Three essays on panel structure models - WANG, Wuyi (Institutional Knowledge at Singapore Management University, 2018)
In panel structure models, individuals can be classified into different groups with the slope parameters being homogeneous within the same group but heterogeneous across groups, both the number of groups and each individual’s group membership are unknown. This dissertation proposes some methods to identify the panel structure models under different specifications, namely, developing a Lasso-type Panel-CARDS method in the linear panel, constructing two sequential binary segmentation algorithms in the nonlinear panel, and using K-means algorithm in the spatial panel. Chapter 2 studies the estimation of a linear panel data model with latent structures. To identify the unknown group structure of vector parameters, we design an algorithm called Panel-CARDS which is a systematic extension of the CARDS procedure proposed by Ke, Fan, and Wu (2015) in a cross-sectional framework. We show that it can identify the true group structure asymptotically and estimate the model parameters consistently at the same time. Simulations evaluate performance and corroborate the asymptotic theory in several practical design settings. The empirical economic application considers the effect of income on democracy by using cross-country data over the period 1961-2000. It reveals the presence of latent groupings in this panel data. Chapter 3 proposes a procedure to identify latent group structures in nonlinear panel data models. 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 can 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. Chapter 4 considers the identification of latent group structures in dynamic spatial models with interactive fixed effects. The model treats three kinds of heterogeneity at the same time, namely, the spatial heterogeneity, individuals’ heterogeneous responses to the same time factors, and heterogeneous slope coefficients. To identify the latent group structures, we adopt quasi-maximum likelihood estimation to get preliminary unconstrained estimators of the slope coefficients. Then we use the K-means algorithm on slope coefficients’ consistent preliminary estimators to get the clusters. The asymptotic analysis shows that this method can identify the true group structure consistently. Therefore, the post-classification estimators have the oracle property. Monte Carlo simulations demonstrate that it has good finite sample performance.