Real Exchange Rate Misalignment: A Panel Co-Integration and Common Factor Analysis

Etienne B Yehoue; Gilles J. Dufrénot

doi:10.5089/9781451861839.001.A001

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Real Exchange Rate Misalignment

A Panel Co-Integration and Common Factor Analysis

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Mr. Etienne B Yehoue

Mr. Etienne B Yehoue
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Gilles J. Dufrénot

Gilles J. Dufrénot https://isni.org/isni/0000000404811396 International Monetary Fund

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Contributor Notes

Author(s) E-Mail Address: lopaduf@aol.com, eyehoue@imf.org

Publication Date:: 01 Aug 2005

eISBN:: 9781451861839

Language:: English

Keywords:: WP; terms of trade; time series; income effect; time series technique; level of significance; moving average; integration estimator

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We combine some newly developed panel co-integration techniques and common factor analysis to analyze the behavior of the real exchange rate (RER) in a sample of 64 developing countries. We study the dynamic of the RER with its economic fundamentals: productivity, the terms of trade, openness, and government spending. We derive a number of common factors that explain the dynamic of the RER in our sample. We find that while some fundamentals such as productivity, terms of trade, and openness are strongly related to these common factors in low-income countries, no such link is found for the middle-income countries. We also derive the misalignment indices, which seem to reproduce recent episodes of overvaluation and undervaluation in a number of countries.

Abstract

I. Introduction

Research related to exchange rate management still remains of interest to economists, despite a relatively vast literature that exists in the area. The real exchange rate (RER)² is not only an important relative price, but also signals the competitiveness of a country vis-à-vis the rest of the world. A number of papers have found that the level of the RER relative to an equilibrium RER, and its stability, importantly influence exports and private investment (e.g., Caballero and Corbo, 1989; Serven and Solimano, 1991). Díaz-Alejandro (1984), drawing from the experience of Latin America, argues that RER misalignment and especially overvaluation with respect to the equilibrium RER can be detrimental to an export-oriented development strategy.

The measurement of the RER misalignment for appropriate policy intervention is then an important issue. However, the literature in this area has not reached a clear consensus. This is because measuring the degree of misalignment is difficult, as it involves measuring an unobserved variable, the equilibrium RER. For many years, policymakers have been relying on a misalignment measure based on the so-called purchasing power parity (PPP) doctrine. It consists of the choice of a base period in which the economy is thought to have been in equilibrium, and then the RER for this year is assumed to be the equilibrium for the rest of the sample period.

This approach is obviously questionable because the equilibrium RER is not a static indicator and moves over time as the economy’s fundamentals move. As a consequence, and rightly pointed out by Elbadawi (1994), the PPP approach runs the risk of identifying as a misalignment what may in fact be an equilibrium movement in the RER.³

Given the limitations of the PPP approach, the 1980s witnessed the emergence of a new literature that tried to estimate the equilibrium exchange rate. It consists of estimating the equilibrium exchange rate using economy fundamentals. Since most of the macroeconomic variables—especially the real exchange rate—are nonstationary, the estimation requires some time series techniques. As a consequence, most studies estimating the equilibrium exchange rate in the 1980s and 1990s focused on individual countries and time series data (e.g., Williamson, 1994). But most of these studies, especially those concerning developing countries where data availability goes back only to the 1960s or 1970s, have to use short time series data or a small sample for the estimation. The consequence is that most of these estimations run the risk of not being robust, leading to nonreliable measures of misalignment. For example, the situation in the CFA zones prior to the 1994 devaluation illustrates this problem. While most observers agreed that the RER in the CFA zones was overvalued, they disagreed on the extent of the overvaluation. This is important, as it determines the degree of policy intervention or devaluation needed. Hence the need to develop empirical models that will deliver reliable measures of misalignment.

Recently, econometric theorists have developed new methods that help to apply some time series techniques to panel data (e.g., Breitung, 2002; Im et al, 2003; Kao and Chiang, 2000). This has reenergized the empirical literature estimating the equilibrium real exchange. As a result, there are some very recent studies estimating the equilibrium RER where countries are pooled and time series techniques are applied to panel data (e.g., Calderon, 2002). However, this very recent literature, which uses panel data co-integration techniques, has not included other shocks such as government shocks that generate deviation from the long-run PPP. This literature also has not taken advantage of the use of factor analysis that allows us to examine the common factors that explain these deviations.

In this paper, we hope to contribute to this literature by tackling these issues. In particular, we implement an empirical analysis that makes use of the new panel data co-integration techniques and includes government shocks. Most importantly, we improve the evaluation of the real exchange rate deviations from the equilibrium by testing the existence of common factors explaining these deviations.

We follow Edwards (1989), and refer to the equilibrium RER as that which prevails when for given sustainable values for other relevant variables, such as terms of trade, capital and aid flows, and technology, the economy achieves both internal and external equilibrium. For our panel unit root analysis, we use both the panel unit root tests proposed by Im, Pesaran, and Shin (1997), and Hadri and Larsson (2001). We make use of the latter, in addition to the former, because it avoids the lack of power for the test by assuming stationarity under the null hypothesis, and is particularly suitable for panel data series with short time dimension, which is the case in this paper.

Given our panel analysis, we pay special attention to the heterogeneity issue. We show evidence of heterogeneous co-integration relationships by comparing the results from a pooled-based estimator with those obtained with an average-based estimator and also by conducting a common factor analysis. This leads us to conclude that a homogenous equilibrium exchange rate is unlikely to exist in panels of developing countries. This directly implies that calculations of misalignment must be based on the average of the individual exchange rate deviations.

In particular, an in-depth evaluation using our common factor analysis reveals that there exists a relatively low degree of homogeneity with regard to the dynamic of the RER in middle-income countries compared to that in low-income countries. Indeed, we find that for the latter there are about 6 or 7 common factors explaining the dynamics of the RER, while this number is only about 4 or 5 for the middle-income countries. We analyze whether these common factors are related to the key fundamentals of the RER. Our results reveal that while some fundamentals, such as productivity, terms of trade, and openness, are strongly related to our common factors in the low-income countries, no such link is found between fundamentals and common factors in the middle-income countries. In other words, while some fundamentals might account for the joint dynamics of the real exchange rate in low-income countries, the RER dynamics in middle-income countries seem to be governed by more heterogeneity.

Based on this analysis, we derive RER misalignments. They show a remarkable success in reproducing the well-known overvaluation and undervaluation episodes in the recent macroeconomic history of a selected number of countries in our sample.

The rest of the paper is organized as follows. The next section specifies the empirical model. Section III describes the data and presents the panel unit root tests. Section IV presents the panel co-integration tests and estimations. Section V lays out the common factor analysis. Section VI analyzes the dynamic of the real exchange rate misalignment. Section VII concludes.

II. Specifying an Empirical Model

Consider N countries with T observations each, the joint distribution of the RER, its fundamentals, and short-run variables can be represented by a vector autoregression (VAR) of finite order p, which in turn has an unrestricted vector error-correction representation of the following form.

\begin{matrix} Δ y_{i t} = α_{i} + ϕ_{i} y_{i t - 1} + β_{i}^{'} X_{i t - 1} + \sum_{j = 1}^{p} δ_{i j} Δ y_{i t - j} + \sum_{k = 1}^{q} ϒ_{i k}^{'} Δ X_{i t - k} + ε_{i t}, & (1) \end{matrix}

where y is the logarithm of the RER and X is the vector of fundamentals and short-run variables which will be described below; i = 1,…, N and t = 1,…, T. This equation says that the RER varies with economic fundamentals. Short-run influences are captured by coefficients in the vector γ_ik. The real exchange rate’s short-term variations can be more or less persistent depending upon the values of the set of parameters δ_ij. For instance, if p = 1, a value of δ_i1 near 1 will lead to very persistent adjustment dynamics. It is also important to know whether the exchange rate evolves toward a target value. This target value can be represented as the value compatible with the level of macroeconomic fundamentals in the long run. Since in the long run none of the variables changes, we can put all the variables expressed in variations equal to zero which yields:

\begin{matrix} y_{i t} \equiv - (β_{i}^{'} / ϕ_{i}) X_{i t □} & (2) \end{matrix}

The double index ij refers to a country i observed at time t. ε_it is a disturbance term distributed as N(0,Ω_i), where Ω_i is the variance-covariance matrix of the elements of the residuals; γ_i and β_i are m×1 vectors where m is the number of regressors. This equation is the long-run co-integration relationship. A central problem is to obtain estimates of the coefficients that are unbiased and consistent.

A direct application of the OLS estimator indeed yields biased estimates (usually, strong autocorrelations remain in the estimated residuals and further, some bias occurs if some of the regressors are not deterministic). Correction methods are twofold. Some are based on parametric regressions (for instance, Stock and Watson (1993) DOLS estimator can be transposed to panels), while others uses nonparametric estimators (for instance, a commonly used estimator is the fully modified OLS estimator).

In practice, equation (1) can be estimated using an approach with two steps. In a first step, a long-run (static) equation is estimated by regressing the current values of the RER on the contemporaneous values of its fundamentals. In a second step, the residuals of this estimation are introduced in a dynamic short-run equation to form an error-correction model. In this paper, we shall concentrate on the first step given that the aim of the paper is to show evidence of heterogeneous long-run relationships between the RER and its fundamentals.

The exogenous variables used in this paper include the terms of trade (TOT), the degree of openness (OPEN), government spending (GOV), and productivity (PROD). Theoretically, the terms of trade’s influence on the RER cannot be signed a priori, as this depends on whether income or substitution effects dominate. The former leads to real currency appreciation (increase in RER) while the latter to real currency depreciation (decrease in RER). An increase in the openness variable is assumed to be arising from a decline in tariff rates, leading to a fall in the domestic prices of importables. This will lead to high demand of foreign currency (to take advantage of cheap imports), and less demand for domestic currency. Hence an increase in the degree of openness is expected to lead to the depreciation of the equilibrium real effective exchange rate. As a result, the openness variable is expected to carry a negative sign.

High government spending is likely to translate into high demand of nontradables, which would lead to a rise in the price of nontradables. According to the definition of RER that we use, which is the ratio of the domestic consumer price index (CPI) to the foreign consumer price index, this will lead to a real appreciation. We expect this variable to be positively signed. Similarly high productivity will make the economy stronger leading to an appreciated equilibrium RER, hence we expect it to carry a positive sign.

In addition to the fundamentals mentioned above, we also introduce a number of control variables. They include net foreign asset payments (NFA), official development assistance (ODA), change in the level of reserve (RESERV), nominal devaluation (DEVAL), and MACRO, which is defined as the ratio of the change in domestic credit to lagged money supply. Higher net foreign asset payments from abroad would lead to higher capital inflows with an upward pressure on the exchange rate. We expect this variable to be positively signed. We also expect the ODA to influence the exchange rate, as a high level of ODA will lead to capital inflows and a high demand of domestic currency leading to an appreciation. Thus, we expect this variable to carry a positive sign. For the same level of money supply, we expect an increase in level of reserve to lead to a currency appreciation. The rate of nominal devaluation is expected to carry a negative sign as it leads to real currency depreciation. Finally, MACRO is an indicator of monetary policy. A high level of this ratio strengthens the central bank balance sheet position, and is expected to lead to a real currency appreciation.

III. Data and Panel Unit Root Tests

A. Data Description

To determine the extent of misalignment, we first need to establish the long-run relationship between the real effective exchange rate and its determinants. To do so, we pool a sample of 64 countries across the world over the period 1979-2000. In what follows, we present the definition and sources of data used in the empirical evaluation.

The dependent variable is the real effective exchange rate. It is the CPI-based multilateral real effective exchange rate. The RER is defined as the ratio of the domestic consumer price index to the foreign consumer price index. The real effective exchange rate is constructed as the trade-weighted average of the real exchange rate where the weights are generated by the IMF based on both bilateral trade shares and export similarity. According to the definition, an increase in the real exchange rate implies a real appreciation of the domestic currency. Data on this variable are from the IMF.

We follow the literature and use a number of fundamentals for the equilibrium exchange rate. They include the terms of trade, the degree of openness of the economy captured by trade, the productivity, and foreign asset interest payments. In our empirical implementation, the terms of trade is defined as the ratio of export price index to import price index. Data on this variable are drawn from the World Bank database. The second fundamental—the extent of openness—is computed as the ratio of the sum of export and import to the gross domestic product (GDP). Data on trade and GDP are from the World Bank.

Concerning the relative productivity, we compute the ratio of GNP per worker for each country in our sample to the GNP per worker in Group of Seven (G-7) countries. To do this, we collect data on labor force and GNP for each country in our sample from the Global Development Finance. We compute the ratio of GNP to labor force to get data on GNP per worker. We apply the same method to the G-7 countries to compute their GNP per worker. We use these two measures to compute the productivity.

With regard to net foreign assets, we use net income from abroad as a proxy. It would be nicer to use the new and cleaner data on foreign assets computed by Kraay, Loayza, Serven, and Ventura (2000), and data on the international interest rate to compute net foreign assets. However, their data cover only 7 countries out of 64 in our sample, and for the moment, there are no complete data on the intermediate variables we need to construct data on foreign asset using their method. We then simply use data on the net income from abroad (NFA) from the World Bank database. It enters as a ratio of GNP.

As government shocks can generate deviations from the long-run PPP, we are also interested in measuring how government spending will affect the equilibrium real exchange especially in this new empirical implementation. We extract data on government spending from the IMF’s International Financial Statistics (IFS). It enters in our regression as a ratio of GNP. Beyond the determinants described above, we also use other variables related to the capital account such as the official development assistance (as a share of GNP). In addition, some monetary policy-related variables—such as the ratio of the change in domestic credit to lagged money supply (MACRO) and nominal devaluation—are also used. The determinants such—as terms of trade, openness, and government spending—enter in our regressions through a logarithmic transformation.

B. Panel Unit Root Tests

A first step before estimating a long-run relationship between the real exchange rate and its determinants is to test for the stationarity of the individual variables. In this paper, we apply two tests proposed respectively by Im, Pesaran, and Shin (1997) (IPS), and Hadri and Larsson (2001) (HL).⁴ The results are shown in Tables 1-4. One observes that the IPS statistics lead one to conclude against the presence of a unit root, thereby implying that the variables are, in general, I(0). However, such a conclusion is neither economically meaningful nor statistically reliable. From a statistical viewpoint, we know that tests based on the null of unit root have low power compared to other tests such as mixing tests.

Table 1.

Panel Unit Root Tests —All Countries

^{^*}The critical value is -2.46 (model with an intercept and a linear time trend) at the 5% level of significance (N=21 and T=22).