Typical VAR models used for policy analysis include only small numbers of variables. One motivation for considering larger VAR models is that policy institutions such as central banks and government organizations consider large panels of time series variables in making policy decisions. If important variables are not included in a VAR model, that model becomes informationally deficient and estimates of the responses to policy shocks will be distorted by omitted-variable bias. Thus, unless a variable is known to be irrelevant, one should ideally include it in the structural VAR model.

Deciding on the relevance of a particular variable for an empirical model is a difficult task because the variables for which data are available may not correspond exactly to the variables used in theoretical models. For example, consider a monetary policy reaction function that includes inflation and the output gap as explanatory variables. It is well known that the output gap is difficult to measure. Hence, one can make the case for including all variables that contain information about the output gap because they could all be important for the analysis of the impact of monetary policy.

Another motivation for considering larger VAR models is that we may wish to examine the impact of monetary policy shocks at a more disaggregate level. For example, one may be interested not only in the response of the overall price level to a monetary policy shock, but also in the response of sub-indices corresponding to specific expenditure components. Such an analysis necessitates the inclusion of disaggregate price level data in the model. Likewise, one may be interested in the output response in specific sectors of the economy. In that case, again, these additional variables have to be included in the analysis.

Conventional unrestricted VAR models do not allow for the situations described above because the inclusion of many additional variables undermines the precision of the model estimates in small samples. Moreover, the extent to which a VAR model can be enlarged is limited by the fact that the number of regressors cannot exceed the number of observations. This restriction can easily become binding when working with large-dimensional VAR models because the number of parameters in a VAR model increases with the square of the number of variables included.