We extend the Prais-Winsten AR(k) generalized least squares (GLS) transformation to panel data within the Beck-Katz panel-corrected standard error (PCSE) framework and implement the method in the community-contributed Stata package xtpraisk. As the panel extension of Prais-Winsten, xtpraisk is the natural comparator to xtscc, the panel extension of Newey-West and implementation of the Driscoll-Kraay estimator. We conduct a Monte Carlo simulation to validate the statistical properties of xtpraisk and compare its finite-sample performance with xtscc. The simulation spans autoregressive orders 1-3, three autocorrelation scenarios, three panel sizes, six series lengths, and five effect sizes, with 2,000 replications per condition. Across all conditions, xtpraisk achieved higher power than xtscc while maintaining near-nominal Type I error rates, confidence interval coverage, and standard error calibration. In contrast, xtscc exhibited systematic standard error underestimation and inflated Type I error at short series lengths, with both deficiencies worsening as autoregressive order increased. Both estimators were essentially unbiased. Misspecification of the autoregressive order did not degrade xtpraisk's inferential performance, and cross-panel correlation and panel size had negligible effects on the relative performance of either estimator. The results indicate that xtpraisk is preferable when both statistical efficiency and valid inference are priorities, particularly under persistent higher-order autocorrelation and short to moderate series lengths.

翻译：我们将普雷斯-温斯顿 AR(k) 广义最小二乘 (GLS) 变换扩展到贝克-卡茨面板校正标准误 (PCSE) 框架下的面板数据，并在用户贡献的 Stata 软件包 xtpraisk 中实现了该方法。作为普雷斯-温斯顿方法的面板扩展，xtpraisk 是与 xtscc（纽威-韦斯特方法的面板扩展及德里斯科尔-克雷估计量的实现）的自然比较对象。我们进行蒙特卡洛模拟以验证 xtpraisk 的统计性质，并比较其与 xtscc 在有限样本中的表现。模拟涵盖自回归阶数 1-3 阶、三种自相关情景、三种面板规模、六种序列长度和五种效应量，每个条件下进行 2,000 次重复。在所有条件下，xtpraisk 的统计功效均高于 xtscc，同时保持接近名义水平的第一类错误率、置信区间覆盖率和标准误校准。相比之下，xtscc 在短序列长度下表现出系统性标准误低估和第一类错误膨胀，且这两种缺陷随自回归阶数增加而恶化。两种估计量均基本无偏。自回归阶数的误设不会降低 xtpraisk 的推断性能，而面板间相关性和面板规模对两种估计量的相对性能影响可忽略。结果表明，当统计效率和有效推断均为优先目标时，特别是存在持续性高阶自相关且序列长度较短至中等的情况下，xtpraisk 更为可取。