Estimating shocks and impulse response functions

This paper examines the issue of how to identify the shocks in a cointegrated VAR when the following assumptions are made: the variables can be classified as endogenous or exogenous, there are as many cointegrating relations as endogenous variables, the cointegrating vectors are identified and they contain at least one exogenous variable. It is shown that with these assumptions it is possible to identify the shocks without the use of further restrictions on the covariance matrix of the disturbances or the short-run dynamics. If the long-run parameters are known the whole model can be estimated by OLS. The analysis is extended to allow the VAR to have both stationary and non-stationary variables. An illustration of the method is provided using the traditional benchmark VAR model involving US data on output, prices, interest rates and money. A liquidity effect is not found using this VAR methodology.