Bias Correction in a Stable AD (1,1) Model: Weak versus Strong Exogeneity

This paper compares the behaviour of a bias-corrected estimator assuming strongly exogenous regressors to the behaviour of a bias-corrected estimator assuming weakly exogenous regressors, when in fact the marginal model contains a feedback mechanism. To this end, the effects of a feedback mechanism on the first-order least-squares coefficient estimation bias is examined through large-sample asymptotics in a stable first-order autoregressive distributed-lag model with weakly exogenous regressors. The derived formulae show explicitly how the bias of the coefficient estimators of the conditional model depends on the parameters that belong to the marginal model. In addition, an explicit approximation in all the system parameters is derived for the first-order bias formula based on strongly exogenous regressors. It is found that the two bias approximations can lead to quite different numerical values. Through a small simulation study, the bias and efficiency of the two bias-corrected estimators is investigated. It appears that the valid bias-corrected estimator based on the whole system is somewhat less biased than the invalid bias-corrected estimator. For a few particular parameter values considered, however, both bias-corrected estimators are inefficient relative to the uncor-rected estimator in terms of mean squared error. Somewhat surprisingly, the invalid bias-corrected estimator based on only the conditional model is on average just as efficient as the valid bias-corrected estimator based on the whole system.