Eliminating the Outside Good Bias in Logit Models of Demand with Aggregate Data

Abstract

The logit model is the most popular tool in estimating demand for differentiated products. In this model, the outside good plays a crucial role because it allows consumers to stop buying the differentiated good altogether if all brands simultaneously become less attractive (for example if a simultaneous price increase occurs). But practitioners lack data on the outside good when only aggregate data is available. The currently accepted procedure is to assume a “market potential” that implicitly defines the size of the outside good (i.e. the number of consumers who considered the product but did not purchase); in practice, this means that an endogenous quantity is approximated by a reasonable guess thereby introducing the possibility of an additional source of error and, most importantly, bias. We provide two contributions in this paper. First, we show that structural parameters can be substantially biased when the assumed market potential does not approximate the outside option correctly. Second, we show how to use panel data techniques to produce unbiased structural estimates by treating the market potential as a fixed effect (known as a “correlated random effect” in the non-linear panel data literature). We explore three possible solutions: a) controlling for the unobservable with market fixed effects, b) specifying the unobservable to be a linear function of the (average) product characteristics, and c) a “demeaned” regression approach. Solution a) is feasible (and preferable) when the number of goods is large relative to the number of markets, whereas b) and c) are attractive when the number of markets is too large. Importantly, we find that all three solutions are nearly as effective in removing the bias. We demonstrate our two contributions in the simple and random coefficients versions of logit via Monte Carlo experiments and with data from the automobile and breakfast cereals markets.

Keywords: Logit model, demand estimation, market potential, differentiated products.comma separated

JEL Classification: C15, C82, D12, D43