Three Essays on Modelling Large Panel Data with a Multilevel Factor Structure

This thesis presents a sequential and comprehensive development of high-dimensional panel data models with a multilevel factor structure. The multilevel factors consist of unobserved global factors that affect all individuals and unobserved local factors that affect individuals within specific blocks.
In Chapter 1, we develop a novel approach based on canonical correlation analysis to identify the number of global factors in the multilevel factor model. We propose two consistent selection criteria: the canonical correlation difference (CCD) and the modified canonical correlations (MCC). Monte Carlo simulations show that CCD and MCC correctly select the number of global factors even in small samples, and they are robust to correlated local factors. In an empirical application, we investigate a multilevel asset pricing model for stock return data in 12 industries in the U.S. market.
Chapter 2 advances a unified econometric framework for the multilevel factor model based on generalized canonical correlation (GCC) analysis. Our approach is valid even if some blocks share common local factors. We establish the consistency of the estimated factors and loadings, as well as their asymptotic normality under fairly standard conditions. As a by-product of estimation, a new selection criterion is developed to estimate the number of global factors. Through Monte Carlo simulations, we confirm the validity of our asymptotic theory and demonstrate its superior performance over existing approaches. We apply the model to a large disaggregated panel data set of house prices in England and Wales.
Chapter 3 considers a panel regression model with multilevel factors. We propose a multilevel iterative principal component (MIPC) method that iteratively updates the slope coefficients and factors. We also propose a model selection criterion based on eigenvalue ratios to determine the number of factors. Given consistent factor estimates, we employ GCC to separately identify the global and local factors. Under a finite number of blocks, we show the consistency of our estimates and establish the asymptotic normality of the bias-corrected estimator for the slope coefficients. Monte Carlo simulations demonstrate the good finite sample performance of MIPC. We apply our method to an analysis of the energy consumption and economic growth nexus using a cross-country panel data categorized by regions.