  It is well known that in the presence of heteroscedasticity ordinary least
squares estimator is not efficient. I propose a generalized automatic least
squares estimator (GALS) that makes partial correction of heteroscedasticity
based on a (potentially) misspecified model without a pretest. Such an
estimator is guaranteed to be at least as efficient as either OLS or WLS but
can provide some asymptotic efficiency gains over OLS if the misspecified model
is approximately correct. If the heteroscedasticity model is correct, the
proposed estimator achieves full asymptotic efficiency. The idea is to frame
moment conditions corresponding to OLS and WLS squares based on miss-specified
heteroscedasticity as a joint generalized method of moments estimation problem.
The resulting optimal GMM estimator is equivalent to a feasible GLS with
estimated weight matrix. I also propose an optimal GMM variance-covariance
estimator for GALS to account for any remaining heteroscedasticity in the
residuals.
