Black market exchange rate versus the official rate in testing the PPP: an application of a non-linear test.
The purchasing power parity theory (PPP) is perhaps one of the most important theories in economics that has received the largest attention in the literature (1). In its absolute form, the theory claims that in the long run the exchange rate between two currencies will be equal to the ratio of two corresponding national price levels. One implication of the theory is that a country can fight inflation by managing the value of its currency in terms of the currency of its major trading partners. For a successful policy, the relative prices and the nominal exchange rate should converge over time and form a stationary process. Thus, one way of testing the PPP is to test for the mean-reverting property of the nominal exchange rate that incorporates changes in relative prices into its mean-reverting process, that is, testing for stationarity of the real exchange rate.
Early studies that tested for stationarity of the real exchange rates or other formulation of the PPP mostly rejected it. Examples include Taylor (1988), Carbae and Ouliaris (1988, 1991), McNown and Wallace (1989), Layton and Stark (1990), Kim (1990), Bahmani-Oskooee and Rhee (1992), and Bahmani-Oskooee (1995). Examples of those who have supported the PPP include Bahmani-Oskooee and Barry (1997), Lothian and Taylor (1996), and Bahmani-Oskooee (1998). (2) Most of these studies relied upon the standard Augmented Dickey-Fuller (ADF) test in which the null hypothesis of nonstationarity or unit root is tested against a linear stationarity. Recently Kapetanios et al. (2003, KSS hereafter) have developed a new test that is based on a non-linear exponential smooth transition autoregressive (ESTAR) procedure in which the null is still unit root but the alternative is non-linear stationarity in a time-series variable. Application of this new test by most recent studies reveals that the new test supports the PPP more often than the standard ADF test implying that the mean-reverting process of real exchange rates follows a non-linear path. Examples in this later group of studies include Sarno (2000), Taylor et al. (2001), Liew et al. (2004), Chortareas and Kapetanios (2004), Sarno et al. (2004), and Bahmani-Oskooee and Gelan (2006).
One common feature of all of the studies mentioned above is that they have all relied upon the official exchange rates in testing the PPP. There is another part of the literature that includes studies that have used black market exchange rates in testing the PPP in less-developed countries (LDCs). The main argument for using the black market or parallel exchange rates in testing the PPP is that they serve as a proxy for floating exchange rates in LDCs. The literature reviewed by Bahmani-Oskooee and Goswami (2005) reveals that PPP is supported more often when the black market exchange rate is used in the testing procedure. Studies in this group are Culbert (1975), Edwards (1989), Phillips (1988), Bahmani-Oskooee (1993), El-Sakka and McNaab (1994), Baghestani (1997), Sanchez-Fung (1999), Luintel (2000), Kouretas and Zarangas (2001), Nagayasu (2000), and Bahmani-Oskooee and Goswami (2005).
Although the above-mentioned studies validate the PPP by using the black market more often than the official exchange rate, support for the PPP is not unanimous across the countries. In this paper, we try to test the PPP by using both the official as well as the black market exchange rates. In doing so we employ both the standard ADF test and the KSS test to determine whether the mean-reverting properties of the real black market exchange rates are on a non-linear but stationary path. To this end, we introduce the KSS test in the next section. The penultimate section reports the results with concluding remarks in the final section.
THE RELATIVELY NEW KSS TEST (3)
The standard ADF test sets the stage for testing the null of non-stationarity or unit root against the alternative of stationarity of a time-series variable that follows a linear path. In order to see the difference between the standard ADF test and the new KSS test, we outline the standard ADF test first, as in equation (1) for a time-series variable Z.
[DELTA][Z.sub.t] = [delta][Z.sub.t-1] + [n.summation over (k=1)] [[rho].sub.k] [DELTA][Z.sub.t-1] + [[epsilon].sub.t] (1)
Kapetanios et al. (2003) built upon the standard ADF test outlined by (1) and introduce a new test, but a relatively more powerful one, in which the null hypothesis is still unit root but the alternative hypothesis is a non-linear stationary smooth transition autoregressive (STAR) process. They demonstrate that in small samples the linear ADF test suffers from some upward size distortion whereas the size of their new non-linear test rarely rises above the 5% level. Furthermore, the goodness of fit is substantially better under the exponential smooth transition autoregressive (ESTAR) specification as compared to the simple autoregressive specification. The new test is based on the following ESTAR specification:
[DELTA][Z.sub.t] = [lambda][Z.sub.t-1][1 - exp(-[theta][Z.sup.2.sub.t-1]] + [[mu].sub.t] (2)
In (2) the time-series variable [Z.sub.t] could be raw data, the de-meaned data, or the de-trended series. (4) In (2), like (1), the null of unit root, that is, [theta]-0, is tested against the alternative of [theta] > 0. However, Kapetanios et al. (2003) show that since [lambda] is not identifiable under the null, (2) could be approximated by (3) using the Taylor series.
[DELTA][Z.sub.t] = [delta][Z.sup.3.sub.t-1] + [[omega].sub.t] (3)
Furthermore, to make the residuals in (3) white noise, they include the augmented terms as in (4):
[DELTA][Z.sub.t] = [delta][Z.sup.3.sub.t-1] + [n.summation over (k=1)][[rho].sub.k[DELTA][Z.sub.t-k] + [[omega].sub.t] (4)
Comparing (4) to (1) we gather that in (4) non-linearity is reflected by raising the lagged value of the time-series variable under consideration to power three rather than to power one. Again the null of unit root, that is, [delta] = 0 is tested against the alternative of [delta] > 0 by the familiar t ratio obtained for [delta]. However, the new test has a new distribution for which the critical values are tabulated by Kapetanios et al. (2003). For selecting the lag length on the augmented term, we follow Kapetanios et al. (2003, p. 365) and rely upon significance of augmented terms. Since this t ratio is for a non-linear model as outlined by (4), we shall denote it by [t.sub.NL].
In this section we apply the standard ADF test outlined by equation (1) as well as the non-linear ADF test outlined by equation (4) to the official and the black market real exchange rates from 24 developing countries. The CPI data to be used in constructing the real exchange rates and the official exchange rates come from the International Financial Statistics of the IMF and the black market exchange rates come from Reinhart and Rogoff (2004). (5) Study period differed from one country to another depending on the availability of the black market exchange rate as shown in Table 1.
The results of the unit-root tests applied to both real official and real black market exchange rates (in log form) are reported in Table 2.
Reported in Table 2 are four statistics. The t-ratio from the standard ADF test that includes only a constant term is denoted by ADFc. In applying the non-linear test, since there is no constant in (4), following Kapetanios et al. (2003) we de-mean the data and apply the test to de-meaned data. The t-ratio for this non-linear test is reported as [t.sub.NL-demeaned]. Following the literature, these two tests are used to examine the mean-reverting properties of real exchange rates or reversion to a constant as a way of testing PPP.
Let us first concentrate on the results for the real official exchange rate (Table 2). The linear ADF test rejects the null of unit root only in three countries, providing support for PPP (ie, Argentina, Egypt, and Suriname). These cases are identified by a * next to their statistics. However, when we shift to the non-linear test results, the null of unit root is rejected in 11 countries. Therefore, like previous research, when the official exchange rate is used, the non-linear test supports the PPP more often than the linear or standard ADF test.
Now consider the results in Table 2 when the real black market exchange rate is used to carry out the unit root tests. The null of unit root is rejected in three countries by the linear ADF test. However, when we shift to the nonlinear test, the null is rejected in 13 countries. Again, the non-linear test rejects the null much more frequently than the linear test. Comparing these results to those of the official exchange rates, the non-linear tests support the PPP more often than the standard linear tests. But they support the PPP even more when the real black market exchange rate is used compared to the real official rate.
As an additional exercise, we tested the reversion in real exchange rates to a trend. This amounts to including a constant and a trend term in the standard ADF test. The statistic is denoted by [ADF.sub.t]. As for the non-linear test, again since there is no trend term in (4), following Kapetanios et al. (2003) we de-trend the data and apply the test to de-trended data. The statistic for this test is denoted by [t.sub.NL-detrend]. Table 3 reports the results.
From Table 3 we gather that the standard ADF test supports trend stationarity of the official exchange rate only in one country (ie, Syria) whereas, when the black market exchange rate is used, the null of trend stationarity is supported in five countries (ie, Costa Rica, Ethiopia, Kenya, Pakistan, and South Africa). Again, the null is rejected more often when the black market exchange rate is used in the testing procedure. The same is true when we consider the non-linear tests. The null of unit root is rejected by the [t.sub.NL-detrend] for 10 countries when the official exchange rate is used. However, it is rejected for 17 countries when the black market exchange rate is used.
Several studies have interpreted reversion to a trend as a method of testing the productivity bias hypothesis. The hypothesis asserts that in the long run, movement in the real exchange rate is determined by productivity differentials. (6) Our results show that the productivity bias hypothesis is supported more often when the black market exchange rate rather than the official rate is used to test the hypothesis. This supports Bahmani-Oskooee and Gelan (2006) who used regression analysis for testing the productivity bias hypothesis and showed that the hypothesis is supported more often when the black market exchange rate is used in the testing procedure.
SUMMARY AND CONCLUSION
The absolute PPP asserts that in the long run the exchange rate between two currencies should be equal to the ratio of two corresponding prices. One implication of the theory is that when the nominal exchange rate and relative prices are combined and form a long-run cointegrating relationship, their linear combination, which reflects the movement in the real exchange rate, must be stationary or mean reverting to support the PPP.
Most previous studies that tested the mean-reverting properties of the real exchange rate relied upon the standard ADF test, which sets the stage for testing the null hypothesis of non-stationarity or unit root against the alternative of linear stationarity. Since introduction of a new test by Kapetanios et al. (2003) the emphasis has shifted to determine whether the mean-reverting property of real exchange rates are on a non-linear path. Almost all studies that have used the relatively new non-linear test have shown that the new test validates the PPP more often than the standard ADF test. All these studies, however, have used the real official exchange rates to support their assertion.
There is yet another group of studies that has emphasised the use of black market exchange rates in testing the PPP on the grounds that such rates are proxies for the floating exchange rates. The floating exchange rate system lubricates the adjustment path between exchange rates and relative prices, thus supporting the PPP more often than the fixed exchange rate system. Although almost all studies have shown that using the black market exchange rate supports the PPP more often than using the official exchange rate, this conclusion is not unanimous and is based on the application of standard and linear ADF tests.
In this paper, we test the PPP by using the standard ADF as well as the new non-linear ADF test. The main purpose here is to determine whether the non-linear test validates the PPP more often than the standard ADF test when we employ the black market exchange rates. To this end, we use data from 24 developing countries. Two main conclusions stand out. First, the non-linear test provides support for the PPP more often than the standard ADF test when either the official exchange rate or the black market rate is used. Second, concentrating on the non-linear tests PPP receives somewhat more support when the black market exchange rate is used in testing the PPP as compared to using the official exchange rate. The same is true when we test reversion to a trend as a means of testing the productivity bias hypothesis. This hypothesis receives relatively more support when the non-linear test is applied to black market exchange rates as compared to official rates.
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(1) Valuable comments of two anonymous referees and Richard Perlman are greatly appreciated. Remaining errors, however, are ours.
(2) For a review article, see Rogoff (1996). A few studies have supported the PPP, for example, Bleaney (1991), Beach et al. (1993), Moosa (1994), Bahmani-Oskooee and Barry (1997), Lothian and Taylor (1996), and Bahmani-Oskooee (1998).
(3) This section closely follows Bahmani-Oskooee et al. (2007a, b).
(4) [mu] is an error term with usual properties.
(5) The data are actually on Reinhart's website at http://www.puaf.umd.edu/faculty/papers/ reinhart/reinhart.htm.
(6) See for example Bahmani-Oskooee et al. (2007b).
MOHSEN BAHMANI-OSKOOEE & ALTIN TANKU
The Center for Research on International Economics and The Department of Economics, The University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA. E-mail: email@example.com
Table 1: Study period for each country Country Starting date Ending date Algeria 1974Q1 1998Q4 Argentina 1968Q4 1998Q4 Chile 1973Q1 1998Q4 Costa Rica 1957Q1 1998Q4 Egypt 1957Q1 1998Q4 Ethiopia 1970Q3 1998Q4 Indonesia 1968Q1 1998Q4 India 1957Q1 1998Q4 Jordan 1976Q1 1998Q4 Kenya 1966Q4 1998Q4 Malaysia 1957Q1 1998Q4 Myanmar 1970Q1 1998Q4 Mexico 1957Q1 1998Q4 Morocco 1959Q1 1998Q4 Nigeria 1970Q3 1998Q4 Pakistani 1957Q1 1998Q4 Paraguay 1957Q1 1998Q4 Philippine 1957Q1 1998Q4 South Africa 1957Q1 1998Q4 Sri Lanka 1957Q1 1998Q4 Suriname 1970Q3 1998Q4 Syria 1970Q3 1998Q4 Thailand 1965Q1 1998Q4 Turkey 1980Q1 1998Q4 Table 2: The results for mean reversion of the real official and the black market exchange rate Official exchange rate Country [ADF.sub.c] [t.sub.NL-demeaned] Algeria -0.48730 -0.82218 Argentina -2.7161 * -4.0398 * Chile -1.0987 -1.3953 Costa Rica -1.1423 -4.8530 * Egypt -2.6673 * -2.3525 Ethiopia -2.1103 -1.5793 India -0.036137 -1.6294 Indonesia 0.60163 -8.0719 * Jordan -2.0881 -1.6661 Kenya -1.4377 -3.0284 * Malaysia -1.0527 -3.5438 * Myanmar -0.70773 -0.96901 Mexico -2.4185 -1.8229 Morocco -2.0961 -3.2377 * Nigeria -1.6962 -2.5996 Pakistani 0.14959 -0.023946 Paraguay -1.5300 -2.1968 Philippine -2.1561 -0.88850 South Africa -1.6778 -5.4370 * Sri Lanka -0.86966 -0.86564 Suriname -2.9486 * -3.4762 * Syria -1.4530 -3.2904 * Thailand -1.2475 -6.9223 * Turkey -1.8554 -3.8390 * 10% Critical value -2.57 -2.66 Black market exchange rate Country [ADF.sub.c] [t.sub.NL-demeaned] Algeria -1.7331 -1.4106 Argentina -2.3959 -6.9858 * Chile -1.7609 -1.3149 Costa Rica -2.8778 * -6.0357 * Egypt -1.8641 -3.4307 * Ethiopia -1.7763 -0.89291 India -1.4264 -2.0218 Indonesia 0.20028 -7.6739 * Jordan -1.5256 -1.5419 Kenya -3.7860 * -3.1587 * Malaysia 0.059040 -4.1983 * Myanmar -2.1250 -2.9965 * Mexico -2.2236 -3.9350 * Morocco -1.7957 -1.7174 Nigeria -1.7088 -3.1691 * Pakistani -1.0578 -1.4942 Paraguay -1.4322 -1.9730 Philippine -2.1277 -5.2079 * South Africa -3.2575 * -3.3577 * Sri Lanka -2.1161 -1.4978 Suriname -1.8716 -3.0207 * Syria -1.4784 -1.9948 Thailand -0.97783 0.25155 Turkey -2.2565 -3.3951 * 10% Critical value -2.57 -2.66 Note: Critical values come from Kapetanios et at. (2003, p. 364). Table 3: The for trend-stationarity of the real official and the black market exchange rate Official exchange rate Country [ADF.sub.t] [t.sub.NL-detrended] Algeria -2.2443 -1.4841 Argentina -2.7548 -3.9591 * Chile -0.83752 -1.1328 Costa Rica -1.9987 -3.6371 * Egypt -2.9633 -2.8591 Ethiopia -2.3088 -2.0881 India -2.0691 -2.7175 Indonesia -1.0974 -8.9847 * Jordan -2.5144 -3.1149 Kenya -2.1501 -3.1605 * Malaysia -2.5051 -4.5851 * Myanmar -1.3843 -1.7461 Mexico -2.5391 -1.7750 Morocco -2.8014 -2.9015 Nigeria -1.7084 -2.8037 Pakistani -2.7075 -4.4616 * Paraguay -2.5966 -2.6481 Philippine -2.9038 -2.7762 South Africa -2.6334 -5.4858 * Sri Lanka -1.1876 -1.6419 Suriname -2.9267 -3.4349 * Syria -3.3356 * -3.9554 * Thailand -2.0011 -8.1923 * Turkey -2.5308 -2.3250 10% Critical value -3.12 -3.13 Black market exchange rate Country [ADF.sub.t] [t.sub.NL-detrended] Algeria -2.0589 -3.5951 * Argentina -2.6656 -6.7001 * Chile -1.8507 -0.73845 Costa Rica -3.6053 * -6.6801 * Egypt -2.3080 -3.4316 * Ethiopia -3.2922 * -4.0022 * India -2.2356 -3.1398 * Indonesia -1.4868 -8.3244 * Jordan -1.6160 -6.1116 * Kenya -3.8344 * -3.4926 * Malaysia -1.4677 -5.7319 * Myanmar -1.9652 -2.9212 Mexico -2.3406 -4.0544 * Morocco -2.1817 -3.1416 * Nigeria -2.4589 -3.5022 * Pakistani -3.2837 * -4.7848 * Paraguay -2.0312 -2.3147 Philippine -2.9599 -6.0179 * South Africa -4.0747 * -3.6068 * Sri Lanka -2.2071 -4.9789 * Suriname -1.8404 -3.1131 Syria -1.7789 -2.3754 Thailand -1.9121 0.26016 Turkey -2.8861 -2.1510 10% Critical value -3.12 -3.13 Note: Critical values come from Kapetanios et al. (2003, p. 364).
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|Author:||Bahmani-Oskooee, Mohsen; Tanku, Altin|
|Publication:||Comparative Economic Studies|
|Date:||Dec 1, 2007|
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