Validating approximate slope homogeneity in large panels

In this paper, we introduce new inference methods for slope homogeneity in large regression panels. While most existing tests are developed for the hypothesis of slope homogeneity (equality of all individual slopes), we propose to test the more realistic relaxation of approximate slope homogeneity (similarity of all slopes). We present new test statistics for dense and sparse alternatives to approximate homogeneity. In the dense setting, the main focus of this paper, we develop statistics that converge to pivotal limits even under simultaneous temporal and intersectional dependence. We also demonstrate uniform consistency of these statistics against large classes of local alternatives. As a complementary diagnostic tool, we propose tests against sparse alternatives that are sensitive to excessive heterogeneity in a minority of slopes. Such tests can play an important role in the analysis of populations with diverse but small subgroups. A simulation study and a data example underline the usefulness of our approach.