(When) Should cointegrating regressions be detrended? The case of a German money demand function

If an economic relationship is superimposed by a linear time trend, the regression without detrending is misspecified. The estimators of such a regression do not converge to the true parameter values. First, the asymptotic limit arising from such misspecified regressions is characterized. Second, we observe with data before 1975 a significant time trend but no cointegrating relation between real money (M1), income and a long-term interest rate. The price level as a significant omitted variable is considered as an economic explanation for this feature. We find a price elasiticity larger than one. Third, with data after the breakdown of Bretton Woods (and the beginning of monetary targeting by the Bundesbank), real money, income and the interest rate alone are cointegrated. The long-run estimates seem to be fairly stable with data after the German union provided a step dummy accounts for a break in the mean.