Identification through Heteroscedasticity: What If We Have the Wrong Form?

Recent literature proposes estimators that utilize the heteroscedasticity in the error terms to identify the coefficient of the endogenous regressor in a standard linear model, while these estimators do not require extra exogenous variables as the excluded instruments. The assumed forms of heteroscedasticity differ across estimators, but it is often not straightforward how to justify the validity of such assumption a-priori. This simulation study investigates the robustness of the two most popular estimators under different forms of heteroscedasticity. The results show that both estimators can be substantially biased under wrong assumptions on the form of heteroscedasticity. Moreover, the overidentification test proposed for one estimator can have low power against the wrong form of heteroscedasticity. This study also explores the use of the maximum likelihood framework and the use of Akaike Information Criteria (AIC) to distinguish these two models. The simulation results show that it has good performance.