Bootstrapping a Stable AD Model: Weak vs Strong Exogeneity.

Through Monte Carlo experiments the effects of a feedback mechanism on the accuracy in finite samples of ordinary and bootstrap inference procedures are examined in stable first and second-order autoregressive distributed-lag models with non-stationary weakly exogenous regressors. The Monte Carlo is designed to mimic situations that are relevant when a weakly exogenous policy variable affects (and is affected by) the outcome of agents' behaviour. In the parameterizations we consider, it is found that small sample problems undermine ordinary first-order asymptotic inference procedures irrespective of the presence and importance of a feedback mechanism. We examine several residual based bootstrap procedures, each of them designed to reduce one or several specific types of bootstrap approximation error. Surprisingly, the bootstrap procedure which only incorporates the conditional model overcomes the small sample problems reasonably well. Often (but not always) bluer results are obtained if the bootstrap also resamples the marginal model for the policy makers' behaviour. Copyright 1996 by Blackwell Publishing Ltd