Essays on large panel data models with two-way heterogeneity - WANG, Yiren (Institutional Knowledge at Singapore Management University, 2023)
This dissertation consists of two papers that contribute to the estimation and inference theory of the panel data models with two-way slope heterogeneity. The first paper considers the panel quantile regression model with slope heterogeneity along both individuals and time. By modelling this two-way heterogeneity with the low-rank slope matrix, the slope coefficient can be estimated via the nuclear norm regularization followed by sample-splitting, row- and column-wise quantile regression, and debiasing. The inferential theory for the final slope estimator along with its factor and factor loading is derived. Two specification tests are proposed: one tests whether the slope coefficient is a constant over one dimension (individual or time) without assuming the slope coefficient is homogeneous over the other dimension under the case that the true rank of the slope matrix equals one, and the other tests whether the slope coefficient follows the additive structure under the case that the true rank of slope matrix equals two. The second paper focuses on the estimation and inference of the linear panel model with interactive fixed effects and two-way slope heterogeneity. Specifically, individual coefficients are allowed to form by a latent group structure cross-sectionally, and such a structure can change after an unknown structural break. A multi-stage estimation algorithm is proposed, which involves nuclear norm regularization, break detection, and a K-means procedure, to estimate the break date, the number of groups, and the group structure. Under some regularity conditions, the break date estimator, number of groups estimator, and the group structure estimator can be shown to enjoy the oracle property. Monte Carlo studies and empirical applications are conducted to illustrate the finite sample performance of the proposed algorithms and estimators.