Abstract

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)))$O(1/(n(T-1)))$$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.

摘要

我们为空间面板数据模型中的高斯最大似然估计量开发了新的高阶渐近技术，具有固定效应、时变协变量和空间相关误差。我们的鞍点密度和尾部面积近似特征的相对阶次误差O ( 1 / ( n ( T− 1 ) ) )$氧（1/（n（\mathrm{时间}-1）））$$O(1/(n(T-1)))$其中n为横截面尺寸，T时间序列维度。主要的理论工具是非同分布环境中的倾斜埃奇沃斯技术。密度近似总是非负的，不需要重采样，并且尾部是准确的。关于密度近似的蒙特卡罗实验和存在干扰参数的测试说明了我们的近似相对于一阶渐近和埃奇沃斯展开的良好性能。对 OECD（经济合作与发展组织）国家投资储蓄关系的实证应用表明，基于一阶渐近法和鞍点技术的测试结果之间存在分歧。本文的补充材料（包括可用于复制作品的材料的标准化描述）可作为在线补充材料获得。