A Framework for the Analysis of Time-varying Treatment E ects: How The Timing of Grade Retention

In this paper, we develop a method to estimate time-varying treatment e ects in situations where dynamic selection into treatment may confound estimates of the treatment e ect. Doing so, emphasizes an important policy tool, the timing of treatment. We illustrate the challenges in using conventional approaches to control for selection in a static setting for a dynamic setting. The method we develop assumes that the unobservables that jointly determine selection into treatment and the treatment e ects can be modeled through a factor structure. We demonstrate how this method recovers a much richer set of counterfactuals than can be recovered with existing methods. We then apply our method to the study of grade retention using the Early Childhood Longitudinal Study of Kindergartners. We nd evidence of dynamic selection and that the e ect depends both on the time at which the student is retained and the time elapsed since retention. ∗First draft: December 26, 2007. Navarro's work was supported by the Institute for Research on Poverty at the University of Wisconsin-Madison. We thank participants at the Applied Microeconomics lunch at UW-Madison, Anirban Basu, David Meltzer and especially John Kennan and Chris Taber for providing helpful comments. †Department of Economics, University of Wisconsin-Madison. email: [email protected] ‡Department of Economics, University of Wisconsin-Madison. email: [email protected] §Department of Economics, University of Wisconsin-Madison. email: [email protected]