Testing linearity in cointegrating smooth transition regressions

Abstract

This paper develops statistical tests that can be used to test linearity in cointegrating smooth transition regression models. These tests extend previous similar tests by considering I(1) regressors instead of stationary or mixing regressors and they also allow for more general transition mechanisms than in previous studies. As is typical in cointegrating regressions, the regressors and errors of the model can be serially and contemporaneously correlated. In order to allow for this feature, an endogeneity correction based on a leads‐and‐lags approach is employed. The proposed tests are very simple to use because ordinary least squares techniques and standard chi‐square limiting distributions apply. Simulation experiments indicate that the tests have reasonable finite sample properties. Empirical applications to a U.K. money demand function illustrate the practical usefulness of the tests.

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