Identifying Latent Structures in Panel Data
This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized regression techniques. We focus on linear models where the slope parameters are heterogeneous across groups but homogenous within a group and the group membership is unknown. Two approaches are considered — penalized least squares (PLS) for models without endogenous regressors, and penalized GMM (PGMM) for models with endogeneity. In both cases we develop a new variant of Lasso called classiﬁer-Lasso (C-Lasso) that serves to shrink individual coeﬀicients to the unknown group-speciﬁc coeﬀicients. C-Lasso achieves simultaneous classiﬁcation and consistent estimation in a single step and the classiﬁcation exhibits the desirable property of uniform consistency. For PLS estimation C-Lasso also achieves the oracle property so that group-speciﬁc parameter estimators are asymptotically equivalent to infeasible estimators that use individual group identity information. For PGMM estimation the oracle property of C-Lasso is preserved in some special cases. Simulations demonstrate good ﬁnite-sample performance of the approach both in classiﬁcation and estimation. An empirical application investigating the determinants of cross-country savings rates ﬁnds two latent groups among 56 countries, providing empirical conﬁrmation that higher savings rates go in hand with higher income growth.
Su, Liangjun; Shi, Zhentao; and Phillips, Peter C.B., "Identifying Latent Structures in Panel Data" (2014). Cowles Foundation Discussion Papers. 2379.