana. In the accessible literature, the determinants of efficiency of commercial banks in Ghana have been explored by Saka et al (2012). This chapter fills the research gap under this thematic research area and contributes to the existing literature and policy debate on the determinants of productivity in the RCBs industry.
The rest of this chapter is organized as follows. Section 2 provides the econometric methods, empirical model specifications, and the description of the data used for the analyses. A description of the variables used is also presented alongside with the summary statistics.
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Section 3 presents the empirical results and discussions on the determinants of total factor productivity change and its components. Section 4 provides the chapter summary and conclusion.
7.2 Econometric Methods, Empirical Model, and Data Description 7.2.1 Econometric Methods A number of panel estimation strategies have been used to exploit the drivers of productivity in the extant literature, including Pooled-OLS, Tobit models, fixed effect estimator and random effect estimator (see Sharma et al, 2013). To ensure robustness across the various panel estimation techniques, we adopt three common linear panel estimators and models, namely, the Pooled-OLS (POLS), fixed effect (FE) technique, and the random effect (RE) technique.
Generally, the linear panel model is specified with intercept and slope parameters that vary over both individual and time, as presented as follows (Equation 7.4): ′ 𝑦𝑖𝑡 = 𝛼𝑖𝑡 + 𝑥𝑖𝑡 𝛽𝑖𝑡 + 𝑢𝑖𝑡 , 𝑖 = 1, … , 𝑁, 𝑡 = 1, … , 𝑇,
(7.4)
where yit is a scalar dependent variable, xit is a 𝐾 × 1 vector of independent variables, uit is a scalar disturbance term, i indexes individual (or bank) in a cross section, and t indexes time. To allow for the estimation of the general model, further restrictions are placed on the extent to which 𝛼𝑖𝑡 and 𝛽𝑖𝑡 vary with i and t, and on the behavior of the error uit.
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Using the explanatory already described, we estimate the productivity effects of bank specific and macroeconomic factors, using the three different models with DEA and SFA variants. First, and as a benchmark, we use the pooled OLS (POLS model). POLS regressions do not take into account unobserved bank heterogeneity, which is equivalent to assuming that the unobserved bank specific effect, αi, is identical for all RCBs (constant parameters). The POLS model is written as in Equation 7.5: ′ 𝑦𝑖𝑡 = 𝛼 + 𝑥𝑖𝑡 𝛽 + 𝑢𝑖𝑡 (𝑢𝑖 = 0)
(7.5)
If this assumption is violated, POLS estimates will be biased and inconsistent. 15 We, therefore, also estimate random effect models (RE model). The RE model assumes the bank specific effect (heterogeneity), αi, is randomly distributed across individual RCBs and is not correlated with the set of explanatory variables and, then, estimates error variance specific to groups (or times). Hence, ui is an individual specific random heterogeneity or a component of the composite error term. This is why a random effect model is also called an error component model. The intercepts and slopes of regressors are the same across individual RCBs. The difference among individuals (or time periods) lies in their individual specific errors, not in their intercepts. The RE model is specified in Equation 7.6 as: ′ 𝑦𝑖𝑡 = 𝛼 + 𝑥𝑖𝑡 𝛽 + (𝑢𝑖 + 𝜈𝑖𝑡 )
(7.6)
An RE model reduces the number of parameters to be estimated but will produce inconsistent estimates when individual specific random effect is correlated with regressors (Greene, 2008: 200-201). An RE model is estimated by generalized least squares (GLS).
15
The role of unobserved bank heterogeneity was analyzed by applying random and fixed effects panel estimators.
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Finally, and to allow also for correlation between αi with the explanatory variables, we also estimate a fixed effects model (FE model). Note that the individual bank specific effect, αi, may not alone be correlated with the explanatory variables but also the idiosyncratic error term, if yit and xit are simultaneously determined. Still, another problem is a potential erroneous measurement of individual BSF variables, due to accounting errors and omissions. The FE model is written as follows in Equation 7.7 as: ′ 𝑦𝑖𝑡 = (𝛼 + 𝑢𝑖 ) + 𝑥𝑖𝑡 𝛽 + 𝜈𝑖𝑡
(7.7)
This fixed effect model is estimated by least squares dummy variable (LSDV) regression (OLS with a set of dummies) and within effect estimation methods.
Adopting the derivation in Guillaumont et al (2006), the methodology of Generalized Method of Moments (GMM) for dynamic panel data analyses, proposed by Arellano and Bond (1991) and then further developed by Blundell and Bond (1998), is also employed here to control for endogeneity in our estimations and dynamics in the panel.16
Consider the following model in Equation 7.8: 𝑦𝑖𝑡 = 𝛾1 𝑋𝑖𝑡 + 𝛾2 𝑍𝑖𝑡 + 𝜇𝑖 + 𝜀𝑖𝑡 ,
𝑖 = 1, … , 𝑁;
𝑡 = 1, … , 𝑇
(7.8)
where X is a vector of strictly exogenous covariates, Z denotes a vector of predetermined covariates and endogenous covariates (predetermined variables are assumed to be correlated with past errors, while endogenous ones are assumed to be correlated with past and present
16
The literature on the GMM estimator is enormous and continually expanding. Useful recent summary of GMM estimation and some further discussion can be found in e.g., Baltagi (2005, Chapter 8), Green (2000, Chapter 11) and Wooldridge (2002, Chapter 8 and Chapter 14).
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errors), 𝜇𝑖 is the unobserved group-level effect, and 𝜀𝑖𝑡 is the error term, with the assumption that 𝜇𝑖 and 𝜀𝑖𝑡 are independent for each i over all t, and that there is no autocorrelation in the 𝜀𝑖𝑡 . First, in order to eliminate the unobservable group-specific effects, we difference Equation 7.8, and then, it can be rewritten as: 𝑦𝑖𝑡 − 𝑦𝑖𝑡−1 = 𝛾1 (𝑋𝑖𝑡 − 𝑋𝑖𝑡−1 ) + 𝛾2 (𝑍𝑖𝑡 − 𝑍𝑖𝑡−1 ) + (𝜀𝑖𝑡 − 𝜀𝑖𝑡−1 )
(7.9)
Second, instrumental-variable approaches are applied to deal with the endogeneity of explanatory variables in Equation 7.9, where the predetermined and endogenous variables in first differences are instrumented with appropriate lags of the specified variables in levels, while strictly exogenous regressors are first-differenced for use as instruments in the firstdifferenced equation.
However, the efficiency of this instrumental approach might be relatively weak, given the fact that lagged levels are often poor instruments for first differences. Therefore, Blundell and Bond (1998) propose the system-GMM estimator, in which the first-differenced estimator (i.e., Equation 7.9) is combined with the estimator in levels (i.e., Equation 7.8) to form a more efficient “system estimator”. For the first-differenced equation, the instruments are the same as that discussed above, for the levels equation, predetermined and endogenous variables in levels are instrumented with appropriate lags of their own first differences, while the strictly exogenous regressors can directly enter the instrument matrix for use in the levels equation.
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The GMM estimator has been widely used in recent empirical works, particularly in the studies of macroeconomics and finance. This method has a number of advantages. For instance, Beck et al (2000) argue that the GMM panel estimator is good in exploiting the time-series variation in the data, accounting for unobserved individual specific effects, allowing for the inclusion of lagged dependent variables as regressors, and, therefore, providing better control for the endogeneity of all the explanatory variables. According to Blundell and Bond (2000) and Blundell, Bond and Windmeijer (2001), the system GMM estimator not only improves precision of estimates but also reduces the finite sample bias (cited in Baltagi, 2005).
7.2.2 Empirical Model The study specified the following empirical models in equations to evaluate the effect of the potential determinants of productivity change (TFP) and its two components, i.e., technical efficiency change (EFFCH) and technical change (TECH), identified for RCBs in Ghana. TFP, EFFCH and TECH are successively employed as the dependent variables for both DEA and SFA scores. Among the explanatory variables are bank specific indicators (total assets, staff productivity index, profit before tax, efficiency indicators, loan-loss provisions) and macroeconomic factors (t bill rate, inflation rate, and real GDP growth rate) considered as conventional determinants that generally affect all RCBs17. A time dummy and a regional dummy are also included to capture the transitions to technical change and unobserved regional-level specific effects, respectively.
17
Chapter 4 of the thesis discussed the environmental factors (determinants) that affect total factor productivity changes and components of banks..
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The estimations for TFP enable us to assess the aggregate effects of the factors on productivity, while the estimations for the EFFCH and those of TECH allow us to better identify the channels through which the determinants contribute to RCBs’ productivity growth. More specifically, the econometric models for estimation can be described as follows:
𝑇𝐹𝑃𝑖,𝑡 = 𝛼0𝑖 + 𝛼1 𝐵𝑆𝐹𝑖,𝑡 + 𝛼2 𝑀𝐴𝐶𝑖,𝑡 +𝛼3 𝑇𝑡 + 𝛼4 𝜙𝑖 + 𝜀𝑖,𝑡
(7.1)
𝐸𝐹𝐹𝐶𝐻𝑖,𝑡 = 𝛽0𝑖 + 𝛽1 𝐵𝑆𝐹𝑖,𝑡 + 𝛽2 𝑀𝐴𝐶𝑖,𝑡 +𝛽3 𝑇𝑡 + 𝛽4 𝜑𝑖 + 𝜂𝑖,𝑡
(7.2)
𝑇𝐸𝐶𝐻𝑖,𝑡 = 𝛿0𝑖 + 𝛿1 𝐵𝑆𝐹𝑖,𝑡 + 𝛿2 𝑀𝐴𝐶𝑖,𝑡 +𝛿3 𝑇𝑡 + 𝛿4 𝜃𝑖 + 𝜔𝑖,𝑡
(7.3)
where BSF is a vector of bank specific factors; MAC is a vector of macroeconomic factors; T is the time trend; 𝜙, 𝜑, and 𝜃 denote the unobservable regional-level specific effects; and ε, η, and ω are the error terms. i = 1,2,…,107. t=1, 2,…, 15.
Following Guillaumont et al (2006) and Beck et al (2000), this study also uses the systemGMM (GMM-SYS) estimator to investigate the determinants of productivity of RCBs in Ghana. This is to deal with the potential endogeneity of some of the right hand side variables in the models specified in Equations 7.1 to 7.3. Given the size of the sample, the study adopted the GMM-SYS framework with the small sample correction tool proposed by Windmeijer (2005). In line with the principle of estimating dynamic panel models, TFP and the components are modeled as an autoregressive process (see Elsayed and Paton, 2005 and Sigel and Vitaliano, 2007, among others). Therefore, Equations 7.1 to 7.3 are re-specified for the GMM-Sys as: 170
𝑇𝐹𝑃𝑖,𝑡 = 𝛼0𝑖 + ∑𝑡𝑚 𝛾𝑚 𝑇𝐹𝑃𝑖,𝑡−𝑚 + 𝛼1 𝐵𝑆𝐹𝑖,𝑡 + 𝛼2 𝑀𝐴𝐶𝑖,𝑡 +𝛼3 𝑇𝑡 + 𝛼4 𝜙𝑖 + 𝜀𝑖,𝑡 (7.10) 𝐸𝐹𝐹𝐶𝐻𝑖,𝑡 = 𝛽0𝑖 + ∑𝑡𝑚 𝜌𝑚 𝐸𝐹𝐹𝐶𝐻𝑖,𝑡−𝑚 + 𝛽1 𝐵𝑆𝐹𝑖,𝑡 + 𝛽2 𝑀𝐴𝐶𝑖,𝑡 +𝛽3 𝑇𝑡 + 𝛽4 𝜑𝑖 + 𝜂𝑖,𝑡 (7.11) 𝑇𝐸𝐶𝐻𝑖,𝑡 = 𝛿0𝑖 + ∑𝑡𝑚 𝜗𝑚 𝑇𝐸𝐶𝐻𝑖,𝑡−𝑚 + 𝛿2 𝐵𝑆𝐹𝑖,𝑡 + 𝛿3 𝑀𝐴𝐶𝑖,𝑡 +𝛿4 𝑇𝑡 + 𝛿5 𝜃𝑖 + 𝜔𝑖,𝑡
(7.12)
where 𝛾, 𝜌, 𝑎𝑛𝑑 𝜗 are parameters for the lagged dependent variables, 𝑚 = 1,2, … 𝑡 is the time lag order. All other notations are as defined previously. All the models were estimated with standard errors robust to heteroscedasticity and autocorrelation in the data to check for estimator efficiency.
7.2.3 Data Description Our data set consists of a quarterly sample of 107 RCBs from 2009q1 to 2012q3. The dependent TFP, EFFCH, and TECH were derived from the DEA and SFA estimates in the previous chapter. The independent variables, bank specific factors (BSF) and macroeconomic factors (MAC), included in the empirical models are described here as follows.
The bank specific factors included in the estimations are total assets (TAsset), staff productivity index (SPI), and profit before tax (PBT). The bank-specific variables were included as the key variables of interest, because they are internal to individual RCBs. They were obtained from the ARB-Apex Bank Efficiency Monitoring Unit (EMU).
Total assets (TAsset) is included as a proxy for bank size. The relationship of total assets on bank productivity is highly mixed. Nakamura (1993) and Mester et al’s (1998) information advantage hypothesis suggests that total asset (firm size) can have a negative effect on
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productivity. The authors put forward that it is possible for small banks to have a greater access to credit information and less agency problems than larger banks. They indicate that management of small banks tends to be closer to the customer and the loan officer, and this enhances performance. However, Rhodes and Rutz (1982) and Clark (1986) do not agree to the information advantage hypothesis. They argue that total assets (firm size) rather have a positive effect on technical efficiency and productivity growth. Their expense preference hypothesis suggests that managers of small banks are rather risk averse. They are likely to then invest in less risky loans and investments so as to enjoy a ‘quiet life’. This process will tend to result in rejection of possible lucrative and viable loan advances for the bank, thereby, leading to poor performance relative to the larger RCBs.
Staff productivity index (SPI), which is a proxy for the productivity of employees, is also included and its effect on productivity change explored. SPI specifies the performance of the bank employees in undertaking the intermediation operations of the RCBs. Literature suggests that staff productivity index measured as (Deposit + Loans)/Staff. This can be broken down and explained. The first part is deposit per staff = total deposits/staff, serving as a proxy for the potency of the bank in liquidity support, and the second part is total loans per staff calculated as total loans/staff, which represents the efficiency of the bank in terms of how funds are distributed in rewarding investments. The SPI, which is a composite of the first two ratios, describes the potency of the bank in liquidity support and efficient fund allocation. This SPI, as a measure of staff productivity, is expected to have a positive and significant effect on bank productivity changes (Kumar and Gulati, 2010).
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Profit before tax (PBT) is a proxy for profitability of the rural bank. It is expected that highly profitable RCBs will be more productive than their less-profitable peers (Sharma et al, 2013). Profits signifies effieicncy (Ahmed, 2014).
The macroeconomic determinants include inflation rate, GDP growth rate, and Treasury bill rate. The macroeconomic stability variables are used as external control variables that affect all RCBs equally in the economy of Ghana. The variables are described here. They were obtained from the Bank of Ghana Statisitcal Bulletins (2009-2012).
Inflation (Infl) is used to serve as a proxy for financial stability in the estimations. A negative effect confirms the assumption that RCBs are not able to adjust their cost behavior to maintain performance and productivity as their loanable funds shrink. The reverse is also possible, since some level of inflation could cause a high demand for financial intermediation by customers and, thereby, increase banks’ productivity. Among other studies, Kasman and Yildirim (2006) and Pasiouras (2008) argue that high inflation may affect behavior and induce banks to compete through excessive financial intermediation. Demirguc-Kunt et al (2004) find a robust positive effect of inflation on productivity (bank margins and overhead costs).
The 91-day Treasury bill rate (Tbill) is also included to explore the effect of the rent-seeking behavior of managers of RCBs and as a measure of the benchmark interest on lending to the public and private sectors, and the cost of borrowing by banks in Ghana. It is expected that this variable will have a negative effect on productivity change in Ghana. This is because
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investing in treasury bills acts as the opportunity cost of engaging in financial intermediation by way of shifting loanable funds from the private sector to investment in government treasury bills and bonds. In Ghana, most RCBs engage in a high investment of funds in treasury bills at the expense of lending to private businesses (Aryeetey and Nissanke, 2005: 51, IMF, 2008: 33, and Opoku-Yeboah, 2008). A possible counter effect is that higher Tbill rates might lead managers of RCBs to put their funds in low-risk, high-yielding, short-term assets such as Tbills and reduce the level of financial intermediation to the private sector and, thereby, reduce loan productivity18. This is consistent with Opoku-Yeboah (2008) in a study of trends in Treasury bill investment and loans by RCBs in Ghana. Opoku-Yeboah (2008) found out, among others, that banks in Ghana invest more in Tbills than Loans, in unstable environments, but RCBs, in particular, invest more in Tbills in stable periods, and even that, irrespective of the level of the Tbill rate, banks continuously increase their investments in Tbills.
Lastly, the effect of real GDP growth (rgdpgr) is used as a proxy for general economic wellbeing. Since a robust economy is growth-enhancing in all aspects of economic activity, it is expected that this variable will have a positive effect on productivity changes of the RCBs. Maude’s et al (2002) concluded that banks that operate in expanding markets – proxy by the real growth rate of GDP – present higher levels of profit efficiency and by extension, productivity.
Considering investments in Tbills as alternative sources of accruing profit;it competes for RCBs’ scarce loanable funds. Therefore, an increase in Tbill rate causes RCBs to regress on loan productivity. The more attractive the rates, the more likely that the intermediary functions of RCBs suffers. 18
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A summary of the variables and priori expected signs are provided in Table 7.1 below. All variables are in natural log with the exception of inflation rate and real GDP growth rate. Table 7.1 Expected Signs of Explanatory Variables Determinants
Symbol
Expected Sign
Total Assets
lnTAssets
±
Staff Productivity Index
lnSPI
+
Profit before Tax
lnPBT
±
Inflation Rate
Infl
±
Real GDP Growth
rgdpgr
±
91-Day Treasury Bill Rate
lnTbills
−
Table 7.2 presents the summary statistics of the data used in the various regression models specified. Generally, it is observed from Table 7.2 that all the bank specific variables (TAssets, PBT, SPI) have high variance compared to the macroeconomic variables (Infl, Tbill, rgdpgr). This may be the case because all banks operate in the same economy and are affected equally by the macroeconomic conditions.
Table 7.2: Summary Statistics for Dependent and Independent Variables Variable Obs. Mean Std. Dev. Min Dea-tfpch 1498 1.00024 0.0444 0.847 Dea-effch 1498 1.002443 0.0482 0.841 Dea-tech 1498 0.998459 0.0313 0.902 Sfa-tfp 1498 1.023112 0.1752 0.264 Sfa-effch 1498 1.013333 0.1761 0.257 Sfa-tech 1498 1.010095 0.0214 0.945 1498 lnTAsset 15.43719 0.9383 12.282 1498 lnPBT 11.39169 1.4006 5.577 1498 lnSPI 11.67499 0.5095 9.684 1498 Tbill 0.164 0.0644 0.090 1498 Infl 0.132 0.0439 0.090 1498 Rgdpgr 0.09 0.0455 0.020
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Max 1.187 1.197 1.099 3.655 3.672 1.067 17.707 15.920 13.040 0.280 0.200 0.190
7.3 Empirical Results This section presents the empirical results of the determinants of productivity growth of RCBs in Ghana. In each subsection, we first present the results for the static panel regressions (i.e., POLS, RE, and FE), followed by the dynamic panel GMM-System regression. The appropriate robustness tests using F-tests and the modified Wald test for groupwise heteroskedasticity in fixed effect regression model (xttest3), and tests for the error component model for random effects and serial correlation (xttest1), are conducted for the POLS, RE, and FE. In the case of the GMM-Sys, for each regression, we test our specification with the Hansen test for instrument validity, and, then, with the Arellano-Bond test for second-order serial correlation AR(2). The results of tests suggest that our instruments are valid, and that there exists no evidence of second serial correlation in our regressions. The two-step GMM-Sys was preferred for the AR(3) and AR(4) autoregressive dynamic models estimated with the data. Results from the estimation of the empirical model are provided in Tables 7.3–7.8.
The rest of this section is structured as follows: first, the determinants of productivity growth (TFP) are presented in Section 7.3.1, followed by the determinants of efficiency change (EEFCH) in Section 7.3.2, and, then, the determinants of technical change in 7.3.3. The presentation is based on results obtained from both DEA and SFA productivity changes and components.
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Table 7.3: Determinants of Total Factor Productivity (TFP) - Static Analysis (POLS, RE, and FE Estimators)
Variables LnTAsset
LnSPI LnPBT
(1) POLS 0.0007
(2) POLS 0.0017
(3) RE 0.0007
DEA (4) RE 0.0017
(0.0022) 0.0018 (0.0034) 0.0022* (0.0012)
(0.0022) 0.0039 (0.0037) -0.0033***
(0.0011) 0.00175 (0.0013) -0.0022***
(0.0012) 0.00390*** (0.0014) -0.0033***
(0.0008)
(0.0009) 0.259*** (0.0293) 0.200*** (0.0237) 0.0128*** (0.0039) -0.0594*** (0.0175)
1,498
Constant
-0.0074 (0.0282)
(0.0012) 0.259*** (0.0427) 0.200*** (0.0455) 0.0128** (0.0058) -0.0594 (0.0366)
Obs. R-sq. F-test Firms
1,498 0.003 1.551
1,498 0.029 8.246***
L.rgdpgr Infl LnTbill
-0.00744 (0.0110)
Robust standard errors in parentheses
1,498 0.029
(5) FE -0.0087*
(6) FE -0.0027
(7) POLS -0.0075
(8) POLS -0.0075
(9) RE -0.0075
SFA (10) RE -0.0075
(11) FE -0.058*
(0.0044) 0.0113** (0.0048) 0.0035*** (0.00118)
(0.0055) 0.0120** (0.0049) -0.0049***
(0.0096) 0.0170 (0.0147) 0.0096**
(0.0097) 0.0214 (0.0177) 0.0091*
(0.0093) 0.0170 (0.0103) 0.0096**
(0.0093) 0.0214* (0.0126) 0.0091*
(0.0299) 0.0533 (0.0351) 0.0075*
(0.0013) 0.265*** (0.0311) 0.208*** (0.0452) 0.0137*** (0.0047) -0.0681 (0.0835)
(0.0044)
(0.0048) 0.0705 (0.136) 0.158 (0.149) -0.0026 (0.0149) -0.259 (0.173)
(0.0047)
(0.0051) 0.0705 (0.139) 0.158 (0.147) -0.0026 (0.0125) -0.259 (0.173)
(0.0038)
0.0416 (0.0264) 1,498 0.005 4.665***
-0.180 (0.123)
-0.180 (0.118)
1,498 1,498 1,498 1,498 1,498 0.032 0.009 0.010 0.010 19.872*** 5.573*** 2.857*** 107 107 107 *** p
