Identifying Latent Group Structures in Nonlinear Panels

We propose a procedure to identify latent group structures in nonlinear panel data models where some regression coefficients are heterogeneous across groups but homogeneous within a group and the group number and membership are unknown. To identify the group structures, we consider the order statistics for the preliminary unconstrained consistent estimators of the regression coefficients and translate the problem of classification into the problem of break detection. Then we extend the sequential binary segmentation algorithm of Bai (1997) for break detection from the time series setup to the panel data framework. We demonstrate that our method is able to identify the true latent group structures with probability approaching one and the post-classification estimators are oracle-efficient. The method has the advantage of more convenient implementation compared with some alternative methods, which is a desirable feature in nonlinear panel applications. To improve the finite sample performance, we also consider an alternative version based on the spectral decomposition of certain estimated matrix and link the group identification issue to the community detection problem in the network literature. Simulations show that our method has good finite sample performance. We apply this method to explore how individuals' portfolio choices respond to their financial status and other characteristics using the Netherlands household panel data from year 1993 to 2015, and find three latent groups.