 Cross-Section Estimation of Long-Run Relations Using Time-Compressed DataSerena Ng and Nikolay Gospodinov Abstract: 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. Date: 2026-08 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2608.25901 Access Statistics for this paper More papers in Papers from arXiv.org |
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