Cointegrating Regressions with Time Heterogeneity

This article considers the cointegrating regression with errors whose variances change smoothly over time. The model can be used to describe a long-run cointegrating relationship, the tightness of which varies along with time. Heteroskedasticity in the errors is modeled nonparametrically and is assumed to be generated by a smooth function of time. We show that it can be consistently estimated by the kernel method. Given consistent estimates for error variances, the cointegrating relationship can be efficiently estimated by the usual generalized least squares (GLS) correction for heteroskedastic errors. It is shown that the U.S. money demand function, both for M1 and M2, is well fitted to such a cointegrating model with an increasing trend in error variances. Moreover, we found that the bilateral purchasing power parities among the leading industrialized countries such as the United States, Japan, Canada, and the United Kingdom have been changed somewhat conspicuously over the past thirty years. In particular, it appears that they all have generally become more tightened during the period.