Multiple Fixed Effects in Theoretical and Applied Econometrics

Abstract

This dissertation studies nonlinear panel data models with multiple fixed effects. The first two chapters consider the adaptability of estimation methods for nonlinear panel data models to multiple fixed effects. The first chapter investigates whether existing methods can be modified to eliminate multiple fixed effects in the logit model and for Manski's (1987) maximum score estimator. I find that it is possible to generalize the conditional maximum likelihood approach of Rasch (1960,1961) to include two fixed effects for the former, but not for the latter. Monte Carlo simulations show that the conditional logit estimator presented in the chapter is as precise and less biased than other logit estimators. An application to trade data further highlights the importance of properly accounting for two fixed effects. The second chapter considers other nonlinear models. I find that it is possible to generalize the conditional maximum likelihood approach to include two fixed effects for the Poisson, Negative Binomial and Gamma regression models. I also find a moment condition allowing to consistently estimate the parameters for a multiplicative model with two fixed effects. Monte Carlo simulations show that both the Poisson estimating the fixed effects and the conditional Poisson estimator presented in the chapter perform well, while the conditional Negative Binomial estimator is less biased than its counterpart estimating the fixed effects. An application to trade data using the conditional Poisson estimator produces estimates of the gravity model parameters that differ significantly from those obtained with traditional estimators. The third chapter uses patent citations data to study the effect of geographical and technological distance on the diffusion of knowledge between regions of the U.S. I find strong evidence of localization, both geographically and technologically. The elasticity of distance is remarkably stable over time and is substantially higher for the first 18 months following the cited patent grant date. The effect of geographical and technological distance varies across technological categories, with ideas in the computers sector diffusing farther and faster. To deal with the count data nature of citations, I apply the multiple fixed effects Poisson and Negative Binomial estimators developed in the previous chapter.