The Effect of Model Selection Uncertainty on the Error Bands for Impulse Response Functions in Vector Error Correction Models

Conventional asymptotic and bootstrap methods for finite-order autoregressive models condition on the estimated lag-order of the model, which is later, used to construct the error bands for impulse response functions. Even if the estimated lag order is believed to be correct, this procedure ignores the sampling uncertainty of the lag order. An earlier study by Kilian (1998) introduced an endogenous lag order bootstrap algorithm that reflected the true extent of sampling uncertainty in the regression estimates. Applications of Kilian’s method to vector autoregressive (VAR) and vector error correction (VEC) assumed that the true cointegration rank is known. This paper modifies the application of kilian’s method on VEC models by endogenizing the cointegration rank besides the lag order. Monte Carlo simulations results from two U.S. economy models show that ignoring cointegration rank uncertainty may seriously undermine the coverage accuracy of bootstrap confidence intervals for VEC impulse response estimates. Endogenizing the cointegration rank choice is shown to improve coverage accuracy at low additional computational cost