The Purchasing Power Parity Revisited: New Evidence for 16 OECD Countries from Panel Unit Root Tests with Structural Breaks
Paresh Kumar Narayan
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The Purchasing Power Parity Revisited: New Evidence for 16 OECD Countries from Panel Unit Root Tests with Structural Breaks
ABSTRACT
There is a plethora of studies that investigate evidence for mean reversion in exchange rates in an attempt to unravel support for purchasing power parity (PPP). At best, the empirical results are mixed. In this paper, we apply a range of univariate unit root tests including the suite of tests recommended by Ng and Perron (2001) and LM unit root suggested by Im et al. (2002) to test for PPP for 16 OECD countries. In addition to incorporating structural breaks in the exchange rate series in univariate LM tests, we also incorporate structural breaks in the LM panel unit root tests. Our main finding from univariate, tests with and without structural breaks and panel LM test with one break, is that there is no mean reversion of real exchange rates, inconsistent with PPP hypothesis. However when we incorporate two structural breaks, for most countries based on the univariate LM test, we find mean reversion in real exchange rate series. Moreover, LM panel unit root test with two structural breaks provides overwhelming support for PPP.
KEYWORDS: PPP, real exchange rate, unit root tests
JEL: C22, F21
1. Introduction
Since the work of Edison (1987), Frankel (1986) and Galliot (1970) a consensus view has emerged on the theoretical front supporting the fact that convergence of the purchasing power parity (PPP), which asserts that the change in exchange rates between two currencies is determined by the relative prices of the two countries, is slow. Consequently, PPP is deemed a long period theory and is considered an essential building block in international monetary economics.
Over the last couple decades, a plethora of studies have emerged on PPP. To obtain evidence for or against PPP, the extant literature has taken two directions. One group of studies (see, inter alia, Mark, 1990; Grilli and Kaminsky, 1991; Flynn and Boucher, 1993; Serletis, 1994; Framkel and Ross, 1996; Wu, 1996; Serletis and Zimonopoulos, 1997; Lothian, 1997; Papell, 1997; Cheung and Lai, 1998; Taylor and Sarno, 1998; Culver and Papell, 1999; Dueker and Serletis, 2000) apply a range of unit root tests.[1] The central idea here is that if the real exchange rate is characterized by a unit root then the PPP hypothesis is violated, while if the real exchange rate is found to be mean reverting then this is taken as strong evidence in favour of long run PPP. The second group of studies (see, inter alia, Karfakis and Moschos, 1989; Kim, 1990; Patel, 1990; Bleaney, 1991; Cheung and Lai, 1993; Coe and Serletis, 2002) has applied cointegration tests on the relationship between nominal exchange rate and the domestic and foreign prices levels. The central idea here is that for PPP to hold there should be no cointegration relationship between nominal exchange rate and the domestic and foreign price levels.
The fact that empirical research has not reached a consensus view on whether or not PPP holds makes this subject that much more interesting and attractive. Early studies (Roll, 1979; Frankel, 1981; Darby, 1983; Adler and Lehman, 1983; Edison, 1985; Huizinga, 1987; Enders, 1988) failed to find evidence of PPP in the long run. This finding has been corroborated by several recent studies (see, inter alia, Mark, 1990; Grilli and Kaminsky, 1991; Flynn and Boucher, 1993; Serletis, 1994; Serletis and Zimonopoulos, 1997; Dueker and Serletis, 2000) based on univariate unit root tests. On the other hand, there are studies (Framkel and Ross, 1996; Wu, 1996; Lothian, 1997; Papell, 1997; Cheung and Lai, 1998; Taylor and Sarno, 1998; Culver and Papell, 1999) that find evidence supporting the validity of PPP.
The mixed results on PPP are often attributed to the low power of the univariate unit root tests.[2] There are two avenues for increasing the power of univariate unit root tests. One is to increase the sample size, while the other is to adapt a panel data approach. For the latter approach, Quah (1994) proposed the panel test idea showing its prowess in gaining information from cross-sectional dimensions in inferring non-stationarity from panel data.[3] Hence, from within the group of studies based on unit root tests, there has emerged a subset of literature that apply panel unit root test procedures to examine mean reversion in real exchange rate (see, for instance, Frankel and Rose, 1996; Serletis and Zimonopolous, 1997; Papell, 1997; Papell and Theodoridis, 1998; O’Connell, 1998; Fleissig and Strauss, 2000; Taylor, 2002; Ho, 2002). Despite attempts to increase power of the unit root tests by undertaking the panel data approach, there are still conflicting empirical results. For instance, Serletis and Zimonopoulos (1997) test PPP for seventeen OECD countries for the period 1975:1 to 1995:4. They apply the conventional Dickey-Fuller test and the Perron and Vogelsang (1992) one break test to the exchange rate series based on the US dollar and the Deutschemark. Their main finding is that the unit root null hypothesis cannot be rejected – evidence against long run PPP. Moreover, Papell (1997) using quarterly real exchange rate data based on the US dollar for 21 industrialized countries over the period 1973 to 1994 cannot reject the unit root null. The same result is found by Papell and Theodoridis (1998) who extend the sample through to 1996. These results are corroborated by O’Connell (1998). However recently, Ho (2002) using data for 30 countries over the period 1980 to 1999 finds real exchange rate to be mean reverting, consistent with PPP hypothesis. In addition, Papell (2002) incorporates structural breaks in univariate and panel tests for unit roots and finds that there is strong evidence against unit root, and thus evidence of PPP, for panels of between 11 and 15 atypical countries. He also finds that unit root tests that do not account for structural change provide no evidence of PPP for the same panels.
In this paper, we add to the literature along the lines of Papell (2002) by incorporating structural breaks in the real exchange rate series for 16 OECD countries. However, our study differs from Papell in two important ways:
1. We use a range of new developed univariate unit root tests, namely the Dickey Fuller generalized least squares and the point optimal tests recommended by Elliot et al. (1996) and the suite of tests recommended by Ng and Perron (2001), which essential builds upon the conventional augmented Dickey and Fuller (1979, 1981) and Phillips and Perron (1988) tests; and
2. We use the Lagrangian Multiplier panel unit root test developed by Im et al. (2002), which has the advantage of utilizing both panel data and structural breaks when testing for a unit root. Other appealing features of this test are: each country is allowed to have unique fixed effects, differing time trend coefficients, and varying persistence parameters; the structural breaks are allowed to vary for different countries; heterogeneous break points, which are endogenously determined, are allowed; time specific fixed effects are allowed to capture any common year structural breaks; and the optimal number of augmentation terms in the unit root tests are allowed to be heterogeneous and determined jointly with the breaks. Following Perron (1989), the consensus view is that a structural break can be mistaken for non-stationarity. It follows that most previous finding on the non-stationarity of the real exchange rate may be attributed to the failure to allow for structural breaks. Hence, a contribution of this paper is that not only do we examine mean reversion in a panel setting but we also use a new panel test that allows for structural breaks in the data series.
The rest of the paper is organized as follows. In the next section, we give a brief account of PPP formulation followed by a brief overview of the econometric methodology. The empirical results are presented and discussed in the penultimate section, while in the final section we provide some concluding remarks.
2. The PPP formulation
The real exchange rate is calculated as follows:
Here, is the nominal exchange rate (the domestic currency price of one unit of foreign currency) and and are the foreign and domestic price levels, respectively. Equation (1) can be written in log form as follows:
If the real exchange rate follows a first-order autoregressive process
Here, is a serially uncorrelated error process and is a constant. Long-run PPP requires so that the real exchange rate is a stationary process. If , then there is a unit-root in the real exchange rate series, implying that shocks to the real exchange rate are permanent and long run PPP does not hold.
3. Methodology
In this section, we provide a brief explanation of the five univariate unit root tests used in the empirical analysis in this paper. These tests are the conventional Augmented Dickey and Fuller (1979, 1981) test, the Phillips and Perron (PP, 1988) test, the Kwiatkowski-Phillip-Schmidt-Shin (KPSS, 1992), the modified Dickey-Fuller test based on generalized least squares (DFGLS) and Elliot, Rottenberg and Stock (1996) point optimal test (ESROP), and the suite of tests advocated by Ng and Perron (NP, 2001).
3.1. Augmented Dickey and Fuller test
The ADF test is based on the auxiliary regression:
The ADF auxiliary regression tests for a unit root in ; denotes the deterministic time trend; is the lagged first differences to accommodate serial correlation in the errors, ; and , , and are the parameters to be estimated. Equation (4) tests for the null hypothesis of a unit root against a mean stationary alternative in . Equation (5), by contrast, tests the null hypothesis of a unit root against a trend stationary alternative. The null and the alternate hypotheses for a unit root in are:
: :
While relevant critical values are available from various sources, we use the approximate critical values compiled by MacKinnon (1991). For any given sample size, if the estimate of is not significantly different from zero then the null hypothesis of a unit root cannot be rejected. On the other hand if , then the alternative hypothesis of a mean stationary or trend stationary hypothesis holds.
3.2. The PP test
The PP test is also based on Equations (4) and (5), but without the lagged differences. While the ADF test corrects for higher order serial correlation by adding lagged difference terms to the right-hand side, the PP test makes a non-parametric correction to account for residual serial correlation. Monte Carlo studies suggest that the PP test generally has greater power than the ADF test (see Banerjee et al., 1993: 113).
3.3. The KPSS test
The KPSS (1992) test for unit root differs from the ADF and the PP test in that the series is assumed to be (trend-) stationary under the null. Put differently, the KPSS test reverses the null and the alternative hypothesis. The KPSS statistic is based on the residuals from the ordinary least squares regression which takes the following form:
where t is a linear deterministic trend, is a stationary error, and is a random walk; , where are i.i.d. . The initial value of is treated as fixed and is interpreted as an intercept. The test is conducted by first regressing on a constant and a trend (t), allowing one to obtain the residuals. The KPSS statistic is defined as:
where , is the partial sum of the residuals, is a consistent non-parametric estimate of the disturbance variance and is the sample size. Kwiatkowski et al. (1992) show that the statistic has a nonstandard distribution, and critical values are provided therein. If the calculated value of is large, then the null of stationarity for the KPSS test is rejected.
3.4. ERSPO and DFGLS tests
Elliot, Rothenberg and Stock (ERS, 1996) propose two modified versions of the Dickey-Fuller t test – the DFGLS and Point Optimal tests – which have substantially improved power over the ADF test when an unknown trend is present. The efficient unit-root test of Elliot et al. (1996) is based on the point optimal test of the alternative hypothesis , where , and is the sample size. The DFGLS test is based on the following equation[4]:
where represents the locally demeaned process obtained from:
In this case for a locally detrended series with a constant and a linear trend, and for a series without a linear trend. is the slope coefficient from the least squares regression of on , where and , and . Following Elliot et al. (1996), is set equal to -13.5. The null hypothesis of is tested against the alternative .
3.5. The NP test
There has emerged a broad consensus view that the widely used ADF and the PP tests can have severe nominal size distortions when the underlying data-generating process contains a moving average root near unity (see, inter alia, 1989; Phillips and Perron, 1988; Ng and Perron, 1995). To correct for severe size distortions, Ng and Perron (2001) propose new model selection procedures and estimation strategy that produces good power and reliable size. They consider the following model: