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

大量实证文献表明，企业、工人、学校或银行彼此不同，而经济模型中考虑主体异质性往往是准确定量预测的关键。该项目开发了新技术来捕获异质性的相关来源，这些异质性来源在数据中不能直接观察到，但可以通过对个人选择或其他结果的重复观察来推断。灵活地对具有个体特定参数的代理之间未观察到的差异进行建模在计算和统计推断方面提出了重要的挑战。该项目开发的方法基于降维方法，将异构代理分为少量类型。 离散方法提供了一种降低异质性维度的方法。出于计算和统计原因，这可能是有利的。然而，有限混合等现有方法面临着计算挑战，并且它们大多是在群体中异质性是离散的强假设下进行研究的。研究人员通过开发计算上易于处理的两步估计器并在缺乏此类实质性假设的情况下研究其特性，扩大了离散方法的范围。这项研究还说明了这些方法在应用中的有用性，特别是在允许未观察到的异质性提出重要挑战的结构模型中，以及在具有两侧异质性的模型中。

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.