Abstract
Demand models produce biased results when applied to data aggregated across stores with heterogeneous promotional activity. We show how to modify extant aggregate demand frameworks to avoid this problem. First a consumer-level model is developed, which is then integrated over the heterogeneous stores to arrive at aggregate demand. Our approach is highly practical since it requires only standard scanner data of the type produced by the major vendors. Using data for super-premium ice cream, we apply the proposed methodology to the random coefficients logit demand framework.
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Notes
A confidentiality agreement with ACNielsen prohibits retailer names from being revealed. This example does not indicate whether the dataset employed contains the Jewel supermarket chain in Chicago.
Boatwright et al. (2004) is a recent example that uses this methodology to avoid aggregation bias.
In addition, UPCs vary by package size. Most brands of super-premium ice cream are available only in pint-sized containers, however, with larger package sizes representing a small fraction of category sales. We therefore omit them from the analysis by restricting the dataset to pint-sized cartons.
City-chain subscripts are dropped from the control variables for ease of notation.
Following Train (1999), we discard the first 10 elements of the Halton sequence since early elements tend to be correlated. Therefore, we generate a sequence of 1,010 elements, rather than 1,000.
In the representative store model we drop the i subscript from X ijt since the included variables are identical across all consumers.
It is unclear whether “Display Only” or “Feature Only” is higher ranked. We obtain similar results when we let “Display Only” outrank “Feature Only.”
Parameter ρ does not vary over time and is identical across retailers. We make this simplifying assumption since only 15% of the dataset's observations identify the joint promotional distribution. A more flexible specification can be employed in situations where it is practical to do so.
A second advantage is that including the error term within the utility function facilitates use of instrumental variables. This is not an issue here since we lack valid instruments. Supplemental material available upon request details the reasons why valid instruments do not exist for this product category.
We calculate the variance matrix of the parameter estimates using the standard GMM formulas, where the first order conditions from the log-likelihood function are used as moment conditions. Refer to Hamilton (1994) for discussion of this “quasi maximum likelihood” approach of obtaining robust standard errors.
We also considered the following alternative framework. We let \( \{ \pi _t^g \} _{g \in G} \) be a weighted average of two distributions: the distribution that arises when ρ=0 and the distribution when ρ=1. Using this specification, we obtain the same joint distribution as before, where each brand's promotions are positively correlated to the maximum possible extent.
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Acknowledgements
Helpful comments from two anonymous referees, the editor, Peter Rossi, and Luke Froeb, Hajime Hadeishi, Daniel Hosken, Rob McMillan, Charles Romeo, David Schmidt, Shawn Ulrick, and John Yun are greatly appreciated. The views expressed in this paper are those of the author, and do not necessarily represent the views of the Federal Trade Commission or any individual Commissioner.
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Tenn, S. Avoiding aggregation bias in demand estimation: A multivariate promotional disaggregation approach. Quant Market Econ 4, 383–405 (2006). https://doi.org/10.1007/s11129-006-9011-3
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DOI: https://doi.org/10.1007/s11129-006-9011-3