Testing whether real exchange rates are stationary and thus obtaining evidence on the absolute version of the purchasing power parity (PPP) hypothesis is first done using the Augmented Dickey-Fuller (ADF) statistic to test for a unit root. Then, to mitigate the low power of the ADF test, several alternatives have been used for the same purpose. Unit root tests are applied to Turkish real exchange rates (RER) to test the absolute version of the PPP hypothesis.
Pesaran, on the other hand, performs the same decomposition for the perturbation terms of the autoregressions used to test for a root of unity. After the pi and the dtr have been determined, the first step in the LLC approach is to check for the differences in the variances of the εit. Finally, in the case of the Hadri approximation, the null hypothesis is the stationarity of the series rather than the non-stationarity.
In other words, I assume that the variances of the out are the same for each series. This hypothesis can be tested under two different assumptions regarding the variances of the εit. Instead, as in the case of the individual CADFs, critical values are generated by Monte Carlo and presented in Pesaran (2007).
The distribution of the ADF test when applied to Fˆ1t remains the same as when applied to qit.
The Data
The UK, on the other hand, is also an EU country, but the plot of its RER with Turkey is somewhat different from the other four. However, the RER with Switzerland, which is a non-EU European country, is quite similar to the range for these four EU countries. This is also true of the RERs with the other EU countries in the panel.
I further note that the RERs with non-European countries; namely Japan, Saudi Arabia and the US show very different patterns, but such countries are a minority in the panel. So it wouldn't be surprising to discover a very strong dependence between the series that make up this particular panel.
Empirical Results
The critical values for the KPSS tests are obtained from Table 1 of Kwiatowski et al (1992). Looking at the results for the intercept + trend model, the number of series found stationary by the ADF test is halved for Italy, Norway, Sweden and the UK. The Hadri result is consistent with the individual KPSS results for the intercept + trend case in Table 1, but the same cannot be said for the intercept-only case where the stationary series are in the majority.
This also applies to the LLC, IPS, P, Pm and Z results, especially for the intercept + trend case. The LLC, IPS, and Z tests are still significant for the intercept-only case, but at a lower level, while the P and Pm tests are no longer significant. Regarding the individual ADF tests, only the series for Denmark and Saudi Arabia are significant for the intercept-only case, and only the series for Norway in the constant + trend case; all on the 10%.
In the single intercept case, on the other hand, SURADF tests for series due to Belgium, France, Germany and. CIPS, is insignificant for both cases, while CADF is significant (at the 10% level) for the Danish and Saudi Arabian series in the intercept only case (same as in the imputed data solution) and for the Danish series in intercept + trend case. Note that the null hypothesis of a unit root is rejected, at the 10% level, for the common factor in the intercept-only case, but not for the intercept + trend case.
In the case of intercept only, the null hypothesis is rejected only for the idiosyncratic component of the Dutch series, while it is rejected for the idiosyncratic component of the Japanese series in the case of intercept + trend. The ADF statistics for the idiosyncratic components in the case of interception only also have the usual Dickey-Fuller distribution. The critical values related to the ADF test on the idiosyncratic components for the intercept + trend case come from Table 1 of Schmidt and Lee (1991) and correspond to T = 200.
Critical values for the KPSS statistics in the intercept only case are from Kwiatowski et al (1992), Table 1. Critical values for the KPSS statistics in the intercept + trend case are from Table 1 of Shin (1994). In the single intercept case, I found the KPSS statistic for Fˆ to be 0.335 and the critical value at the 10% level to be 0.347, I do not reject the null hypothesis that Fˆ is stationary.
I was also able to apply Hadri's approach to the idiosyncratic components in the intercepted-only case, but not to eˆit1 since they are not asymptotically independent. However, in the case of intercept + trend, the KPSS results agree exactly with the ADF results as applied to eˆit; namely only the Japanese series appears to be I(0), the rest are all I(1).
Conclusions
On the other hand, when using first-generation unit root panel tests, all tests with a zero unit root supported the PPP hypothesis, while both Hadri tests rejected the stationarity of the series. When the data were detrended, LLC, IPS, and Z still supported the PPP hypothesis in the case of the intercept alone, but at a lower level of significance, while none of the panel unit root tests rejected the null when the trend term was added. The common component also dominated the variance of each qi, meaning that it was a factor contributing to the rejection of the null when univariate and most panel tests were directly applied to qit in the intercept-only case and non-rejection in the intercept + trend case.
In fact, when the univariate ADF and KPSS tests were applied to the idiosyncratic components in the latter case, only one series was found to be I(0). In short, the support obtained for the absolute version of the PPP hypothesis by applying the first generation panel procedures directly to the qit appears to be due to ignoring the dependence between the series. The procedures where this dependence is accounted for either give very weak support to the PPP hypothesis (drop-only case) or strongly favor the presence of a unit root in the series.
Thus, it is not surprising to find that testing for a root of unity in a panel of Turkish RERs, while the majority of the series originate from continental Europe and resemble the German series, does not provide any evidence in support of the PPP hypothesis . This strong simultaneous movement in the series is apparently not sufficiently compensated for by cross-sectional heterogeneity, so that the zero of a root of unity is not rejected when inter-series dependence is taken into account, especially when a trend is included in the series. . Wallace (2001), “Misleading inferences from panel unit root tests with an illustration of purchasing power parity,” Review of International Economics.
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