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

Recent literature propose estimators that utilize heteroscedasticity of the error terms to identify the coefficient of the endogenous regressor without using excluded instruments. The assumed forms of heteroscedasticity differ across estimators. This study investigates the robustness of the two most popular estimators under different forms of heteroscedasticity through simulations. The results show that both estimators can be substantially biased under the wrong 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 Alkaline Information Criteria (AIC) to distinguish these two models. The simulation results show that it has good performance.