Identification and sequential estimation of panel data models with insufficient exclusion restrictions

This paper presents estimators for nonparametric panel data models with additive fixed effects. We analyze a model in which the entire regressor vector, consisting of time-varying as well as time-invariant regressors, is correlated with the individual fixed effect but there are insufficient exclusion restrictions to permit direct instrumental variables estimation of the model. It is shown that when the model satisfies the Additive Interactive Regression (AIR) representation of Andrews and Whang (Economic theory 6 (1990) 466–480), a sequential estimator consistently estimates the model. The limiting distribution of scalar nonlinear functionals of the model is shown to be standard normal. Finite sample properties of the estimator are considered in a Monte Carlo simulation study, and used to estimate the returns to education in a cohort of mature men from the National Longitudinal Survey.