Estimation of and testing for random effects in dynamic panel data models

In this article, estimation of moments up to the fourth order of random effects and errors is first investigated for dynamic panel data models. Using the QR decomposition of a matrix, the moments of random individual effects and errors are estimated without affecting each other so that the estimation procedure is simple to implement, and the asymptotic behavior of estimation is derived. On the basis of these estimations, we construct a test for the existence of individual effects. This test is asymptotically normally distributed under the null hypothesis without any distributional assumptions on the individual effects and errors other than moments. A power study shows that our test is able to detect local alternatives that are distinct from the null at a parametric rate. Monte Carlo simulations are carried out for illustration.