Estimation and Inference in Nonlinear Models with Multidimensional Heterogeneity

该项目将开发新的统计工具，使用具有多种未观察到的异质性来源的模型来分析经济变量之间的关系。解释这种丰富的异质性在经济应用中是重要的，因为即使在具有相同可观察特征的个体之间，变量之间的关系也是异质的。例如，两个年龄、性别和种族相同的人在高中毕业时的收入回报可能会有很大差异。 研究人员将分析具有多维潜在或不可观察变量的非线性模型，这些变量允许观察到的和未观察到的异质性的丰富模式。它们包括具有随机系数和/或因子误差结构的二进制和其他有限响应模型。 这些模型中感兴趣的对象通常是异质效应的汇总度量，例如平均值或分位数。具有多维异质性的非线性模型提出了理论和实践挑战，例如要报告的效应的选择和计算，以及与估计效应相关的采样不确定性的量化。该项目旨在解决所有这些挑战的一个重要类别的模型估计的横截面和面板数据。更具体地说，该项目将处理：（1）总结和报告具有多维异质性的非线性模型中的效应，（2）开发分布回归的统计特性，作为对横截面和面板数据应用中的连续和离散响应的分位数效应进行建模、估计和推断的灵活工具，（3）具有因子误差结构的有限响应面板模型固定效应估计量的偏差修正;（4）具有多维异质性的二元响应模型的识别。 所提出的方法将说明从劳动经济学，卫生经济学和国际贸易的几个实证应用。

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.