The interpretation of coefficients of the vector autoregressive model

Johansen (2002) suggests a counterfactual experiment that can be implemented in the vector autoregressive model to interpret the coefficients of an identified cointegrating relation. This article proposes an alternative counterfactual experiment ("design of experiment") that, contrary to the one suggested by Johansen, does not imply a dichotomy of short run and long run values. The experiment interprets the coefficients of an identified cointegrating relation. It is based on the idea that the coefficients, and some operations with them, are projections - at different horizons - conditional on paths of the variables of the model and on exogenous shocks in the error terms of the equations of a structural VAR. The model dynamics can be used to test if these values can be generated by exogenous shocks in these error terms. 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 checking coefficients, of the matrix with the contemporaneous correlations among variables, for the correct sign and significance in a structural VAR. It can be an important complement to the impulse response function analysis.