Partial Effects in Time-Varying Linear Transformation Panel Models with Endogeneity

This article develops a new estimator for an average partial effect in nonlinear panel models, where outcomes are time-varying monotonic transformations of latent variables that include fixed effects and endogenous regressors. The partial effect can be time-varying and the counterfactual shift is scale invariant—key advantages over the linear model. We exploit a conditional moment restriction and address the ill-posed nature of recovering the transformation functions using nonparametric instrumental variable techniques. Our estimator for the partial effect satisfies root-n asymptotic normality. We apply our method to data from the Trends in International Mathematics and Science Study, and find evidence that traditional instruction is strongly associated with improved achievement in both mathematics and science.