Aggregation Bias in Estimating Log‐Log Demand Function

Zizhuo Wang, Chaolin Yang, Hongsong Yuan and Yaowu Zhang

Production and Operations Management, 2021, vol. 30, issue 11, 3906-3922

Abstract: In this study, we consider the problem of estimating demand functions using historical sales data. In particular, we study how using aggregate data may result in bias in such estimations. We consider a log‐log demand model, and two ways of how the price in the aggregate data is calculated, simple average price or weighted average price. We study whether there exists estimation bias in each of the two cases as well as the direction of the bias. We show that in general, the correlation between “average price” and “price dispersion” in each time period has an effect on the direction of the bias. We then propose ways to reduce the aggregation bias. We prove that when the price processes satisfy certain mild conditions, our debiasing procedure can recover the true parameters asymptotically. We also obtain statistical properties of the debiased parameters. We perform numerical experiments on both synthetic and real data to demonstrate the effectiveness of our approach. The numerical results show that our proposed bias mitigation approach has the potential of effectively reducing the bias in both synthetic and practical settings.

Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/poms.13488

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:popmgt:v:30:y:2021:i:11:p:3906-3922

Ordering information: This journal article can be ordered from
http://onlinelibrary ... 1111/(ISSN)1937-5956

Access Statistics for this article

Production and Operations Management is currently edited by Kalyan Singhal

More articles in Production and Operations Management from Production and Operations Management Society
Bibliographic data for series maintained by Wiley Content Delivery ().