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Discussion Paper

Testing Linearity in Cointegrating Relations with an Application to Purchasing Power Parity

This paper develops a linearity test that can be applied to cointegrating relations. We consider the widely used RESET specification test and show that when this test is applied to nonstationary time series its asymptotic distribution involves a mixture of noncentral chi-squared distributions, which leads to severe size distortions in conventional testing based on the central chi-squared. Nonstationarity is shown to introduce two bias terms in the limit distribution, which are the source of the size distortion in testing.