Estimating overidentified linear models with heteroskedasticity and outliers

Résumé 0

A large degree of overidentification causes severe bias in TSLS. A conventional heuristic rule used to motivate new estimators in this context is approximate bias. This paper formalizes the definition of approximate bias and expands the applicability of approximate bias to various classes of estimators that bridge OLS, TSLS, and Jackknife IV estimators (JIVEs). By evaluating their approximate biases, I propose new approximately unbiased estimators, including UOJIVE1 and UOJIVE2. UOJIVE1 can be interpreted as a generalization of an existing estimator UIJIVE1. Both UOJIVEs are proven to be consistent and asymptotically normal under a fixed number of instruments and controls. The asymptotic proofs for UOJIVE1 in this paper require the absence of high leverage points, whereas proofs for UOJIVE2 do not. In addition, UOJIVE2 is consistent under many-instrument asymptotic. The simulation results align with the theorems in this paper: (i) Both UOJIVEs perform well under many instrument scenarios with or without heteroskedasticity, (ii) When a high leverage point coincides with a high variance of the error term, an outlier is generated and the performance of UOJIVE1 is much poorer than that of UOJIVE2.