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Estimating Discrete Joint Probability Distributions for Demographic Characteristics at the Store Level Given Store Level Marginal Distributions and a City-Wide Joint Distribution

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  • Charles Romeo

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    Abstract

    This paper provides a solution to the problem of estimating a joint distribution using the associated marginal distributions and a related joint distribution. The particular application we have in mind is estimating joint distributions of demographic characteristics corresponding to market areas for individual retail stores. Marginal distributions are generally available at the census tract level, but joint distributions are only available for Metropolitan Statistical Areas which are generally much larger than the market for a single retail store. Joint distributions over demographics are an important input into mixed logit demand models for aggregate data. Market shares that vary systematically with demographics are essential for relieving the restrictions imposed by the Independence from Irrelevant Alternative property of the logit model. We approach this problem by formulating a parametric function that incorporates both the city-wide joint distributional information and marginal information specific to the retail store’s market area. To estimate the function, we form moment conditions equating the moments of the parametric function to observed data, and we input these into a GMM objective. In one of our illustrations we use four marginal demographic distributions from each of eight stores in Dominick’s Finer Foods data archive to estimate a four dimensional joint distribution for each store. Our results show that our GMM approach produces estimated joint distributions that differ substantially from the product of marginal distributions and emit marginals that closely match the observed marginal distributions. Mixed logit demand estimates are also presented which show the estimates to be sensitive to the formulation of the demographics distribution. Copyright Springer Science + Business Media, Inc. 2005

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    File URL: http://hdl.handle.net/10.1007/s11129-005-0259-9
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    Bibliographic Info

    Article provided by Springer in its journal Quantitative Marketing and Economics.

    Volume (Year): 3 (2005)
    Issue (Month): 1 (January)
    Pages: 71-93

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    Handle: RePEc:kap:qmktec:v:3:y:2005:i:1:p:71-93

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    Web page: http://www.springerlink.com/link.asp?id=111240

    Related research

    Keywords: mixed logit; discrete joint probability distributions; generalized method of moments;

    References

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    1. Levinsohn, James & Berry, Steven & Pakes, Ariel, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Scholarly Articles 3436404, Harvard University Department of Economics.
    2. Amil Petrin, 2002. "Quantifying the Benefits of New Products: The Case of the Minivan," Journal of Political Economy, University of Chicago Press, vol. 110(4), pages 705-729, August.
    3. Aviv Nevo, 2003. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Microeconomics 0303006, EconWPA.
    4. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
    5. Peter Davis, 2006. "Spatial competition in retail markets: movie theaters," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 964-982, December.
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    Cited by:
    1. Paap, R. & van Dijk, A., 2006. "Explaining individual response using aggregated data," Econometric Institute Research Papers EI 2006-05, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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