RDP 8711: Deviations from Purchasing Power Parity: The Australian Case 4. Testing the Models on Australian Data

The choice of lags in testing equation 10 is entirely arbitrary. However, in the effort to incorporate both short-run and long-run factors, models with lag lengths of 6 months, 12 months and 18 months are examined.

(a) Heteroskedasticity issues

He expect heteroskedasticity to be present in exchange rate data for Australia because of the changes in regime that have occurred – most notably the switch from a crawling peg to floating exchange rates. In the more general model, we are also aware of the problem of increasing variance of commodity prices in the lattor half of the floating exchange rate period.

Consequently, whon estimating the models, we tested for heteroskedasticity using a procedure developed by White (1980). The results are shown in Table 7. The null hypothesis of no heteroskedasticity is consistently rejected in the post float period when commodity prices are included in the model – but not otherwise.

Corrections for heteroskedasticity are made using the procedure developed by White. Tables 2 to 6 show estimation results for both the uncorrected and corrected models.

(b) Test statistics

The hypothesis that the parameters for the lagged explanatory variables are jointly insignificantly different from zero (no serial correlation) is tested using the F-statistic in the original model and the Wald statistic in the corrected model. The individual coefficients in each regrossion which are significant at the 95% level, according to their t-statistics, are also reported.

These tests assume independent and identically distributed errors – there should be no remaining autocorrelation in the error terms. We use the Breusch-Godfrey test to determine whether first-order autocorrelation exists in each model. Test results shown in Table 8 indicate that in general first order autocorrelation is not present.

The results for both models are presented in Tables 2 to 6, along with the marginal significance levels. The random walk model is rejected when the marginal significance level is greater than 0.99.

(c) The results

In Table 2 we present results for the case of the real exchange rate defined in terms of the U.S. dollar exchange rate, using quarterly data. Recall that we are testing the null hypothesis that the random walk model of deviations from PPP is the true model.

Over the full sample period, and both the managed and floating rate subperiods, it is difficult to reject the random walk hypothesis when the commodity price terms are excluded. The random walk hypothesis for the case of four lags is rejected when commodity prices are included over the floating rate period. Corrections for heteroskedasticity appear to be important to this finding.

Table 3 contains results for the same tests, but where the real exchange rate is defined in terms of a trade-weighted basket of currencies. The results are summarised as follows:

• over the full sample period the results are much the same as for the case of the U.S. dollar (i.e. the random walk model is not rejected by the data);
• over the sample period containing only managed exchange rate regimes the random walk hypotheses is again not rejected; and
• over the floating rate period the random walk model of deviations from PPP is rejected once terms of trade affects are taken into account. In this case the correction for heteroskedasticity appears to be crucial to the results.

The small number of quarterly observations during the floating rate period led to difficulties in placing much weight on our results. This motivated us to carry out tests for the real effective exchange rate using monthly observations. Since the terms of trade is not available on this basis, the Reserve Bank's index of commodity prices is used as a proxy for the terms of trade effect. This series is available only from July 1984. Consequently. only the model that ignores commodity price effects could be tested on monthly data over the full sample period (Table 4). and over the period of managed exchange rates (Table 5). In both of these cases the random walk hypothesis was not rejected by the monthly data.

The results for the post-float period using monthly data and the more general test of the random walk hypothesis (Table 6) are of more interest, and are summarised as follows:

• the random walk model of deviations from PPP is not rejected by the monthly data if commodity prices are ignored; but
• the random walk model is rejected by the monthly data over the period of floating exchange rates if commodity prices are included. Corrections for heteroskedasticity appear to be crucial for obtaining this result.

This latter finding provides evidence that behaviour of the real exchange rate since the float is not a random process – it may reflect movements in the equilibrium real exchange rate following from sustained changes in commodity prices.