Purchasing power parity and uncovered interest parity: another look using stable law econometrics

In this study, we will re-examine the long-run PPP and UIP relationships by using standard cointegration test procedures but with critical values that are appropriate under infinite variance errors. These tests are performed using monthly observations over the period January 1973--December 1999 for Belgium, Canada, Denmark, France, Germany, Italy, Japan, Netherlands, Norway, Spain, Sweden and United Kingdom against the United States;Finite variance errors are a basic assumption for the distribution theory used to evaluate test statistics for the analysis of cointegration in PPP and UIP. But some recent studies have suggested that many financial variables, such as exchange rate returns, stock market returns, interest rate movements and commodity price movements, may have infinite variance. In this study we estimate the stability indices of the exchange rate, price index, and nominal interest rate series, and find evidence that most of them have an index of stability alpha less than 2. That is, it appears from the evidence that a stable non-Gaussian model may be more appropriate for these series in our data. Phillips-Perron unit root tests, along with the critical values in Caner (1998), implemented for determining the order of integration of those series generally cannot reject the null of a unit root. The finding of the non-Gaussian stable errors and the unit root in those series provide the motivation for re-doing the cointegration tests for the PPP and UIP relationships;For the PPP hypothesis, the results obtained by the multivariate likelihood-based cointegration tests demonstrate that while with the normal error assumption the results show some evidence of supporting the weak-form PPP relationship with the United States, weak-form PPP with the stable error assumption receives stronger support from the data. However, the restrictions for strong-form PPP are rejected. For the UIP hypothesis, the unrestricted cointegration results are consistent and strongly supportive of long-run UIP relationship with the United States under the assumption of stable errors. However, like PPP, the restrictions for strict UIP relationship are rejected.