利用时间压缩数据对长期关系进行横截面估计
Cross-Section Estimation of Long-Run Relations Using Time-Compressed Data
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中文总结 AI 辅助
该论文针对时间压缩的I(1)数据，提出横截面回归可得到超一致且渐近正态的长期关系估计量，通过实证应用验证了部分宏观变量间长期关系的可靠性。
中文摘要 AI 辅助
许多关于长期关系的实证研究基于对平均化或长差分数据的横截面回归，这些数据实质上压缩了T×N面板的时间维度。我们分析一类时间压缩的I(1)数据，表明它们具有放大的变异性，原因在于非平稳面板的横截面方差会随时间“扩散”。无论回归元是平稳、非平稳还是高度持久的，时间压缩数据中的横截面回归都可能产生超一致且渐近正态的估计量。达到最快收敛速率√NT需要一种压缩方案，该方案不仅能放大非平稳信号，还能稀释回归噪声。遗漏的固定效应会阻碍噪声稀释，但估计量仍保持超一致性。不过，当数据存在强均值回复或收敛趋势时，扩散效应会被削弱，这一问题似乎与温度数据相关。我们考虑三项应用，发现消费与收入、增长/通胀与人口变量之间的长期关系得到了较好确定，但增长与升温温度之间的估计关系较为脆弱。
英文摘要
Many empirical investigations of long-run relations are based on cross-section regressions in averaged or long differenced data that effectively have the time dimension of a $T\times N$ panel compressed. We analyze a class of time-compressed I(1) data and show that they have magnified variability stemming from the fact that the cross-section variance of a non-stationary panel `fans out' with time. Cross-section regressions in time compressed data can potentially yield estimates that are super-consistent and asymptotically normal, whether the regressors are stationary, non-stationary, or highly persistent. The fastest convergence rate of $\sqrt{N}T$ requires a compression scheme that not only magnifies the non-stationary signal, but also dilutes the regression noise. Omitted fixed effects preclude noise dilution but the estimates remain super-consistent. However, the fanning out effect can be weakened when the data have a strong force for mean-reversion or convergence, a problem that seems relevant for temperature data. We consider three applications and find that the long-run relation between consumption and income, and between growth/inflation and demographic variables are reasonably well determined, but the estimated relation between growth and warming temperature is fragile.
