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.

Measuring Substitution Patterns in Differentiated-Products Industries

“…A growing number of papers using our instruments confirm these results. The Differentiation IVs introduced in this paper have now been used to obtain precise estimates of substitution patterns in a variety of applied contexts, ranging from demand for cars (Miravete, Moral, andCoşar, Grieco, andTintelnot 2018), scanner data (Miller and Weinberg (2017), Sullivan (2020), Dube, Hortacsu, and Joo (2020)), and school choice (Singleton 2019). See also Conlon and Gortmaker (2019) for additional Monte-Carlo simulation results.…”

Determinants of economies of scope in retail

“…Having annual data, we do not model stock-outs. 21 See, e.g.,Anderson et al (1987),Anderson and De Palma (2006), andDube et al (2020).22 The demand system is similar to the logit discrete choice system, but the price is in logs.…”

Spatial Economics for Granular Settings

“… See Sotelo (2019) for a discussion of the relationship between the multinomial and Poisson pseudo-maximumlikelihood estimators in the context of gravity models. In practice, we use the Stata package ppmlhdfe ofCorreia, Guimarães, and Zylkin (2020).17 This selection bias also has substantial implications for the estimated fixed effects, as discussed in Appendix C. Recent research in industrial organization draws attention to the problems associated with zero-valued market shares(Quan and Williams, 2018;Gandhi, Lu, and Shi, 2019;Dubé, Hortaçsu, and Joo, 2020).…”