Block F-tests would be useful in analysing the causality in a VAR with cointegrating variables since they reveal which of the variables in the system would have a significant impact on the future value of each of the variables in the system. The F-test is however limited as it fails to show whether a
77 shock of the variables has a positive or negative impact on the other variables in the system. The F-test also fails to provide insight into how long it will take for the shock to work through the system (Brooks, 2008:299). The variance decomposition and impulse response analysis overcome these limitations and will be employed in this study.
Impulse response takes into account how the dependent variables in a VAR system respond to the shocks of each of the explanatory variables. If there are n variables in the system, then n2 impulse responses can be generated. This is achieved by expressing the VAR model as a vector moving average and if the system is stable the shock should generally die out. An impulse response does not die out to zero, however it approaches some non-zero value which reflects the non-stationarity of the system where an impulse can have a permanent effect (Lϋtkepohl, 2005:264).
Variance decomposition on the other hand reveals the proportion of the movements in the dependent variables that are due to their own shocks versus the shocks of the exogenous variables.
With the variance decomposition analysis it is generally observed that own series shocks explain most of the error variance of the series in the VAR. Generally variance decomposition and impulse response analyses provide similar information (Brooks, 2008:300).
Once the long-run model for the real exchange rate has been estimated, the next step is to determine the extent of the real exchange rate misalignment. This will be discussed in the following section.
4.5 THE HODRICK-PRESCOTT FILTER AND EXCHANGE RATE MISALIGNMENT The Hodrick-Prescott (H-P) filter is a smoothing technique which is used to obtain the long-run (permanent) trend component of a series. The H-P filter is a linear two-sided filter that computes the smoothed series s of y, by minimising the variance of y around s, subject to penalty that
The penalty parameter λ controls the smoothness of the series σ. The larger the penalty parameter, the smoother the σ. The default penalty parameter used is λ = 1600 for quarterly data.
78 The H-P filter is used to smooth the explanatory variables in the long-run model. The permanent (smoothed) series of the explanatory variables along with the long-run coefficients from the VECM are used to compute the permanent equilibrium exchange rate (PEER). Exchange rate misalignment is thus the difference between the actual REER and the PEER. To compute the percentage exchange rate misalignment we apply the method used in Dufrenot and Yehoue (2005:17) and Aliyu (2007:22) where
100 ] /
)
[(actualREER PEER PEER nment
RERmisalig 4.9
4.6 CONCLUSION
Against the theoretical background of the determination of the equilibrium exchange rate, the equilibrium exchange rate model is defined as the relationship between the REER and its determinants. This chapter provides the definitions of the determinants as well as a brief discussion of their effects on the REER. The next step would be to test for cointegration among the variables.
An important condition for this test is that the variables should be non-stationary; hence this chapter provides a brief description of the ADF and KPSS tests for unit root and stationarity respectively.
The Johansen method tests for the number of cointegrating equations using the Trace test and the maximum Eigenvalue test. This is carried out after selecting an appropriate lag using the information criteria. If there is evidence of a cointegrating equation the VECM is estimated in order to gain the long- and short-run coefficients of the exchange rate model. If a model performs well in the diagnostic checks, impulse response and variance decomposition analyses will be applied in order to assess the magnitude and effect of shocks of the explanatory variables on the REER.
The H-P filter is used to smooth out the explanatory variables in the long-run model, in order to obtain their permanent values. Along with the estimated long-run coefficients, the PEER is computed. Exchange rate misalignment is thus the difference between the actual REER and the PEER. The next chapter will apply these techniques to quarterly data from Ghana and Nigeria in order to assess the extent of RER misalignment in these countries over the study periods.
79 CHAPTER 5
EMPIRICAL ANALYSIS AND FINDINGS 5.1 INTRODUCTION
Chapter 4 provides the analytical framework which reviews the estimation techniques which will be used to model the equilibrium exchange rates as well as to find the degree of possible real exchange rate misalignment. This chapter applies these proposed analytical techniques on quarterly data from Ghana and Nigeria from 1980 to 2006 and from 1980 to 2007 respectively. The findings in this chapter provide the answers to the questions which were posed at the onset of this study such as:
which variables are the short- and long-run determinants of the equilibrium REER in Ghana and in Nigeria? Is the REER endogenous to the model? Based on these findings, is there exchange rate misalignment in Ghana and in Nigeria and if there is, to what extent? The Johansen (1995) approach, the Vector Error Correction model as well as orthogonalised impulse response and variance decomposition analyses are applied to answer the first two questions, while the Hodrick-Prescott filter is applied to answer the remaining question. Section 5.2 presents the empirical findings and Section 5.3 will conclude.