Exchange Rate Dynamics and Monetary Fundamentals

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Exchange rates have a strong influence in an economy. They perform the dual function as a nominal anchor for domestic prices and the maintenance of ...
Exchange Rate Dynamics and Monetary Fundamentals: A Cointegrated SVAR Approach for Nigeria

Ekpeno L. Effiong

Department of Economics University of Uyo P.M.B. 1017, Uyo Akwa Ibom Nigeria

[email protected] [email protected] +234 802 789 0160

Revised Manuscript

Exchange Rate Dynamics and Monetary Cointegrated SVAR Approach for Nigeria

Fundamentals:

A

Abstract Are monetary fundamentals important determinants of the exchange rate behaviour in Nigeria? This paper examines the validity of both short and long-run versions of the monetary exchange rate model for the Nigerian naira-U.S. dollar exchange rate from 1987:1 to 2011:4 within a cointegrated SVAR framework. Apart from the long-run relationship, the short-run contemporaneous interactions are examined for the monetary exchange rate model. The results show the existence of a unique long-run relationship between the exchange rate and monetary fundamental which is theoretically consistent with the monetary model. The short-run evidence is not entirely consistent with the monetary exchange rate model although the impulse response of the exchange rate to shocks in the monetary fundamentals mirrors the predictions of the monetary model. However, only the interest rate differential is significant and explains most of the variations in the nominal exchange rate in the short-run. Keywords: Monetary fundamentals, Nominal exchange rate, Monetary exchange rate model, Nigeria, Cointegrated SVAR. JEL Classification: C22, C32, E4, F31, F41.

1. Introduction Exchange rates have a strong influence in an economy. They perform the dual function as a nominal anchor for domestic prices and the maintenance of international competitiveness. Since the collapse of the Bretton Woods system in the early 1970s and the transition to the modern float era, exchange rates have become increasingly volatile and intractable across the globe. The intractability of exchange rate can harm an economy’s internal and external balance and, hence disrupt economic progress. In recent times, the central focus in the exchange rate economics literature has been to explain the behaviour of exchange rate with reference to a reliable set of macroeconomic fundamentals. Few models have been thrown up in the literature to facilitate proper

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understanding of the movement of exchange rate. These models flow from the monetary approach to exchange rate determination which has become the standard instrument of analysis in international finance. The monetary exchange rate models (i.e. flexible and sticky models) posit a link between exchange rate and a set of monetary fundamentals. The monetary exchange rate model in its standard form assumes that the exchange rate (the price of a currency in relation to another) is determined by the fundamentals of supply and demand for money. The flexible-price formulation of the monetary model uses the log differentials between the domestic and foreign monetary aggregates, outputs and interest rates as the basic fundamentals that affect exchange rate behaviour (see Frankel, 1976; Bilson, 1978). As such, any misalignment and widening of the fundamentals would reflect in the exchange rate dynamics. Like other economic models, the monetary exchange rate model has not been spared from empirical validation. Since the seminal work of Meese and Rogoff (1983) that found the naïve random walk models to outperform the conventional monetary models in explaining exchange rate behaviour, and the reverse predictions of Mark (1995), Chinn and Meese (1999) and Mark and Sul (2001), the focus in the literature has transcended towards testing the existence of long-run equilibrium relationship between the exchange rate and the monetary fundamentals. Using cointegration approach, the validity of the monetary exchange rate model has been examined for both developed and developing countries (e.g. MacDonald and Taylor, 1991, 1994; Rapach and Wohar, 2002; Kulkarni and Ishizaki, 2002; Chin et al., 2007; Liew et al., 2009) and particularly for Nigeria (see Jimoh, 2004; Nwafor, 2006; Alao et al., 2011; Adawo and Effiong, 2013) However, few studies have attempted to combine the short and long run properties of data to analyse both the short and long-run validity of the monetary exchange rate model (see Loria et al., 2010).

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2.5 2 1.5 1 .5 1985m1

1990m1

1995m1

2000m1

2005m1

2010m1

Fig. 1: Log nominal exchange rate (naira/dollar), monthly series. The objective of this paper is to investigate the monetary exchange rate model for a developing economy like Nigeria for both short and long run validity during the flexible exchange rate era (1987:1 – 2011:4). The focus on Nigeria is unique for two reasons. First, the Nigeria exchange rate (naira-dollar rates) has been immensely volatile as depicted in Figure 1 above which reflects instability in Nigeria’s exchange rate management. Secondly, evidence of the monetary model in Nigeria have focused only on testing for the existence of long-run relationship while the short-run instantaneous correlations between the exchange rate and the monetary fundamentals remains untouched. Building on Loria et al. (2010), a cointegrated SVAR approach is employed as it allows for the estimation of the instantaneous correlations (in the short run) between the exchange rate and the monetary fundamentals after accounting for the existence of a long-run exchange rate equation in the estimation procedure. The balance of the paper is as follows: Section 2 presents a review of related literature while Section 3 provides a theoretical framework of the monetary exchange rate model. Section 4 discusses the econometric estimation strategy and the data while section 5 presents the empirical findings. Section 6 provides the concluding remarks.

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2. Review of Related Literature The monetary exchange rate model literature has grown exponentially since the postBretton Woods float. The interest of researchers has been to determine a reliable set of fundamental economic variables influencing the exchange rate behaviour in the wake of its increasing volatility and intractability. Emphasis has been on testing the predictability performance and long-run validity of the monetary model using standard cointegration techniques. Several studies have estimated various versions of the monetary model with mixed evidence. Meese and Rogoff (1983) in their seminal contribution finds that the out-of-sample forecasting performance of these models fails to outperform a simple random walk model at short horizons. However, studies by Mark (1995), Chinn and Meese (1995), MacDonald and Taylor (1994) have shown that for a small set of monetary fundamentals, the out-of-sample forecast improves upon the random walk model. The robustness of these results has been questioned by Berben and van Dijk (1998) and Berkowitz and Giorgianni (2001) based on the assumption of a stable cointegrating relationship. Recent studies admit the possibility albeit difficulty in beating the random walk forecast (see for example, Mark and Sul, 2001; Rapach and Wohar, 2002). On the other hand, researchers have examined the long-run relationship of the monetary exchange rate model using cointegration approach1. Groen (1999) emphasized the importance of cointegration in establishing a long-run link between nominal exchange rate and monetary fundamentals. In the absence of cointegration, the long-run predictability of the monetary model breaks down (Mark, 1995; Chinn and Meese, 1995; Groen, 1999). MacDonald and Taylor (1991) examined the long-run validity of the monetary model of exchange rate by employing the Johansen’s multivariate cointegration technique and provide 1

Macdonald and Talylor (1991) argue that the multivariate cointegration technique is more appropriate than the two-step cointegration methodology in testing the monetary model. This has become widely used in the literature.

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supportive evidence for both the US dollar and British pound. Choudhry and Lawler (1997) applied both Johansen-Juselius and Engle-Granger cointegration tests for Canada and found the existence of a long-run relationship for Canadian dollar-US dollar. This evidence is further supported by Kouretas (1997). Dutt and Ghosh (2000) found evidence in favour the monetary model for the nominal Japanese yen-US dollar exchange rates. Liew et al. (2009) reports a long-run relationship for Thailand’s exchange rate based on the flexible-price monetary model. Lee et al. (2007) and Long and Samareth (2008) using different cointegration approaches found evidence in support of the monetary model for the Philippines; while same conclusion is reached for Malaysia by Chin et al. (2007). Another strand of the literature finds little evidence in favour of the monetary exchange rate model (e.g. Meese, 1986; McNown and Wallace, 1989; Sarantis, 1994; Cusham, 2000). Sarantis (1994) applied the Johansen cointegration framework to investigate three variants of the long-run monetary approach to exchange rate determination and found no statistical evidence supporting long-run equilibrium relationship consistent with the flexible-price monetary model. Cusham (2000) found cointegration relationship for the monetary model using Canadian – US dollar exchange rate but since the estimated cointegrating coefficients were inconsistent with those predicted by the monetary model, he concluded that the data does not support the monetary model. The long-run relationship for the monetary exchange rate model has also been examined using panel data framework and long historical data with supportive evidence (e.g. Groen, 2000; Mark and Sul, 2001; Crespo-Cuaresma et al., 2004; Uz and Ketenci, 2007; Rapach and Wohar, 2002). Groen (2000) and Mark and Sul (2001) follow the first approach and tested for a stable long-run relationship between nominal exchange rate and monetary fundamentals using panel cointegration tests for the post-Bretton Woods. Both found strong evidence of cointegration among nominal exchange rates, relative money supplies, and real output levels. Uz and Ketenci (2007) tested the monetary model using panel data for ten new members of the European Union and Turkey over the period 1993:1 and 2005:4 and found 5

strong evidence of cointegration between exchange rates and monetary model. CrespoCuaresma et al. (2004) used the panel cointegration techniques for six Central and Eastern European countries2 to estimate the monetary exchange rate model supplemented with the Balassa-Samuelson effect and found that the monetary model provides a good explanation of the fluctuations in nominal exchange rates. Rapach and Wohar (2002) follows the second approach using long span of data with results supporting a simple long-run monetary model of the U.S. dollar exchange rate determination for France, Italy, the Netherlands and Spain; moderate support for Belgium, Finland and Portugal; and weaker support for Switzerland. For Nigeria, the literature on exchange rate determination based on the monetary exchange rate model is increasing. Jimoh (2004) tested the monetary model of exchange rate determination in Nigeria during the floating regime between 1987 and 2001 (quarterly series) using the two-step cointegration methodology. He found that the monetary approach fits the Nigerian exchange rate behaviour. Nwafor (2006) applied the Johansen’s multivariate cointegration procedure to the naira-dollar exchange rates for the period 1986 and 2002 (quarterly series) and found at least one cointegrating vector which suggests the existence of a long-run monetary model of exchange rate in Nigeria. Alao et al. (2011) examined the flexible price monetary model for the naira-US dollar exchange rates using time series data for the period 1986-2008. Applying Johansen cointegration test, they found that one cointegrating vector and concluded that the variability of the nominal naira-dollar exchange rate was consistent with flexible price model. Adawo and Effiong (2013) while using the Johansen cointegration methodology found evidence of the monetary exchange rate model over the floating exchange rate regime with the estimated long-run parameters being theoretically consistent with the predictions of the monetary exchange rate model.

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This includes Czech Republic, Hungary, Poland, Romania, Slovakia and Slovenia.

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Further evidence on the monetary model is provided by Loria et al. (2010) who examined both the long-run and short-run validity of Bilson’s variant of the monetary model for Mexico between 1994 and 2007 using a cointegrated SVAR model. They found robust short and long-run relationships between Mexican monetary aggregates and the exchange rates consistent with Bilson’s prediction, thus concluding that the monetary model provides a good framework to understand Mexico’s currency behaviour. This paper contributes to the literature on exchange rate determination based on Bilson’s variant of the flexible-price monetary model by extending the analysis to uncover the short-run contemporaneous interactions between the nominal naira-dollar exchange rate and monetary fundamentals. The forecast variance decomposition of the underlying shocks to the nominal exchange rate from innovations in the monetary fundamentals is examined in addition to the impulse response analysis. To our knowledge, no study has adopted this approach for Nigeria. Hence, it is imperative to re-validate the monetary model of exchange rate for Nigeria. 3. The Monetary Exchange Rate Model Framework The monetary approach to exchange rate has been the standard instrument of analysis in international finance. The main features of the monetary approach to exchange rate determination start with the flexible-price formulation (Frankel, 1976; Bilson, 1978). The standard monetary model contains three basic building blocks: monetary market equilibrium, purchasing power parity (PPP) and uncovered interest parity (UIP)3. The starting point of the monetary approach is the definition of exchange rate as the relative price of two monies in terms of the relative supply and demand for money. The money

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The UIP asserts that with open markets, expected changes in the nominal exchange rate are equal to the interest ) ( ) denotes the market expectation of rate differential. This is expressed as ( ), where ( the change in the exchange rate.

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demand relationships between the domestic and foreign country can be expressed as a monetary equilibria as follows: ( ) ( ) where

,

,

and

denote the log-levels of the domestic money supply, price level

income level and interest rate level respectively at time t;

and

are positive constants;

asterisks denote foreign variables. In the monetary model, the real interest rate is assumed to be exogenous in the long-run and determined in the world markets because of the assumption of perfect mobility of capital and goods. Another building block of the monetary approach is the absolute power purchasing parity (PPP) which holds that goods market arbitrage will tend to move the exchange rate until prices in both domestic and foreign countries are equalized. Therefore, the monetary approach assumes that PPP holds continuously so that: ( ) where

is the log-level of the nominal bilateral exchange rate (the domestic price of the

foreign currency). The domestic money supply determines the domestic price level and hence the exchange rate is determined by the relative money supplies. Solving for (

) by

subtracting equation (2) from (1), the nominal exchange rate becomes as follows: (

)

(

)

(

)

( )

which is the fundamental monetary exchange rate model equation. For simplicity, the model assumes that the income elasticities and interest rate semi-elasticity of money demand are the same for domestic and foreign countries. Therefore, equation (4) reduces to the following: (

)

(

)

(

) 8

(5)

Based on equation (5), the monetary model postulates that exchange rate movement may )

be determined by the differentials of money supply, income and interest rate [( (

)

(

)]. Accordingly, the transmission mechanism that maintains the

monetary market equilibrium through changes in the nominal exchange rate is as follows: an increase in the domestic money supply relative to the foreign counterpart produces an equiproportionate depreciation of the currency; income differential and interest rate differential have negative and positive impact on the exchange rate respectively. Therefore, income and interest rate differentials will produce exchange rate appreciation and depreciation respectively. In addition, the elasticities for the domestic and foreign money supply are assumed to be identical although both variables have opposite effects on the exchange rate. The same assumption holds for the domestic and foreign interest rate variables. 4. Econometric Estimation Strategy and Data4 The structural VAR methodology (see Sims, 1986; Amisano and Giannini, 1997) offers a reliable econometric tool in validating the monetary model of exchange rate in Nigeria. Contrary to the traditional a-theoretic VAR (Sims, 1980), economic theory plays an important role in the modelling (identification) process of the SVAR framework. As a result, the SVAR methodology combines time series analysis and economic theory in determining the dynamic responses of economic variables to independent disturbances (or shocks). The standard VAR approach includes only lags of variables due to assumption of stationary. The reduced VAR form is represented as follows: (6) where

is a vector of endogenous variables;

is a vector of deterministic of components

such as constants, trends, and seasonal or intervention dummies;

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This section draws liberally from Loria et al. (2010).

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is a vector of independent

multivariate normal disturbances. Equation (6) fails to offer explanation on the contemporaneous effects among each variables which are hidden in the correlation structure of the covariance matrix from

. This implies that the innovations in

will be

contemporaneously correlated. A deeper examination of the so-called primitive VAR leads us to better understanding of such difficulty (Enders, 1995; Loria et al., 2010): (7) where matrix B contains the contemporaneous interactions among the variables such that the errors in

are cross correlated, while matrix A contains all the lagged interactions

among the same variables. A deeper observation of equations (6) and (7) shows that C = B-1A and

= B-1 ; which means that the reduced VAR errors are linear combinations of the

uncorrelated shocks

. Unlike the standard Cholesky decomposition, the contemporaneous

interactions of interest as contained in matrix B can be recovered by imposing restrictions. The essence is to compute the impulse-response functions in traditional VAR analysis5, so as to satisfy the necessary identification conditions. This states that the number of non-zero elements in matrix B must be equal or less than (n2 – n/2). However, the SVAR analysis allows imposing restrictions that identifies the contemporaneous interactions from the disturbances of the reduced VAR model. Following

Amisano and Giannini (1997) and Loria et al (2010), a general SVAR

framework admits a VAR representation with non-stationary time series as the take-off point for the specification of an SVAR model. In the presence of cointegration among economic variables, the structuralization of the model takes place at two distinct stages. First, the identification of the long-run equilibrium; and second is the identification of the short-run

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The parametric restrictions contained in matrix B are based on economic theory.

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interactions. The final structure of the instantaneous equations is achieved by means of two matrices (A and B) as follows: ( )

( ) ( )

where

is a vector of the reduced VAR disturbances and

is a vector of the primitive VAR

disturbances. In addition, it is assumed that E( ) = 0 and E = (

)=

. Matrices A and B

encapsulates the contemporaneous relationships of interest and the diagonal matrix of normalized variances of the structural innovations

respectively. The final structure is

obtained starting from an exactly identified model and moving to an over-identified model by imposing statistically valid theoretical restrictions. The likelihood ratio test is used to confirm the validity of the imposed constraints. The SVAR methodology is performed in three steps. First, the reduced VAR model is estimated and a matrix of disturbances computed. Second, the matrices A and B are estimated from the computed disturbances using the Full Information Maximum Likelihood (FIML). Third, the instantaneous reactions of the system to individual shocks are estimated and the impulse-response function graphed. The validity of both short and long run monetary model for the naira-dollar exchange rate is tested using the Cointegrated SVAR approach. The testing procedure involves the estimation of the long-run monetary model of exchange rate cointegration equation and the imposition of restrictions in the covariance matrix of the reduced-form VAR model to compute the contemporaneous correlations suggested by the short-run version of the monetary model. The structuralization of a VAR takes three distinct steps in the presence of cointegration. First, an appropriate VAR representation for the set of variables in terms of choosing the lag order, the cointegration rank and associated deterministic polynomial, and identification of the space

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spanned by the cointegrating vectors (Johansen, 1995, Loria et al., 2010). Specifically, the Johansen’s maximum likelihood procedure for testing the existence of a cointegration relationship is applied to the monetary model of exchange rate equation given as follows: (

)

(

)

(

)

(10)

The expected coefficient signs for the long-run monetary model must be

,

> 0 and

< 0.

If one of the cointegrating relationships is consistent with the expected coefficients in equation (10), then the monetary model of exchange rate holds in the long-run. The second step is called the structuralization stage. Here, the error correction form of the VAR model is used to identify the short-run associations between the exchange rate and its monetary fundamentals hidden in the covariance matrix of the residuals of the multivariate model. Consequently, the structuralization of the flexible-price monetary model of exchange rate is given as: ( ) where

( (

) (

)

) and ( )

) (

The variance-covariance matrix of VAR in its error correction form in equation (9) is used to recover the short-run model coefficients. Based on the monetary model of exchange rate, the following set of theoretical constraints is imposed on matrix A as follows:

[

][

(

)

(

)

(

)

]

[

][

(

)

(

)

(

)

]

(12)

The final structure of the short-run monetary model can be written as the following equation: (

)

(

)

(

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)

(13)

The expected coefficient signs of the short-run monetary model must be

,

> 0 and