Modeling the Real Exchange Rates in WAEMU and CEMAC
- Charalambos Tsangarides, Carlo Cottarelli, Gian Milesi-Ferretti, and Atish Ghosh
- Published Date:
- September 2008
The CFA franc arrangement dates back to the mid-1940s and is among the longest-standing fixed exchange rate regimes world-wide.1 The zone includes France on one side and two monetary unions in Central and West Africa on the other, namely, the Communauté Économique et Monétaire de l’Afrique Centrale (Economic and Monetary Community of Central Africa, or CEMAC) and the Union Économique et Monétaire ouest Africaine (West African Economic and Monetary Union, or WAEMU), respectively.2 The CFA franc was pegged first to the French franc prior to 1999, and then to the euro thereafter; it was devalued only once in 1994 to correct for domestic and external imbalances that emerged during the 1980s and 1990s. Over the past two years the CFA franc—along with the euro to which it is pegged—appreciated by more than 25 percent in nominal terms vis-à-vis the U.S. dollar, putting pressure on the region’s competitiveness. This has led to a renewed interest in the prospects of and the outlook for the CFA franc.
Assessing competitiveness and necessary exchange rate or other appropriate policy actions requires as a first step a quantitative analysis of the actual and equilibrium exchange rates and measurement of the degree of potential exchange rate misalignment. In this chapter, we estimate the paths of the long-run equilibrium real effective exchange rates (EREERs) and potential misalignments for the two monetary unions of the CFA franc zone over the period 1970–2005. We posit a long-run relationship between the real effective exchange rate and a set of determinants motivated by the Edwards (1989) fundamental equilibrium exchange rate approach and apply the Johansen (1995) cointegration methodology to test for and estimate such a relationship.
Our empirical findings can be summarized as follows. First, we show that the proposed fundamentals account for most of the fluctuation in real effective exchange rates: increases in the terms of trade, government consumption, and productivity improvements tend to cause the exchange rate to appreciate, whereas increases in investment and openness lead to a depreciation. Second, based on these fundamentals, we estimate that although both the WAEMU and CEMAC real exchange rates were slightly more appreciated than their estimated long-run equilibrium levels at end-2005, the estimated misalignments are not statistically significant. Finally, we identify a feedback effect for both CEMAC and WAEMU, which suggests that following a shock there is reversion to the time-varying long-run equilibrium, with the speed of reversion about two times faster in WAEMU than in CEMAC.
The rest of the chapter is organized as follows. The next section lays down the theoretical foundation for the empirical exercise in the chapter. This is followed by an overview of our empirical methodology and a discussion of the data and variables. We then present the cointegration analysis, which includes model selection and testing for cointegration, as well as the estimation of the long-run cointegrating vectors and speed-of-adjustment parameters. Next, we compute the equilibrium exchange rate—using the extracted permanent component of the fundamentals and the estimated cointegrating vectors—and the exchange rate misalignment. Finally, we offer some concluding remarks.
Theory and Empirical Formulation
Modeling Approaches to EREER Estimation
The literature offers a number of different approaches to calculating the EREER,3 among them traditional uncovered interest parity and purchasing power parity theories and more recent approaches, such as the fundamental equilibrium exchange rate approach, the underlying internal-external balance approach, and the behavioral equilibrium exchange rate approach.
The uncovered interest parity and purchasing power parity arbitrage conditions are common starting points when movements in the exchange rate are analyzed. The uncovered interest parity condition is more informative in explaining the rate of change (or the adjustment path back to equilibrium) than the level of the exchange rate. Uncovered interest parity by itself has not been successful at predicting exchange rate movements, partly because uncovered interest parity estimation does not account for possible shifts in the equilibrium exchange rate. Along the same lines, the purchasing power parity theory posits that price levels are equalized when measured in the same currency, which suggests that the real equilibrium exchange rate should be constant and equal to unity. However, empirical work on testing purchasing power parity (see, for example, Rogoff, 1996, and MacDonald, 2000) is not very supportive of the theory, which suggests that alternative approaches are needed. To explain the persistence in real exchange rates, it is possible to combine uncovered interest parity and purchasing power parity and estimate a cointegrating relationship among relative prices, nominal interest rate differentials, and the nominal exchange rate (see, for example, Johansen and Juselius, 1992). This approach is known as the capital enhanced equilibrium exchange rate (CHEER) approach, which has produced higher speed-of-convergence estimates than other simple purchasing power parity models.
Another popular approach used to estimate equilibrium exchange rates is the underlying internal-external balance (UIEB) approach (also known as the macroeconomic balance approach). This approach defines the equilibrium real exchange rate as the rate that satisfies both internal and external balance. For the underlying balance to hold, planned output must equal aggregate demand (the sum of domestic demand and net trade), with the real exchange rate playing the role of relative price, which must move to equilibrate demand and supply. The most popular variants of the UIEB approach are the fundamental equilibrium exchange rate (FEER) approach of Edwards (1989), Williamson (1994), and Wren-Lewis (1992), the desired equilibrium exchange rate (DEER) approach, and the natural real exchange rate (NATREX) approach of Stein (1994).4
Finally, a method with a shorter time horizon is the behavioral equilibrium exchange rate (BEER) approach associated with Clark and MacDonald (1999). BEER modeling aims to use a technique that captures movements in real exchange rates over time, not just movements in the medium- or long-term equilibrium level. Partly reflecting this, the emphasis in the BEER approach is largely empirical, with variables used to represent long-run fundamentals in the same way they would influence FEERs.
As Driver and Westaway (2004) emphasize, there is no single definition of “equilibrium exchange rate.” The choice of approach depends on the question of interest, and in particular the time horizon. In addition to methodological issues (for example, definition and measurement of the REER), the choice among approaches must therefore be made in terms of the question of interest. Approaches may differ, for example, in the treatment of dynamics and the time frame they concentrate on.
The FEER Approach
FEER is a well-recognized approach for calculating EREERs. It is particularly appropriate for assessing whether movements of the REER represent misalignments or signal that the EREER itself has shifted as a result of changes in economic fundamentals. The FEER methodology is well suited to our analysis for a number of reasons. First, traditional purchasing power parity and uncovered interest parity theories cannot be used. Testing the validity of purchasing power parity reduces to testing whether the REER series is stationary; this is easily refuted in the data, as the REER series contain a unit root, thus rejecting the purchasing power parity theory and its implications. Additionally, certain characteristics of the WAEMU economies (for example, the importance of a single commodity export, capital account restrictions, and the lack of a forward foreign exchange market) affect the plausibility of interest rate parities and uncovered interest parity. Second, the Edwards model was designed to describe nominal misalignments in fixed exchange rate regimes. Third, we believe that FEER model fundamentals represent more accurately the current situation of the WAEMU economies,5 and the FEER period of analysis (medium to longer run) is most relevant to our analysis.
The Edwards dynamic model of a three-good (exportables, importables, and nontradables) small open economy with a fixed exchange rate provides a coherent method of identifying the fundamental variables that are associated with the EREER.6 In that model, the equilibrium exchange rate is defined as the exchange rate that results when internal and external equilibria are attained simultaneously in an economy. Internal equilibrium is achieved when the market for nontradable goods clears in the present and is expected to clear in the future because price and wage flexibility ensure that the condition of internal balance (demand equal to supply) is satisfied. External equilibrium is achieved when the current account balance is “sustainable.” Since only real factors (the fundamentals) can influence the EREER, the model can be used to describe nominal misalignments by separating factors that can affect the long-run EREER, with permanent changes and short-run misalignments of the nominal exchange rate stemming from policy variables.
In the long run, the EREER is determined by the following fundamentals:7
e = e (terms of trade, government spendiing, trade controls, productivity, investment).
The model predictions suggest the following expected signs for the fundamentals:
- Terms of trade of goods. The terms of trade affect the REER through the wealth effect. A positive terms-of-trade shock induces an increase in domestic demand, hence an increase in the relative price of nontradable goods, which leads to a REER appreciation. Alternatively, viewed from an internal-external balance angle, an increase in the terms of trade leads to an increase in real wages of the export sector and a trade surplus. For external balance to be restored, the REER must appreciate. Hence, the expected sign is positive.
- Government spending. This is a proxy for government demand for nontradables. Changes in the composition of government spending affect the long-run equilibrium in different ways, depending on whether the spending is directed toward traded or nontraded goods.8 If government spending is primarily directed toward nontradable (tradable) goods, an increase in government consumption will result in an appreciation (depreciation) of the REER. The expected sign is ambiguous in the absence of a breakdown of government spending in tradable and nontradable goods.
- Degree of trade controls/restrictions. As trade controls or barriers are reduced, the total amount of trade is expected to increase. The demand for imports leads to external and internal imbalances that require a depreciation to correct. Therefore, the expected sign is negative. We proxy the reduction in trade controls and restrictions with openness.9
- Productivity. This captures the Balassa-Samuelson effect. An increase in the productivity of tradables versus nontradables of one country relative to a foreign country raises the first country’s relative wages. This increases the price of nontradables relative to that of tradables and, hence, causes a REER appreciation. The expected sign is positive.
- Investment. Edwards suggests that inclusion of investment in the theoretical model results in supply-side effects that are dependent on the relative factor intensities across sectors, and as a result, the expected sign may a priori be ambiguous. However, given developing country evidence that investment may have a high import content, a rise in the investment share of GDP could shift spending toward traded goods and thus depreciate the REER, suggesting an expected negative sign.
Overview of the Econometric Methodology
Our econometric estimation proceeds in several steps. In the first step, we model the REER as a function of a set of determinants motivated by the FEER approach, based on Edwards (1989).
In the second step, we establish whether a long-run relationship exists between the posited fundamentals and the REER, then estimate the relationship. An analysis of the exchange rate and its fundamentals usually suggests that the processes involved are nonstationary (or I(1)), which has implications with respect to the use of the appropriate statistical methodology. Estimating a regression of the exchange rate on the fundamentals using conventional methods like ordinary least squares may result in a spurious correlation problem because of the nonstationary nature of the data. Although running the regression in first differences of the data may correct for spurious correlations, it also removes any potential long-run relationship that may exist among the levels of the variables of interest, namely, the exact relationship we are interested in identifying and estimating.
One fruitful way to eliminate spurious correlations while maintaining the true long-run relationship between the exchange rate and the fundamentals is to estimate the model in a cointegration framework. Formally, two or more nonstationary series are said to be cointegrated if there exists a linear combination of them that is stationary. Intuitively, despite the fact that the exchange rate and the fundamentals are individually nonstationary, trending away from their initial values, they may move closely together in the long run, such that a linear combination of them is stationary. When this is true, the exchange rate and the fundamentals are said to be cointegrated. As a result, we examine the hypothesis that there exist economically meaningful linear combinations of the I(1) series that are stationary (or I(0)). Therefore, the Johansen (1988, 1991, 1995) maximum-likelihood procedure is first used to test for the existence of a long-run cointegrating relationship between the exchange rate and its fundamentals.
In the estimation’s third step, we compute the long-run (or equilibrium) levels of the fundamentals by extracting the permanent component of each of the series. Potential methods for estimating the permanent component of the fundamentals include the approaches of Hodrick and Prescott (1997), Quah (1992), Kasa (1992), and Gonzalo and Granger (1995). The Gonzalo-Granger method is the most theoretically appealing, because in that method, the decomposition is derived by construction so that the transitory component does not Granger-cause the permanent component in the long run, which implies that a temporary shock does not have a permanent effect on the series.
In the fourth and final step of our estimation, we combine the estimates of the long-run relationship between the fundamentals and the exchange rate with the extracted permanent component of the fundamentals to derive the long-run equilibrium path of the real effective exchange rate. Exchange rate misalignments (and associated error bands) are then computed.
Data and Univariate Analysis
We begin with a look at the data used in the empirical exercise, as knowledge of the time-series properties of the data will guide our modeling strategy. The theoretical background discussed in the previous section suggests focusing on the following variables: the natural logarithm of the real effective exchange rate (LREER), the natural logarithm of the terms of trade (LTTT), the natural logarithm of government consumption as a share of GDP (LNCGR), the natural logarithm of real GDP per capita relative to trading partners (LPROD) to capture the Balassa-Samuelson effect, the natural logarithm of openness to GDP (LOPEN), and the natural logarithm of the ratio of investment to GDP (LNIR).
The data sets for both the CEMAC and WAEMU regions consist of annual observations for the period 1970–2005.10 The real effective exchange rate and the fundamentals referred to in the last paragraph for the period 1975–2005 are plotted for the CEMAC and WAEMU regions in panels (a) and (b), respectively, of Figure 8.A.1. Some interesting patterns are worth highlighting. Economic performance under the CFA arrangement was initially favorable, with growth in line with experiences in other African countries but with markedly lower inflation. However, by the 1980s and early 1990s, increasing domestic and external imbalances emerged: high current account deficits, low levels of international reserves and pressures on the exchange rate eventually forced a devaluation of the CFA franc in 1994 by 50 percent vis-à-vis the French franc. This sole devaluation is generally seen as a success, as it restored external competitiveness in the region and supported a resumption of growth. In contrast, measures to enhance the resilience of the exchange arrangement seem to have had less of an impact. Efforts initiated in 1994 to deepen regional integration in the context of two common markets failed to increase internal trade and factor mobility. Similarly, notwithstanding free capital markets in the region, financial markets remain shallow and segmented.11
The 1994 devaluation was followed by a steady appreciation of the REER (see Table 8.A.1 and Figure 8.A.2). First, for CEMAC, the real effective exchange rate (REERC) appreciated cumulatively by about 33 percent through December 2000 and by a further 16 percent from January 2001 to December 2005 (the latest appreciation essentially owing to the strengthening of the euro, to which the CFA franc is pegged). By December 2005, REERC was at 85 percent of its predevaluation level. For WAEMU, the real effective exchange rate (REERW) appreciated cumulatively by about 22 percent through December 2000 and by a further 12 percent from January 2001 to December 2005. By December 2005, the REERW was at 76 percent of its predevaluation level.
We observe significant variations around the regional averages (see Figure 8.A.3). In the WAEMU region (panel (b)), Benin has experienced the highest appreciation since the 1994 devaluation and Senegal the lowest, with their REERs appreciating by December 2005 to between 58 percent (Senegal) and 91 percent (Benin) of their predevaluation levels. In the CEMAC region, there has been a somewhat wider variance in REERs compared to WAEMU, partly as a result of the new oil producers in that region. Equatorial Guinea had the highest appreciation (115 percent of its predevaluation level) and Gabon the lowest appreciation (70 percent of its predevaluation level) among CEMAC member countries over the period in question.
For both regions, we observe a persistent decline in real GDP per capita with respect to trading partners starting in about 1977 and continuing until the end of the sample period (see Figure 8.A.1); we also observe an increase in investment starting in the 1990s, and a quite volatile pattern of terms of trade, with an average increase in the 2000s as a result of favorable export commodity prices: oil for CEMAC and cotton, cocoa, and gold for WAEMU. Further, for the CEMAC region only, we observe a surge in foreign direct investment in 2000–03 associated with oil-related construction in Chad and Equatorial Guinea, whereas in WAEMU, foreign direct investment slowed during that period. Next, for CEMAC, government consumption was slightly increasing until about 1990 with a net decline since then. Finally, for WAEMU, there has been an overall decline in the government consumption ratio since the mid-1980s.
There are significant differences between the two regions. Within WAEMU some countries are semi-industrial and more developed than others (such as Senegal and Côte d’lvoire), and some are low-income landlocked countries close to the Sahara (Mali and Niger). WAEMU countries are net oil importers. The eight WAEMU countries had a total population of 76 million inhabitants in 2003 and a combined GDP of US$37 billion. This is about the same population and GDP as Vietnam. The six CEMAC countries had a total population of 34 million inhabitants in 2003 and a combined GDP of US$28 billion. This is about the same population as Tanzania, and the same GDP as Kazakhstan. With five of six CEMAC members now net oil exporters, economic developments and prospects in that region are dominated by oil market developments. Except for Cameroon, each CEMAC member country has a dominant export commodity accounting for 80 percent or more of total primary exports.
We now take a closer look at the univariate time-series properties of the data, which involves testing for unit roots or the order of integration of the various series under consideration. Figure 8.A.1 shows a somewhat trending behavior in the series, and the autocorrelations are quite strong and persistent. Nelson and Plosser (1982) find that many macroeconomic and aggregate level series are shown to be well modeled as stochastic trends, that is, integrated of order one, or I(1) Simple first-differencing of the data will remove the nonstationarity problem, but with a loss of generality regarding the long-run equilibrium relationships among the variables.
We performed the standard augmented Dickey-Fuller (ADF) tests on both levels and first differences of the variables of interest. Table 8.A.2 displays the results for the CEMAC and WAEMU samples. Based on those results, we cannot reject the null hypothesis of a unit root for all variables in levels. However, we can strongly reject the null of a unit root in first differences. Hence, we conclude that all our variables are I(1) in levels or, equivalently, stationary in first differences.12
Model Selection and Estimation
VAR Model Specification
The Johansen procedure begins with specifying a vector of variables Yt assumed to be in vector autoregressive form:
where Yt is a (6 x 1) vector:
π0 is a (6 x 1) vector of constants, πi are (6 x 6) matrices of coefficients on lags of Yt, Dt is a vector of dummy-type variables, p is the lag length, and et is a (6 x 1) vector of independent and identically distributed errors assumed to be normal with zero mean and covariance matrix Ω. As such, the VAR comprises a system of six equations, with the right-hand side of each equation comprising a common set of lagged and deterministic regressors.
For both CEMAC and WEAMU, the VARs include LREER and the five fundamentals—LTTT, LNCGR, LNIR, LPROD, and LOPEN13—as well as a constant term and dummy variables. For the CEMAC region, the VAR includes five impulse dummies, one each for 1994, 1976, 1978, 1985, and 2001; for WAEMU, the VAR includes three impulse dummies, one each for 1994, 1974 and 1979 together, and 2003.14
The use of these dummy variables can be justified on both economic and statistical grounds. Economically, for WAEMU, the impulse dummies for 1994, 1974 and 1979, and 2003, respectively, capture the devaluation, the first and second oil price shocks, and the Côte d’lvoire crisis. For CEMAC, the impulse dummy for 1994 captures the devaluation; the dummies for 1976 and 1978 capture large changes in the real GDP growth of Gabon (40 percent and -28 percent in 1976 and 1978, respectively); the dummy variable for 1985 primarily captures a favorable terms-of-trade effect in Cameroon right before the collapse of oil prices in 1986;15 and the dummy variable for 2001 captures the effect of the surge in foreign direct investment relating to oil construction and investment and, to some extent, a terms-of-trade increase. Statistically, an examination of the residuals of the VARs fitted without the impulse dummies reveals outliers in excess of three standard deviations and further induces misspecification in the residuals. The inclusion of the dummy variables results in a substantial improvement in the fit of the model, much better residual diagnostics, and statistically stable/constant VARs, as shown in the next subsection.16
Lag Length, Residual Diagnostics, and Model Constancy
The Johansen procedure assumes that the parameters of the VAR are constant over time and that VAR residuals are white noise. In addition, the lag length of the VAR is not known a priori, so some testing of lag order must be done. Therefore, prior to conducting the cointegration tests, the appropriate lag length of the VAR must be determined and a constant/stable model found. VAR residuals should also appear close to the assumption of white noise.
The number of lags to use in the VAR model is unknown at the beginning. A large number of lags is likely to produce an overparameterized model. Too few lags, on the other hand, may induce autocorrelation in the residuals and hence violate the assumption of white noise. Our selection methodology starts with a VAR with an initial maximum of p lags, which is assumed here to be three, given considerations surrounding data frequency and sample size. Then we estimate a VAR that includes two lags on each variable, denoted VAR(2), and test whether the simplification from the VAR with three lags, VAR(3), to VAR(2) is statistically valid. The process is repeated sequentially down to a VAR with a single lag, VAR(1). We select the VAR with the fewest number of lags that can reasonably explain the dynamics in the data system and that can produce residuals close to being white noise.
Table 8.A.3 reports F-statistics (and their associated p-values) for testing the validity of these simplifications. The F-statistic tests the null hypothesis that the data are generated by a VAR model with i lags, VAR(i), as opposed to a VAR model with a lag length that is greater than i, for i = (2, 1). For both WAEMU and CEMAC, the simplification from VAR(3) to VAR(2) is statistically valid, whereas for CEMAC the simplification from VAR(2) to VAR(1) is rejected at the 5 percent significance level, but for WAEMU, this simplification is accepted at the 5 percent level. Hence, we proceed with the analysis using the VAR(2) model for CEMAC and the VAR(1) model for WAEMU.
Table 8.A.4 reports residual diagnostic tests for the VAR(2) model for CEMAC and the VAR(1) model for WAEMU: a Breusch-Godfrey Lagrange multiplier (LM) test for serial autocorrelation up to the second lag, the Jarque-Bera test for normality, and White’s test for heteroscedasticity. The null hypotheses for these tests are, respectively, that no residual autocorrelation exists, that the residuals are normally distributed, and that no residual heteroscedasticity exists.17 None of the diagnostic tests reject the null hypothesis at the 5 percent significance level. Hence, the VAR residuals appear serially uncorrelated, normal, and homoscedastic.18
Although the VAR residual properties appear to meet the white-noise standard, the data-generating process may have undergone changes, raising concerns about the stability of the coefficient estimates. An important aspect of diagnostic checking is then to test for model constancy/stability. For that purpose, we employ recursive estimation techniques and conduct recursively estimated Chow tests.
The basic idea behind recursive estimation is to fit the VAR over an initial sample of observations, then fit it over successive time periods by increasing the sample size by one additional observation for each estimation. The last estimation involves the total sample size. Panels (a) and (b) of Figure 8.A.4 show the results from recursively estimating the CEMAC and WAEMU VARs, respectively. Specifically, the figure shows, for both CEMAC and WAEMU VARs, recursively estimated Chow statistics for each equation of the VAR (denoted Ndn plus the name of the associated variable) and for the VAR system as a whole (denoted Ndn CHOWs). For a given plot and year, the Chow statistic tests the null hypothesis that the coefficients estimated up to that year are the same as those estimated for the entire sample. The Chow statistics are normalized by the 1 percent critical value, so that the horizontal line at 1 gives the critical value. The results from the various plots strongly suggest that the estimated coefficients of the VARs are constant over time.19
In summary, the foregoing analysis indicates that the VARs for CEMAC and WAEMU are empirically well behaved and hence are suitable starting points for the cointegration analysis, which proceeds in several steps: testing for the existence of cointegration, interpreting and identifying the relationship(s), and performing inference tests on the coefficients from theory and weak exogeneity. Testing permits reduction of the unrestricted general model to a final restricted model without loss of information.
Vector Error Correction Representation
The VAR specification in Equation (8.1) provides the basis for cointegration analysis. Adding and subtracting various lags of Yt yields an expression for the VAR in first differences:
where Δ denotes the difference operator, Γi = -(πi+1 + … + πp) is a (6 x 6) coefficient matrix, and
where I is the identity matrix.
If π is a zero matrix, then modeling in first differences is appropriate. The matrix π may be of full rank or of rank less than full but greater than zero. When rank (π) = 6, then the original series are stationary; modeling in differences is unnecessary. But if 0 < rank(π) ≡ r < 6, then the matrix π can be expressed as the outer product of two full column rank (6 x r) matrices α and β where π = αβ’. This implies there are 6 - r unit roots in πY. The VAR model can then be expressed in error correction form:
The matrix β’ contains the cointegrating vector(s) and the matrix α has the weighting elements for the rth cointegrating relation in each equation of the VAR. The matrix rows of β’Yt-1 are normalized on the variable(s) of interest in the cointegrating relation(s) and interpreted as the deviation(s) from the long-run equilibrium condition(s). In this context, the columns of α represent the speed of adjustment to long-run equilibrium.20 The estimated vector ρ can be used to provide a measure of the equilibrium real exchange rate and also to quantify the misalignment gap between the prevailing real exchange rate and its equilibrium level. The estimated a captures the speed at which the real exchange rates converge to the equilibrium level.
Testing for Cointegration
Table 8.A.5 presents the initial tests for cointegration for the CEMAC and WAEMU samples. The table reports the trace and max-eigenvalue test statistics together with their associated p-values. The trace statistic tests the null hypothesis that there are at most r cointegrating vectors against the alternative that there are more than r cointegrating vectors, whereas the max-eigenvalue statistic tests the null that there are r cointegrating vectors against the alternative that r + 1 such vectors exist. The null hypothesis of no cointegration is strongly rejected by both test statistics for both samples. In addition, there is no evidence that more than one cointegrating vector exists. Therefore, we conclude that there exists one cointegrating vector for each sample.
Cointegrating Vectors and Speed of Adjustment
The Long-Run and Short-Run Relationships
The cointegration analysis suggests that there exists a long-run relationship between the REERs and their identified fundamentals for both the CEMAC and WAEMU regions. Table 8.1 displays the results of estimating the VARs/vector error correction mechanisms in Equation (8.3) for the CEMAC and WAEMU samples. The resulting cointegration equations are consistent with the predictions from economic theory, as the estimated coefficients (all representing elasticities) have the expected signs and are strongly significant.
The long-run relationship between the REER and the fundamentals variables is shown in the top panel of the table. For both the CEMAC and WAEMU samples: (1) the terms of trade are positively correlated with the REER, indicating that an improvement in terms of trade would result in an appreciation of the long-run EREER through a possible wealth effect; (2) government consumption has a positive (appreciating) impact on the REER, suggesting that most government spending is directed toward nontradables; (3) the relatively high long-term impact of technological progress (proxied by the relative real GDP per capita) confirms the Balassa-Samuelson effect; (4) investment is negatively correlated with the REER, confirming the hypothesis that investment shifts spending toward traded goods; and (5) increases in openness are associated with depreciation of the REER through increases in imports.
|ln(Real Effective Exchange Rate)||CEMAC||WAEMU|
|Estimates of the cointegrating relationships|
|ln(terms of trade)||0.70***||0.58***|
|Estimates of the feedback coefficients|
|D[ln(real effective exchange rate)]||-0.12**||-0.24***|
|D[ln(terms of trade)]||0.26||-0.15|
|Half-life of deviation||5.6||2.9|
However, there appear to be important differences in the marginal impact of the fundamentals on the REER for the two regions. For example, a 1 percent increase in technological progress is associated with a 0.59 percent appreciation of the REER in CEMAC but a mere 0.26 percent appreciation in WAEMU. Also, a 1 percent increase in the level of government consumption as a fraction of GDP is associated with a 0.4 percent appreciation of the REER in CEMAC but a 0.7 percent appreciation in WAEMU.
The bottom panel of the table shows the feedback coefficients. Some are estimated to be significantly different from zero, which suggests that the corresponding fundamentals are not weakly exogenous with respect to the parameters of the cointegrating vector, and in the face of any deviation from the long-run equilibrium, these variables jointly respond and move the system back to equilibrium. Furthermore, for both CEMAC and WAEMU, the feedback coefficient for the error correction equation (DLREER) is negative and significantly different from zero, suggesting stability of the error correction mechanism. In fact, these estimates suggest very different speeds of adjustment for the two regions. For the CEMAC region, on average, about 0.12 percent of the gap between the actual and equilibrium REER is eliminated every year, which implies that, in the absence of further shocks, about half of any gap would be closed within 5.6 years of the shock that induced it. However, for the WAEMU region, the adjustment is faster, with 0.24 percent of such a gap eliminated every year, implying that in the absence of further shocks, about half the gap would be closed within 2.9 years, almost half the time estimated for CEMAC. However, larger deviations (such as the ones caused by the 1994 devaluation) may take much longer to absorb. In comparison to those obtained in other studies, both the WAEMU and CEMAC adjustment speeds are reasonable.21
Impulse Response Analysis
To get a sense of the dynamic interaction of our variables, we conduct impulse response analysis using the cointegrated VAR model. Impulse response functions show how a shock to one of the fundamentals directly affects the fundamental itself and is transmitted to all of the other endogenous variables through the dynamic (lag) structure of the VAR. Figure 8.A.5 traces the effect of a one-time one-standard-deviation shock to one of the innovations of current and future values of the fundamentals on the impulse (and accumulated) response functions of the real effective exchange rate.22 For both CEMAC and WAEMU, the accumulated impulse response functions are consistent with the theoretical priors described in the long-run coefficients: positive investment and openness shocks have a long-run depreciating effect on the exchange rate, whereas the opposite is true for a positive terms of trade, government consumption, and productivity shocks. In addition, and in line with the findings regarding adjustment speed discussed previously, the WAEMU nonaccumulated impulse response functions stabilize in a much shorter period, in about half the time it takes the CEMAC impulse response functions to stabilize.
Estimation of Equilibrium
Extracting the Permanent Component of the Fundamentals
The presence of cointegration implies that the vector Yt may be thought of as being driven by a smaller number of common trends or permanent components. The permanent component YtP is taken to be the measure of equilibrium, whereas YtT measures transitory fluctuations. There are a number of alternative methods of extracting the permanent component of the series. All of these methods attempt to determine common trends driving the real exchange rate and other identified fundamentals and to identify real shocks, which are considered to be permanent, and nominal shocks, which are considered to be transitory.23
We apply two different decomposition methods to the fundamentals’ time series, namely, the Hodrick-Prescott (HP) (1997) filter and the Gonzalo-Granger (GG) (1995) decomposition. Construction of the permanent component of the fundamentals series using the HP filter has become a popular choice among business cycle analysts. The HP filter is obtained by solving the following minimization problem:
where λ is an arbitrary constant that penalizes the variability in the smoother so that when λ = 0 the smooth component is the data themselves and no smoothing takes place. Conversely, as λ grows large, the smooth component is a linear trend.
As can be seen from Equation (8.4), the flexibility of the HP filter is both a virtue and a downfall: the filter depends on the choice of λ, which makes the resulting cyclical component and its statistical properties highly sensitive to this choice. Further, it is not possible to calculate an approximately “optimal” λ, for each series via estimation. Although this method produces smooth permanent-component series, it lacks a sound theoretical basis. Therefore, we use it only for illustration purposes.24
The GG decomposition is more theoretically appealing. It is based on the assumption that shocks to the transitory component (that is, misalignments) do not affect the permanent component (that is, the equilibrium). The decomposition is derived so that first, the transitory component does not Granger-cause the permanent component in the long run and second, the permanent component is a linear combination of contemporaneous observed variables. The first restriction implies that changes in the transitory component will have no effect on the long-run values of the variables; the second restriction makes the permanent component observable and assumes that the contemporaneous observations contain all the information necessary to extract the permanent component.25 Drawing from Gonzalo and Granger (1995), a brief sketch of the GG procedure follows.
Continuing from the VECM in Equation (8.3), define the orthogonal complements α┴ and β┴ as the eigenvectors associated with the unit eigenvalues of the matrices I - α(α’α)-1α’ and I - β(β’β)-1β’, respectively, where α’┴α = 0 and β’┴β = 0. If the vector Yt is of reduced rank, Gonzalo and Granger (1995) show that the elements of Yt can be explained in terms of a smaller number (6 - r) of variables called common factors, ft, plus some I(0) components, and the transitory part, YtT:
If the common factors are linear combinations of the variables Yt so that ft = B1Yt and the permanent-transitory decomposition is given by Equation (8.5), then the only linear combination of Yt such that YT has no long-run impact on Yt is ft = α┴Yt. This identification of the common factors allows the decomposition of Yt into a permanent and a transitory part, as follows:
Gonzalo and Granger (1995) show that innovations to the transitory components of the endogenous variables do not affect the long-run (equilibrium) forecast for Yt captured by the permanent component. Thus, cyclical deviations of the fundamentals are removed in the construction of the equilibrium exchange rate. Defined this way, the transitory components will have no effect on the long-run values of the variables captured by the permanent components.
Further, following results in Proietti (1997) and Johansen (2001), it is possible to calculate error bands around the permanent component of the series.26 First, note that the moving-average representation for ΔYt in Equation (8.3) follows from the Granger Representation Theorem (see Johansen, 1995), with a solution for the levels, Yt, given by
where C(1) = β┴(α’┴Γ(1)β┴)-1α┴, C*(L) is a polynomial in the lag operator, η are deterministic variables, and A is a function of the initial conditions such that β’A = 0. The matrix C(1) measures the long-run effect of shocks to the system, and
is a function of the short-run coefficients. Then it can be shown that an equivalent decomposition to Equation (8.6) into stationary and nonstationary parts is
Finally, by means of Johansen (2001) and the permanent-transitory decomposition in Equation (8.8), error bands can be derived for the non-stationary component of the process. Let ei denote the unit vector. The 95 percent confidence interval associated with the permanent component of the ith variable is
Estimates of Misalignment
As discussed previously, we use two methods to derive the permanent component of the fundamentals: the HP filter (used for illustrative purposes only) and the GG decomposition (which is more theoretically appealing).27 The cointegrating vectors estimated earlier in the chapter and the extracted permanent component of the fundamentals are then combined to calculate the equilibrium real effective exchange rate. Finally, misalignments are calculated as the difference between the actual and equilibrium real effective exchange rates.
Panels (a) and (b) of Figure 8.1 display the evolution of the actual and the estimated EREER (using the HP filter) for the CEMAC and WAEMU regions, respectively, for the period 1985–2005. Panels (a) and (b) of Figure 8.2 apply the GG decomposition to construct the estimated EREER for CEMAC and WAEMU, respectively. Interestingly, although the HP filter method carries no theoretical basis, EREERs estimated using the HP method are very close to the ones estimated by the theoretically attractive GG decomposition (especially for CEMAC). Panels (a) and (b) of Figure 8.3 estimate the misalignments for CEMAC and WAEMU, respectively, along with the error bands derived using Equation (8.9), in order to identify statistically significant misalignment episodes.
The actual WAEMU and CEMAC REERs went through a period of overvaluation prior to 1994 (with the actual REERs well above the equilibrium level in the case of CEMAC, but less so for WAEMU), which suggests that the 1994 CFA devaluation was warranted. After 1994 and a few years of correction, both the CEMAC and WAEMU REERs remained, in principle, above their equilibrium levels for the rest of the period of analysis as a result of changes in the fundamentals, which differed for the two regions. In particular, the CEMAC REER temporarily exceeded its equilibrium level in 1999 and then again during the period 2001–04, with statistically significant misalignments during those episodes. In the case of WAEMU, there were no statistically significant misalignments after the devaluation until a short period in 2003–04. Finally, in 2005, our analysis shows that although both the CEMAC and WEAMU REERs were slightly above their estimated long-run equilibrium levels, neither of these overvaluations was statistically significant. This suggests that at end-2005, both the CEMAC and WAEMU REERs were broadly in line with their long-run equilibrium values.
Figure 8.1.Actual and Hodrick-Prescott Equilibrium Real Effective Exchange Rates
Taking the latter period of the sample (2000–05), it is useful to analyze the contribution of each of the fundamentals to the appreciation of the REERs.28 For WAEMU, in the period 2001–05, the REER appreciated by about 12 percent as a result of increases in the terms of trade and government consumption (accounting for an appreciation of the equilibrium real exchange rate on the order of about 9 percent each), and the increases in investment and openness and decreases in the productivity index contributed to REER depreciations of 2, 1, and 3 percent, respectively. In the case of CEMAC, the 13 percent appreciation of the REER in the 2001–05 period can be decomposed into an appreciation of about 23 percent as a result of increases in terms of trade and depreciations caused by government consumption and productivity decreases (2 percent and 7 percent, respectively) and an increase in openness (about 1 percent).
Figure 8.2.Actual and Gonzalo-Granger Equilibrium Real Effective Exchange Rates Figure 8.3.Estimated Misalignment Episodes
Using a dynamic model of a small open economy and the Johansen (1988) cointegration methodology, this chapter has analyzed the WAEMU and CEMAC regions’ equilibrium real effective exchange rates and assessed whether the movements in the aggregate real exchange rates are consistent with the underlying macroeconomic fundamentals. We have shown that much of the long-run behavior of the real effective exchange rates for the two regions can be explained by fluctuations in the terms of trade, government consumption, investment, openness, and productivity. Our analysis has pointed out, however, that although the paths of the two regions’ equilibrium exchange rates have evolved similarly, there are important differences in the marginal impacts of the fundamentals as well as the speed of adjustment to equilibrium in response to shocks, with the exchange rate in WAEMU reverting to equilibrium twice as fast as that in CEMAC.
Based on the estimated paths of the WAEMU and CEMAC equilibrium real effective exchange rates, there is a clear pattern of overvaluation before 1994 (suggesting that the exchange rate adjustment in that year was warranted). The real appreciation of the CFA exchange rate has brought the CEMAC and WAEMU REERs above their underlying long-run equilibrium values, as evident from the short periods of temporary overvaluations in the latter part of the period studied. Nevertheless, in 2005, the levels of the real effective exchange rates were in line with the estimated equilibrium real effective exchange rate paths, without any statistically significant misalignment.
A complete analysis of the environment that affects the short-term sus-tainability of the CFA franc arrangement would require an examination of possible pressures on balance of payments flows and reserve levels, losses of competitiveness, unfavorable market perceptions, and sustained deviations from equilibrium exchange rates. For the last of these, fixed exchange rate regimes can be sustainable in theory, as long as actual deviations from long-term equilibrium rates are small and mean-reverting. In contrast, if deviations are one-sided and build up to longer-term significant misalignments, it is generally argued that, in addition to demand-side management policies, real exchange rate action may be needed to restore balance.29
The data sets for both the CEMAC and WAEMU samples consist of annual observations for the period of 1970–2005. The regional aggregate variables for CEMAC and WAEMU were constructed using national annual observations and GDP weights. Equatorial Guinea did not join CEMAC until 1985 and was therefore excluded from analysis (and because of poor-quality data as well). Similarly, Guinea-Bissau was excluded from the WAEMU average, as it joined the union only in 1997.
The countries’ real effective exchange rate prior to 1980 was unavailable in the IMF’s Information Notice System database and was constructed based on consumer price indices from the World Economic Outlook with partner weights renormalized. The “foreign” variable (used for the calculation of the productivity proxy) was calculated as the renormalized weighted average of six trading partners based on the INS weights for the real effective exchange rate. For CEMAC, the partner countries (weights) were France (0.43), the United States (0.15), Germany (0.13), Japan (0.11), Italy (0.10), and Belgium (0.08). For WAEMU, the partner countries (weights) were France (0.42), Germany (0.15), the United States (0.14), Japan (0.11), Italy (0.10), and the Netherlands (0.09).
The variables used in the study presented in the chapter and the sources of data for each are as follows:
|LREER||Natural logarithm of the real effective exchange rate. Sources: IMF, Information Notice System and staff calculations.|
|LNCGR||Natural logarithm of ratio of public consumption expenditure to GDP. Source: IMF, World Economic Outlook.|
|LTTT||Natural logarithm of terms of trade. Source: IMF, World Economic Outlook.|
|LNIR||Natural logarithm of ratio of gross capital formation to GDP.|
|Source: IMF, World Economic Outlook.|
|LPROD||Natural logarithm of real per capita GDP relative to main trade partners, normalized to 1 in 2000 with weights as discussed in the chapter. Source: IMF, World Economic Outlook.|
|LOPEN||Natural logarithm of ratio of sum of exports and imports to GDP. Source: IMF, World Economic Outlook.|
|BFDIR||Ratio of net foreign direct investment (current prices) to GDP.|
|Source: IMF, World Economic Outlook.|
|January 1994-December 1998||January 1999-December 2000||January 2001-December 2005|
|Period percentage change|
|Real effective exchange rate||51.2||-11.3||13.4|
|Nominal effective exchange rate||15.2||-8.7||7.1|
|Relative price index||31.8||-2.3||5.8|
|Cumulative percentage change|
|Real effective exchange rate||42.9||-9.8||16.3|
|Nominal effective exchange rate||14.4||-7.4||10.0|
|Relative price index||28.7||-1.8||6.2|
|Period percentage change|
|Real effective exchange rate||35.4||-8.8||9.4|
|Nominal effective exchange rate||13.2||-8.2||7.0|
|Relative price index||25.4||0.0||0.6|
|Cumulative percentage change|
|Real effective exchange rate||31.0||-8.9||11.5|
|Nominal effective exchange rate||12.7||-8.3||8.5|
|Relative price index||23.0||0.9||0.5|
|VAR(3) to VAR(2)||F(36,15)||1.14||0.407|
|VAR(3) to VAR(1)||F(72,22)||1.64||0.096|
|VAR(2) to VAR(1)||F(36,42)||2.07||0.012y**|
|VAR(3) to VAR(2)||F(36,24)||1.38||0.205|
|VAR(3) to VAR(1)||F(72,33)||1.56||0.081|
|VAR(2) to VAR(1)||F(36,51)||1.53||0.080|
rejection of the null hypothesis at the 5 percent level of statistical significance.
rejection of the null hypothesis at the 5 percent level of statistical significance.
|Test and Equation||Value||p-value|
|AR 1-2 test [F(2,13)]|
|Normality test [%2(2)]|
|Heteroscedasticity test [%2(24)]|
|AR 1-2 test [F(2,23)]|
|Normality test [%2(2)]|
|Heteroscedasticity test [%2(12)]|
|Number of hypothesized cointegrating equations: CEMAC||Eigenvalue||Trace Statistic||p-value|
|At most 1||0.64||55.63||0.40|
|At most 2||0.50||32.34||0.60|
|At most 3||0.40||16.57||0.68|
|At most 4||0.16||4.71||0.84|
|At most 5||0.03||0.63||0.43|
|The trace test indicates one cointegrating equation at the 5 percent level of statistical significance.|
|At most 1||0.64||23.29||0.52|
|At most 2||0.50||15.77||0.69|
|At most 3||0.40||11.86||0.57|
|At most 4||0.16||4.08||0.84|
|At most 5||0.03||0.63||0.43|
|The max-eigenvalue test indicates one cointegrating equation at the 5 percent level of statistical significance.|
|Number of hypothesized cointegrating equations: WAEMU||Eigenvalue||Trace Statistic||p-value|
|At most 1||0.54||49.03||0.68|
|At most 2||0.38||26.73||0.86|
|At most 3||0.26||12.78||0.90|
|At most 4||0.12||4.17||0.88|
|At most 5||0.01||0.31||0.58|
|The trace test indicates one cointegrating equation at the 5 percent level of statistical significance.|
|At most 1||0.54||22.30||0.60|
|At most 2||0.38||13.95||0.82|
|At most 3||0.26||8.60||0.86|
|At most 4||0.12||3.87||0.87|
|At most 5||0.01||0.31||0.58|
|The max-eigenvalue test indicates one cointegrating equation at the 1 percent level of statistical significance.|Figure 8.A.1.Cointegration Variables Figure 8.A.2.Exchange Rates and Relative Prices Figure 8.A.3.Real Effective Exchange Rates of Member Countries Figure 8.A.4.Model Stability Tests Figure 8.A.5.Impulse Response Functions
- Search Google Scholar
- Export Citation
AbdihY. and C.Tsangarides2006“FEER for the CFA Franc,”IMF Working Paper 06/236 (Washington: International Monetary Fund).
AcemogluD.S.JohnsonJ.A.Robinson and Y.Thaicharoen2003“Institutional Causes, Macroeconomic Symptoms: Volatility, Crises and Growth,”Journal of Monetary EconomicsVol. 50 (January) pp. 49–123.
AlberolaE.S.GarciaCerveroJ.H.Lopez and A.Ubide1999“Global Equilibrium Exchange Rates—Euro, Dollar, ‘Ins,’ ‘Outs,’ and Other Major Currencies in a Panel Cointegration Framework,”IMF Working Paper 99/175 (Washington: International Monetary Fund).
CashinP.L.Cespedes and R.Sahay2002“Keynes, Cocoa, and Copper: In Search of Commodity Currencies,”IMF Working Paper 02/223 (Washington: International Monetary Fund).
CerraV. and S.C.Saxena2002“What Caused the 1991 Currency Crisis in India?”IMF Staff PapersVol. 49 (September) pp. 395–425.
ClarkP.B. and R.MacDonald1999“Exchange Rates and Economic Fundamentals: A Methodological Comparison of Beers and Feers,” in Equilibrium Exchange Ratesed. by R.MacDonald and J.L.Stein (Norwell, Massachusetts: Kluwer Academic Publishers).
DavidsonJ.E.H.D.F.HendryF.Srba and J.S.Yeo1978“Econometric Modelling of the Aggregate Time-Series Relationship Between Consumers’ Expenditure and Income in the United Kingdom,”Economic JournalVol. 88 (December) pp. 661–92.
DoornikJ.A. and D.F.Hendry2001Modeling Dynamic Systems Using PcGive 10Vol. 2 (London: Timberlake Consultants Press).
DornbuschR.1982“Stabilization Policies in Developing Countries: What Have We Learned?”World DevelopmentVol. 10 (September) pp. 701–708.
DriverR.L. and P.F.Westaway2004“Concepts of Equilibrium Exchange Rates,”Working Paper No. 248 (London: Bank of England).
EasterlyW. and R.Levine2003“Tropics, Germs, and Crops: How Endowments Influence Economic Development,”Journal of Monetary EconomicsVol. 50 (January) pp. 3–39.
EdwardsS.1989Real Exchange Rates Devaluation and Adjustment: Exchange Rate Policy in Developing Countries (Cambridge, Massachusetts: MIT Press).
EdwardsS.1994“Real and Monetary Detriments of Real Exchange Rate Behavior: Theory and Evidence from Developing Countries,” in Estimating Equilibrium Exchange Ratesed. by J.Williamson (Washington: Institute for International Economics).
EdwardsS.and S. van Wijnbergen,1986“The Welfare Effects of Trade and Capital Market Liberalization,”International Economic ReviewVol. 27 (February) pp. 141–48.
ElbadawiI. and N.Majd1996“Adjustment and Economic Performance Under a Fixed Exchange Rate: A Comparative Analysis of the CFA Zone,”World DevelopmentVol. 24 (May) pp. 939–51.
EngelsF.P.Konstantinou and J.Sondegaard2005“The UK Productivity Slowdown and the Strength of the Sterling”(unpublished).
FaruqeeH.P.Isard and P.R.Masson1999“A Macroeconomic Balance Framework for Estimating Equilibrium Exchange Rates,” in Equilibrium Exchange Ratesed. by R.MacDonald and J.L.Stein (Norwell, Massachusetts: Kluwer Academic Publishers).
FoudaS. and D.Stasavage2000“The CFA Franc Zone After EMU: Status Quo, Reform, or Dissolution?”World EconomyVol. 23 (February) pp. 221–33.
GonzaloJ. and C.Granger1995“Estimation of Common Long-Memory Components in Cointegrated Systems,”Journal of Business and Economic StatisticsVol. 13 (January) pp. 27–35.
HadjimichaelM.T. and M.Galy1997“The CFA Franc Zone and the EMU,”IMF Working Paper 97/156 (Washington: International Monetary Fund).
HarbergerA.1986“Economic Adjustment and the Real Exchange Rate,” in Economic Adjustment and Exchange Rates in Developing Countriesed. by S.Edwards and L.Ahamed (Chicago: University of Chicago Press).
HinkleL. and P.J.Montiel1999Exchange Rate Misalignment: Concepts and Measurement for Developing Countries (Washington: World Bank).
HodrickR.J. and E.C.Prescott1997“Postwar U.S. Business Cycles: An Empirical Investigation,”Journal of Money Credit and BankingVol. 29 (February) pp. 1–16.
JohansenS.1988“Statistical Analysis of Cointegrating Vectors,”Journal of Economic Dynamics and ControlVol. 12 (June-September) pp. 231–54.
JohansenS.1991“Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models,”EconometricaVol. 59 (November) pp. 1551–80.
JohansenS.1995Likelihood-Based Inference in Cointegrated Vector Autoregressive Models (Oxford: Oxford University Press).
JohansenS.2001“The Interpretation of Common Trends, Impulse Responses and Cointegrating Coefficients in the Cointegrated VAR Model”(unpublished).
JohansenS.and K. Juselius,1992“Testing Structural Hypotheses in a Multivariate Cointegration Analysis of the PPP and the UIP for UK,”Journal of EconometricsVol. 53 (June-September) pp. 211–44.
JPMorgan2000“An Introduction to J.P. Morgan’s Emerging Markets Real Exchange Rate Model: Theory and Econometrics” (New York).
KasaK.1992“Common Stochastic Trends in International Stock Markets,”Journal of Monetary EconomicsVol. 29 (February) pp. 95–124.
MacDonaldR.2000“Concepts to Calculate Equilibrium Exchange Rates: An Overview,”Economic Research Group, Discussion Paper No. 3/00 (Frankfurt: Deutsche Bundesbank).
MacDonaldR. and L.Ricci2003“Estimation of the Equilibrium Real Exchange Rate for South Africa,”IMF Working Paper 03/44 (Washington: International Monetary Fund).
MacDonaldR. and J.L.Stein1999Equilibrium Exchange Rates (Boston: Kluwer Academic).
MaravallA.1993“Stochastic Linear Trends: Models and Estimators,”Journal of EconometricsVol. 56 (March) pp. 5–37.
MassonP. and C.Pattillo2001Monetary Union in West Africa (ECOWAS)?IMF Occasional Paper No. 204 (Washington: International Monetary Fund).
MassonP. and C.Pattillo2004The Monetary Geography of Africa (Washington: Brookings Institution Press).
MathisenJ.2003“Estimation of the Equilibrium Real Exchange Rate for Malawi,”IMF Working Paper 03/104 (Washington: International Monetary Fund).
MontielP.J.1999“The Long-Run Equilibrium Real Exchange Rate: An Analytical Model,” in Exchange Rate Misalignment: Concepts and Measurement for Developing Countriesed.L.E.Hinkle and J.P.Montiel (Washington: World Bank).
MussaM.1974“Tariffs and the Distribution of Income: The Importance of Factor Specificity, Substitutability and Intensity in the Short and Long Run,”Journal of Political EconomyVol. 82 (November-December) pp. 1191–204.
NelsonC.R. and C.R.Plosser1982“Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications,”Journal of Monetary EconomicsVol. 10No. 2 pp. 139–62.
ObstfeldM. and K.Rogoff1996Foundations of International Macroeconomics (Cambridge,Massachusetts: MIT Press).
OsbatC.R.Ruffer and B.Schnatz2003“The Rise of the Yen vis-à-vis the (‘Synthetic’) Euro: Is It Supported by Economic Fundamentals?”ECB Working Paper SeriesNo. 224 (Frankfurt am Main: European Central Bank).
PesaranM.H. and Y.Shin1998“An Autoregressive Distribution-Lag Modelling Approach to Cointegration Analysis,” in Econometrics and Economic Theory in the 20th Century: The Ragnar Frisch Centennial Symposiumed. by S.Strom (Cambridge: Cambridge University Press), pp. 371–413.
ProiettiT.1997“Short-Run Dynamics in Cointegrated Systems,”Oxford Bulletin of Economics and StatisticsVol. 59 (August) pp. 405–22.
QuahD.1992“The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds,”EconometricaVol. 60 (January) pp. 107–18.
RogoffK.1996“The Purchasing Power Parity Puzzle,”Journal of Economic LiteratureVol. 34 (June) pp. 647–68.
SarnoL. and M.Taylor2002The Economics of Exchange Rates (Cambridge: Cambridge University Press).
StasavageD.1997“The CFA Franc Zone and Fiscal Discipline,”Journal of African EconomiesVol. 6 (March) pp. 132–67.
SteinJ.L.1994“The Natural Real Exchange Rate of the US Dollar and Determinants of Capital Flows,” in Estimating Equilibrium Exchange Ratesed. by J.Williamson (Washington: Institute for International Economics), pp. 133–76.
WilliamsonJ.1994“Estimates of FEERs,” in Estimating Equilibrium Exchange Ratesed. by J.Williamson (Washington: Institute for International Economics), pp. 177–243.
Wren-LewisS.1992“On the Analytical Foundations of the Fundamental Equilibrium Exchange Rate,” in Macroeconomic Modelling of the Long Runed. by C.P.Hargreaves (Aldershot,U.K.: Edward Elgar).
CEMAC includes Cameroon, the Central African Republic, Chad, Republic of Congo, Equatorial Guinea, and Gabon. WAEMU includes Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau, Mali, Niger, Senegal, and Togo. Strictly speaking, there are two different currencies called CFA franc, the West African CFA franc and the Central African CFA franc. In fact, they are distinguished only by the meaning of the abbreviation CFAF. In the West African union, CFAF stands for franc de la Communauté Financière de l’Afrique, and in the Central Africa union, CFAF stands for franc de la Cooperation Financière Africaine.
Driver and Westaway (2004) provide a complete taxonomy of the different empirical approaches on equilibrium exchange rate estimation used in the literature.
In the DEER approach, the theoretical assumptions are as in FEER, but the external balance is based on optimal policy. The NATREX approach has a longer time horizon than the FEER and DEER approaches and adds the assumption of portfolio balance.
The equation that underpins BEER analysis suggests that the REER set of fundamentals includes real interest rate differentials, terms of trade, net foreign assets, and government debt, and the horizon of the analysis is shorter. Some of the BEER model fundamentals may have been more relevant for our sample of countries in the pre-1994 years (given the significantly high debt levels).
An increase in the REER is defined as an appreciation.
See, for example, Montiel (1999) for a discussion on this. It is worth noting, however, that most empirical studies using this framework tend to find a positive relationship between the REER and government consumption.
Openness as a measure of trade restrictions is used by Montiel (1999). Edwards (1989) uses two alternative measures (import tariffs, as ratio of tariff revenues, and the spread between the parallel and official rates), which he acknowledges to have important limitations.
The ADF test results in Table 8.A.2 are based on a specification with a constant term included (see the table’s notes). We experimented with specifications that include both a constant and a deterministic time trend. The results were virtually unchanged from those reported in Table 8.A.2.
Recall that all the variables are in natural logarithm.
Impulse dummies take the value of one for the year(s) they represent and zero otherwise.
Cameroon started oil production in 1976, reaching a peak in 1985. Oil production steadily declined through the mid-1990s.
We thank David Hendry for his suggestions on the inclusion of dummy variables.
These diagnostic tests are performed on each equation of the VAR separately. Vector/system tests performed on the entire system yield the same results as single-equation tests.
If the coefficient is zero in a particular equation, that variable is considered to be weakly exogenous, and the VAR can be conditioned on that variable.
Mathisen (2003) and Cashin, Cespedes, and Sahay (2002) estimate an adjustment speed with half-life of less than a year for Malawi; MacDonald and Ricci (2003) estimate a half-life of two to two-and-a-half years for South Africa; Rogoff (1996) estimates a longer half-life of three to five years.
Generalized impulses are used. As described by Pesaran and Shin (1998), this method constructs an orthogonal set of innovations that does not depend on the VAR ordering.
Moreover, as also discussed in Cerra and Saxena (2002), if simple smoothing processes were sufficient to arrive at the equilibrium values for the fundamental series, then presumably the same smoothing process could be employed to arrive at the equilibrium real exchange rate series, without the need for the VECM estimation.
This approach has been used by Osbat, Ruffer, and Schnatz (2003) and Engels, Konstantinou, and Sondegaard (2005). Another methodology for constructing asymptotic standard errors for the GG decomposition is discussed and applied in Alberola and others (1999).
As discussed, the choice of the degree of smoothing is arbitrary, with larger (smaller) factors generating smoother (less smooth) equilibrium real exchange rate paths. As a robustness check, the equilibrium real exchange rates in Figure 8.1 are derived by applying to the explanatory variables an HP filter based on the average of five smoothing factors (10, 30, 50, 100, and 300).
This analysis is based on estimated elasticities and estimates of cumulative variable changes, similar to “sources of growth” accounting. Owing to the associated residuals, the magnitudes of the REER appreciations discussed here may not be directly comparable to those presented in Table 8.A.1.