Approximately Exact Inference in Dynamic Panel Models

This paper develops a general method for conducting exact small-sample inference in models which allow the estimator of the (scalar) parameter of interest to be expressed as the root of an estimating function, and which is particularly simple to implement for linear models with a covariance matrix depending on a single parameter. The method involves the computation of tail probabilities of the estimating function. In the context of dynamic panel models, both the least squares and maximum likelihood paradigms give rise to estimating functions involving sums of ratios in quadratic forms in normal variates, the distribution of which cannot be straightforwardly computed. We overcome this obstacle by deriving a saddlepoint approximation that is both readily evaluated and remarkably accurate. A simulation study demonstrates the validity of the procedure, and shows the resulting estimators to be vastly superior over existing ones