A Lagrange Multiplier-Type Test for Idiosyncratic Unit Roots in the Exact Factor Model

In this article, an exact factor model is considered, and a Lagrange multiplier-type test is derived for a homogeneous unit root in the idiosyncratic component. It is shown that under sequential asymptotics, its null limiting distribution is standard normal, regardless of whether the factors are integrated, cointegrated or stationary. In a simulation study, the size and local power of the Lagrange multiplier-type test and some popular non-likelihood-based tests are compared. The simulation results show that the Lagrange multiplier-type test has the highest local power as the panel dimensions tend to infinity, with the actual size tending to the nominal size.