Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models, The Review of Economics and Statistics, Vol. 72, No. 1 (Feb., 1990), pp. 116-125

A systems cointegration rank test is proposed that is applicable for vector autoregressive (VAR) processes with a structural shift at unknown time. The structural shift is modeled as a simple shift in the level of the process. It is proposed to estimate the break date first on the basis of a full unrestricted VAR model. Two alternative estimators are considered and their asymptotic properties are derived. In the next step the deterministic part of the process including the shift size is estimated and the series are adjusted by subtracting the estimated deterministic part. A Johansen type test for the cointegrating rank is applied to the adjusted series. The test statistic is shown to have a well-known asymptotic null distribution that does not depend on the break date. The performance of the procedure in small samples is investigated by simulations.

An error correction model for the demand for real M3 money is constructed for the period of 1976–1994 with real GNP, the GNP deflator, as well as a short-term and a long-term interest rate as explanatory variables. Quarterly, seasonally unadjusted data are used in estimating the model. It is found that there is a clear structural break due to the German unification in 1990. On the other hand, once this structural break is accounted for, a stable relation is found which resists a series of specification tests. These include a number of recent tests of parameter constancy and linearity. Our specification is at variance with findings reported by some other researchers, notably the Deutsche Bundesbank.