Real exchange rate stationarity in developing countries a new panel test.

ABSTRACT

This article examines the mean reversion behavior of the real exchange rate for panels with cross sectional dependency. The study is conducted using a newly developed nonlinear IV unit root test for a panel of 41 developing countries. The test allows for a general dependency structure among the innovations that generate data for each of the cross-sectional units, is asymptotically normal, and does not require any tabulation of the critical values. Using the US dollar as a numeraire and annual data that extends from 1971 and up to 2000, we were able to reject the null of unit root for the full panel and for sub panels for Africa, Latin America and for high inflation countries.

1. INTRODUCTION The purchasing power parity (PPP) exchange rate is the exchange rate that would make the purchasing power of a unit of a currency the same in two countries if expressed in terms of one common currency, under these conditions the same basket of goods and services should cost the same when expressed in terms of the same currency. The above refers to what is called the absolute version of the PPP theory. The relative version of the theory says that the nominal exchange rate change over time such that the price of the same basket of goods in the two economies change at the same rate. One implication of the PPP is that the real exchange rate should not change starting from an equilibrium position. If the real exchange rate is constant, then its movement will be viewed as deviations from PPP, in this case, PPP would serve as a good approximation of economic behavior in the long run. Policy makers will then be able to make predictions about future movement in the exchange rate or decide on fixing parties between currencies based on some exchange rate derived based on the real exchange rate. If the real exchange rate could not found to be constant, (non-stationary) then PPP would not be of much help to policy makers. In addition, the importance of the PPP stems from the fact that most theories of international finance are based on PPP theory, as result policy advice again may depend on the validity of PPP.

While empirical evidence for PPP has been mixed, recently there has been increasing evidence in favor of PPP in industrial countries. These studies used mostly the panel test procedure. Among these studies are (Wu, 1996); (MacDonald,1996); (Oh, 1996); (Jorion and Sweeney, 1996); (Papell, 1997) and (Papell & Theodoridis, 1998; 2001) to mention some Studies for developing countries have found mixed evidence for PPP. (Bahmani-Oskooee, 1993) Used Engle-Granger technique on 25 less developed countries and fond evidence for PPP only on few cases among major trading partners, (Mahdavi and Zhou, 1994) applied the Johansen technique on a sample of less developed countries and concluded that PPP is likely to hold among high inflation countries, (Salehizadeh M & Taylor R, 1999) used the technique of cointegration and found mixed results in a sample of 27 developing countries. The majority of the Studies on the validity of PPP theory in developing countries used ADF tests and cointegration techniques and have found only little evidence for PPP. Studies that tests for cointegration have been criticized for having low power against stationary alternatives. The ADF statistics have been found to have low power with short time span; they tend not to reject the unit root null even if it is false. One way to deal with this problem is to increase the sample size or to resort to the panel test procedure so as to increases the power of the unit root tests. One of the recent studies employing the panel tests is the study by (Holmes M, 2001). The study has tested for relative purchasing power parity among a sample of thirty less developed countries using the test advocated by (Im, Pesaran and Shin, 1997). The test is based on the calculation of the average augmented Dickey-Fuller statistic and deals with the problem of cross correlations by demeaning the data. Cross correlations is caused by the common components induced by the numeraire country's base currency and price index. The study concluded that only a few units in the world panel drive the result for PPP. (O'Connell, 1998) has shown that in the presence of cross correlation even demeaning may not be enough if countries in the panel are group wise highly correlated. In this study, we reexamine for the PPP theory using a newly developed nonlinear IV panel unit root testing procedure due to (Yoosoon, C 2002). The study differs from other studies in the way that cross correlation is dealt with. The test allow for general dependency structure among the innovations that generate data for each of the cross-sectional units, is asymptotically normal, and does not require any tabulation of the critical values. It is based on a nonlinear IV estimation of the usual Augmented Dickey-Fuller type regression for each cross-sectional unit, using as instruments nonlinear transformations of the lagged levels. A t-ratio statistic that has limiting standard normal distribution under the null hypothesis is constructed for testing the unit root based on the nonlinear IV estimator for the AR coefficient. (Yoosoon C, 2002) has shown that the individual IV t-ratio statistics are asymptotically independent even across dependent cross-sectional units. Consequently, the average of these independent individual IV t-ratio statistics is considered as a statistic for testing joint unit root null hypothesis for the entire panel. This study test for PPP in 41 developing countries using annual data and bilateral dollar exchange rate. We allowed for heterogeneous dynamic AR structure and selected the lag length based on the BIC. The data used covers the period from 1971 and up to 2000. The rest of this paper is organized as follows: section 2 is on the methodology, section 3 describe the data used in the study and the univarite ADF test results, section 4 is on the Panel test results, section 5 is the conclusion

2. METHODOLOGY:

The actual IV Z test statistic is simply defined as a standardized sum of the individual IV t-ratios. Consider the following regression

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The IV panel unit root test can be done based on the above regression. To deal with cross sectional dependency the IV test relies on an instrument generated by non-linear function F as

(2) F ([y.sub.i, t-1])

for the lagged level [y.sub.i, t-1] and for the lagged differences

(3) [x'.sub.it] = ([DELTA] [y.sub.i, t-1] ... [DELTA] [y.sub.i, t-pi])

the variables themselves are used as instruments, hence for the entire regressors ([y.sub.i, t-1], [x'.sub.it])', the instrument is given by

(4) (F([y.sub.i, t-1]), [x.sub.it])' = (F ([y.sub.i, t-1]), [DELTA] [y.sub.i, t-1] ... [DELTA] [y.sub.i, t-pi])'

The instrument is required to be regularly integrable and correlated with the regressor [y.sub.i, t-1]. The augmented auto regression (1) can be written in matrix form as

(5) [y.sub.i] = [y.sub.li] [[alpha].sub.i] + [X.sub.i] [[beta].sub.i] + [[epsilon].sub.i] = [Y.sub.i][y.sub.i] + [[epsilon].sub.i]

Where [[beta].sub.i] = ([[alpha].sub.,i1],.... [[alpha].sub.i, p]), [Y.sub.i] = ([y.sub.li,,] [X.sub.i]), and [y.sub.i] = ([[alpha.sub.i], [[beta].sub.i). For the augmented auto regression (5) the estimator [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of [y.sub.i] is the IV estimator. The IV estimator [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for the AR [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] coefficient correspond to the first element of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], see (Yoosoon C, 2002) for details. To test for the joint unit root null hypothesis [H.sub.o]:[[alpha].sub.i]=1 for all i=1, ..., N the test uses an average statistics based on the individual t-statistics for testing [alpha] = 1 in (1) constructed from the nonlinear IV estimator. The average IV ratio test statistics is defined as

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [Z.sub.i] is the individual nonlinear IV t- ratio statistic. The normalized sum of the individual IV t ratios has standard normal limit distribution as long as [T.sub.min] [right arrow] [infinity] and [T.sup.1/4.sub.min] log [T.sub.max]/[T.sup.3/4.sub.min] [right arrow] 0, where [T.sub.min], [T.sub.max] denote the minimum and the maximum number of time series observations respectively. The usual sequential asymptotics, upon which most of the asymptotic theories for panel unit root models heavily rely, are not required. The number of cross-sectional units may thus allowed to be arbitrarily small or large. The finite sample properties of the IV t-ratio statistic are examined in (Yoosoon C, 2002) paper and compared to t-bar statistic by (Im et al. ,1997). The test generally performed better than the t-bar test in terms of both finite sample sizes and powers.

3. THE DATA:

The data set is taken from the international financial statistics IFS CD ROM. The price series used to construct the real exchange rates is the consumer price index the CPI; it is the only price series available for most countries in the panel. The US dollar is used as a numeraire. The test is implemented with the data sampled at annual frequencies extending from 1971 and up to 2000, with 30 observations. The use of the annual series is justified since we are interested in the long run behavior rather than short-term volatility. The real exchange rate between each country and say, for example, the US is defined as

(7) [y.sub.t] = ln ([e.sub.t] [P.sup.US.sub.t]/[P.sub.t])

Where [y.sub.t] is the real exchange rate between a given country's currency and the US dollar;[P.sub.t.sup.US] is the US CPI ; [P.sub.t] is a given country's CPI; [e.sub.t] the nominal exchange rate between a country's currency and the US$. Forty-one Countries are included in the panel; these are:

Africa: 1) Burundi, 2) Cote D Ivoire, 3) Egypt, 4) Ethiopia, 5) Gabon 6) Mauritius, 7)Gambia, 8) Ghana, 9) Morocco, 10) Nigeria, 11) Sierra Leone, 12) Swaziland 13) Sudan, and 14) Kenya

Latin America: 1) Chile, 2) Colombia, 3) Costa Rica, 4) Dominican Republic, 5)Ecuador, 6) El Salvador, 7) Guatemala, 8) Haiti, 9) Honduras, 10) Mexico, 11) Panama, 12) Paraguay and 13) Venezuela,

Asia: 1) Korea, 2) Singapore, 3) Malaysia, 4) Philippines, 5) Indonesia, 6) Thailand, 7) Srilanka, and 8) Iran

Others: 1) Cyprus, 2) Turkey, 3) Malta, 4) Trinidad and Tobago, and 5) Netherlands Antilles, and 6) Jamaica

Some of the countries in the panel have experienced frequent exchange rate regime changes and some of them maintain pegged exchange rates; it has been argued that the same specification of the PPP hypothesis is not applicable to countries that adopt different exchange rate regimes (Liu, 1992). The PPP as along run phenomena, however, should apply irrespective of the exchange rate regime. Evidence to support this view is found in (Lothian and Taylor, 1996) they show that the stationary process estimated for the pre 1973 data (that is before the floating regime for the industrial countries) perform well in out of sample forecasting for post 73 period. (Froot, Kim, and Rogoff ,2001) showed surprising stability of deviations from the low of one price over seven hundred years in England and Holland, specifically, they showed that movements in cross-country relative prices of the same good constituted the major source of variation in real exchange rates. They show that this occurs while the nominal exchange rates were far less volatile and so, local-currency pricing (sticky prices) apparently far less important. More recently, (Kuo and Mikkola, 2001) found evidence for PPP form a panel of industrial countries over the 1947-1996 period. They concluded among other things, that PPP as along run relationship has nothing to do with the exchange rate regime. To conclude, while deviations from the law of one price (LOP) or PPP may be stationary, the sources of the deviations can interchange between the nominal exchange rate changes, the relative prices changes or both. The empirical evidence suggests that exchange rate regime have no impact on real exchange rate long run mean reversion behavior.

To formally test for unit root in the real exchange rates the augmented (Dickey-Fuller 1979, 1981) tests were conducted first. Table 1 contains the summery of our ADF unit root test results for each of the individual series in the panel. The test was carried for original sample period 1971-2000, using the following equation

(8) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Where [y.sub.t] log of the real exchange rate, [[mu].sub.j] country specific constant term to control for non time dependant heterogeneity across countries the [y.sub.i]'s are lagged coefficient in the process describing [y.sub.t], [[alpha].sub.j] = [[rho].sub.j]-1. Lag specification is done according to the BIC procedure. I report the ADF result in table 1 .The null hypothesis that the real exchange rates data contains unit root could be rejected for only two countries in the panel (Singapore at % 5 and Sierra Leone at 1% levels of significance). Accordingly, each of the remaining real exchange rates in this panel is nonstationary according to the ADF test procedure.

4. THE IV PANEL APPROACH:

As we indicated earlier, it is known that the ADF statistics has low power with short time span see for example (Maddala, and Kim, 1998). They tend not to reject the unit root null even if it is false. One way to deal with this problem is to increase the sample size. We were only able to use a sample extending from 71 to 2000. In the following section, we turn to a panel test procedure and use both the IV test to examine the null of unit root in our panel of real exchange rate series. The main advantage of the panel test procedure over the standard augmented Dickey-Fuller test is that it exploits the extra information provided by the pooled cross sectional time series and dramatically increases the power of the tests. We first applied the test to the full panel 41 countries and the null of unit root was rejected at 1% according the IV Z test. To respond to the cautionary note by (Taylor and Samo, 1998) that the result of panel unit root test may be driven by as low as one stationary series in the panel series we checked the robustness of the result to dropping the stationary series based on the ADF test result. After dropping Sierra Leone and Singapore (as they appeared stationary based on the univariate ADF result), the null is still rejected in each case at 5% level of significance. Although the rejection is now lower, this result indicates that the result is not driven by the stationary series in the panel Table 2. We then reorganized the panel based on main regions (Africa, Asia, and Latin America), as a result, we have three panels to test each for PPP. The result of applying the test on each sub panel is reported in table 2. The null of unit root was rejected in case of Africa and Latin America but accepted incase of Asia. The acceptance of the null in case of Asia given a stationary Asian real exchange rate (Singapore) again indicates that the result is not driven by the stationary exchange rates in the world panel. It has been argued that PPP is more likely to hold among high inflation countries. High inflation results in loss of competitiveness that (in many cases) requires devaluations to restore competitiveness. The process of nominal exchange rate adjustment accelerates real exchange rate mean reversion. As a result, we have tested for PPP among a selected group of high inflation countries (countries with annual inflation of 20% or more during 1971-2000). The countries included in this panel are Chile, Colombia, Ecuador, Ghana, Iran, Jamaica, Mexico, Nigeria, Sierra Leone, Turkey, and Venezuela. The null is also rejected at 5% level of significance in this case table 2. Our over all result is generally consistent with the results obtained by (Mark J. Holmes, 2001) on the world panel and the African sub panel. The difference is that we found evidence for mean reversion in case of Latin America, high inflation countries. It should also be pointed here that the existence of stationary univarite real exchange rate had no impact in the result incase of Asia.

The full panel organized by region is as follows:

Africa: 1) Burundi, 2) Cote D Ivoire, 3) Egypt, 4) Ethiopia, 5) Gabon 6) Mauritius, 7) Gambia, 8) Ghana, 9) Morocco, 10) Nigeria, 11) Sierra Leone , 12) Swaziland 13) Sudan, and 14) Kenya

Latin America: 1) Chile, 2) Colombia, 3) Costa Rica, 4) Dominican Republic, 5) Ecuador, 6)El Salvador, 7) Guatemala, 8) Haiti, 9) Honduras, 10), Mexico, 11) Panama, 12) Paraguay and 13) Venezuela

Asia: 1) Korea, 2) Singapore, 3) Malaysia, 4) Philippines, 5) Indonesia, 6) Thailand, 7) Srilanka, and 8) Iran

Others: 1) Cyprus, 2) Turkey, 3) Malta, 4) Trinidad and Tobago, and 5) Netherlands Antilles, 6) Jamaica High Inflation Countries: 1) Chile, 2)Colombia, 3)Ecuador, 4)Ghana, 5)Iran, 6)Jamaica, 7)Mexico, 8)Nigeria, 9)Sierra Leone, 10)Turkey, and 11)Venezuela

5. CONCLUSION:

In this study, we reexamine for the real exchange rate mean reversion behavior in 41 developing countries using annual data and bilateral dollar exchange rate. The study differ from other studies in that cross correlation is directly dealt with using a newly developed nonlinear IV panel unit root testing procedure due to (Yoosoon, C ,2002). The test is based on nonlinear IV estimation of the usual Augmented Dickey-Fuller type regression for each cross-sectional unit, using as instruments nonlinear transformations of the lagged levels. The actual test statistic is simply defined as a standardized sum of individual IV t -ratios. We allowed for heterogeneous dynamic AR structure and selected the lag length based on the BIC. The data used covers the period from 1971 and up to 2000. We found evidence for mean reversion in the full panel and even after dropping the series that appeared stationary at the univarite testing level. We also found evidence for mean reversion for sub panels in case of Africa, Latin America and for high inflation countries. We did not find Evidence of mean reversion for Asia, although Singapore real exchange rate appeared stationary based on ADF test. The lack of evidence in case of Asia could be because Asian economies are better integrated with Japan than with the US, consequently, their prices and exchange rates may be stable against the Japanese prices and exchange rate.

TABLE 1

UNIVARIATE UNIT ROOT TEST

COUNTRY                 ADF

Burundi                 -0.74863
Chile                   -2.1272
Colombia                -1.3935
Cost Rica               -1.8545
Coteivoire              -2.1553
Cyprus                  -1.9351
Dominican               -1.2192
Ecuador                 -0.87069
Egypt                   -2.7203
Elsalvdor               -1.1489
Ethiopia                -0.0069357
Gabon                   -0.75838
Gambia                  -0.48395
Ghana                   -1.1051
Guatemala               -1.2333
Haiti                   -2.5237
Honduras                -1.2275
Iran                    -2.228
Jamaica                 -1.5318
Kenya                   -1.6907
Malaysia                -0.30737
Malta                   -1.9859
Mauritius               -1.087
Mexico                  -2.6203
Morocco                 -1.8422
Netherlands Antilles    -2.5718
Nigeria                 -2.1396
Panama                   0.087978
Paraguay                -1.0489
Philippines             -1.7198
Sra Leone               -3.6694 *
Singapore               -3.5208 *
Srilanka                -2.3199
Swaziland               -1.9718
Thailand                -0.87025
Trinidad and Tobago     -2.3546
Turkey                  -1.4417
Venezuela               -1.3135
Sudan                   -2.6848
Korea                   -1.6588
Indonesia               -0.41415

Where * represent the 5% level of significance

TABLE 2

PANEL UNIT ROOT TEST RESULTS

                     The Z IV Test    P Value        N     T

The Full Panel              -2.393    [0.0084] **    41    30
Less 1 Stationary           -2.064    [0.0195] *     40    30
Less 2 Stationary           -1.931    [0.0267] *     39    30
Africa                      -2.116    [0.0172] *     14    30
Asia                        -0.017    [0.4932]        8    30
Latin America               -1.771    [0.0383] *     13    30
HiGh Inflation              -1.903    [0.0285] *     11    30

* & ** represent the 1 and the 5% levels of significance respectively.

REFERNCES:

Bahmani-Oskooee, M., "Purchasing Power Parity Based on Effective Exchange Rate and Cointegration", World Development, Vol. 21, 1993, 1023-31.

Dickey, D. and Fuller, W., "Distribution of the Estimators for Autoregressive Time Series with a Unit Root", Journal of the American Statistical Association, Vol.74, 1979, 427-431.

Dickey, D., and Fuller, W.A.," Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root", Econometrica, Vol.49, 1981, 1057-1072.

Holmes M. "New Evidence on Real Exchange Rate Stationarity and Purchasing Power Parity in Less Developed Countries" Journal of Macroeconomics, Vol. 23(4), 2001, 601-614

Im, K. S., M. H. Pesaran, and Y. Shin, "Testing for Unit Roots in Heterogeneous Panels", Discussion paper, Department of Applied Economics, University of Cambridge December 1997

Jorion, P., and R. Sweeney., "Mean Reversion in Real Exchange Rates: Evidence and Implications for Forecasting," Journal of International Money and Finance, Vol.15, 1996, 535-550.

Lothian, J. and Taylor, M., "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries", Journal of Political Economy, Vol. 104, 1996,488-509

MacDonald, R., "Panel Unit Root Tests and Real Exchange Rates", Economic Letters, Vol. 50, 1996, 7-11.

Maddala, G.S., and Kim, I.M., Unit Roots, Cointeqration, and Structural Change Cambridge University Press, 1998

Mahdavi, Saeid, and Su Zhou. "Purchasing Power Parity in High Inflation Countries: Further Evidence." Journal of Macroeconomics, Vol. 16, 1994, 403-22.

O'Connell, P.G.J., "The Overvaluation of Purchasing Power Parity", Journal of International Economics, Vol.44, 1998, 1-19.

Oh, K. "Purchasing Power Parity and Unit Root Tests Using Panel Data," Journal of International Money and Finance, Vol.15, 1996, 405-418.

Papell, D. "Searching for Stationarity: Purchasing Power Parity under the Current Float," Journal of International Economics, Vol.43, 1997, 313-332.

Papell, D., and H. Theodoridis "Increasing evidence of purchasing power parity over the current float", Journal of International Money and Finance, Vol. 17 (1) 1998, 41-50

Papell, D., and H. Theodoridis "The Choice of Numeraire Currency in Panel Tests of Purchasing Power Parity," Journal of Money, Credit, and Banking, Vol.33, 2001, 790-803.

Salehizadeh M, Taylor R "A test of purchasing power parity for emerging economies" Journal of International Financial Markets, Institutions and Money, Vol.9, 1999, 183-193

Taylor, Mark P., and Lucio Sarno. "The Behavior of the Real Exchange Rate During the Bretton Woods Period." Journal of International Economics Vol.46, 1998, 281-312.

Shen Kuo, B, and Mikkola Anne "How Sure Are We about Purchasing power Parity? Panel Evidence with the Null of Stationary Real Exchange Rates, "Journal of Money, Credit, and Bankinq, Vol.33, 2001, 767-789.

Froot, K., and Rogoff, K. "The Law of One Price over 700" revision of NBER working Paper May 1995, No. 5132

Wu, Y., "Are Real Exchange Rates Nonstationary? Evidence from a Panel-Data Test, "Journal of Money, Credit, and Banking Vol.28, 1996, 54-63.

Yoosoon Chang "Nonlinear IV unit root tests in panels with cross-sectional dependency "Journal of Econometrics, Vol. 110, 2002, 2,261-2.

Dr. K Hassanain earned his Ph.D. at Iowa State University in 12/1997. Currently he is an assistant professor of economics at the UAE University, UAE Alain and the chair of the collage of business resources committee. He also represents the collage at the university level on resources related matters