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，在经济模型中考虑代理人的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异质性的相关来源，这些来源不能直接在数据中观察到，但可以通过重复观察个人选择或其他结果来推断。灵活建模具有个体特定参数的智能体之间未观察到的差异在计算和统计推断方面提出了重要挑战。本项目开发的方法基于降维方法，将异质代理分组为少量类型。离散方法提供了一种降低异构维数的方法。这在计算和统计上都是有利的。然而，现有的方法，如有限混合，面临着计算上的挑战，它们大多是在强假设异质性在群体中是离散的情况下进行研究的。研究者拓宽了离散方法的范围，通过发展计算上易于处理的两步估计，并在没有这些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实用性，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，以及在具有双边异质性的模型中。

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.