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

Bahmani-Oskooee, Mohsen ; Kutan, Ali M. ; Zhou, Su 等

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 [y.sub.t] is the de-meaned or detrended series of interest, [epsilon] is an i.i.d, error with zero mean and constant variance, and [1 -exp (-[theta][y.sup.2.sub.t-1]) is the exponential transition function adopted in the test to present the nonlinear adjustment. The null hypothesis of a unit root in [y.sub.t] (i.e., [DELTA][y.sub.t] = [[epsilon].sub.t]) implies that [theta] = 0, so that the term [1 -exp (-[theta][y.sup.2.sub.t-1]) is 0. If [theta] is positive, it effectively determines the speed of mean reversion.

The KSS test hence directly focuses on the 0 parameter by testing the null hypothesis of nonstationarity [H.sub.0]: [theta] = 0 against the alternative hypothesis of nonlinear mean-reversion, [H.sub.1]: [theta] > 0. Because [theta] in Equation 1 is not identified under the null, it is not feasible to directly test the null hypothesis. KSS thus reparameterize Equation 1 by computing a first-order Taylor series approximation to specification (1) to obtain the auxiliary regression specified by Equation 2:

[DELTA][y.sub.t] = [delta][y.sup.3.sub.t-1] + error. (2)

For a more general case where the errors in Equation 2 are serially correlated, Equation 2 is extended to

[DELTA][y.sub.t] = [p.summation over (j=1)][[rho].sub.j] [DELTA][y.sub.t-j] + [delta][y.sup.3.sub.t-1] + error, (3)

with the p augmentations to correct for serially correlated errors. The null hypothesis to be tested with either Equation 2 or 3 is [H.sub.0]: [delta] = 0 against the alternative of [H.sub.1]: [delta] < 0. KSS show that the t-statistic for [delta] = 0 against [delta] < 0, i.e., [t.sub.NL], does not have an asymptotic standard normal distribution, and they therefore tabulate the asymptotic critical values of the [t.sub.NL] statistics via stochastic simulations.

We estimate the [t.sub.NL] statistics with both regression Equations 2 and 3 and refer to them as [t.sub.NL11] and [t.sub.NL12], respectively, for de-meaned data, and [t.sub.NL21] and [t.sub.NL22], respectively, for detrended data. The de-meaned or detrended data are obtained by first regressing each series on a constant or on both a constant and a time trend, respectively, and then saving the residuals. The conventional ADF test statistics are also estimated, denoted as [t.sub.ADF1] for the model with a constant only, and [t.sub.ADF2] for the model with both a constant and a time trend. The rejection of the null by the KSS test with de-meaned data or by the ADF test that only includes a constant indicates reversion in REER to a constant mean, supporting PPP. If there is no evidence of reversion to a constant mean, but we are able to reject the null by the KSS test with detrended data or by the ADF test that includes a constant and trend, this would be an indication of linear or nonlinear reversion in REER to a trend, supporting the Balassa-Samuelson effect.

Following the suggestion of KSS (2003, p. 365), the number of augmentations p for either the ADF tests or the KSS tests is selected based on the significance testing procedure in Ng and Perron (1995). The maximum number of p was set to 24 mostly because the data are monthly, and insignificant augmentation terms were excluded.

3. Data, Sample Period, and the Empirical Results

The tests discussed in the previous section are applied to the monthly real effective exchange rates of 24 Asian, 18 African, 25 European, and 21 Latin American LDCs. Data of the REERs of African and Latin American LDCs (except Mexico) and five European LDCs (Armenia, Cyprus, Macedonia, Malta, and Moldova) are collected from the International Monetary Fund (IMF)'s International Financial Statistics online. Those of Mexico and Turkey are from the OECD Economic Indicators. For the other 19 European countries and 24 Asian LDCs, the data of their REERs are obtained from the Information Notice System of the IMF. The sample period for each country is reported in tables along with the test results. Because the available data for most countries begin around 1980, we start our sample from 1980. For some countries, the sample period starts later than 1980; this is either due to the data availability or the exclusion of the periods with existing large breaks in their REERs during the 1980s or the early 1990s. The ending month of the samples is August 2005 for most of the countries and is July 2003 or October 2003 for some countries when their samples have some missing observations in 2003-2004.

We report the results of the KSS test along with the standard ADF statistic for 24 Asian LDCs in Table 1. Tables 2-4, report the results for 18 African, 25 European, and 21 Latin American LDCs, respectively. The exact sample periods are listed in Tables 14.

As indicated before, six statistics are reported. The test statistic of the standard ADF that only includes a constant is denoted by [t.sub.ADF1]. TWO tests outlined by Equations 2 and 3 are applied to de-meaned data. The KSS test with no augmented terms that is based on Equation 2 is denoted by [t.sub.NL11], and the one with augmented terms that is based on Equation 3 is denoted by [t.sub.NL12]. These are the statistics for testing PPP. The comparable statistic with a trend in the ADF is [t.sub.ADF2] and the two KSS statistics without and with augmentation for detrended data are [t.sub.NL21] and [t.sub.NL22], respectively. They are utilized to test the Balassa-Samuelson effect.

Concentrating on the first three tests, we gather from Tables 1-4, that the null of nonstationarity in REER is rejected by [t.sub.ADF1] at the 10% level of significance in 12 countries--Cambodia, Pakistan, Samoa, Singapore, Vietnam, Morocco, Zambia, Ukraine, Chile, Costa Rica, Ecuador, and Mexico. Thus, the REER of these countries reverts to a constant mean linearly. However, there are 19 additional countries in which the null of nonstationarity of REER is only rejected by [t.sub.NL11] or [t.sub.NL12] but not by [t.sub.ADF1], implying a nonlinear mean reversion in these countries (again, rejection of the null is based on the 10% level of significance, which is the level we use throughout the paper). The list includes Indonesia, Korea, Lao, Maldives, Sri Lanka, Thailand, Sierra Leone, Togo, Armenia, Bulgaria, Croatia, Moldova, Slovak Republic, Slovenia, Turkey, Uzbekistan, Paraguay, St. Kitts and Nevis, and St. Vincent and Grenades. Thus, the KSS test validates PPP in more countries than the standard ADF test. Putting the three tests together, the results support PPP at least by one of the three statistics in a total of 31 out of 88 countries (35%). (13)

Our results, based on using real effective exchange rates, are similar to those of Cerrato and Sarantis (2006), who applied the KSS test to the real bilateral exchange rates of 35 less-developed countries using the U.S. dollar as the numeraire currency. Their results revealed that PPP was supported by the standard ADF test in five countries and by the KSS test in 10 additional countries for a total of 15 out of 35 countries, i.e., in 43% of the cases. (14) Obviously, the difference could be attributed to using REER in this paper against real bilateral exchange rates in Cerrato and Sarantis (2006). Liew, Baharumshah, and Chong (2004), who applied KSS tests to real bilateral exchange rates of 11 Asian countries, showed that there is no mean reversion in the real bilateral exchange rate of India when the Japanese yen is used as the numeraire. However, when the U.S. dollar was used as the numeraire, PPP was validated by the KSS test. Moreover, when the dollar was used as the numeraire, there was support for nonlinear mean reversion in 8 out of 11 countries (73%), and when the yen was used as the numeraire, nonlinear mean reversion was supported in 6 out of 11 countries (55%). In none of the countries was linear mean reversion supported by the standard ADF test in Liew, Baharumshah, and Chong (2004). Indeed, incidence of nonlinear mean reversion was much higher in Liew, Baharumshah, and Chong (2004) than in this study or in Cerrato and Sarantis (2006). One explanation could be that Liew, Baharumshah, and Chong (2004) used quarterly data that included observations from the pre- and post-1973 period. Clearly, the structural break that took place in 1973 because of a shift in the international monetary system could introduce nonlinearity into real exchange rates that could increase the incidence of nonlinear mean reversion and reduce the incidence of linear mean reversion. All in all, these two studies are consistent with ours in that all three studies reveal that the nonlinear KSS test provides more support for PPP than for the linear ADF test.

We next discuss the evidence with respect to mean reversion to a trend, i.e., the Balassa-Samuelson type effects. As indicated before, for this purpose we rely on the last three statistics in Tables 14 for the 57 countries for which there is no evidence of PPP. Concentrating on [t.sub.ADF2], the null of nonstationarity is rejected in favor of reversion to a linear trend in 4 out of 57 countries. The list includes Belize, Malawi, Papua New Guinea, and Romania. However, when we consider the nonlinear tests, there are nine additional countries for which the null is rejected in favor of nonlinear reversion to a trend either by [t.sub.NL21] or [t.sub.NL22] but not by [t.sub.ADF2]. Again, it appears that nonlinear tests provide more support for the productivity bias hypothesis as compared with linear tests. Overall, Balassa-Samuelson type effects receive support in a total of 13 out of 88 countries, of which four are transition economies (Albania, Czech Republic, Macedonia, and Romania). All in all, evidence for mean reversion in REER to a constant mean or to a trend is found for 44 out of 88 countries, i.e., in 50% of the cases.

Does the membership of a country in a trade association have some impact on the time series behavior of its REER? If we just look at the test results of Asian LDCs, the answer might be in the affirmative. The nonstationarity of REER is rejected for seven out of nine members of the Association of Southeast Asian Nations, but only for 5 out of 15 other Asian economies, implying that the REERs of the countries in a trade association are more likely to be stationary. However, the results of African, European, and Latin American LDCs may suggest the opposite: Belonging to a trade bloc does not seem to make a notable difference for the behavior of a country's REER. There is evidence for the stationarity of REERs for only 7 out of 15 African LDCs who are members of the Southern African Customs Union, the Common Market for Eastern and Southern Africa, the Economic Community of Central African States, or the Economic Community of West African States, and for two of the three remaining African LDCs in our sample who are not members of any of these regional trade blocs. For the 10 new EU entrants, the null of a unit root in their REERs is rejected for only three of them. Yet, the same null is rejected for 10 of the other 15 European LDCs in our study. Among the 21 Latin American LDCs in our sample, the null hypothesis is rejected for Paraguay and Uruguay (two Mercosur members), Mexico (a North American Free Trade Agreement [NAFTA] member), and Chile (who signed free-trade agreements with each of the NAFTA countries), but only for 5 out of 15 countries in either the Andean Community or the Caribbean Community or in the Central American Common Market.

4. Country Characteristics and Mean Reversion of REER

Cheung and Lai (2000), Alba and Park (2003), and Alba and Papell (2006) show that country characteristics are significantly linked to both adherence to and deviations from long-run PPP. PPP may hold better for countries with a higher ratio of openness to trade because PPP theory is based on arbitrage of tradable goods across countries. Evidence for PPP could be higher for countries subject to high inflation because prices adjust more quickly to ensure that the parity holds. On the other hand, PPP may hold less for highest-income or lowest-income countries because they have a relatively higher or lower productivity of tradable goods sector than that of their major trading partners. (15) Table 5 reports some country characteristics, the number of countries in each group, the number of cases in which REER reverts to a constant mean, the number of countries in which REER reverts to a trend, and the number of countries in which REER reverts to a constant mean or a trend.

We measure openness by the average of the sum of merchandise exports and imports as a share of gross domestic product (GDP), and measure GDP growth by the average of annual percentage growth rate of PPP-adjusted per capita real GDP. Inflation is measured by the average annual change in CPI. The data are collected from the Worm Development Indicators (2005). Two measures of nominal exchange rate flexibility are calculated by the standard deviations of the logs of monthly exchange rates: national currency per SDR and national currency per U.S. dollar. These exchange rates are obtained from the International Financial Statistics online.

For each characteristic, we divide the 88 countries in our sample into four groups, based on the magnitude of the measure of the country against the particular criterion. For example, for nominal exchange rate flexibility, the 22 countries with the smallest or the largest standard deviations of the logs of monthly exchange rates are grouped as "lowest flexibility" or "highest flexibility," respectively. The countries falling in between the range of the smallest and the largest standard deviations are classified as "moderately low flexibility" and "moderately high flexibility," respectively. Each group includes 22 countries except for the characteristics of inflation and GDP growth, where some groups include 21 countries because the price indices of Antigua and Barbuda, Tajikistan, and Uzbekistan, and the GDP of Netherlands Antilles are not available.

From Table 5 we gather that PPP is validated (i.e., REER reverts to a constant mean) somewhat more often for countries with highest inflation (10 out of 21 cases or 48%) or highest nominal exchange rate flexibility (12 out of 22 cases or 55%) as compared with the countries in the three lower quartiles. Turning to countries in which REER reverts to a trend, we see mixed outcome between country characteristics and the number of cases in each group. For example, there are four countries in the lowest and highest quartiles of the exchange rate flexibility category for which REER reverts to a trend. In the inflation category, there are eight countries in the last two quartiles versus five countries in the first two quartiles, supporting the notion that the REER reverts to a trend more frequently in relatively high-inflation countries. The opposite is true in the openness and GDP growth categories. This may imply that the Balassa-Samuelson effect is not as sensitive to country characteristics as PPP.

As an additional exercise we combine the two columns and report the results in the last column of Table 5, which reflects the number of countries in each group for which the null of the unit root is rejected in favor of reversion to a constant mean or a trend. The combined results once again suggest that reversion in REER to a constant mean or to a trend is more likely to occur for countries with highest inflation (14 out of 21 cases or 67%) or highest nominal exchange rate flexibility (16 out of 22 cases or 73%). Further inspection revealed that most of the 14 countries in the highest inflation group with reversion in their REER do belong to the highest exchange rate flexibility category. The exceptions were Albania, Armenia, and Croatia, which belonged to the first group but not to the second group. Similarly, most of the 16 countries with reversion in their REER in the highest exchange rate flexibility group also belonged to the highest inflation category, except Algeria, Chile, Costa Rica, Indonesia, and Paraguay, which are within the highest exchange rate flexibility group but not in the highest inflation group. Thus, for the former three countries, we can attribute the reversion of their REER to high inflation, while high exchange rate flexibility may contribute to the reversion in REER for the latter five countries. In the remaining 11 countries that belonged to both groups, perhaps a combination of both high inflation and high exchange rate flexibility have contributed to the mean reversion of REER. (16)

Note that PPP or reversion in REER does not seem to be closely related to the openness of the countries, nor does it hold or emerge less for the countries with highest or lowest real GDP growth. (17) Besides, reversion in REER could be attributed to rather high inflation and/or exchange rate flexibility while the position in the lower quartiles would not be much relevant. (18) An explanation for this is that when high inflation and nominal shocks in developing countries dominate real factors such as openness and productivity growth, REERs would respond to large nominal shocks quickly to ensure parity or revert to equilibrium. (19)

5. Summary and Conclusions

Since the introduction of unit-root testing procedures, many studies have tested the stationarity or mean-reverting properties of RERs by using the ADF test in which the null of nonstationarity or unit root is tested against an alternative hypothesis of linear stationarity. Not much support for PPP is produced by the standard ADF test. However, when the new test that incorporates nonlinearity in the mean reverting properties of the real exchange rate into the testing procedure is employed, PPP is validated by most authors, though generally for industrial countries with no comprehensive evidence for developing and transition countries.

The main purpose of this paper is to test PPP by using the conventional ADF test as well as the KSS test (which could be considered a nonlinear version of the ADF test) that assumes the alternative hypothesis to be nonlinear stationarity. Our study differs from previous research in that we concentrate on the experience of as many developing countries and transition economies as possible. Furthermore, rather than using the real bilateral exchange rate between one country and her major trading partner, we use real effective exchange rate, which is a more comprehensive measure of movement in the overall value of a country's currency and hence it is a test of PPP based on multiple trading partners.

Monthly real effective exchange rates were available for 24 countries from Asia, 18 from Africa, 25 from Europe, and 21 from Latin America for a total of 88 less-developed countries in the sample. The results could be best summarized as follows: While the standard or linear version of the ADF test supports PPP in 12 countries, the nonlinear version of the ADF test supports PPP in an additional 19 countries, implying that the real effective exchange rates of developing countries revert to their mean following a nonlinear path more often than a linear path. Therefore, studies modeling real exchange rates or testing PPP in developing countries by using the standard ADF test may have significant inference bias.

In addition to testing PPP, unlike previous research, we also test mean reversion in the real effective exchange rates to a trend, which is considered to be a method of testing the Balassa-Samuelson effect or the productivity bias hypothesis within the unit-root testing framework. We found, again, more evidence supporting nonlinear reversion to a trend than linear reversion. The standard linear ADF test supported reversion to a trend in four countries, whereas nonlinear ADF supported nonlinear reversion to a trend in nine additional countries. Thus, productivity bias hypothesis seems to be supported in 13 countries. One recommendation that follows from our study is that researchers should use both linear and nonlinear tests to determine the appropriate data generating process for real exchange rates.

Another important finding is that the productivity bias hypothesis or the Balassa-Samuelson effect does not appear to be a particularly important factor in the behavior of REER for the transition economies as claimed in some previous studies. This suggests that transition-specific factors, such as changes in product quality, shift in consumer preferences toward Western goods, and adjustments in administered or regulated prices do not seem to dominate real exchange movements in these economies. Furthermore, evidence on country characteristics suggested that reversion to a constant mean or to a trend occurs more often in high-inflation countries and in countries with high nominal exchange rate flexibility.

Valuable comments of two anonymous referees are greatly appreciated. We also thank Aleg Bulir for his help with data. Any error, however, is ours.

Received September 2006; accepted March 2007.

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Taylor, Mark P., David A. Peel, and Lucio Sarno. 2001. Nonlinear mean-reversion in real exchange rates: Toward a solution to the purchasing power parity puzzles, International Economics Review 42:1015-42.

World Bank. 2005. "World Development Indicators." CD-Rom. Washington, DC: World Bank.

(1) For a review of the literature, see Lothian and Taylor (2005) and Sarno (2005).

(2) Panel unit root studies, among others, include Papell and Theodoridis (2001) and Alba and Park (2003). Taylor, Peel, and Sarno (2001), Kapetanios, Shin, and Snell (2003), Chortareas and Kapetanios (2004), Sarno, Taylor, and Chowdhury (2004), and Lothian and Taylor (2005), among others, employ nonlinear real exchange rate adjustment models to examine PPP.

(3) Taylor (2003) and Lothian and Taylor (2005) review related theories and summarize the available empirical evidence. Overall, evidence from limited studies indicates that RERs exhibit some nonlinear adjustment patterns.

(4) For application of nonlinear tests versus a test based on structural breaks under the gold standard, see Heywood and Papell (2002) and Paya and Peel (2004).

(5) Other notable studies are Sarno (2000) and Liew, Baharumshah, and Chong (2004). They test PPP for 11 Middle Eastern and 11 Asian countries, respectively, using bilateral real exchange rates. Alba and Papell (2006) investigate PPP for a very diverse group of 84 developed and developing countries, using panel unit root tests and real bilateral exchange rates. Their focus is on the role of individual country characteristics on PPP, rather than how PPP holds in developed versus developing countries, however.

(6) Alba and Park (2003) also report some ADF test results as some preliminary evidence to their panel unit root tests. Hence, our results based on nonlinear adjustment processes may be considered an extension of their ADF tests.

(7) Available studies either focus on the sources of real exchange movements (e.g., Dibooglu and Kutan 2001; Kutan and Wyzan 2005: De Broeck and Slok 2006; and Egert, Lommatzsch, and Lahreche-Revil 2006) or estimating equilibrium real exchange rates (for a survey, see Egert. Halpern, and MacDonald 2006).

(8) The only study we are aware of testing PPP for transition economies is Payne. Lee, and Hofler (2005), but only for one country, Croatia. They find evidence against PPP.

(9) See Egert, Halpern, and MacDonald (2006) and Egert, Lommatzsch, and Lahreche-Revil (2006).

(10) On the other hand, evidence shows that the introduction of the euro in 1999 reduced the variability and the persistence of bilateral RER shocks in the most recent EU members (Kutan and Zhou 2008). This may slow down or even reverse the trend appreciation observed in these former transition economies.

(11) For a review article on productivity bias hypothesis and PPP, see Bahmani-Oskooee and Nasir (2005).

(12) This section draws on Bahmani-Oskooee, Kutan, and Zhou (2007), who apply the KSS methodology to 23 OECD countries.

(13) Note that out of 19 countries, eight are transition economies. These economies during our sample period had significant central bank interventions to manipulate the value of their domestic currencies to stay competitive in international markets. More important, market participants tend to have different opinions regarding the equilibrium level of RER in the transition economies. This is expected because these countries did not have much market economy until the early 1990s, so there was some speculation regarding the correct equilibrium value of real exchange rates. The debate has intensified over time because many of the transition countries were or had been in the process of entering the euro zone, and they, therefore, needed an estimate of the equilibrium exchange rates prior to a permanent link to the euro. Hence, besides central bank interventions, different beliefs among market participants regarding the equilibrium level of real exchange rates have likely contributed to the nonlinear reversion to the mean in these countries.

(14) Concentrating only on nonlinear mean reversion, our results support PPP in 19 out of 88 countries, i.e., in 22% of the eases. The comparable figure in Cerrato and Sarantis (2006) is 10 out of 35 countries or 29%. This analysis is based on the fact that in countries where PPP is supported by both the ADF and KSS test, the reversion to mean is linear.

(15) A detailed description of country characteristics for each region is not reported, but it is available upon request from the authors.

(16) These 11 countries are Bulgaria, Ecuador, Lao, Malawi, Mexico, Romania, Sierra Leone, Turkey, Ukraine, Uruguay, and Zambia.

(17) Using data on dollar-based real exchange rates for 94 countries, Cheung and Lai (2000) also find that openness and per capita GDP growth are not linked to the persistence of deviations from PPP.

(18) Note that there are 12 cases of mean reversion within the 22 moderately less open economies category. Further inspection of the relevant data revealed that among these 12 cases, one had high inflation, two had high exchange rate volatility, and three had high inflation and high exchange rate volatilities. That is, six of them exhibit high inflation and/or high exchange rate volatility.

(19) From Table 5 we gather that in each category out of 88 countries in the sample, PPP is supported in a total of 31 countries. In 13 of the remaining countries in which PPP is not supported, the Balassa-Samuelson type effect may explain the failure of PPP. In the remaining 44 countries, deviation of relative prices from the equilibrium rate is due to other factors such as speculation, trade restrictions, arbitrage activities, transportation cost, nontradable goods, monetary instability, etc. (see Davutyan and Pippenger 1985).

Mohsen Bahmaniu-Oskooee, * Ali M. Kutan, ([dagger]) and Su Zhou ([double dagger])

* The Center for Research on International Economics and the Department of Economics, The University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA; E-mail bahmani@uwm.edu; corresponding author.

([dagger]) Department of Economics and Finance, Southern Illinois University, Edwardsville, IL 62026-1102, USA; The Emerging Markets Group, Sir Cass Business School, 106 Bunhill Row, London EC1Y 8TZ; The William Davidson Institute, University of Michigan, 724 East University Avenue, Wyly Hall, First Floor, Ann Arbor, MI 48109-1234, USA; E-mail akutan@siue.edu.

([double dagger]) Department of Economics, University of Texas at San Antonio, San Antonio, TX 78249-0633, USA; E-mail szhou@utsa.edu.

Table 1. Unit Root Test Results for Asian LDCs

Country Sample Period

Bangladesh 1980:1-2005:8
Cambodia 1992:1-2005:8
China 1980:1-2005:8
Fiji 1980:1-2005:8
Hong Kong,
 China 1980:1-2005:8
India 1980:1-2005:8
Indonesia 1980:1-2005:8
Korea 1980:1-2005:8
Lao 1988:1-2005:8
Malaysia 1980:1-2005:8
Maldives 1992:1-2005:8
Myanmar 1980:1-2005:8
Nepal 1980:1-2005:8
Pakistan 1980:1-2005:8
Papua New
 Guinea 1980:1-2005:8
Philippines 1980:1-2005:8
Samoa 1980:1-2005:8
Singapore 1980:1-2005:8
Solomon Islands 1980:1-2005:8
Sri Lanka 1980:1-2005:8
Thailand 1980:1-2005:8
Tonga 1980:1-2005:8
Vanuatu 1980:1-2005:8
Vietnam 1990:1-2005:8

Country [t.sub.ADF1] [t.sub.NL11] [t.sub.NL12]

Bangladesh 1.32 1.37 1.39
Cambodia -4.21 *** -5.73 *** -4.90 ***
China 2.53 2.59 1.41
Fiji 1.77 0.90 1.01
Hong Kong, 1.26 1.17 1.88
 China 1.57 1.44 1.27
India 2.30 -2.94 ** -3.08 **
Indonesia 2.54 -2.78 * -4.44 ***
Korea 2.45 -3.15 ** -3.25 **
Lao 1.32 0.93 1.41
Malaysia 1.52 -3.29 ** 1.91
Maldives -2.30 -2.75 1.23
Myanmar 1.60 1.81 1.98
Nepal -3.14 ** -4.14 *** -3.22 **
Pakistan 1.10 2.22 2.16
Papua New 1.80 1.67 1.40
 Guinea -2.93 ** 2.31 2.35
Philippines -2.75 * 1.25 -2.92 *
Samoa 2.18 1.92 1.89
Singapore 2.56 2.21 -2.94 **
Solomon Islands 1.27 2.57 -2.80 *
Sri Lanka 1.84 1.95 1.76
Thailand 1.85 2.12 2.06
Tonga -2.90 ** -3.70 *** -4.83 ***
Vanuatu -1.85 -2.12 -2.06
Vietnam -2.90 ** -3.70 *** -4.83 ***

Country [t.sub.ADF2 [t.sub.NL21] [t.sub.NL22]

Bangladesh 2.51 1.92 2.07
Cambodia -4.27 *** 2.46 2.80
China 1.81 1.47 2.64
Fiji 1.62 0.99 1.60
Hong Kong, 1.05 1.56 1.61
 China 0.85 0.65 1.96
India 1.69 3.04 -3.61 **
Indonesia 2.66 2.40 -4.16 ***
Korea 2.47 3.06 -3.54 **
Lao 2.61 1.76 2.62
Malaysia 1.13 -3.33 * 1.97
Maldives -0.66 0.58 -4.28 ***
Myanmar 1.47 2.47 2.68
Nepal 1.65 2.74 2.63
Pakistan -3.58 ** -3.60 ** -4.25 ***
Papua New 2.15 1.65 1.48
 Guinea 1.35 2.41 2.11
Philippines 2.75 1.20 2.83
Samoa 1.96 1.90 2.14
Singapore 2.65 1.91 2.49
Solomon Islands 2.49 -5.23 *** -6.70 ***
Sri Lanka 2.56 2.21 1.98
Thailand 1.43 2.46 2.40
Tonga 2.68 -3.41 ** -4.69 ***
Vanuatu -1.43 -2.46 -2.4
Vietnam -2.68 -3.41 ** -4.69 ***

[t.sub.ADF1] and [t.sub.ADF2] are the standard ADF test statistics
for the null of stationarity and the null of trend stationarity,
respectively, of the variable in the study. [t.sub.NL11] and
[t.sub.NL12] are the KSS test statistics for the de-meaned data using
the models without and with augmentations, respectively. [t.sub.NL21]
and [t.sub.NL22] are the KSS test statistics for the detrended data
using the models without and with augmentations, respectively. The
10, 5, and 1% asymptotic critical values for [t.sub.ADF1] are -2.57,
-2.86, and -3.43, respectively, and those for [t.sub.ADF2] are -3.12,
-3.41, and -3.96, respectively. The 10, 5, and 1% asymptotic critical
values for [t.sub.NL11] and [t.sub.NL12] are -2.66, -2.93, and -3.48,
respectively, and those for [t.sub.NL21] and [t.sub.NL22] are -3.13,
-3.40, and -3.93, respectively, taken from Kapetanios, Shin, and Snell
(2003, p. 364).

*, **, and *** denote rejection of the null hypothesis at the 10, 5,
and 1% significance levels, respectively.

Table 2. Unit Root Test Results for African LDCs

Country Sample Period [t.sub.ADF1] [t.sub.NL11]

Algeria 1980:1-2005:8 -1.34 -0.72
Burundi 1980:1-2005:8 -1.50 -1.45
Cameroon 1980:1-2003:7 -1.39 -1.90
Central African
 Rep. 1980:1-2003:10 -1.35 -1.94
Cote d'Ivoire 1980:1-2003:7 -1.94 -2.13
Equatorial Guinea 1985:1-2005:8 -1.20 -2.41
Gabon 1980:1-2005:8 -1.04 -1.49
Gambia 1986:1-2005:8 0.35 0.26
Ghana 1986:1-2005:8 -1.77 -1.35
Lesotho 1980:1-2003:7 -0.91 -1.50
Malawi 1980:1-2003:7 -1.34 -1.76
Morocco 1980:1-2005:8 -2.90 ** -3.14 *
Sierra Leone 1987:1-2005:8 -2.15 -4.51 ***
South Africa 1980:1-2005:8 -1.79 -1.27
Togo 1980:1-2003:10 -1.94 -2.95 **
Tunisia 1980:1-2005:8 -2.09 -1.81
Uganda 1990:1-2005:8 -0.82 -1.55
Zambia 1980:1-2005:8 -3.05 ** -4.15 ***

Country [t.sub.NL12] [t.sub.ADF2]

Algeria -1.85 -2.41
Burundi -1.88 -2.43
Cameroon -1.40 -2.16
Central African
 Rep. -1.64 -2.78
Cote d'Ivoire -2.18 -2.10
Equatorial Guinea -0.57 -2.00
Gabon -1.23 -1.87
Gambia -0.32 -1.10
Ghana -1.98 -2.43
Lesotho -1.96 -2.06
Malawi -1.30 -3.57 **
Morocco -2.41 -2.84
Sierra Leone -3.71 *** -2.22
South Africa -1.57 -2.14
Togo -2.13 -2.72
Tunisia -1.80 -1.92
Uganda -1.46 -2.46
Zambia -4.32 *** -2.91

Country [t.sub.NL21] [t.sub.NL22]

Algeria -1.12 -3.64 **
Burundi -2.83 -3.42 **
Cameroon -2.51 -1.92
Central African
 Rep. -2.56 -2.47
Cote d'Ivoire -2.76 -2.91
Equatorial Guinea -1.77 0.10
Gabon -3.22 * -2.99
Gambia -1.07 -1.71
Ghana -1.33 -1.97
Lesotho -1.92 -2.62
Malawi -2.26 -1.79
Morocco -2.30 -2.18
Sierra Leone -4.19 *** -3.34 *
South Africa -2.86 -3.64 **
Togo -2.91 -1.88
Tunisia -1.74 -2.70
Uganda -2.74 -2.85
Zambia -3.73 ** -3.82 **

[t.sub.ADF1] and [t.sub.ADF2] are the standard ADF test statistics
for the null of stationarity and the null of trend stationarity,
respectively, of the variable in the study. [t.sub.NL11] and
[t.sub.NL12] are the KSS test statistics for the de-meaned data using
the models without and with augmentations, respectively. [t.sub.NL21]
and [t.sub.NL22] are the KSS test statistics for the detrended data
using the models without and with augmentations, respectively. The
10, 5, and 1% asymptotic critical values for [t.sub.ADF1] are -2.57,
-2.86, and -3.43, respectively, and those for [t.sub.ADF2] are -3.12,
-3.41, and -3.96, respectively. The 10, 5, and 1% asymptotic critical
values for [t.sub.NL11] and [t.sub.NL12] are -2.66, -2.93, and -3.48,
respectively, and those for [t.sub.NL21] and [t.sub.NL22] are -3.13,
-3.40, and -3.93, respectively, taken from Kapetanios, Shin, and Snell
(2003, p. 364).

*, **, and *** denote rejection of the null hypothesis at the 10, 5,
and 1% significance levels, respectively.

Table 3. Unit Root Test Results for European LDCs

Country Sample Period [t.sub.ADF1] [t.sub.NL11]

Albania 1992:1-2005:8 -1.07 -1.14
Armenia 1994:1-2005:8 -0.82 -2.91 *
Azerbaijan 1994:1-2005:8 -0.95 -1.67
Belarus 1994:1-2005:8 -1.22 -1.93
Bulgaria 1992:1-2005:8 -0.80 -2.69 *
Croatia 1992:1-2005:8 -2.18 -6.64 ***
Cyprus 1980:1-2005:8 -1.95 -2.51
Czech Republic 1992:1-2005:8 -1.10 -1.14
Estonia 1992:6-2005:8 -2.45 -1.82
Hungary 1992:1-2005:8 0.77 0.46
Kyrgyz Republic 1994:1-2005:8 -2.40 -1.65
Latvia 1992:6-2005:8 -1.26 -0.53
Lithuania 1994:1-2005:8 -2.17 -1.70
Macedonia 1992:6-2005:8 -1.71 -1.62
Malta 1980:1-2005:8 -2.42 -1.72
Moldova 1994:1-2005:8 -2.45 -4.44 ***
Poland 1992:1-2005:8 -1.79 -1.70
Romania 1992:1-2005:8 -0.75 0.32
Russia 1994:1-2005:8 -1.95 -1.11
Slovak Republic 1992:1-2005:8 -1.08 -0.50
Slovenia 1992:6-2005:8 -1.49 -4.41 ***
Tajikistan 1992:1-2005:8 -1.55 -2.60
Turkey 1980:1-2005:8 -2.01 -2.27
Ukraine 1992:1-2005:8 -2.79 * -2.56
Uzbekistan 1994:1-2005:8 -1.44 -2.96 **

Country [t.sub.NL12] [t.sub.ADF2]

Albania -1.57 -2.51
Armenia -0.84 -1.75
Azerbaijan -2.44 -2.14
Belarus -1.73 -1.98
Bulgaria -2.70 * -3.71 **
Croatia -4.95 *** -3.35 *
Cyprus -2.46 -1.44
Czech Republic -1.27 -2.92
Estonia -2.00 -2.30
Hungary 0.05 -2.19
Kyrgyz Republic -1.94 -1.79
Latvia -1.03 -1.24
Lithuania -1.52 -1.06
Macedonia -2.18 -2.17
Malta -2.38 -1.40
Moldova -5.84 *** -2.40
Poland -2.13 -2.32
Romania -0.89 -3.50 **
Russia -1.85 -1.93
Slovak Republic -3.25 ** -3.24 *
Slovenia -3.44 ** -1.98
Tajikistan -2.52 -1.10
Turkey -2.74 * -1.81
Ukraine -4.75 *** -2.86
Uzbekistan -2.85 * -2.25

Country [t.sub.NL21] [t.sub.NL22]

Albania -2.50 -3.93 ***
Armenia -3.11 -0.97
Azerbaijan -1.81 -2.44
Belarus -1.81 -1.25
Bulgaria -4.10 *** -4.34 ***
Croatia -6.59 *** -6.00 ***
Cyprus -1.25 -1.49
Czech Republic 3.23 * -3.27 *
Estonia -1.03 -1.37
Hungary -2.21 -2.50
Kyrgyz Republic -1.90 -2.01
Latvia -0.02 -1.01
Lithuania -0.35 -0.99
Macedonia -2.50 -3.51 **
Malta -2.01 -2.79
Moldova -4.45 *** -5.89 ***
Poland -2.07 -2.53
Romania -2.58 -3.89 **
Russia -1.33 -1.96
Slovak Republic -0.88 -3.82 **
Slovenia -3.23 * -2.29
Tajikistan -2.18 -2.17
Turkey -1.77 -2.20
Ukraine -2.56 -4.60 ***
Uzbekistan -2.99 -2.85

[t.sub.ADF1] and [t.sub.ADF2] are the standard ADF test statistics
for the null of stationarity and the null of trend stationarity,
respectively, of the variable in the study. [t.sub.NL11] and
[t.sub.NL12] are the KSS test statistics for the de-meaned data using
the models without and with augmentations, respectively. [t.sub.NL21]
and [t.sub.NL22] are the KSS test statistics for the detrended data
using the models without and with augmentations, respectively. The
10, 5, and 1% asymptotic critical values for [t.sub.ADF1] are -2.57,
-2.86, and -3.43, respectively, and those for [t.sub.ADF2] are -3.12,
-3.41, and -3.96, respectively. The 10, 5, and 1% asymptotic critical
values for [t.sub.NL11] and [t.sub.NL12] are -2.66, -2.93, and -3.48,
respectively, and those for [t.sub.NL21] and [t.sub.NL22] are -3.13,
-3.40, and -3.93, respectively, taken from Kapetanios, Shin, and Snell
(2003, p. 364).

*, **, and *** denote rejection of the null hypothesis at the 10, 5,
and 1% significance levels, respectively.

Table 4. Unit Root Test Results for Latin American LDCs

Country Sample Period [t.sub.ADF1] [t.sub.NL11]

Antigua and
 Barbuda 1980:1-2005:8 -2.01 -1.32
Belize 1980:1-2005:8 -2.40 -0.95
Bolivia 1986:1-2005:8 -1.50 -0.56
Chile 1980:1-2005:8 -4.64 *** -3.66 ***
Colombia 1980:1-2005:8 -2.28 -1.23
Costa Rica 1981:1-2005:8 -2.75 * -2.05
Dominica 1980:1-2005:8 -2.33 -1.98
Dominican
 Republic 1980:1-2005:8 -2.39 -2.46
Ecuador 1980:1-2005:8 -2.86 ** -3.39 ***
Grenada 1980:1-2003:7 -1.46 -1.58
Guyana 1990:1-2005:8 -2.18 -2.10
Mexico 1980:1-2005:8 -3.61 *** -3.29 **
Netherlands
 Antilles 1980:1-2003:7 -2.21 -1.10
Nicaragua 1992:1-2005:8 -2.28 -1.17
Paraguay 1980:1-2003:7 -2.29 -2.68 *
St. Kitts and
 Nevis 1980:1-2005:8 -1.82 -2.15
St. Lucia 1980:1-2003:7 -1.72 -2.42
St. Vincent
 and Grens. 1980:1-2005:8 -2.02 -2.56
Trinidad and
 Tobago 1986:1-2005:8 -1.94 -2.06
Uruguay 1983:1-2003:7 -1.46 -1.28
Venezuela 1980:1-2003:7 -1.82 -1.74

Country [t.sub.NL12] [t.sub.ADF2]

Antigua and
 Barbuda -1.70 -2.79
Belize -2.19 -3.54 **
Bolivia -1.07 -1.75
Chile -3.96 *** -3.67 **
Colombia -1.51 -1.97
Costa Rica -2.94 ** -2.77
Dominica -2.32 -2.73
Dominican
 Republic -2.20 -2.17
Ecuador -3.03 ** -2.14
Grenada -1.73 -1.73
Guyana -1.87 -1.54
Mexico -4.03 *** -5.79 ***
Netherlands
 Antilles -1.36 -2.86
Nicaragua -1.98 -2.30
Paraguay -2.07 -1.95
St. Kitts and
 Nevis -3.17 ** -1.90
St. Lucia -2.40 -1.73
St. Vincent
 and Grens. -2.99 ** -2.19
Trinidad and
 Tobago -1.84 -2.06
Uruguay -1.89 -1.19
Venezuela -1.71 -1.79

Country [t.sub.NL21] [t.sub.NL22]

Antigua and
 Barbuda -1.88 -2.41
Belize -1.10 -2.35
Bolivia -2.36 -2.89
Chile -2.79 -3.22 *
Colombia -0.90 -1.59
Costa Rica -1.96 -2.77
Dominica -2.03 -2.39
Dominican
 Republic -1.80 -1.93
Ecuador -2.65 -2.36
Grenada -1.67 -1.83
Guyana -1.32 -1.61
Mexico -5.51 *** -6.65 ***
Netherlands
 Antilles -1.65 -2.23
Nicaragua -1.47 -2.38
Paraguay -1.75 -0.23
St. Kitts and
 Nevis -2.32 -3.39 *
St. Lucia -2.41 -2.38
St. Vincent
 and Grens. -2.67 -3.12
Trinidad and
 Tobago -1.84 -1.57
Uruguay 0.03 -3.14 *
Venezuela -1.64 -1.60

[t.sub.ADF1] and [t.sub.ADF2] are the standard ADF test statistics
for the null of stationarity and the null of trend stationarity,
respectively, of the variable in the study. [t.sub.NL11] and
[t.sub.NL12] are the KSS test statistics for the de-meaned data using
the models without and with augmentations, respectively. [t.sub.NL21]
and [t.sub.NL22] are the KSS test statistics for the detrended data
using the models without and with augmentations, respectively. The
10, 5, and 1% asymptotic critical values for [t.sub.ADF1] are -2.57,
-2.86, and -3.43, respectively, and those for [t.sub.ADF2] are -3.12,
-3.41, and -3.96, respectively. The 10, 5, and 1% asymptotic critical
values for [t.sub.NL11] and [t.sub.NL12] are -2.66, -2.93, and -3.48,
respectively, and those for [t.sub.NL21] and [t.sub.NL22] are -3.13,
-3.40, and -3.93, respectively, taken from Kapetanios, Shin, and Snell
(2003, p. 364).

*, **, and *** denote rejection of the null hypothesis at the 10, 5,
and 1% significance levels, respectively.

Table 5. Mean Reversion of REER and Country Characteristics

 Number of
 Countries
 with the REER
 Number of Reverting to a
Country Group Countries Constant Mean

Openness (%)
Least open (<44) 22 6
Moderately less open (44-62) 22 12
Moderately more open (62-85) 22 7
Most open (>85) 22 6
GDP growth (%)
Lowest (<0.11) 21 6
Moderately low (0.11-2) 22 8
Moderately high (2-3.65) 22 8
Highest (>3.65) 22 9
Inflation (%)
Lowest (< 5.3) 22 9
Moderately low (5.3-11) 21 5
Moderately high (11-23) 21 6
Highest (> 23) 21 10
Nominal exchange rate (log of national currency per SDR) flexibility
Lowest (<0.22) 22 5
Moderately low (0.22-0.4) 22 8
Moderately high (0.4-0.92) 22 6
Highest (>0.92) 22 12
Nominal exchange rate (log of national currency per U.S. dollar)
 flexibility
Lowest (<0.2) 22 5
Moderately low (0.2-0.36) 22 9
Moderately high (0.36-0.86) 22 5
Highest (>0.86) 22 12

 Number of
 Countries
 Number of with REER
 Countries with the Reverting to a
 REER Reverting Constant Mean
Country Group to a Trend or to a Trend

Openness (%)
Least open (<44) 6 12
Moderately less open (44-62) 2 14
Moderately more open (62-85) 3 10
Most open (>85) 2 8
GDP growth (%)
Lowest (<0.11) 6 12
Moderately low (0.11-2) 3 11
Moderately high (2-3.65) 2 10
Highest (>3.65) 2 11
Inflation (%)
Lowest (< 5.3) 2 11
Moderately low (5.3-11) 3 8
Moderately high (11-23) 4 10
Highest (> 23) 4 14
Nominal exchange rate (log of national currency per SDR) flexibility
Lowest (<0.22) 4 9
Moderately low (0.22-0.4) 2 10
Moderately high (0.4-0.92) 3 9
Highest (>0.92) 4 16
Nominal exchange rate (log of national currency per U.S. dollar)
 flexibility
Lowest (<0.2) 4 9
Moderately low (0.2-0.36) 2 11
Moderately high (0.36-0.86) 3 8
Highest (>0.86) 4 16

Openness is the average of the sum of exports and imports measured
as a share of GDP. GDP growth is the average of annual percentage
growth rate of PPP-adjusted per capita real GDP. Inflation is the
average annual change in CPI. Nominal exchange rate volatility is
the standard deviation of the log of the monthly exchange rate.
Real effective exchange rate volatility is the standard deviation
of the rate used in this study for the unit root tests.