Examining impulse response functions in cointegrated systems

A system of reduced forms with cointegrated variables may be estimated in two ways: as a vector autoregression in levels, or as a vector error correction model. The latter is a restricted version of the former. If there is cointegration, imposing this restriction will yield more efficient estimates. However, at short horizons, vector error correction estimates are known to perform poorly relative to those from a vector autoregression. We examine how this property affects impulse response functions. A Monte Carlo experiment, and an example, suggest that impulse response functions of the two models are similar at short horizons, but different at long horizons. This suggests that the loss of efficiency from vector autoregression estimation is not critical at the commonly used short horizon. Our results complement parallel arguments focusing on forecast errors made by Clements and Hendry (1995), Hoffman and Rasche (1996), and Lin and Tsay (1996).