Likelihood Inference for Dynamic Panel Models

The likehood principle is applied to the problem of inference in dynamic panel models. The prin ciple states that the likelihood function contains "... all the information which the data provide concerning the relative merits of..." alternative parametric hypotheses. The usual asymptotic theory of maximum likelihood is based on a qua dratic approximation to the likelihood function in the nearby neighborhood of a local maximum of the function. One needs to look at the entire function more broadly in order to ascertain the true significance of the data for the hypo theses under consideration, not only because of the possibilities of multiple local maxima and boundary solutions, but also because the data are typically differentially informative with respect to different regions of the parameter space. In order to handle cases in which the likelihood function depends on more than two parameters, the devices of "concentrating" and of "slicing" or sectioning the function in the direction of a hyperplane or surface reflecting the varia tion of all but two of the parameters are introduced. The likelihood functions for two basic dynamic panel models: (1) a model involving individual-specific effects which reflect the influence of latent time-persistent variables; (2) a model involving individual-specific time trends which reflect the nonstationarity introduced by trending latent variables, are derived. The methods are applied to the analysis of cross-country economic growth. The findings demonstrate the power and feasibility of general methods of likelihood inference, especially to reveal problems of inference and areas of ignorance.