Inconsistency of the OLS estimator of the partial adjustment-adaptive expectations model

Following elimination of unobservable quantities it is assumed that the disturbance in the partial adjustment-adaptive expectations model follows a first-order moving average. The inconsistency of OLS is derived and calculated for different parameter values. The results indicate that the inconsistency in the estimate of the long-run elasticity is very small but that the short-run elasticity is likely to be seriously overestimated. Also, if OLS is used, it is quite probable that the model will be incorrectly rejected in favour of the partial adjustment (or the adaptive expectations) model by itself.