Weights in Regressions

Solon et al. have a new paper on the use of weights in empirical analysis. Not only does the paper have a great title, but it addresses one of the more hairy issues in empirical work, when and how to use weights:

We discuss three distinct potential motives for weighting when estimating causal effects: (1) to achieve precise estimates by correcting for heteroskedasticity, (2) to achieve consistent estimates by correcting for endogenous sampling, and (3) to identify average partial effects in the presence of unmodeled heterogeneity of effects. In each case, we find that the motive sometimes does not apply in situations where practitioners often assume it does.

There is, of course, no foolproof recipe:

In situations in which you might be inclined to weight, it often is useful to report both weighted and unweighted estimates and to discuss what the contrast implies for the interpretation of the results. And, in many of the situations we have discussed, it is advisable to use robust standard error estimates.