Econometrica: May 2015, Volume 83, Issue 3

Grouped Patterns of Heterogeneity in Panel Data
p. 1147-1184

S. Bonhomme and E. Manresa

This paper introduces time‐varying grouped patterns of heterogeneity in linear panel data models. A distinctive feature of our approach is that group membership is left unrestricted. We estimate the parameters of the model using a “grouped fixed‐effects” estimator that minimizes a least squares criterion with respect to all possible groupings of the cross‐sectional units. Recent advances in the clustering literature allow for fast and efficient computation. We provide conditions under which our estimator is consistent as both dimensions of the panel tend to infinity, and we develop inference methods. Finally, we allow for grouped patterns of unobserved heterogeneity in the study of the link between income and democracy across countries.

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Supplement to "Grouped Patterns of Heterogeneity in Panel Data"

This zip file contains the replication files for the manuscript.

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Supplement to "Grouped Patterns of Heterogeneity in Panel Data"

This supplementary appendix is divided into seven sections. In Section S1 we describe the computational algorithms.  In Section S2 we deal with inference, both from a large-N, T perspective and from a large-N, fixed-T perspective.  In Section S3 we treat the issues of misspecification of the number of groups G and its choice.  In Section S4 we study two extensions of the baseline model, which allow for unit-specific heterogeneity and for group-specific coefficients, respectively.  In Section S5 we deal with several other issues, including the connection with mixture models, and how to incorporate prior information in estimation.  In Section S6 we report the results of a simulation study.  Lastly, in Section S7 we show a number of additional results related to the empirical application.

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