Saddlepoint techniques for spatial panel data models

Abstract: We develop new higher-order asymptotic techniques for the Gaussian maximum likelihood estimator (henceforth, MLE) of the parameters in a spatial panel data model, with fixed effects, time-varying covariates, and spatially correlated errors. To improve on the accuracy of the extant asymptotics, we introduce a new saddlepoint density approximation, which features 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, which yields a density approximation that is always non-negative, does not need resampling, and is accurate in the tails. We provide an algorithm to implement our saddlepoint approximation and we illustrate the good performance of our method via numerical examples. Monte Carlo experiments show that, for the spatial panel data model with fixed effects and $T=2$, the saddlepoint approximation yields accuracy improvements over the routinely applied first-order asymptotics and Edgeworth expansions, in small to moderate sample sizes, while preserving analytical tractability.

This is a joint paper with Jiang C., Ronchetti E., Scaillet O.