"This dissertation concerns nonlinear panel data estimation relevant to the fields of econometrics and applied microeconomics. Panel data is attractive for estimating causal effects when unobserved heterogeneity in cross-sectional units is correlated with explanatory variables. For instance, well-known linear fixed effects and first difference estimators use within-group variation to achieve consistent estimation. However, nonlinear models often better represent limited dependent variables like binary outcomes or counts, and extending traditional panel techniques to these settings can be problematic. For instance, treating heterogeneity as parameters to be estimated usually leads to what is known as the incidental parameters problem. Furthermore, heterogeneous slopes in a conditional mean function can also confound estimation, but fewer remedies exist than do for additive effects. I aim to address these issues in my research with an emphasis on practical applicability. Chapter 1: Finite sample properties of bias-corrected fixed effects estimators for panel binary response models. Maximum likelihood estimation (MLE) of nonlinear unobserved effects panel models is known to be generally inconsistent when treating the heterogeneity as parameters. Several authors have proposed corrections justified by large-T expansions of the inconsistency under conditions like dynamic completeness. Using Monte Carlo (MC) techniques, I find that failure of dynamic completeness can increase bias in slope and average partial effects (APE) estimates in shorter panels, but has little impact on APE for longer panels. I also compare bias-corrections to correlated random effects (CRE) and Conditional MLE using MC and welfare data from the Survey of Income and Program Participation (SIPP). Chapter 2: Exponential panel models with coefficient heterogeneity. If heterogeneous slopes are ignored in exponential panel models, fixed effects Poisson may not estimate any quantity of interest. Existing estimation methods often involve treating only a small subset of the slopes as "random effects" and integrating from the likelihood, increasing computational difficulty. I propose a test to detect slope heterogeneity that, unlike the traditional approach, does not amount to testing for information matrix equality. Additionally, I present a correlated random coefficients approach to identification which allows for estimation of the coefficient means and average partial effects. I test these proposed methods using a Monte Carlo experiment and apply them to the patent-R&D relationship for U.S. manufacturing firms. Chapter 3: Estimation of average marginal effects in multiplicative unobserved effects panel models. This chapter concerns estimation of average marginal effects in static multiplicative unobserved effects panel models for nonnegative dependent variables. While fixed effects Poisson (FEP) consistently estimates the parameters of the conditional mean function, marginal effects generally depend on the unobserved heterogeneity. They would therefore seem inestimable without either additional assumptions or some form of bias correction. I show, however, that Average Partial Effect (APE) and Average Treatment Effect (ATE) estimators that use estimated individual effects are consistent and asymptotically normal. This is in contrast with cases like fixed effects logit, where similar marginal effects estimators suffer from the incidental parameters problem."--Page ii-iii.
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