Non-parametric Panel Data Models with Interactive Fixed Effects

Abstract

This article studies non-parametric panel data models with multidimensional, unobserved individual effects when the number of time periods is fixed. I focus on models where the unobservables have a factor structure and enter an unknown structural function non-additively. The setup allows the individual effects to impact outcomes differently in different time periods and it allows for heterogeneous marginal effects. I provide sufficient conditions for point identification of all parameters of the model. Furthermore, I present a non-parametric sieve maximum likelihood estimator as well as flexible semiparametric and parametric estimators. Monte Carlo experiments demonstrate that the estimators perform well in finite samples. Finally, in an empirical application, I use these estimators to investigate the relationship between teaching practice and student achievement. The results differ considerably from those obtained with commonly used panel data methods.

Dynamic treatment effects

“…Using the analyses of Hu and Schennach (2008), Cunha, Heckman, and Schennach (2010), and Freyberger (2014), it is possible to identify the distributions of factors even when the measurement equations (6) are nonlinear, and to apply the methods just discussed. As noted in the survey by Schennach (2013), there has been considerable progress in identifying factor models using information on higher moments and using nonlinearities intrinsic to the general factor model.…”

Econometric Analysis of Large Factor Models

“…Freyberger (2012) introduced interactive fixed effects into nonlinear panel regression and identified important differences between linear and nonlinear regression results. Su et al (2015) developed a consistent nonparametric test for linearity versus nonlinear models in the presence of interactive effects.…”

Specification test for panel data models with interactive fixed effects

“…Recently nonparametric panel data models with IFE have started to receive attention; see Freyberger (2012), Su and Jin (2012), Jin and Su (2013), and Su and Zhang (2013). Freyberger (2012) considers identification and sieve estimation of nonparametric panel data models with IFE when  is large and  is fixed. Su and Jin (2012) extend the CCE estimation of Pesaran (2006) from the static linear model to a static nonparametric model via the method of sieves.…”