"Efficient estimation of regression models with user-specified parametric model for heteroskedasticity"
Eric Renault, Warwick University
November 1, 2022, 12:00 to 1:00 PM
Several modern textbooks report that, thanks to the availability of heteroskedasticity robust standard errors, one observes the near-death of Weighted Least Squares (WLS) in cross-sectional applied work. We argue in this paper that it is actually possible to estimate regression parameters at least as precisely as OLS and WLS, even when using a misspecified parametric model for conditional heteroskedasticity. Our analysis is valid for a general regression framework (including Instrumental Variables and Nonlinear Regression) as long as the regression is defined by a conditional expectation condition. The key is to acknowledge, as first pointed out by Cragg (1992) that, when the user-specific heteroskedasticity model is misspecified, WLS has to be modified depending on a choice of some univariate target for estimation. Moreover, targeted WLS can be improved by properly combining moment equations for OLS and WLS respectively. Efficient GMM must be regularized to take into account the possible multicolinearity of estimating equations when errors terms are actually nearly homoscedastic.