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Black market exchange rate versus the official rate in testing the PPP: an application of a non-linear test.

INTRODUCTION

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].

THE RESULTS

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.

REFERENCES

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Bahmani-Oskooee, M. 1993: Black market exchange rates versus official exchange rates in testing purchasing power parity: An examination of iranian rial. Applied Economics 25: 465-472.

Bahmani-Oskooee, M. 1995: Real effective exchange rates and the purchasing power parity: Experiences of 19 industrial countries. Economic Notes 24: 239-250.

Bahmani-Oskooee, M. 1998: Do exchange rates follow a random walk process in middle eastern countries? Economies Letters 58: 339-344.

Bahmani-Oskooee, M and Rhee, H-J. 1992: Testing for long-run purchasing power parity: An examination of Korean won. International Economic Journal 6: 93-103.

Bahmani-Oskooee, M and Barry, M. 1997: The purchasing power parity and the Russian ruble. Comparative Economic Studies 39: 82-94.

Bahmani-Oskooee, M and Goswami, GG. 2005: Black market exchange rates and purchasing power parity in emerging Economies. Emerging Markets Finance and Trade 41: 37-52.

Bahmani-Oskooee, M and Gelan, A. 2006: Black market exchange rate and the productivity bias hypothesis. Economics Letters 91: 243-249.

Bahmani-Oskooee, M., Kutan, A. and Zhou, S. 2007a: Testing PPP in the non-linear STAR framework. Economics Letters 94: 104-110.

Bahmani-Oskooee, M, Kutan, A and Zhou, S. 2007b: Do real exchange rates follow a non-linear mean reverting process in developing countries? Southern Economic Journal forthcoming.

Beach, ED, Kruse, NC and Uri, ND. 1993: The doctrine of relative purchasing power parity re-examined. Journal of Economic Studies 20: 3-23.

Bleaney, M. 1991: Does long-run purchasing power parity hold within the European monetary system? Journal of Economic Studies 19: 66-72.

Chortareas, G and Kapetanios, G. 2004: The yen real exchange rate may be stationary after all: Evidence from non-linear unit-root tests. Oxford Bulletin of Economics and Statistics 66: 113-131.

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Corbae, D and Ouliaris, S. 1991: A test of long run purchasing power parity allowing for structural breaks. The Economic Record 67: 26-33.

Culbertson, WP. 1975: Purchasing power parity and black market exchange rates. Economic Inquiry 13: 287-296.

Edwards, S. 1989: Real Exchange Rates, Devaluation, and Adjustment: Exchange Rate Policy in Developing Countries. The MIT Press: Cambridge, pp. 87-127.

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Kapetanios, G, Shin, Y and Snell, A. 2003: Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112: 359-379.

Kim, Y. 1990: Purchasing power parity in the long run: A cointegration approach. Journal of Money, Credit and Banking 22: 491-403.

Kouretas, GP and Zarangas, LP. 2001: Long-run purchasing power parity and structural change: The official and parallel foreign exchange markets for dollars in Greece. International Economic Journal 15: 109-128.

Layton, AP and Stark, JP. 1990: Co-integration as an empirical test of purchasing power parity. Journal of Macroeconomics 12: 125-136.

Liew, VK-s, Ahmad Zubaidi, B and Terence Tai-leung, C. 2004: Are Asian real exchange rates stationary? Economic Letters 83: 313-316.

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Luintel, KB. 2000: Real exchange rate behavior: Evidence from black markets. Journal of Applied Econometrics 15: 161-185.

McNown, R and Wallace, MS. 1989: National price levels, purchasing power parity and cointegration: A test of four high inflation economies. Journal of International Money and Finance 8: 533-545.

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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: bahmani@uwm.edu
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
Geographic Code:1USA
Date:Dec 1, 2007
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