Saddlepoint approximations for spatial panel data models

Document pages: 68 pages

Abstract: We develop new higher-order asymptotic techniques for the Gaussian maximumlikelihood estimator in a spatial panel data model, with fixed effects,time-varying covariates, and spatially correlated errors. Our saddlepointdensity 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 $T$ thetime-series dimension. The main theoretical tool is the tilted-Edgeworthtechnique in a non-identically distributed setting. The density approximationis always non-negative, does not need resampling, and is accurate in the tails.We provide an algorithm and Monte Carlo experiments illustrating its goodperformance over first-order asymptotics and Edgeworth expansions, whilepreserving analytical tractability. An empirical application on theinvestment-saving relationship in OECD countries shows disagreement betweentesting results based on first-order asymptotics and saddlepoint techniques.