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. Supplementary materials for this article, including a standardized description of the materials

available for reproducing the work, are available as an online supplement.