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

I provide an overviewof 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 √ N-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.