Estimating Primary Demand for Substitutable Products from Sales Transaction Data

42 Pages Posted: 7 Sep 2011

See all articles by Gustavo Vulcano

Gustavo Vulcano

Universidad Torcuato Di Tella - School of Business

Garrett van Ryzin

Cornell Tech; Lyft, Inc.

Richard Ratliff

affiliation not provided to SSRN

Date Written: April 1, 2011

Abstract

We propose a method for estimating substitute and lost demand when only sales and product availability data are observable, not all products are displayed in all periods (e.g., due to stock-outs or availability controls), and the seller knows its aggregate market share. The model combines a multinomial logit (MNL) choice model with a non-homogeneous Poisson model of arrivals over multiple periods. Our key idea is to view the problem in terms of primary (or first-choice) demand; that is, the demand that would have been observed if all products had been available in all periods. We then apply the expectation-maximization (EM) method to this model, and treat the observed demand as an incomplete observation of primary demand. This leads to an efficient, iterative procedure for estimating the parameters of the model, which provably converges to a stationary point of the incomplete data log-likelihood function. Every iteration of the algorithm consists of simple, closed-form calculations. We illustrate the effectiveness of the procedure on simulated data and two industry data sets.

Keywords: Demand estimation, demand untruncation, choice behavior, multinomial logit model, EM method

Suggested Citation

Vulcano, Gustavo and van Ryzin, Garrett and Ratliff, Richard, Estimating Primary Demand for Substitutable Products from Sales Transaction Data (April 1, 2011). Columbia Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=1923711 or http://dx.doi.org/10.2139/ssrn.1923711

Gustavo Vulcano

Universidad Torcuato Di Tella - School of Business ( email )

Avda Figueroa Alcorta 7350
Buenos Aires, CABA 1428
Argentina

Garrett Van Ryzin (Contact Author)

Cornell Tech ( email )

2 W Loop Rd
New York, NY 10044
United States

Lyft, Inc. ( email )

San Francisco, CA

Richard Ratliff

affiliation not provided to SSRN ( email )

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