Lag selection in subset VAR models with an application to a US monetary system

Alternative modeling strategies for specifying subset VAR models are considered. It is shown that under certain conditions a testing procedure based on t-ratios is equivalent to sequentially eliminating lags that lead to the largest improvement in a prespecified model selection criterion. A Monte Carlo study is used to illustrate the properties of different procedures. It is found that the differences between alternative strategies are small. In small samples, the strategies often fail to discover the true model. Nevertheless, using subset strategies results in models with improved forecast precision. To illustrate how these subset strategies can improve results from impulse response analysis, a VAR model is used to analyze the effects of monetary policy shocks for the U.S. economy. While the response patterns from full and subset VARs are qualitatively identical, confidence bands from the unrestricted model are considerably wider. We conclude that subset strategies can be useful modeling tools when forecasting or impulse response analysis is the main objective.