Inference and testing breaks in large dynamic panels with strong cross sectional dependence

In this paper we provide a new Central Limit Theorem for estimators of the slope papers in large dynamic panel data models (where both n and T increase without bound) in the presence of, possibly, strong cross-sectional dependence. We proceed by providing two related tests for breaks/homogeneity in the time dimension. The first test is based on the CUSUM principle; the second test is based on a Hausman-Durbin-Wu approach. Some of the key features of the tests are that they have nontrivial power when the number of individuals, for which the slope parameters may differ, is a “negligible” fraction or when the break happens to be towards the end of the sample, and do not suffer from the incidental parameter problem. We provide a simple bootstrap algorithm to obtain (asymptotic) valid critical values for our statistics. An important feature of the bootstrap is that there is no need to know the underlying model of the cross-sectional dependence. A Monte-Carlo simulation analysis sheds some light on the small sample behaviour of the tests and their bootstrap analogues. We implement our test to some real economic data.