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 $O(m^{-1})$ for $m=n(T-1)$ with $n$ being the cross-sectional dimension and $T$ the time-series dimension. The main theoretical tool is the tilted-Edgeworth technique in a non-identically distributed setting. The density approximation is always non-negative, does not need resampling, and is accurate in the tails. We provide an algorithm and Monte Carlo experiments illustrating its good performance over first-order asymptotics and Edgeworth expansions, while preserving analytical tractability. An empirical application on the investment-saving relationship in OECD countries shows disagreement between testing results based on first-order asymptotics and saddlepoint techniques.