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Title: Saddlepoint techniques for spatial panel data models Authors:  Chaonan Jiang - University of Geneva (Switzerland) [presenting]
Davide La Vecchia - University of Geneva (Switzerland)
Elvezio Ronchetti - University of Geneva (Switzerland)
Olivier Scaillet - University of Geneva and Swiss Finance Institute (Switzerland)
Abstract: New higher-order asymptotic techniques are developed 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 error. The first-order asymptotics needs the cross-sectional sample size ($n$) to diverge, while the time dimension ($T$) can be fixed. The resulting approximation to the MLE density has absolute error of order $O(m^{-1/2})$, for $m = n(T-1)$. We illustrate that, when $n$ and $T$ are small, the first-order asymptotics can be inaccurate, specially in the tails -- the parts of the density we are typically interested in, e.g. for the p-values. To improve on the accuracy of the extant asymptotics, we introduce a new saddlepoint density approximation, which features relative error of order $O(m^{-1})$. The main theoretical tool is the tilted-Edgeworth technique, which, by design, yields a density approximation that is always non-negative and does not need resampling. 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.