Estimating Demand for Differentiated Products with Zeroes in Market Share Data

57 Pages Posted: 17 Dec 2019 Last revised: 31 Jan 2020

See all articles by Amit Gandhi

Amit Gandhi

University of Wisconsin - Madison

Zhentong Lu

Government of Canada - Bank of Canada

Xiaoxia Shi

University of Wisconsin - Madison; Yale University

Date Written: January 30, 2020

Abstract

In this paper we introduce a new approach to estimating differentiated product demand systems that allows for products with zero sales in the data. Zeroes in demand are a common problem in product differentiated markets, but fall outside the scope of existing demand estimation techniques. Our solution to the zeroes problem is based on constructing bounds for the conditional expectation of the inverse demand. These bounds can be translated into moment inequalities that are shown to yield consistent and asymptotically normal point estimator for demand parameters under natural conditions for differentiated product markets. In Monte Carlo simulations, we demonstrate that the new approach works well even when the fraction of zeroes is as high as 95%. We apply our estimator to supermarket scanner data and find that correcting the bias caused by zeroes has important empirical implications, e.g., price elasticities become on the order of twice as large when zeroes are properly controlled.

Suggested Citation

Gandhi, Amit and Lu, Zhentong and Shi, Xiaoxia, Estimating Demand for Differentiated Products with Zeroes in Market Share Data (January 30, 2020). Available at SSRN: https://ssrn.com/abstract=3503565 or http://dx.doi.org/10.2139/ssrn.3503565

Amit Gandhi

University of Wisconsin - Madison ( email )

716 Langdon Street
Madison, WI 53706-1481
United States

Zhentong Lu (Contact Author)

Government of Canada - Bank of Canada ( email )

234 Wellington Street
Ontario, Ottawa K1A 0G9
Canada

Xiaoxia Shi

University of Wisconsin - Madison ( email )

1180 Observatory Drive
Madison, WI 53706
United States

Yale University

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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