Hypothesis testing for slope heterogeneity for three dimensional panel data model

Abstract

Tests for slope heterogeneity play important roles in panel data analysis nowadays as we can see several tests have been proposed in the last decades. However, those tests were proposed for classical panel models while multi-dimensional panel data have been becoming more available and are important in applications. Therefore, the main goal of this thesis is to derive a heterogeneity test statistic that is applicable for three-dimensional panel data model. Our test is the Lagrange multiplier test statistic based on the conditional Gaussian likelihood function of a sufficient statistic. The test is asymptotically normally distributed when the number of levels of considered direction tends to infinity and the number of time periods is fixed. Simulation results show that the proposed test has good size under considered specifications.