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Across-Design Uncertainty in Short Pricing Panels: Inference and Identification

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  • Pedro Cadahia Delgado

Abstract

Short observational pricing panels often contain many data points but very few actual price changes. This paper shows that this sparsity creates a hidden source of error that standard statistical methods miss. When estimating price effects, most of the uncertainty does not come from sample size within a panel, but from the specific history of price movements observed. Standard confidence intervals fail because they only measure variation within the panel, ignoring this broader design-level error. Using simulations, we find that this cross-design variation accounts for most of the estimation error, causing standard methods to significantly understate uncertainty. First, we show that cross-design error decreases predictably as the total volume of price variation increases. Second, adding more data from regions that share the same price trends does not fix the issue; true precision improves only when combining data across units with independent price trajectories. Third, applying a simple variance-component adjustment across independently priced units restores accurate statistical coverage. We confirm these findings in real-world store scanner data, showing that products and pricing zones behave as if they have far fewer independent price movements than their raw counts suggest. Ultimately, reliable inference in passive pricing data requires genuine, independent variation, which can be achieved through controlled regional price testing.

Suggested Citation

  • Pedro Cadahia Delgado, 2026. "Across-Design Uncertainty in Short Pricing Panels: Inference and Identification," Papers 2608.21334, arXiv.org, revised Sep 2026.
  • Handle: RePEc:arx:papers:2608.21334
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    1. Whitney Newey & Kenneth West, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    2. Harold D. Chiang & Kengo Kato & Yukun Ma & Yuya Sasaki, 2022. "Multiway Cluster Robust Double/Debiased Machine Learning," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1046-1056, June.
    3. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2009. "Dealing with limited overlap in estimation of average treatment effects," Biometrika, Biometrika Trust, vol. 96(1), pages 187-199.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    5. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2011. "Robust Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 238-249, April.
    6. Peter M. Aronow & Cyrus Samii, 2016. "Does Regression Produce Representative Estimates of Causal Effects?," American Journal of Political Science, John Wiley & Sons, vol. 60(1), pages 250-267, January.
    7. Jean-Pierre Dubé & Sanjog Misra, 2023. "Personalized Pricing and Consumer Welfare," Journal of Political Economy, University of Chicago Press, vol. 131(1), pages 131-189.
    8. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2020. "Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis," Econometrica, Econometric Society, vol. 88(1), pages 265-296, January.
    9. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    10. Timothy B. Armstrong & Michal Kolesár, 2020. "Simple and honest confidence intervals in nonparametric regression," Quantitative Economics, Econometric Society, vol. 11(1), pages 1-39, January.
    11. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, June.
    12. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    13. J. Miguel Villas-Boas & Russell S. Winer, 1999. "Endogeneity in Brand Choice Models," Management Science, INFORMS, vol. 45(10), pages 1324-1338, October.
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