Vector autoregressive (VAR) models have been intensively used for macro policy analysis since Sims (1980) suggested VAR models for macroeconomic analysis. VAR models employ minimal restrictions compared with traditional large-scale models, which impose a large number of incredible restrictions. As a result, VAR models have been used to document data-oriented empirical evidence on the effects of macroeconomic policies. VAR models were commonly used in the early years to analyze the role of macro policies in business cycle fluctuations. For example, how much does monetary shock contribute to output fluctuations? VAR analysis was later performed as an empirical counterpart of the theoretical model. For example, impulse responses from VAR models are compared with those from Dynamic Stochastic General Equilibrium (DSGE) models to examine the success and failure of theories. Simple recursive VAR models introduced by Sims (1980) were frequently used in the early years because such models were regarded as models with atheoretical (or normalizing) restrictions. However, subsequent studies showed that the results were usually sensitive to the ordering among variables.
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