Bias and MSE Analysis of the IV Estimator Under Weak Identification with Application to Bias Correction∗
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چکیده
We provide results on properties of the IV estimator in the presence of weak instruments, beginning with the derivation of analytical formulae for the asymptotic bias (ABIAS) and mean squared error (AMSE). We also obtain approximations for the ABIAS and AMSE formulae based on an asymptotic scheme; which, loosely speaking, requires the expectation of the first stage F-statistic to converge to a finite (possibly small) positive limit as the number of instruments approaches infinity. The approximations so obtained are shown, via regression analysis, to yield good approximations for ABIAS and AMSE functions. One consequence of the asymptotic framework adopted here is that when the sample size and the number of instruments are allowed to approach infinity in a particular sequential manner, we obtain consistent estimators for the ABIAS and AMSE. This in turn suggests a number of bias corrected OLS and IV estimators, which we outline and examine. We also note that, under stronger but more primitive conditions than used in this paper, our bias-corrected estimators can be justified on the basis of a pathwise asymptotic scheme which takes the number of instruments to infinity as a function of the sample size, although this particular result is proved elsewhere. Finally, we note that the bias-corrected IV estimators proposed here are also robust in the sense that they would remain consistent in a conventional asymptotic setup where the model is fully identified. A series of Monte Carlo experiments documents the gains in bias reduction when our bias adjusted estimators are used instead of standard IV and OLS estimators. JEL classification: C12, C22.
منابع مشابه
ALTERNATIVE APPROXIMATIONS OF THE BIAS AND MSE OF THE IV ESTIMATOR UNDER WEAK IDENTIFICATION WITH AN APPLICATION TO BIAS CORRECTION By
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تاریخ انتشار 2001