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The Interpretation of Coefficients of the Vector Autoregressive Model

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  • Elcyon Caidado Rocha Lima

Abstract

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.

Suggested Citation

  • Elcyon Caidado Rocha Lima, 2005. "The Interpretation of Coefficients of the Vector Autoregressive Model," Discussion Papers 1072, Instituto de Pesquisa Econômica Aplicada - IPEA.
  • Handle: RePEc:ipe:ipetds:1072
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    1. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
    2. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
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