On the Behavior of Inconsistent Instrumental Variable Estimators

Results published recently by Hendry (1979) for the limiting distribution of inconsistent instrumental variable estimators in misspecified dynamic systems are incorrect. In particular, Hendry's derivations involve the use of an appropriate control variate and lead to an expression for the covariance matrix of the limiting distribution which, in general, omits many additional terms. Correct formulae are given in the present paper and the accuracy of the asymptotic distribution in finite samples is investigated in a simple case using the know exact small sample distribution. On the basis of our exact results, we argue for caution in the use of response surface regressions of the type recommended by Hendry in Monte Carlo experiments; and we emphasize the need for qualifying statements concerning the parameter environments in which the adequacy of these regressions has been substantiated.