Collaborative Research: Dimension Reduction Methods for Estimating Economic Models with Panel Data

大量的实证文献表明，企业、工人、学校或银行彼此不同，而在经济模型中考虑代理异质性往往是准确定量预测的关键。该项目开发了新的技术来捕捉相关的异质性来源，这些来源在数据中没有直接观察到，但可以通过对个人选择或其他结果的重复观察来推断。智能体与个体特定参数之间未观察到的差异的合理建模在计算和统计推断方面提出了重要的挑战。该项目中开发的方法基于降维方法，将异构代理分组为少量类型。 离散方法提供了一种降低异质性维数的方法。出于计算和统计原因，这可能是有利的。然而，现有的方法，如有限混合面临计算的挑战，他们大多是在强假设下，异质性是离散的人口研究。研究人员扩大了离散方法的范围，通过开发计算上易于处理的两步估计量，并在没有这种实质性假设的情况下研究它们的性质。这项研究还说明了这些方法在应用中的有用性，特别是在结构模型中，允许未观察到的异质性提出了重要的挑战，并在模型与双侧异质性。

A vast empirical literature has demonstrated that firms, workers, schools, or banks differ from each other, and that accounting for agent heterogeneity in economic models is often key for accurate quantitative predictions. This project develops new techniques to capture relevant sources of heterogeneity which are not directly observed in the data, but can be inferred using repeated observations of individual choices or other outcomes. Flexibly modeling unobserved differences between agents with individual-specific parameters raises important challenges in terms of computation and statistical inference. The approach developed in this project is based on dimension reduction methods whereby heterogeneous agents are grouped into a small number of types. Discrete methods provide a way to reduce the dimensionality of heterogeneity. This may be advantageous for both computational and statistical reasons. However, existing methods such as finite mixtures face computational challenges, and they are mostly studied under the strong assumption that heterogeneity is discrete in the population. The investigators broaden the scope of discrete methods, by developing computationally tractable two-step estimators and studying their properties in the absence of such substantive assumptions. This research also illustrates the usefulness of these methods in applications, particularly in structural models where allowing for unobserved heterogeneity raises important challenges, and in models with two-sided heterogeneity.