Testing for Unit Roots in Panel Data: An Exploration Using Real and Simulated Data
Bronwyn H. Hall and Jacques Mairesse,
UC Berkeley, INSEE-CREST, and NBER

Abstract

This paper explores the univariate time series properties of commonly used variables in firm-level panels: sales (turnover), employment, R&D, investment, and cash flow. We focus on two questions: 1) whether GMM offers a solution to the problem of modeling the dynamics of short panels that contain unobservable individual-specific effects, and 2) whether the behavior of these series is consistent with stationarity. In particular, we note that the results of the usual GMM estimator are greatly affected by whether the data is trend stationary (exhibits regression to individual firm means) or difference stationary (evolves as a random walk, possibly with a non-zero drift), making the test for unit roots an important pre-condition for choosing estimation strategy. Using simulation, we demonstrate that some of the tests for nonstationarity of panel data that have been proposed in the literature either have low power or can be misleading for panels of our dimension. We go on to explore the use of likelihood-based tests when there is parameter heterogeneity (leading to an incidental parameter problem). We then report the results of our preferred tests, and find that although our data displays close to unit root behavior, in most cases it rejects nonstationarity in favor of stationarity with a very high autoregressive coefficient, but no individual-specific effect.