Resurrecting weighted least squares

Linear regression models form the cornerstone of applied research in economics and other scientific disciplines. When conditional heteroskedasticity is present, or at least suspected, the practice of reweighting the data has long been abandoned in favor of estimating model parameters by ordinary least squares (OLS), in conjunction with using heteroskedasticity consistent (HC) standard errors. However, we argue for reintroducing the practice of reweighting the data, since doing so can lead to large efficiency gains of the resulting weighted least squares (WLS) estimator over OLS even when the model for reweighting the data is misspecified. Efficiency gains manifest in a first-order asymptotic sense and thus should be considered in current empirical practice. Crucially, we also derive how asymptotically valid inference based on the WLS estimator can be obtained even when the model for reweighting the data is misspecified. The idea is that, just like the OLS estimator, the WLS estimator can also be accompanied by HC standard errors without knowledge of the functional form of conditional heteroskedasticity. A Monte Carly study demonstrates attractive finite-sample properties of our proposals compared to the status quo, both in terms of estimation and making inference.