Saddlepoint Approximations for Spatial Panel Data Models

We develop new higher-order asymptotic techniques for the Gaussian maximum likelihood estimator in a spatial panel data model, with fixed effects, time-varying covariates, and spatially correlated errors. Our saddlepoint density and tail area approximation feature relative error of order O(1/(n(T-1))) with n being the cross-sectional dimension and T the time-series dimension. The main theoretical tool is the tilted-Edgeworth technique in a nonidentically distributed setting. The density approximation is always nonnegative, does not need resampling, and is accurate in the tails. Monte Carlo experiments on density approximation and testing in the presence of nuisance parameters illustrate the good performance of our approximation over first-order asymptotics and Edgeworth expansion. An empirical application to the investment-saving relationship in OECD (Organisation for Economic Co-operation and Development) countries shows disagreement between testing results based on the first-order asymptotics and saddlepoint techniques. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.