On the asymptotic distribution of impulse response functions with long run restrictions

In this paper, the asymptotic distribution of the parameters of the moving average representation of structural VAR models with long run restrictions is derived. Moreover, it is shown that the structural model can easily be estimated in a two step procedure, where the reduced form model parameters serve as input for the structural parameters. The proposed model structure is very general, including the common trends model, in the sense that all identification schemes that can be expressed as linear zero restrictions on the contemporaneous or long-run impact of the structural shocks are allowed for. The asymptotic distribution of the moving average parameters can be used to determine asymptotic confidence intervals of impulse response functions or to perform tests of hypotheses concerning forecast error variance decompositions. The relevance of the correction for long run restrictions to the asymptotic distribution is shown in an example on German interest rates.