This paper considers the cointegrating regression with errors whose variances change smoothly over time. The model can be used to describe a longrun cointegrating relationship, the tightness of which varies along with time. Heteroskedasticity in the errors is modelled nonparametrically and is assumed to be generated by a smooth function. We show that it can be consistently estimated by the kernel method. Given consistent estimates for error variances, the cointegrating relationship can be efficiently estimted by the usual GLS correction for heteroskedastic errors. It is shown that the US money demand function, both for M1 and M2, is well fitted to such a cointegrating model with growing variance. Moreover, we found that the bilateral purchasing power parities among many industrialized countries including the US, Germany, Japan, Canada, and the UK have been changed somewhat conspicuously over the past twenty years. They all had been monotonically loosened in the 70's and 80's, but most of them became tightened in the 90's.
