Jeffrey M. Wooldridge studies inverse probability weighted (IPW) M-estimation for general missing data problems. He extends previous work by allowing selection probabilities to depend on unobserved variables and shows that estimating these probabilities can lead to more efficient estimators than using known probabilities. He also discusses the "double robustness" property in treatment effect estimation, where at least one of the models for the outcome or selection probability must be correctly specified for consistent estimation. Wooldridge considers various cases, including censored duration data, variable probability sampling, and treatment effects with potentially misspecified models. He demonstrates that IPW estimation can be more efficient than unweighted estimation, especially when selection probabilities are estimated. The paper also addresses the conditions under which IPW estimation is appropriate and provides asymptotic variance formulas for weighted and unweighted estimators. Wooldridge concludes that IPW estimation is generally more efficient than unweighted estimation, even when selection probabilities are misspecified, and that the unweighted estimator can be more efficient under certain conditions. The paper provides a general framework for IPW estimation under various missing data mechanisms and discusses the implications for econometric inference.Jeffrey M. Wooldridge studies inverse probability weighted (IPW) M-estimation for general missing data problems. He extends previous work by allowing selection probabilities to depend on unobserved variables and shows that estimating these probabilities can lead to more efficient estimators than using known probabilities. He also discusses the "double robustness" property in treatment effect estimation, where at least one of the models for the outcome or selection probability must be correctly specified for consistent estimation. Wooldridge considers various cases, including censored duration data, variable probability sampling, and treatment effects with potentially misspecified models. He demonstrates that IPW estimation can be more efficient than unweighted estimation, especially when selection probabilities are estimated. The paper also addresses the conditions under which IPW estimation is appropriate and provides asymptotic variance formulas for weighted and unweighted estimators. Wooldridge concludes that IPW estimation is generally more efficient than unweighted estimation, even when selection probabilities are misspecified, and that the unweighted estimator can be more efficient under certain conditions. The paper provides a general framework for IPW estimation under various missing data mechanisms and discusses the implications for econometric inference.