Robust tests for time-invariant individual heterogeneity versus dynamic state dependence

We derive tests for persistent effects in a general linear dynamic panel data context. Two sources of persistent behavior are considered: time-invariant unobserved factors (captured by an individual random effect) and dynamic persistence or “state dependence” (captured by autoregressive behavior). We will use a maximum likelihood framework to derive a family of tests that help researchers learn whether persistence is due to individual heterogeneity, dynamic effect, or both. The proposed tests have power only in the direction they are designed to perform, that is, they are locally robust to the presence of alternative sources of persistence, and consequently, are able to identify which source of persistence is active. A Monte Carlo experiment is implemented to explore the finite sample performance of the proposed procedures. The tests are applied to a panel data series of real GDP growth for the period 1960–2005.