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

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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.