Discretizing Unobserved Heterogeneity

Abstract

We study panel data estimators based on a discretization of unobserved heterogeneity when individual heterogeneity is not necessarily discrete in the population. We focus on two-step grouped-fixed effects estimators, where individuals are classified into groups in a first step using kmeans clustering, and the model is estimated in a second step allowing for group-specific heterogeneity. We analyze the asymptotic properties of these discrete estimators as the number of groups grows with the sample size, and we show that bias reduction techniques can improve their performance. In addition to reducing the num-ber of parameters, grouped fixed-effects methods provide effective regularization. When allowing for the presence of time-varying unobserved heterogeneity, we show they enjoy fast rates of convergence depending of the underlying dimension of heterogeneity. Finally, we document the finite sample properties of two-step grouped fixedeffects estimators in two applications: a structural dynamic discrete choice model of migration, and a model of wages with worker and firm heterogeneity.JEL codes: C23, C38.

A Distributional Framework for Matched Employer Employee Data

“…We show this strategy is helpful in alleviating small‐sample biases arising from low mobility rates. In companion work (Bonhomme, Lamadon, and Manresa ()), we further studied the theoretical properties of approaches based on an initial clustering step, viewing discrete estimation as an approximation to individual or firm heterogeneity.…”

“… Similarly as in most of the literature on discrete estimation, this result is derived under the assumption that the population of firms consists of a finite, known number of classes. In Bonhomme, Lamadon, and Manresa (), we considered a setting where the discrete modeling is viewed as an approximation to an underlying, possibly continuous, distribution of firm unobserved heterogeneity, and we provided consistency results and rates of convergence. …”

A Distributional Framework for Matched Employer Employee Data

“…We show this strategy is helpful in alleviating small-sample biases arising from low mobility rates. In companion work (Bonhomme et al, 2017) we further study the theoretical properties of approaches based on an initial clustering step, viewing discrete estimation as an approximation to individual or firm heterogeneity.…”

“…Similarly as in most of the literature on discrete estimation, this result is derived under the assumption that the population of firms consists of a finite number of classes. InBonhomme et al (2017) we consider a more general setting where the discrete modeling is viewed as an approximation to an underlying, possibly continuous, distribution of firm unobserved heterogeneity, and we provide consistency results and rates of convergence. In this alternative asymptotic framework, estimation error in the classification generally affects post-classification inference.…”

Synthetic Difference In Differences

“…for i = 1, ..., N − 1 and t = 1, ..., T − 1, where c ω and c λ are tuning parameters. For our result, we also make generative assumptions that let us characterize the behavior of nearest neighbor matching with noisy data; see Bonhomme, Lamadon, and Manresa [2017] for related results on the behavior of clustering panel data.…”