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

大量的实证文献表明，公司、工人、学校或银行彼此不同，考虑经济模型中的代理人异质性往往是准确定量预测的关键。这个项目开发了新的技术来捕捉相关的异质性来源，这些来源不是在数据中直接观察到的，但可以通过对个人选择或其他结果的重复观察来推断。用特定于个体的参数灵活地建模代理之间未观察到的差异在计算和统计推理方面提出了重要的挑战。本项目中开发的方法基于降维方法，从而将不同种类的代理分成少数几种类型。离散方法提供了一种降低异质性维度的方法。出于计算和统计两方面的原因，这可能是有利的。然而，现有的方法，如有限混合面临着计算方面的挑战，而且它们大多是在强假设下进行研究的，即种群中的异质性是离散的。研究人员通过开发易于计算的两步估计器，并在没有这种实质性假设的情况下研究它们的性质，拓宽了离散方法的范围。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带来重大挑战的结构模型中，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.