Chapter 6: Vector autoregressive models
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Multivariate simultaneous equations models were used extensively for macroeconometric analysis when Sims (1980) advocated vector autoregressive (VAR) models as alternatives. At that time longer and more frequently observed macroeconomic time series called for models which described the dynamic structure of the variables. VAR models lend themselves to this purpose. They typically treat all variables as a priori endogenous. Thereby they account for Sims’ critique that the exogeneity assumptions for some of the variables in simultaneous equations models are ad hoc and often not backed by fully developed theories. Restrictions, including exogeneity of some of the variables, may be imposed on VAR models based on statistical procedures. VAR models are natural tools for forecasting. Their set-up is such that current values of a set of variables are partly explained by past values of the variables involved. They can also be used for economic analysis, however, because they describe the joint generation mechanism of the variables involved. Structural VAR analysis attempts to investigate structural economic hypotheses with the help of VAR models. Impulse response analysis, forecast error variance decompositions, historical decompositions and the analysis of forecast scenarios are the tools which have been proposed for disentangling the relations between the variables in a VAR model.

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