Random-Coefficients Logit Demand Estimation with Zero-Valued Market Shares

Abstract

Although typically overlooked, many purchase datasets exhibit a high incidence of products with zero sales. We propose a new estimator for the Random-Coefficients Logit demand system for purchase datasets with zero-valued market shares. The identification of the demand parameters is based on a pairwise-differencing approach that constructs moment conditions based on differences in demand between pairs of products. The corresponding estimator corrects nonparametrically for the potential selection of the incidence of zeros on unobserved aspects of demand. The estimator also corrects for the potential endogeneity of marketing variables both in demand and in the selection propensities. Monte Carlo simulations show that our proposed estimator provides reliable small-sample inference both with and without selection-onunobservables. In an empirical case study, the proposed estimator not only generates different demand estimates than approaches that ignore selection in the incidence of zero shares, it also generates better out-of-sample fit of observed retail contribution margins.

A Random Coefficients Model of Seafood Demand: Implications for Consumer Preferences and Substitution Patterns

“…Comparing the count of products reveals that on average 27% of products sold in a given county-month had zero market share for some week within that month. The results comparing monthly with quarterly are similar, and suggest that the bias for high-frequency data described in Dube, Hortaçsu, and Joo (2020) would be an issue.…”

“…The BLP model treats every product that is sold in a market as part of the consideration set, but that also means that any product with zero market share is assumed to have been out of the consideration set. This can lead to bias in high-frequency data (Dube, Hortaçsu, and Joo 2020), so we aggregate the data to the quarterly level to alleviate this concern and to reduce the computational burden, giving us a total of 640 markets. 4 At the quarterly level, the model still accounts for the seasonal availability of fresh Pacific salmon.…”

Estimating demand for differentiated products with zeroes in market share data

“…The bounds are used to construct a set of moment inequalities, which are valid in the presence of the zeroes, and more generally in the presence of sampling error in market shares. 1 The moment inequalities can be directly used for parameter inference with the help of set inference methods in the econometrics literature but for computational reasons, 1 In the last couple of years, new aggregate demand models have been considered that accommodate zeroes in market share data in Dube, Hortacsu, and Joo (2020) and Lima (2021). Dube et al model the products with zero market shares as ones that are not in any consumer's consideration set.…”

“…11 In the last couple of years, new aggregate demand models have been considered that accommodate zeroes in market share data in Dube, Hortacsu, and Joo (2020) and Lima (2021). Dube et al model the products with zero market shares as ones that are not in any consumer's consideration set.…”