A1407
Title: Robust variance estimation and inference for spatial panel data without weight matrices
Authors: Shuichi Nagata - Kwansei Gakuin University (Japan) [presenting]
Abstract: In panel data regression with cross-sectional dependence, robust inference typically requires specifying a spatial weight matrix or a distance metric, both of which are subject to misspecification. A time-direction aggregation estimator, constructed from cross-sectionally summed scores, avoids this requirement by absorbing arbitrary spatial correlation within each period. Under alpha-mixing random field conditions on a lattice, the associated t-statistic converges to a t-distribution with $T-1$ degrees of freedom as $N$ grows with $T$ fixed and no serial correlation, mirroring a classical result for the individual-direction estimator under growing $T$ with $N$ fixed. Monte Carlo experiments with spatial AR(1) errors confirm that (i) size is nearly invariant to spatial correlation strength and depends primarily on $T$, (ii) using $t(T-1)$ critical values brings size close to the nominal level for moderate $T$, (iii) a spatial HAC estimator exhibits substantial size distortion even with correct distances, worsened by misspecification, and (iv) these properties are robust to heavy-tailed and skewed innovations. Two-way fixed effects estimation plays a key role by imposing zero-sum constraints on scores across both panel dimensions, enabling the $N$-$T$ symmetric asymptotic structure.
