This study aimed at assessing the technical efficiency of fish farmers in Ibadan metropolis of Oyo. State, Nigeria using the stochastic frontier production function ...
Technical Efficiency of Small Scale Farmers: An Application of the Stochastic Frontier Production Function to Fish Farmers in Ibadan Metropolis, Oyo State, Nigeria. O.W. Osawe1, A.J. Adegeye2, B.T. Omonona3 1
Department of Agricultural Economics, University of Ibadan, Oyo State, Nigeria
2
Professor in the Department of Agricultural Economics, University of Ibadan, Oyo State, Nigeria 3
Department of Agricultural Economics, University of Ibadan, Oyo State, Nigeria
Abstract This study aimed at assessing the technical efficiency of fish farmers in Ibadan metropolis of Oyo State, Nigeria using the stochastic frontier production function analysis. Primary data were collected using a set of structured questionnaire from 82 fish farmers in Ibadan metropolis, Oyo State, Nigeria. The stochastic frontier function estimated for the 82 respondents showed that the mean efficiency value was 0.906. Majority of the fish farmers of about 65.9 percent are over 90 percent efficient and about 34.1 percent had technical efficiency ranging from 50 percent to 90 percent, based on the use of input. The distribution of results also showed that fish farmers in Ibadan metropolis are more efficient in the use of inputs though not all the inputs. There are farmers who gain more by reducing the inputs (e.g. labour use) for the same level of output. Changing the input combinations can thereby increase the farm level of efficiency. The farmers in the study area therefore need to use their available input intensively and rationally so as to produce better output and be technically efficient. INTRODUCTION Nigerian agriculture is dominated by the small scale farmers who produce the bulk of food requirements in the country. Despite their unique and pivotal position, the small holder farmers belong to the poorest segment of the population and therefore, cannot invest much on their farms. The vicious circle of poverty among these farmers has led to the unimpressive
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performance of the agricultural sector. While several efforts have been undertaken to raise production and productivity of these farmers so as to achieve food security, such efforts have had negative implications for the environment. As the population density increases, farmers must produce even more food than before. With the population increases today, people are being pushed to new lands and many into marginal lands. One of the enormous challenges in the drive to increase food to feed the growing population will be to raise productivity and efficiency in the agricultural sector. More so that Nigeria’s rapid population growth has outstripped the nation’s capacity to grow food. From 1980 - 1990, Nigeria’s population grew by 3.1% a year, while agricultural production lagged far behind - growing at just 2.5% a year (Ojo, 1990). Given the various agricultural programmes and policies implemented over the years to increase agricultural productivity in Nigeria, it then becomes imperative to quantitatively measure the current level of and determinants of technical efficiency and policy options available for raising the present level of efficiency, given the fact that efficiency of production is directly related to the overall productivity of the agricultural sector vis-à-vis the fishery sub-sector.. Agriculture plays basic roles in the economic development of Nigeria. It provides food for the growing population, employment for over 65% of the population, raw materials and foreign exchange earnings for the development of the industrial sector (FAO, 1992). However, the ability of Nigerian agriculture to perform these roles in development varies over the years. Nigerian agricultural sector experienced staggering growth before and after the implementation of the Structural Adjustment Programme (SAP). Between 1980 and 1986 (just before the implementation SAP) Nigerian agricultural sector experienced an average growth rate of 0.5 while this rose to 3.8 between 1987 and 1992 (after the implementation of SAP). However, the growth rate decline to an average of 2.9 between 1993 and 1996. The reasons behind this decline
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are not far-fetched going by the sudden resurgence of the oil sector and the neglect of the agricultural sector by the government of Nigeria. The collapse of the oil market in the early 1980s brought into focus the fact that the Agricultural sector could not meet domestic food requirements, provide raw materials for industry or earn substantial foreign exchange through export of crops. Realising this fact, the federal government in 1986 introduced the Structural Adjustment Programme (SAP). SAP was introduced to alter and restructure the productive and consumption patterns in the economy in order to eliminate price distortion, heavy dependence on oil revenue and importation of consumer and producer goods. With respect to specific agricultural sector policies, the core of the measures under SAP included institutional reforms, improved pricing policy and specific production scheme for local staples. Prominent among the institutional reforms were the abolition of the Commodity Marketing Boards and the privatization of many agricultural enterprises formerly run by the public sector. In addition, the government introduced an agricultural policy in 1988. The policy blueprint adequately reflected the new government philosophy of minimum administrative control of economic activities and a wide scope for free market forces in the economy, a greater role for the private sector and more emphasis on efficiency and productivity as well as economic self-reliance (Ajibefun et al, 2006). With the introduction of agricultural policies in 1988, the Nigerian small-scale farmers became the central focus. The reason, according to Okuneye (1989), is due to the fact that the nation’s agriculture has always been dominated by small-scale farmers, who represent substantial proportion of the total population and produce about 90-95 percent of the total agricultural output in the country. It is against this background, that Nigerian governments, at various times adopted different agricultural development programmes aimed at raising the production, efficiency and
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productivity of these farmers. The programmes included the Agricultural Development Project, National Agricultural Insurance Scheme, National Directorate of Employment, River Basin Development Authority, Green Revolution, National Agricultural Land Development Programme, the Agricultural Credit Guarantee Scheme, National Accelerated Food Production Programme and many other programmes. Given the various agricultural programmes and policies implemented over the years to raise farmers’ efficiency and productivity, it then becomes imperative to quantitatively measure the current level of and determinants of technical efficiency and policy options available for raising the present level of efficiency, given the fact that efficiency of production is directly related to the overall productivity of the agricultural sector vis-à-vis the fishery sub-sector. From the foregoing, there is a crucial need to raise agricultural productivity; as such growth is the most efficient means of alleviating poverty and protecting the environment. For Nigeria, raising productivity per area of land is the key to effectively addressing the challenges of achieving food security. From the available literature, only few studies have been carried out on technical efficiency of farmers in the African setting. Such studies includes Adesina and Djato, 1997; Ajibefun and Abdulkadri, 1999; Ajibefun, Battese and Daramola, 1996. Of these studies, none has investigated policy options for raising farmers’ technical efficiency vis-à-vis the fishery sub-sector. Nigeria being a coastal country has about 1,280 kilometer square marine areas and about 124,878 kilometer square of inland waterways. But in spite of this potential, domestic fish production is grossly inadequate to meet even domestic demand. It is noteworthy to state that, the socioeconomic welfare of a particular nation is dependent on the level of productivity of the
agricultural and industrial sectors of that economy. Therefore, if this level of productivity is hampered or not maximized, the economy will suffer as in the case of the Nigerian agricultural sector, which has been suffering from poor productivity due largely to inadequate supply of input and at the right quality. It is in this wise that, it is expedient for us to examine the level of technical efficiency of input use of the agricultural sector vis-à-vis, the fishery sub-sector. The measurement of farm efficiency is an important area of research both in the developed and developing world (Tadesse and Krishnamoorthy, 1997). Odulaja and Kiros, (1996) mentioned that at least 73 % of all rural Africans are small-scale farmers, but despite the fact that such a high percentage of the population are farmers, food demand is still not being met from this source. This suggests that policy interventions should always be linked to efficiency. There is a need therefore, to study the input and output technical efficiencies of small-scale fish farmers, because this will serve as a source of guide for investment decisions of farmers and the basis for policy recommendations to the government. The issue of inputs used and outputs made, pose a lot of problems to small-scale fishery producers. Consequently, information on the various inputs at the optimum formulation that contribute significantly to maximization of output would be of much benefit to intending fish farmers. Potential Advantages Derived from Integration of Aquaculture into other Small-Scale Farming System
There are several potential advantages that can be derived from integrating aquaculture with other smallholder farming system components:
•
Decreased Risk: The diversification of farming systems to include aquaculture diminishes the risks associated with small-scale farming. This is because pond water not only yields fish, an edible and tradable commodity, but can also contribute to crop irrigation and livestock watering in the dry season, thereby increasing the viability of year-round production.
•
Improved Food and Economic Security: The extra production from aquaculture can imply an increased availability of protein for household consumption.
•
Enhanced Production: Certain edible plants, such as Chinese water spinach and water chestnuts, can be cultivated in fishponds.
•
Multiple Uses of Ponds: The water in aquaculture ponds need not only serve to culture fish. In parts of South Asia, fishponds are used for bathing and irrigating homestead fruit and vegetables, others for disposing of domestic wastewater.
•
Environmental Benefits: Where farm wastes are produced in significant quantities, their application into aquaculture ponds not only leads to a more efficient system, but prevents them from being disposed into the environment.
PRODUCTION IN TERMS OF INPUTS AND OUTPUT Commodity (i.e. goods and services) that are demanded and supplied are produced by transforming other goods and services called inputs into those commodities which are usually termed output or product (Adegeye and Dittoh, 1985). They also further stressed that the process of transforming input into output is what is called Production, while output is also called Product. Adegeye and Dittoh (1985) categorized factors of production into four: firstly, there are the natural resources such as land, water and local climate which are given by God, but which
could be made productive by man; secondly, we have labour which is the human resources or manual input; thirdly, there is capital, sometimes defined as “a means of production” because it is a man-made input; and finally there is management or entrepreneurship which is a qualitative kind or input that is, the effective harnessing of land, labour and capital resources. Total production or output refers to the total quantity of goods produced at a particular time as a result of the use of all the factors of production (Anyaele, 1987). The study concluded that total product depends mainly on the quantity of all factors of production that are applied in production. TECHNICAL EFFICIENCY: DEFINITION, MEASURES AND DETERMINANTS Efficiency measures have received considerable attention from both theoretical and applied economists. Leibenstein (1966) stated that there had been a spirited exchange about the relative importance of the various components of firm efficiency. Farrell (1957), proposed an approach which distinguished between technical and allocative efficiencies with the former referring to the ability of producing a given level of output with a minimum quantity of inputs and given technology. The latter refers to the choice of the optional input proportions given relative prices. Economic or total efficiency is the product of technical and allocative efficiencies. Farrell’s model, which is known as a deterministic non-parametric frontier (Forsund et al., 1980) attributed any deviation from the frontier inefficiency and imposes no functional form on the data. Several extensions of Farrell’s deterministic model have been made by Aigner and Chu (1968), Timmer (1970), Afriat (1972), Richmond (1974), Schmidt (1976), and Greene (1980) among others. For this study, the stochastic frontier production function was used to estimate the technical efficiency for the sampled farmers. Efficiency of a production system or unit means a
comparison between observed and optimal values of its output and inputs. The comparison can take the form of the ratio of observed to maximum potential output obtainable from the given inputs. In this comparison, the optimum is defined in terms of production possibilities, and efficiency is technical. A farm is said to be technically inefficient if too little output is being produced from a given bundle of inputs. Hence, enterprise inefficiency involves excessive usage of all inputs. Farrell (1957) in his study, illustrated his ideas using two inputs X1 and X2 to produce output Y. Frontier technology can be reflected by the unit isoquant, in a two-dimensional plane, with the input-output ratios as the vertical and horizontal axes such as SS1 in Figure 1. Given the efficient isoquant SS1 and the isocost line AA1, the technical efficiency measure of Farrell is given by: TE = OQ/OP
x2/y S A
P Q
R
Q1 S1
0
A1
x1/y
Figure 1: Farrell Efficiency Measures. Knowledge of the unit isoquant of the fully efficient farm, represented by SS1 in figure 1, permits the measurement of technical efficiency. If a given farm uses quantities of inputs defined by the point P, to produce a unit of output, the technical inefficiency of that farm could be represented by the distance QP, which is the amount by which all inputs could be proportionally reduced
without a reduction in output. This is usually expressed in percentage terms by the ratio QP/OP, which represents the percentage by which all inputs could be reduced. The technical efficiency (TE) of a farm is most commonly measured by the ratio, TE = OQ/OP, which is equivalent to one minus QP/OP. This will take a value between zero and one, and hence provides an indication of the degree of technical inefficiency of a farm. A value of one indicates that the farm is fully technically efficient. The position of individual farms relative to the frontier, whether on the frontier or below the frontier, would be influenced by factors such as environmental, structural and farm characteristics. These characteristics could include the share of production, size of farms, tenure, specialization, degree of mechanization, operator’s characteristics, geographical location, management practices and strategies as well as business organization and arrangement of farms (Sall, 1997; Hoppe et al, 1996 and Hoppe et al, 2001). The theoretical definition of a production function has been based on expressing the maximum amount of output obtainable from given input bundles with fixed technology. This is regarded as estimating average production function. This definition assumes that technical inefficiency is absent from the production function. Following pioneering but independent works by Aigner, Lovell and Schmidt (1977), Battese and Corra (1977) and Meeusen and van den Broeck (1977), serious consideration has been given to the possibility of estimating the so-called frontier production functions, in an effort to bridge the gap between theory and empirical work. The idea of frontier function can be illustrated with a farm using ‘n’ inputs (X1, X2, .., Xn) to produce output Y. Efficient transformation of inputs into output is characterized by the production function f (Xi) which shows the maximum output obtainable from various input vectors. The stochastic frontier production function assumes the presence of technical inefficiency of production. Hence the function is defined by,
Yi = f (Xi,β) exp (Vi - Ui)
i = 1, 2, ....., n
Where Y is the output of ith farmer, X is the input variables, β’s are production coefficients, the Vi is a random error, which is associated with random factors not under the control of the farmer, while Ui is the inefficiency measure. This model is such that the possible production Yi is bounded above by the stochastic quantity, f (Xi, β) exp (Vi), hence the term stochastic frontier. The random error Vi is assumed to be independently and identically distributed as N(0, σ2v) random variables independent of the Ui’s, which are assumed to be non-negative truncations of the N(0,σ2) distribution. The error terms, εi = (Vi-Ui) is the composed error terms, consisting of Vi, which is the two-sided error term while Ui is the one-sided error term. The components of the error terms are guided by different assumptions about their distribution. The random error represents random variation in the economic environment facing the production unit. The distribution of the inefficiency components can assume different forms, but it is normally assumed to be distributed asymmetrically. However, there is no a priori argument that suggests that one form of distribution is superior to the other, although different assumptions yield different efficiency levels. Meeusen and van den Broeck (1977) and Aigner et al. (1977) assume that Ui has an exponential and a half normal distribution, respectively. Both distributions have a mode of zero. Other specifications of the distribution of Ui include a truncated normal distribution, N (0, σ2u) as proposed by Stevenson (1980); Battese and Coelli (1995), and the gamma density as proposed by Greene (1980). The stochastic frontier model can be estimated by “corrected ordinary least squares” (COLS) method or the “maximum likelihood method”. In this
study, we use the maximum likelihood method, in line with Battese and Coelli (1995), using Battese and Corra (1977) parameterization. The analysis of efficiency, in general, focuses on the possibility of producing a certain level of output from given resources. Production efficiency is usually analyzed by separately examining its two components: technical and allocative efficiency (Wang et al., 1996). Technical efficiency may be defined as obtaining the maximum output from a given set of physical inputs. Technical inefficiency arises when actual or observed output from a given input mix is less than the maximum possible. Allocative efficiency, on the other hand, is defined as the ability to choose optimal input levels for given factor prices (Xu and Jeffrey, 1997). Wang et al. (1996) observed that allocative efficiency is evaluated from the producer’s profit maximization point of view. It does not necessarily reflect social costs and therefore is not necessarily efficient in the sense of social cost benefit assessment. Economic or total efficiency is the product of technical and allocative efficiency. ANALYTICAL FRAMEWORK FOR EFFICIENCY Following Kopp and Diewert (1982), it is assumed that the production frontier is given by Q= g (Xa) ---------------------------------------------equation (1) Where Q us output and Xa is a vector of variable inputs. The technically efficient input vector (Xt) for a given level of output (Q) is derived by solving simultaneously the equation (1) above and the input X1/Xi = Ki (i>1) where Ki is the ratio of observed inputs X1 and Xi at output Q. Assuming that the production frontier is self dual (e.g. Cobb-Douglas), then the corresponding cost frontier derived analytically can be written in general form as:
C = h (P, Q) -----------------------------------------equation (2) Where C is the minimum cost associated with the production of output Q, and P is a vector of input prices. Applying Shepard’s lemma, we obtain: δC/δPi = Xi (P, Q) ----------------------------------equation (3) This is the system of minimum cost input demand equations. Substituting a firm’s input prices and output quantity into the demand system in equation (3), we obtain the economically efficient (Xt’ P) and (Xe’ P) input combinations associated with the firm’s observed output. In addition, the cost of the firm’s actual operating input combination is given by Xa’ P. These three equations for measuring cost can now be used to compute technical (TE) and economic (EE) efficiency indices as follows: TE = (Xt’ P) / (Xa’ P) -------------------------------equation (4) EE = (Xe’ P) / (Xa’ P) -------------------------------equation (5) Finally, allocative efficiency (AE), derived from equation (4) and (5) is given by: AE = (EE) / (TE) = (Xe’ P) / (Xt’ P) ----------------------equation (6) Kopp and Diewert’s decomposition approach is based on a deterministic frontier, which imposes the limiting assumption that any deviation from the frontier is the result of inefficiency; hence, the resulting inefficiency measures are biased (Schmidt, 1985-86). To avoid this problem, we estimate a stochastic production frontier model and use the approach introduced by Jondrow et al (1982) to purge the purely random error from the efficiency
component. To illustrate how the random error is purged, consider the stochastic production frontier: Q = f (Xa) + ε ---------------------------------------equation (7) Where ε = V-U ------------------------------------equation (8) Equation (8), is the component error term (Aigner et al, 1977; Meeusen and Van den Broeck, 1977). The two components V and U are assumed to be independent of each other, where V is the two-sided normally distributed random error [V ~ N(O,σ2v) ] and U is the one-sided efficiency component with a half-normal distribution [U ~ N (O, σ2u) ]. The maximum likelihood estimation of equation (7) provides estimation for β, λ and σ2, where β was defined earlier, λ = σu / σv and σ2 = σ2u + σ2v. Given the assumptions on the distribution of V and U, (Jondrow et al, 1982) showed that, the conditional mean of U, given ε, is equal to: ε (U / ε) = σ* f*(λ ε / σ) - λ ε
---------------------------------equation (9)
1-F* (λ ε / σ) σ
Where f* and F* are respectively the standard normal density and distribution functions, evaluated at λ = ε / σ, and σ*2 = σ2u. σ2u/σ2 Thus, equations (7) and (9) provide estimates for U and V after replacing ε, σ* and λ by their estimates. Subtracting V from both sides of equation (7), we will have:
Q* = f (Xa) – U = Q – V -------------------equation (10) Where Q* is the firm’s observed output adjusted for the statistical noise captured by V. Equation (10) is used to compute the vector Xt and to algebraically derive the cost frontier, which in turn is the basis for obtaining the minimum cost factor demand equations. The algebraic expressions above shows us how the variables determining technical efficiency and in which case, the technical inefficiency are measured. Past Findings and Studies on Technical Efficiency in Agricultural Production using the Stochastic Frontier Production Function The stochastic frontier production function model has the advantage in that it allows simultaneous estimation of individual technical efficiency of the respondent farmers as well as determinants of technical efficiency (Battese and Coelli, 1995). Ines and Sean (2002) said the concept of efficiency is that, if a farm’s actual production point lies on the frontier, it is perfectly efficient. If it lies between the frontiers, then it is technically inefficient with the ratio of the actual to potential production defining the level of efficiency of the individual farm. Reichnider and Stevenson (1991), proposed a stochastic frontier model in which the technical inefficiency effects were dependent on other variables. Kumbhakar, Ghosh and McGuckin (1991) also proposed a stochastic frontier production of Zelluer-Revantur type, in which technical inefficiency effects were assumed to be a function of the values of other observable explanatory variables. Huang et al (1994) specified a non-neutral stochastic frontier production in which the technical inefficiency effects were specified in terms of various firm’s specific variables and interaction among these variables and the input variables in the frontier
Kareem et al (2007) applied the stochastic frontier production function for the analysis of technical, allocative and economic efficiency of different pond systems in Ogun State, Nigeria. The results of the analysis of the mean technical efficiency for both systems revealed that concrete pond system with 88% while earthen pond system was 89%. Similarly, the allocative efficiency results revealed that concrete pond system was 79 percent while earthen pond had 85%. Stochastic frontier production function models revealed that pond area, quantity of lime used, and number of labour used were found to be the significant factors that contributed to the technical efficiency of concrete pond system while pond, quantity of feed and labour are the significant factors in earthen pond system. The results therefore concluded that only years of experience is the significant factor in concrete pond system in the inefficiency sources model. Battese and Coelli (1995), also specified a stochastic frontier production function for panel data in which the technical inefficiency effect were specified in terms of various explanatory variables, possibly including time. Ajibefun and Daramola (1999) used stochastic frontier to predict efficiencies, which happened to vary across poultry farms ranging from 49-85 percent with mean technical efficiency of 68 percent. The sources of inefficiency revealed by the model were age, education and experience of the poultry farmers. Adeoti (2001) used the stochastic frontier model and reported the physical inputs that affect output levels in farms under Fadama and irrigation system to include farm size, family and hired labour, fertilizer and irrigation water with mean technical efficiency of 0.84. The sources of inefficiency include age, literacy status, and ownership of pump and residency status of farmers. Ajibefun (2002) applied the stochastic frontier production function for the analysis of policy issues of technical efficiency of small-scale farmers, an application to Nigerian farmers. The
result of the analysis indicates that the farmers have an average farm size of 1.56 hectares. It also indicated that both family and hired labour were extensively used in farm production. The analysis shows a wide variation in the estimated technical efficiencies, ranging between 0.18 and 0.91, and a mean value of 0.63, indicating a wide room for improvement in the technical efficiency. The results of simulation of policy variables show that the level of technical efficiency would significantly increase with rising level of education and farming experience. Ogunjobi (1999) used the stochastic production frontier to estimate the efficiency in small-scale cocoa farmers in Ondo state of Nigeria. The results of the analysis revealed that technical efficiencies vary between 0.21 and 0.94 with a mean technical efficiency of 0.63. The determinants of technical efficiency among the sampled farmers include farmers’ age, which was found to be negatively related to production efficiency, while education and age of cocoa trees have positive influence on production efficiency. Chukwuji et al (2006) applied the stochastic frontier production function to find the determinants of technical efficiency of gari processing in Delta state, Nigeria. The results of the analysis revealed that there is a wide variation in the level of technical efficiency in Gari processing, ranging from 25 percent to 88 percent, with a mean efficiency level of 65 percent. The technical inefficiency level of processors is attributed to socio – economic characteristics including age of processor, family size, level of formal education, access to production credit, availability of alternative sources of income and membership of Gari Processing Associations. The inefficiency of individual processors was negatively related to all factors and were statistically significant (P < 0.05), except age of processor.
Munir-Ahmad et al (1999) in Pakistan analysed the technical efficiency of rice farmers. The study used the stochastic Cobb-Douglas production function to estimate the farm level efficiency of rice farms, using the data collected for the 1996-1997 cropping season. The results showed that the average technical efficiency of sample farms was 85 percent with a minimum of 57 percent and maximum of 96 percent. The results further showed that visits of agricultural extension agents to the farms or farmers’ visits to extension officers and the availability of agricultural credit played a significant role in improving technical efficiency. Ajibefun et al (2002) presented an empirical study of factors influencing the technical efficiency of food crop farmers in Oyo State, using the stochastic frontier production. The study selected 67 farmers from the sample area and then determined the levels of technical efficiencies. The estimated technical efficiencies of the sampled farmers varied widely, ranging from 19-95 percent with a mean of 82 percent indicating that the farmers are 82 percent efficient in their use of production inputs. Mustafa et al (2005) applied the stochastic frontier production function to examine the technical efficiency of tobacco farming in Southeastern Anatolia, Turkey. The technical efficiencies of tobacco farms in Southeastern Anatolia were estimated with parametric and non-parametric methods. Data obtained from 149 tobacco farms were used in the empirical analysis. Results obtained with an output oriented Data Envelopment Analysis (DEA) were compared to those obtained from Stochastic Frontier Analysis (SFA). According to the results of the DEA model, mean efficiency of tobacco farmers was found to be 0.45 and 0.56 for Constant and Variable Returns to Scale (CRS and VRS) assumptions, respectively. Mean technical efficiency obtained with the SFA model was found to be 0.54. A strong correlation was found between the results obtained with output oriented VRS-DEA and SFA models. Based on these results, it was
concluded that the sampled tobacco farms would be able to increase their technical efficiency by 45 percent through better use of the available resources, while applying current technology. Amaza and Olayemi (1998) examined production efficiency in food crop enterprises in Gombe State, Nigeria. The sample size was 123 food crop farmers and the data was obtained through the use of multi-stage sampling technique. A stochastic frontier production function was used, with the maximum likelihood estimation (MLE) as the analytical tool. The MLE results showed that, land, family labour, hired labour and fertilizer are the major factors that influence the output of food crops. The effect of land area on output was observed to be positive and the coefficient was found to be statistically significant at 1 percent. The coefficient of family labour is found to be negative but significant at 1 percent, thus suggesting that, an excessive use of family labour in production. Hired labour and fertilizer use, according to the analysis have positive effects on output and their coefficients are statistically significant at 5 percent. Maize based enterprises are the most efficient in terms of technical efficiency (TE) followed closely by cowpea-based enterprises with mean technical efficiency indices of 0.73 and 0.72 respectively. In terms of economic efficiency according to the study, cowpea-based enterprise is the most efficient with mean economic efficiency of 0.59.
SAMPLE DATA AND VARIABLES Primary data were collected from a population of small scale fish farmers in Ibadan metropolis for this research work. Different fish farmers from different local government areas in Ibadan metropolis where randomly sampled as respondents and data was collected. Since these small scale fish farmers are few in the study area, fish farming households were randomly picked to
form the sample size at different locations in the study area. A total of 82 respondents were therefore selected for this research work. The data used for this study are cross-sectional data obtained by the use of structured questionnaires, through interview scheduled with the assistance of some agricultural personnel. The questionnaires were administered in selected localities in the chosen towns. Ibadan (Ìlú Èbá-Ọdàn, the town at the junction of the savannah and the forest), the capital of Oyo State, is the third largest city in Nigeria by population (after Lagos and Kano), and the largest in geographical area. It is located in south-western Nigeria, 78 miles (125.5km) inland from Lagos and is a prominent transit point between the coastal region and the areas to the north. Its population is 2,550,593 according to 2006 census results, including 11 local government areas. The population of Ibadan municipal, including five LGAs, is 1 338 659 according to census results for 2006, covering an area of 128 kilometer square. Ibadan occupies a land area of 27, 148 kilometer square. Oyo state is well drained with rivers flowing upland in a north-south direction. The major rivers are Oyan, Ofiki, Ogun, Owu, Shasha Woro. Others are Asejire and Eleyele. Measurement of Variables The variables used are in two ways: (I)
Dependent variable ‘Yi’ is the output, which represents the quantity of harvest measured in kilogram/ha.
(II)
Independent Variables
-
‘X1’ is the pond size as a proxy for farm size
-
‘X2’ is the total quantity of labour use
-
‘X3’ represents total feed used per application
-
‘X4’ represents the stocking rate (pieces)
The a-priori
expectation of the independent variables is that, yield should increase with
increased pond size as a proxy for farm size, optimum labour use, increased quantity of feed with increased stocking rate respectively or vice-versa ceteris paribus. A summary of the values of the variables which were used in our analysis in the determinant of production related characteristics is presented in Table 1. Table 1: Summary of the Variables for Fish Farmers in Ibadan Metropolis of Oyo State, Nigeria. Output / Input Variables
Minimum
Maximum
Mean
Standard Deviation
Total production (Y)
800
19620
2943.841
3542.514
Pond Size (ha) X1
0.001
0.2
0.008
0.024
Total Labour used (Man-days) X2
36.75
324
84.277
55.742
Quantity of Feed (Kg/ha) X3
30
180
46.451
26.017
1000
20000
3170.732
3601.217
Stocking Rate (Kg/ha) X4
Socio-economic Characteristics: Socio-economic characteristics of the respondents were based on their age, sex, educational status, marital status, household size, number of children and cooperative membership.
Farm information data were based on farm size, year of establishment of pond, type of pond, sources of water supply, fish farming practice, sources of fingerlings, type of fish specie cultured The socio-economic variables were considered to see their influence on the estimated technical efficiencies of the fish farmers.
MODEL SPECIFICATION Following Mohammad and Thompson (1998), the functional form used in this study is CobbDouglas, which is specified below as:
N
Yi = A П Xiβi е-Ui+V ------------------------------------------equation (iii) i=1 Where A and βi are unobservable parameters indicating the efficiency parameter and the output elasticity coefficients respectively. The estimating equation becomes: n
LnYi = LnA + ∑ LnXi + еi --------------------------------------equation (iv) i=1 Where еi = Vi – Ui and Ln е = 1 Hence,
n
LnYi = LnA + ∑ βi LnXi + (Vi - Ui) --------------------------------------equation (v) i=1 LnYi = LnA + β1LnX1 + β2LnX2 + ……+ β4LnX4 + (Vi - Ui) ---------equation (vi)
The MLE has however been found to be asymmetrically more efficient than the corrected OLS estimators (Coelli, 1995). Therefore, Maximum Likelihood Estimator (MLE) will provide estimation for γ, λ and σ. Where: σU λ = σV
----------------------------------------------------------------equation (vii)
σ = σ2 u + σ2 v λ2 γ = 1+λ2
---------------------------------------------------------equation (viii)
--------------------------------------------------------------equation (ix)
In the absence of other farm-level data (e.g. farmer’s education, technical assistance etc), which may represent the sources of inefficiency, the effect of farm size alone may be examined by means of a simple quadratic function. The concept of technical efficiency model can be illustrated graphically using a simple example of a two input (x1, x2)-two output (y1, y2) production process (Figure 1). Efficiency can be considered in terms of the optimal combination of inputs to achieve a given level of output (an input-orientation), or the optimal output that could be produced given a set of inputs (an outputorientation). In Figure 1(a), the firm is producing a given level of output (y1*, y2*) using an input combination defined by point A. The same level of output could have been produced by radially contracting the use of both inputs back to point B, which lies on the isoquant associated with the minimum level of inputs required to produce (y1*, y2*) (i.e. Iso (y1*, y2*)). The input-oriented level of technical efficiency (TEI(y, x)) is defined by 0B/0A. However, the least-cost combination of
inputs that produces (y1*, y2*) is given by point C (i.e. the point where the marginal rate of technical substitution is equal to the input price ratio w2/w1) (Kumbhaker and Lovell, 2000). The production possibility frontier for a given set of inputs is illustrated in Figure 1(b) (i.e. an output-orientation). If the inputs employed by the firm were used efficiently, the output of the firm, producing at point A, can be expanded radially to point B. Hence, the output oriented measure of technical efficiency (TEO(y, x)); can be given by 0A/0B. This is only equivalent to the input-oriented measure of technical efficiency under conditions of constant returns to scale. While point B is technically efficient, in the sense that it lies on the production possibility frontier, higher revenue could be achieved by producing at point C (the point where the marginal rate of transformation is equal to the price ratio p2/p1). In this case, more of y1 should be produced and less of y2 in order to maximise revenue. To achieve the same level of revenue as at point C while maintaining the same input and output combination, output of the firm would need to be expanded to point D. (Kumbhaker and Lovell 2000).
Figure 2: Input (a) and output (b) oriented efficiency measures
RESULTS The effect of the sampled socio-economic characteristics of the fish farmers in the Ibadan, Oyo state, Nigeria on technical efficiency of fish farming are described below. Findings as shown in table 2 on the age of the fish farmers show that, about 95 percent of respondents are not up to 60years of age. The average age of the fish farmers is 40years. The implication of this finding is that most respondents sampled are in their active working age. Similarly, fish farmers that are less than 30 years of age are 93.4 percent efficient followed by those of age 30-39 years with average technical efficiency of 92.6 percent. Farmers of age group 50-59 had an average technical efficiency of 0.837. This means that those fish farmers that are in
their prime age are more efficient. This could be attributed to the fact that these groups of farmers are more active and have more time to spend with supervision of the fish farm Table 3 shows the effect of educational status on technical efficiency. Majority of the fish farmers i.e. 56.1 percent had secondary education, 31.7 percent had post secondary education and 12.2 percent had primary education. The implication of this is that most farmers sampled are likely to easily appreciate the need to adopt new technology which will enhance their efficiency level. Similarly, fish farmers that had undergone primary school education were 87.3 percent technically efficient while those with secondary and post secondary education were 90.6 percent and 92.5 percent technically efficient respectively. This agrees with the a priori expectation that technical efficiency should increase with level of education. Similarly, findings as shown in table 4 shows that 43.9 percent accounted for married monogamous fish farmers followed by 26.8 percent singles respondents. 22.0 percent are married polygamous. The implication of this is that there is likely to be more family labour available for farm work since most of the respondents are married. However, 7.3 percent are either divorced or widowed. In the same vein, respondents that are divorced and widowed had higher average technical efficiency of 0.973 and 0.969 respectively. Respondents that are married polygamous had the lowest mean efficiency level of 0.868. Efficiency in fish farming does not increase with increase in labour as shown in table 5. It is shown in the table that fish farm households that are few had higher technical efficiency. Household sizes of 1-3 were 92.5 percent efficient and household sizes of 4-6 were 91.0 percent efficient while household sizes of 10-12 were 86.2 percent efficient. This means efficiency those not increase with increase in households. This agrees with the MLE results that show that yield
did not increase with increase in quantity of labour use measured in man-days that will be discussed later in this work. As expected, efficiency increased with cooperative membership. This is shown in table 6. Members of cooperative organizations were 92.6 percent efficient while non-members were 88.9 percent technically efficient. This could be attributed to the fact that, membership with cooperative organizations means that farmers might have access to information, input at cheaper cost and other intangible benefits that can serve to enhance efficiency level. Table 2: Summary of Distribution of Fish Farmers by Age Age Group (Yrs) 0.91
54
65.9
Mean Efficiency = 0.906
54
60 50
0.51-0.60
40
0.61-0.70 23
Frequency 30
0.81-0.90
20 10
0.71-0.80
2
1
2
>0.91
0 Efficiency Level
Figure 1: Chart Showing the Frequency Distribution of the Technical Efficiency Estimates of Fish Farmers in Ibadan, Oyo State, Nigeria.
Determination of Technical Inefficiency in Fish Production From table 10, the coefficients of feeding regime was positive, indicating that this factor led to increase in technical inefficiency or decrease in TE of fish production in the study area. This result may be due to the fact that the more the farmers feed the fish per day with lesser stock to
commensurate with the carrying capacity of the pond, the lesser their efficiency with respect to input use. Also, the coefficients of educational level, years of experience, pond type and cooperative membership were negative, indicating that these factors led to decrease in technical inefficiency or increase in technical efficiency. This agrees with the a priori expectation that TE should increase with increase in years of schooling and experience since education and experience are expected to be positively correlated with adoption of improved technology and techniques of production (Ojo and Ajibefun, 2000). Similarly, in the results shown tertiary education was significant at 1 percent level, secondary education and cooperative membership were significant at 5 percent levels of significance. Table 10: Estimates of the Technical Inefficiency of Fish Farmers in Ibadan, Oyo State, Nigeria Variables
Coefficient
Constant
-0.342
0.999
-0.342
Feeding regime
0.555
0.991
0.560
Tertiary Education
-0.389
0.095
-4.094***
Secondary Education
-0.198
0.085
-2.329**
Experience
-0.107
0.977
-0.110
Pond type
-0.117
0.999
-0.177
Cooperative membership - 0.452
0.200
-2.260**
***Significant at 1 percent **Significant at 5 percent
Standard Error
T-Statistics
Conclusion and Recommendation This study aimed at determining the input and output technical efficiencies of fish producers in Ibadan metropolis. The maximum likelihood estimate of the frontier production showed clearly that pond size, quantity of feed and stocking rate are the most important inputs in fish production. The stochastic frontier function estimated for the 82 respondents showed that the mean efficiency value was 0.906. Majority of the fish farmers of about 65.9 percent are over 90 percent efficient and about 34.1 percent had TE ranging from 50 percent to 90 percent, based on the use of input. The level of inefficiency was found to be negatively related to coefficients of educational level, years of experience and pond type. This indicated that these factors led to decrease in technical inefficiency or increase in technical efficiency. This result showed that inputs in fish production need to be efficiently used by all farmers so as to produce more output than ever before. Alternatively, some inputs like size of pond and labour used could be reduced at the same level of feed and stocking rate for the farmers to operate at optimal level and be efficient. The elasticities of production for the inputs used are -560.0554, 0.0878, 2.7574 and 0.9862 for pond size, total quantity of labour, total quantity of feed and stocking rate respectively. Those with low values of below 1, point to relative inelastic response. The farmers could intensify more on the use of feed for more output and be technically efficient. Stakeholders in fish production such as research institution, extension agents and fish producers association should intensify effort in the area of sensitizing farmer with respect to the right level of input combinations that can improve efficiency level of fish production in Nigeria. This is so,
since findings have shown that the ration combinations if not strictly adhered to as empirically demonstrated in the study will lead to decrease in efficiency in fish production. It is therefore likely that agricultural production vis-à-vis fish production in Nigeria will need the continuing support of government and international agencies for some time to come until the level of production and efficiency of farmers are increased to sufficiently higher levels through proper enlightenment of the right input combinations.
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