Resurrecting weighted least squares

This paper shows how asymptotically valid inference in regression models based on the weighted least squares (WLS) estimator can be obtained even when the model for reweighting the data is misspecified. Like the ordinary least squares estimator, the WLS estimator can be accompanied by heteroskedasticity-consistent (HC) standard errors without knowledge of the functional form of conditional heteroskedasticity. First, we provide rigorous proofs under reasonable assumptions; second, we provide numerical support in favor of this approach. Indeed, a Monte Carlo study demonstrates attractive finite-sample properties compared to the status quo, in terms of both estimation and inference.