Do real exchange rates follow a nonlinear mean reverting process in developing countries?

• Author: Bahmani-Oskooee, Mohsen

1. Introduction

   The debate on the validity of the purchasing power parity (PPP) hypothesis continues. To test PPP, many researchers rely on evidence from unit root tests regarding the (non) stationarity of real exchange rates (RER). Initial studies, which were based on the augmented Dickey-Fuller (ADF) tests, showed evidence against the theory. The failure of validating PPP has been attributed to the low power of these tests. As a result, the literature has moved on in two new directions: While some researchers have turned to panel unit root tests, others have proposed alternative tests that emphasize a nonlinear stationary process. (1)

   Using either panel or nonlinear unit root tests, several studies have provided fresh evidence on the validity of ppp. (2) However, these studies focus mainly on industrial countries. Empirical evidence on PPP in developing countries has been scant, especially using the recent tests that have higher power against the conventional ADF tests. In the present paper, we fill this gap in the literature by providing comprehensive evidence on the validity of PPP in 88 developing economies. To do so, we use the recently developed exponential smooth transition autoregressive (ESTAR) procedure introduced by Kapetanios, Shin, and Snell (KSS, hereafter) (2003). They have developed a new technique for the null hypothesis of a unit root against an alternative of nonlinear smooth exponential autoregressive (STAR) process. If real exchange rates in developing countries follow nonlinear stationary processes, the alternative hypothesis of the ADF unit root tests based on the linear model would be misspecified. KSS (2003) have illustrated that their tests are more powerful than the ADF tests for the series that may revert to their mean nonlinearly.

   There are several theories outlining why we would expect nonlinear adjustment toward ppp. (3) One potential source arises from nonlinearities in international goods arbitrage because of factors such as transportation costs and trade barriers, causing a price gap among similar goods traded in spatially separated markets. These costs and barriers are much higher in developing countries than industrial countries, suggesting a strong case for nonlinear adjustment toward PPP in these countries. Another reason is the higher level of foreign exchange rate interventions in developing countries. In an effort to manage inflation and manipulate trade flows, these countries tend to intervene much more frequently than industrial countries, causing nonlinearity in the adjustment of the nominal exchange rate, and given sticky prices, in the adjustment of the real exchange rate as well (Sarno and Taylor 2001a; Taylor 2003). Finally, different beliefs among market participants regarding the equilibrium level of real exchange rates is given as another source of nonlinearity (Sarno and Taylor 2001b). Because of information barriers and a high level of government involvement in developing countries, we expect a higher number of heterogeneous economic agents interacting in the foreign exchange markets in these countries, causing some nonlinear adjustment of RER. (4)

   Comprehensive evidence on the validity of PPP in developing countries is scant. To our knowledge, the most inclusive evidence comes from a recent study by Alba and Park (2003). (5) They provide evidence from 65 developing countries during the 1976-1999 period. They find weak evidence on PPP, and PPP tends to hold better for the post-1980 period. Our study provides complementary evidence on their findings regarding the validity of PPP in developing economies in the following sense. While Alba and Park (2003) use panel unit root tests, we base our evidence on the nonlinear ESTAR tests. If RERs exhibit nonlinear behavior, panel unit root tests that assume linear behavior may bias the inferences. (6)

   Besides using a different approach, our study is also different from Alba and Park (2003) in terms of the definition of the real exchange rate we employ: We use real effective exchange rates (REERs) in our analysis, while they employ bilateral RERs against the U.S. dollar. Unit root tests on REERs set a more comprehensive stage to test PPP because they indicate movement in the overall value of a country's currency rather than a movement against the currency of only one trading partner embodied in the real bilateral exchange rate. Testing whether REERs follow nonstationary mean-reverting behavior is also a test of the multicountry version of PPP, rather than that of PPP based on a bilateral trading partner. Overall, we offer complementary evidence on the legitimacy of PPP in developing countries using an alternative approach (nonlinear ESTAR) to that of Alba and Park (2003) and a multicountry framework. Furthermore, we discuss whether the membership of a country in a trade association has some impact on the time series behavior of its REER. Our study is also different from Sarno (2000) and Liew, Baharumshah, and Chong (2004). Although, like ours, they use nonlinear unit root tests, they employ bilateral real exchange rates whereas we use REER. In addition, they provide evidence only from selected Middle Eastern and Asian countries, while we cover all the available data from all the regions of the world.

   In addition to developing countries, we also provide evidence on the so-called transition economies of the former Soviet Union and of Central and Eastern Europe. For the purposes of this study we call them European less-developed economies. These countries' RERs are understudied. (7) However, it is important to investigate these countries' RERs for several reasons, as discussed in detail in Alba and Park (2005). First, most of these countries are in the process of entering the euro zone, and they therefore need an estimate of equilibrium exchange rates prior to a permanent link to the euro. If PPP does not hold well for these countries, then using PPP rates as an equilibrium exchange rate measure, as typically suggested in the literature, may not yield an appropriate exchange rate between these new European Union (EU) members and the euro. Second, it is argued that testing PPP for EU candidate economies has implications for testing income convergence between these economies and their EU partners. Because PPP is generally used in measuring and hence comparing income across countries, the comparison may not be accurate if PPP fails to hold. Alba and Park (2005) consider these issues empirically by providing evidence about the validity of PPP for Turkey. Our study extends their study to other EU candidate economies, as well as the transition economies that are likely to apply for EU membership in the near future. (8)

   We apply the KSS tests to REERs of 88 developing economies, which consist of 24 Asian, 18 African, 25 European, and 21 Latin American less-developed countries (LDCs). Like Alba and Park (2003), our sample focuses on the post-Breton Woods floating period. We employ monthly data, which start around the 1980s for most of the countries, except the European LDCs. The sample period for these countries starts in the early 1990s. The very early years of 1990 are eliminated in estimations because of the erratic changes in RERs due to reforms initiated at the same time.

   In this paper, besides testing PPP, we take an additional step and try to explain productivity differentials as one of the factors that may determine the deviation of PPP-based exchange rates from the equilibrium rate, i.e., the real exchange rate. It is well known that Balassa-Samuelson type effects may be present in developing economies, especially in the transition economies, (9) reflecting the differential rates of productivity growth in traded and nontraded goods sectors of a country relative to that of her major trading partners. Besides the Balassa-Samuelson effects, a trend appreciation of the REER in transition economies would be due to dramatic changes in product quality and a progressive shift in both domestic and foreign consumers' preferences toward domestically produced goods, as well as transition-specific adjustments in administered or regulated prices (Egert and Kutan 2005). In addition, Kutan and Yigit (2007) show that integration into the EU brings about significant productivity gains, which may further cause REER to appreciate in the transition economies, many of which now are the new EU members. (10) Previous research that tested the Balassa-Samuelson effect concentrated on regression analysis in which the real exchange rate was regressed on productivity differentials. (11) Within a unit-root testing procedure, the Balassa-Samuelson effect can be tested by including a time trend in the regression model. If there is evidence of mean reversion in REER, and it is to a constant mean, then we conclude in favor of PPP, while if the reversion in REER is to a trend, indicating the effects of productivity shocks, etc., we consider it as evidence for the existence of the Balassa-Samuelson type effect.

   To this end, we review and outline the KSS test for nonlinear stationarity in section 2. Section 3 reports the results. Section 4 analyzes the economic characteristics of the countries to see whether such characteristics are consistent with the PPP theory. Finally, section 5 concludes.

2. Methodology (12)

   In identifying the order of integration of a time series variable, the ADF test is perhaps the most commonly used test, in which the null is nonstationarity of a variable against an alternative of stationarity. Recently, KSS (2003) expanded the standard ADF test by keeping the null hypothesis as nonstationarity in a time series variable against the alternative of a nonlinear but globally stationary process. They demonstrate that the new test could be based on the following ESTAR specification:

   [DELTA][y.sub.t] = [gamma][y.sub.t-1][1 -exp (-[theta][y.sup.2.sub.t-1]) + [[epsilon].sub.t], [theta] [greater than or equal to] 0, (1)

   where...