Three Essays on Panel and Factor Models

The dissertation includes three chapters on panel and factor models. In the first chapter, we introduce a two-way linear random coefficient panel data models with fixed effects and cross-sectional dependence. We follow the idea of within-group transformation to estimate the parameters of interests. We establish the limiting distributions of the estimators and propose a two-way heterogeneity bias test to check the desirability of the estimation strategy. Specification tests are then proposed to test for the null hypothesis of no slope heterogeneity along either the cross-section or/both the time dimensions. We study the asymptotic properties of the specification tests and employ two bootstrap schemes to rectify the undersize issue of the tests. We apply the specification tests to reveal the heterogeneous relationship between the unemployment rate and youth labor rate in the working-age population. In the second chapter, we devise a simple but effective procedure to test for the existence of bubbles in the idiosyncratic components in the presence of nonstationary or mildly explosive factors in the common components in panel factor models. We study the asymptotic properties of the test and propose a wild bootstrap procedure to improve its finite sample performance. As an illustrative example, we consider testing the bubbles in the idiosyncratic components of cryptocurrency prices. In the third chapter, we consider the tests of bubbles in the common factors when the idiosyncratic errors follow a unit-root or local-to-unity process. We study the asymptotic properties of the proposed tests and show that they have non-trivial power to detect the bubbles in the unobserved common factors under the alternative of local-to-unity. To implement the proposed tests, we propose to use the dependent wild bootstrap method to simulate the critical values in practice.