There Is No Aggregation Bias: Why Macro Logit Models Work

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of Business &Economic Statistics.In this article, we examine the aggregation properties of (nested) logit models to understand their exceptional macro-level performance. The problem of aggregating micro logit models involves integrating nonlinear functions of model parameters over a distribution of consumer heterogeneity. The aggregation problem is analyzed using a mixture of analytic and simulation techniques, with the simulation experiments using actual panel data to calibrate the distribution of heterogeneity. We conclude that the practice of fitting aggregate logit models is theoretically justified under the following three conditions: (1) All consumers are exposed to the same marketing-mix variables, (2) the brands are close substitutes, and (3) the distribution of prices is not concentrated at an extreme value. These conditions are frequently met in store-level scanner data.

Aggregation Bias in Sponsored Search Data: The Curse and the Cure

“…Sinceβ c is a consistent and unbiased estimator of β,β s is biased. This finding is contrary to earlier work by Allenby and Rossi (1991), Gupta et al (1996) and Russell and Kamakura (1994), which prove that aggregation bias in market or store-level scanner data is negligible. Aggregation bias is significantly reduced in their context as products are very close substitutes of each other and the consumers (or house-holds) are exposed to very similar marketing activities.…”

“…However, as pointed earlier, several papers show that aggregation bias is negligible in various marketing data (Allenby and Rossi, 1991;Gupta et al, 1996;Russell and Kamakura, 1994). They argue that aggregation bias is significantly reduced because the products considered in their analysis are very close substitutes.…”

“…Allenby and Rossi (1991) present an analytical proof for the non-existence of aggregation bias in nested logit models of consumer choice when the products are close substitutes of each other, though they assume that the micro-level consumer behavior is approximately linear in the product attributes. More specifically, in the context of sponsored search, Rutz and Trusov (2011) use a latent instrumental variable approach that addresses endogeneity in search auctions.…”

Heterogeneity and Aggregation

“…As an organizing principle, we consider (i) heterogeneity in individual tastes and incomes, (ii) heterogeneity in wealth and income risks faced by individuals and (iii) heterogeneity in market participation. 4 There is a generic tension between the degree of individual heterogeneity accounted for and the ease with which one can draw implications for economic aggregates. We point out how di¤erent types of heterogeneity are accommodated in the di¤erent application areas.…”

Integrated measures of sales, merchandising, and distribution

“…Exceptions are Christen, Gupta, Porter, Staelin, and Wittink (1997), Gupta, Chintagunta, Kaul, and Wittink (1996), Foekens, Leeflang, and Wittink (1994), Link (1995), and Allenby and Rossi (1991). These authors investigate biases introduced by applying econometric techniques to data that has been assembled by aggregating from individuals to stores or stores to markets.…”