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This example looks at nominal and real exchange rates and simple tests for purchasing power parity using regression analysis. The the dollar/pound exchange rate is used.
The EViews program and workfile were originally created for EViews 2.0.
The 3 journal articles are Frenkel (1981), Adler and Lehmann (1983), Abuaf and Jorion (1990).
Frenkel (1981) is one of the first studies to test the behavior of exchange rates in the post-Bretton Wood period. To test the hypothesis of purchasing power parity, he estimates the equation
ln St = a0 + a1 ln(P/P*)t, where S is the spot exchange rate and P/P* the ratio of the price indices in the domestic and foreign country (note: remember that which country is domestic or foreign depends on the way the exchange rate is defined!). If PPP holds, we expect a1 = 1. (Coefficient a0 is irrelevant, because it depends on an unknown equilibrium level of the real exchange rate and/or the base years of the price indices used. To replicate Frenkel's result more closely we need to rebase the price indices.)
Frenkel examines several countries and exchange rates. He finds that the results which involve the US dollar are generally very poor, with insignificant or incorrectly signed coefficients. Results not involving the US dollar are better. Nevertheless, we focus on the result for the dollar/pound and consumer price indices. The data period is June 1973 - July 1979. The estimation method is Two Stage Least Squares (TSLS), with Cochrane-Orcutt correction for first-order serial correlation and instruments constant, time, time squared, lagged values of the dependent and independent variables. The TSLS is used because exchange rate and prices are assumed to be determined simultaneously. Therefore, the price ratio is an endogenous explanatory variable and this requires an instrumental variables estimation method. The OLS estimates would be biased.
Frenkel's Table 7 reports the estimation results
the two coefficients and their standard errors, the standard error of the regression, the Durbin-Watson test-statistic for serial correlation, and the estimated first-order autocorrelation coefficient.
The PPP model a1 = 1 cannot be rejected with the standard t-test on coefficient a1, but neither can the hypothesis a1 = 0 be rejected.
(Note: EViews does not use the Cochrane-Orcutt correction for first-order serial correlation that was used by Frenkel. In addition to the TSLS estimates, the program also generates the OLS estimates, which turn out to be completely different.)
Adler and Lehmann (1983) also test the purchasing power parity hypothesis. The Frenkel (1981) approach is seriously flawed, because the nominal exchange rate and the price ratio are nonstationary variables. In general, these regressions may be 'spurious' and biased (Fuller 1976). (Note: Subsequent development of the Engle-Granger cointegration analysis qualifies this statement.) Adler and Lehmann examine the hypothesis that the real exchange follows a random walk. If this were true, it implies that PPP does not hold.
The estimated model is yt = SUMi=1,n bi yt-i + vt, where yt is the innovation (i.e. log change) in the real exchange rate. The test is bi = 0 for all i. A model in first-differences is used because the alternative test a1= 1 and a2 = ... = an = 0 in a model xt = SUMi=1,n ai xt-i + vt, with real exchange rate levels xt, is generally biased towards finding b1< 1. (Note: Again, cointegration qualifies this statement.) Using first-differences Adler and Lehmann can employ a standard exclusion F-test on the estimated bi to examine PPP.
The model is estimated for many countries and several sample periods. We focus on the results for Great Britain, monthly data 1971.04-1981.05 and 6 lags. Adler and Lehmann's Table IIA reports a F-statistic of 0.13 with an associated marginal significance level less than 0.90 (i.e. the probability that the estimated bi are all zero exceeds 90 percent).
This test does not reject the null-hypothesis of a random walk in the real exchange rate. A bad result for the PPP hypothesis.
Abuaf and Jorion (1990) also test the hypothesis that the real exchange follows a random walk. Again, if this were true, it implies that PPP does not hold. They argue that previous tests, based on first-differenced variables, have little power to reject the random walk model. They develop a test in levels of the real exchange rate and provide the required critical values of the test statistics.
The estimated model is et+1 = k0 + k1 et + SUM j=1,p bj (et-j+1 - et-j), where et is the log real exchange rate. The random walk model implies k1 = 1. This can be tested together with the assumption of either a zero or non-zero k0. Abuaf and Jorion show that, assuming k0 = 0, the test statistics rho = T (k1-1) and tau = (k1-1)/std(k1) have one-sided 10% critical values of -11.1 and -2.57.
The model is estimated for ten countries using real exchange rates against the US dollar and monthly data for January 1973-December 1987. Their Table V provides estimates of the model with no lags of real exchange rate changes. They also suggest to use 12 lags in the more general dynamic specification, but do not provide results for the individual countries. For the British pound Abuaf and Jorion report in Table V
These results do not reject the null-hypothesis of a random walk in the real exchange rate. Therefore, PPP cannot be confirmed.
Examine and compare the results from the original studies with the output from the EViews program. Look for the corresponding estimates and test statistics.
Experiment with the program and data. For example, try to re-estimate when the data sample is extended and uses all available data.
Note: The empirical tests of purchasing power parity presented here are used only to introduce programming in EViews and to introduce econometric analysis on a simple level. The tests and results should not be taken at face value, i.e. as being the final results or as examples of 'best practice' on this specific topic. The literature has since progressed and has provided new evidence on the existence/non-existence of PPP.
Abuaf, N. and P. Jorion, "Purchasing power parity in the long run", Journal of Finance, vol.45 (1) March 1990: 157-74.
Adler, M. and B. Lehmann, "Deviations from purchasing power parity in the long run", Journal of Finance, vol.38 (5) December 1983: 1471-87.
Frenkel, J.E., "Flexible exchange rates, prices and the role of 'news': Lessons from the 1970's", Journal of Political Economy vol.89 (4) 1981: 665-705.