Time-varying linear transformation models with fixed effects and endogeneity for short panels

Abstract

This paper considers a class of fixed-T nonlinear panel models with timevarying link function, fixed effects, and endogenous regressors. We establish sufficient conditions for the identification of the regression coefficients, the time-varying link function, the distribution of counterfactual outcomes, and certain (time-varying) average partial effects. We propose estimators for these objects and study their asymptotic properties. We show the relevance of our model by estimating the effect of teaching practices on student attainment as measured by test scores on standardized tests in mathematics and science. We use data from the Trends in International Mathematics and Science Study, and show that both traditional and modern teaching practices have positive effects of similar magnitudes on the performance of U.S. students on standardized tests in math and science.* We would like to thank Stéphane Bonhomme, Xavier D'Haultfoeuille, Jean-Pierre Florens, Laura Liu, Thierry Magnac for comments and suggestions, and participants at various conferences and seminars. We would also like to thank Jan Bietenbeck for sharing the data.