Uses of entropy and divergence measures for evaluating econometric approximations and inference

This paper provides the uses of the Kullback and Leibler divergence measure in two directions. First a new result on the asymptotic expansion of the Kullback and Leibler divergence is provided which can be used for comparing two distributions. An application to compare two alternative approximate distributions from the unknown true exact distribution of a Student t-statistic in a dynamic regression is given. Second we explore the application of the Kullback and Leibler divergence measure to non-parametric estimation and specification testing in regression models. A non-parametric specification test is proposed.