LATE With Missing or Mismeasured Treatment

Abstract

We provide a new estimator, MR-LATE, that consistently estimates local average treatment effects when treatment is missing for some observations, not at random. If instead treatment is mismeasured for some observations, then MR-LATE usually has less bias than the standard LATE estimator. We discuss potential applications where an endogenous binary treatment may be unobserved or mismeasured. We apply MR-LATE to study the impact of women’s control over household resources on health outcomes in Indian families. This application illustrates the use of MR-LATE when treatment is estimated rather than observed. In these situations, treatment mismeasurement may arise from model misspecification and estimation errors.

Keywords:

• Collective model
• Health
• LATE
• Measurement error
• Misclassification
• Missing treatment
• Resource shares

Supplementary Material

Our appendix, which is available online, contains three main sections. Appendix A provides a graphical illustration of the MR-LATE estimator. Appendix B discusses several details of our empirical application: the derivation of the demand equations for private assignable goods is in Appendix B.1, details on data sources and estimation samples are presented in Section B.2, a validation of our structural estimates is in Appendix B.3, and a discussion of possible violations of the exclusion restriction is in Appendix B.4. Additional figures and tables are in Appendix C.

Acknowledgments

We are grateful to the editor, associate editor and anonymous referees for their detailed and constructive comments. We thank Samson Alva, Erich Battistin, Jonathan de Quidt, Bram De Rock, Laurens Cherchye, Flávio Cunha, Frank DiTraglia, Yingying Dong, Jeremy Fox, Michael Gechter, Mette Gørtz, Rachel Heath, Nikolaj Harmon, Søren Leth-Petersen, Benjamin Solow, Takuya Ura, Kenneth Wolpin, Lina Zhang, Yi Zhang, seminar participants at University of Copenhagen, ECARES, Monash University, Penn State, Rice University, Stockholm University, Tilburg University, UT Austin, and participants at the Winter Meeting of the Econometric Society, NEUDC, SEA Conference, the Annual Conference on Economic Growth and Development at ISI-Delhi, the Texas Econometrics Camp, and the Economic Demography Workshop for their suggestions. All errors are our own.