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Estimation of Random Coefficient Demand Models: Challenges, Difficulties and Warnings


  • Christopher R. Knittel
  • Konstantinos Metaxoglou


Empirical exercises in economics frequently involve estimation of highly nonlinear models. The criterion function may not be globally concave or convex and exhibit many local extrema. Choosing among these local extrema is non-trivial for a variety of reasons. In this paper, we analyze the sensitivity of parameter estimates, and most importantly of economic variables of interest, to both starting values and the type of non-linear optimization algorithm employed. We focus on a class of demand models for differentiated products that have been used extensively in industrial organization, and more recently in public and labor. We find that convergence may occur at a number of local extrema, at saddles and in regions of the objective function where the first-order conditions are not satisfied. We find own- and cross-price elasticities that differ by a factor of over 100 depending on the set of candidate parameter estimates. In an attempt to evaluate the welfare effects of a change in an industry's structure, we undertake a hypothetical merger exercise. Our calculations indicate consumer welfare effects can vary between positive values to negative seventy billion dollars depending on the set of parameter estimates used.

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  • Christopher R. Knittel & Konstantinos Metaxoglou, 2008. "Estimation of Random Coefficient Demand Models: Challenges, Difficulties and Warnings," NBER Working Papers 14080, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:14080
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    References listed on IDEAS

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    Cited by:

    1. Vivienne Pham & David Prentice, 2010. "An empirical Analysis of the Counter-factual: A Merger and Divestiture in the Australian Cigarette Industry," Working Papers 2010.08, School of Economics, La Trobe University.
    2. Lou, Weifang & Prentice, David & Yin, Xiangkang, 2008. "The Effects of Product Ageing on Demand: The Case of Digital Cameras," MPRA Paper 13407, University Library of Munich, Germany.
    3. Liu, Yizao & Lopez, Rigoberto A. & Zhu, Chen, 2014. "The Impact of Four Alternative Policies to Decrease Soda Consumption," Agricultural and Resource Economics Review, Cambridge University Press, vol. 43(01), pages 53-68, April.
    4. Laura Grigolon & Frank Verboven, 2014. "Nested Logit or Random Coefficients Logit? A Comparison of Alternative Discrete Choice Models of Product Differentiation," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 916-935, December.
    5. Hyungsik Roger Moon & Matthew Shum & Martin Weidner, 2012. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers CWP08/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. repec:spo:wpecon:info:hdl:2441/53r60a8s3kup1vc9je5h30d2n is not listed on IDEAS
    7. Rigoberto A. Lopez & Yizao Liu & Chen Zhu, 2013. "Spillover and Competitive Effects of Advertising in the Carbonated Soft Drink Market," Working Papers 18, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    8. Lou, Weifang & Prentice, David & Yin, Xiangkang, 2012. "What difference does dynamics make? The case of digital cameras," International Journal of Industrial Organization, Elsevier, vol. 30(1), pages 30-40.
    9. Jean-Pierre H. Dubé & Jeremy T. Fox & Che-Lin Su, 2009. "Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation," NBER Working Papers 14991, National Bureau of Economic Research, Inc.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • L4 - Industrial Organization - - Antitrust Issues and Policies

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