  Estimating linear regression using least squares and reporting robust
standard errors is very common in financial economics, and indeed, much of the
social sciences and elsewhere. For thick tailed predictors under
heteroskedasticity this recipe for inference performs poorly, sometimes
dramatically so. Here, we develop an alternative approach which delivers an
unbiased, consistent and asymptotically normal estimator so long as the means
of the outcome and predictors are finite. The new method has standard errors
under heteroskedasticity which are easy to reliably estimate and tests which
are close to their nominal size. The procedure works well in simulations and in
an empirical exercise. An extension is given to quantile regression.
