Panel threshold regressions with latent group structures - MIAO, Ke (Institutional Knowledge at Singapore Management University, 2019)
In this paper, we consider the least squares estimation of a panel structure threshold re-gression (PSTR) model where both the slope coeﬃcients and threshold parameters may exhibit latent group structures. We study the asymptotic properties of the estimators of the latent group structure and the slope and threshold coeﬃcients. We show that we can estimate the latent group structure correctly with probability approaching 1 and the estimators of the slope and threshold coeﬃcients are asymptotically equivalent to the infeasible estimators that are obtained as if the true group structures were known. We study likelihood-ratio-based inferences on the group-speciﬁc threshold parameters under the shrinking-threshold-eﬀect framework. We also propose two speciﬁcation tests: one tests whether the threshold parameters are homogenous across groups, and the other tests whether the threshold eﬀects are present. When the number of latent groups is unknown, we propose a BIC-type information criterion to determine the number of groups in the data. Simulations demonstrate that our estimators and tests perform reasonably well in ﬁnite samples. We apply our model to revisit the relationship between capital market imperfection and the investment behavior of ﬁrms and to examine the impact of bank deregulation on income inequality. We document a large degree of heterogeneous eﬀects in both applications that cannot be captured by conventional panel threshold regressions.