Asymptotic Theory for Panel Structure Models∗

This paper proposes and implements a tractable approach to detect group structure in panel data. The mechanism works by means of a panel structure model, which assumes that individuals form a number of homogeneous groups in a heterogeneous population. Within each group, the (linear) regression coefficients are the same, while they may be different across different groups. The econometrician is not presumed to know the group structure. Instead, a multinomial logistic regression is used to infer which individuals belong to which groups. The model is estimated via maximum likelihood. We prove that there always exists a local maximum likelihood estimator (MLE), which is consistent and asymptotically normal, even if the likelihood function is unbounded. The consistency and asymptotic normality of a global MLE are established under the assumption that the time dimension is larger than the number of regressors in the linear regression. An EM (Expectation and Maximization) algorithm is presented to implement the MLE. A simulation study shows that the MLE performs quite well and that the proposed approach is capable of detecting underlying group structure with good precision. JEL Classification: C13; C23; C51