Inverse probability weighted M-estimators for sample selection, attrition, and stratification

I provide an overview of inverse probability weighted (IPW) M-estimators for cross section and two-period panel data applications. Under an ignorability assumption, I show that population parameters are identified, and provide straightforward -consistent and asymptotically normal estimation methods. I show that estimating a binary response selection model by conditional maximum likelihood leads to a more efficient estimator than using known probabilities, a result that unifies several disparate results in the literature. But IPW estimation is not a panacea: in some important cases of nonresponse, unweighted estimators will be consistent under weaker ignorability assumptions.JEL Classification: C13, C21, C23I would like to thank Bo Honoré, Christophe Muller, Frank Windmeijer, and the participants at the CeMMAP/ESCR Econometric Study Group Microeconometrics Workshop for helpful comments on an earlier draft.