Estimation and Inference in Nonlinear Models with Multidimensional Heterogeneity

Trustees Of Boston University, Boston

Investigators

Abstract

The project will develop new statistical tools to analyze relationships between economic variables using models with multiple sources of unobserved heterogeneity. Accounting for such rich heterogeneity is important in economic applications because the relationships between variables are expected to be heterogeneous even among individuals with the same observable characteristics. For example, two individuals with the same age, gender, and race can experience very different returns to high school graduation on earnings. The investigator will analyze nonlinear models with multidimensional latent or unobservable variables, which allow for rich patterns of observed and unobserved heterogeneity. They include binary and other limited response models with random coefficients and/or factor error structure. The objects of interest in these models are often summary measures of the heterogeneous effects such as averages or quantiles. Nonlinear models with multidimensional heterogeneity pose theoretical and practical challenges such as the choice and computation of the effects to report, and the quantification of the sampling uncertainty associated with the estimated effects. This project aims to tackle all these challenges for an important class of models estimated from cross sectional and panel data. More specifically, the project will address: (1) summarizing and reporting effects in nonlinear models with multidimensional heterogeneity, (2) developing the statistical properties of distribution regression as a flexible tool to model, estimate and make inference on quantile effects of continuous and discrete responses in cross sectional and panel data applications, (3) deriving bias corrections for fixed effects estimators of limited response panel models with factor error structure, and (4) identification of binary response models with multidimensional heterogeneity. The methods proposed will be illustrated with several empirical applications from labor economics, health economics, and international trade.