Inferential theory for heterogeneity and cointegration in large panels

© 2020 Elsevier B.V. This paper provides an estimation and testing framework to assess the presence and the extent of slope heterogeneity and cointegration when the units are a mixture of spurious and/or cointegrating regressions. We propose two moment estimators for the degree of heterogeneity (measured by the dispersion of the slope coefficients around their average) and for the fraction of spurious regressions, which are found to be consistent in the whole parameter space. Based on these estimators, two tests for the null hypotheses of slope homogeneity and for cointegration are proposed. Monte Carlo simulations show that both tests have the correct size and satisfactory power.