The Interpretation of Coefficients of the Vector Autoregressive Model

Johansen (2002) suggests a counterfactual experiment that can be implemented inthe vector autoregressive model to interpret the coefficients of an identifiedcointegrating relation.This article proposes an alternative counterfactual experiment (design ofexperiment) that, contrary to the one suggested by Johansen, does not imply adichotomy of short run and long run values. The experiment interprets thecoefficients of an identified cointegrating relation. It is based on the idea that thecoefficients, and some operations with them, are projections?at differenthorizons?conditional on paths of the variables of the model and on exogenousshocks in the error terms of the equations of a structural VAR. The model dynamicscan be used to test if these values can be generated by exogenous shocks in these errorterms. It is also feasible to construct, as was shown by Doan, Litterman and Sims(1984), a plausibility index for these exogenous shocks.The analysis of the proposed conditional projections can be as useful as checkingcoefficients, of the matrix with the contemporaneous correlations among variables,for the correct sign and significance in a structural VAR. It can be an importantcomplement to the impulse response function analysis.