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

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  • Christopher R. Knittel
  • Konstantinos Metaxoglou

Abstract

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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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14080.

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Date of creation: Jun 2008
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Handle: RePEc:nbr:nberwo:14080

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Cited by:
  1. Liu, Yizao & Lopez, Rigoberto A. & Zhu, Chen, 0. "The Impact of Four Alternative Policies to Decrease Soda Consumption," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association.
  2. 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.
  3. 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.
  4. 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 EDIRC Provider-In, School of Economics, La Trobe University.
  5. Weifang Lou & David Prentice & Xiangkang Yin, 2008. "The Effects of Product Ageing on Demand: The Case of Digital Cameras," Working Papers 2008.06, School of Economics, La Trobe University.
  6. 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.
  7. repec:spo:wpecon:info:hdl:2441/53r60a8s3kup1vc9je5h30d2n is not listed on IDEAS
  8. Grigolon, Laura & Verboven, Frank, 2011. "Nested logit or random coefficients logit? A comparison of alternative discrete choice models of product differentiation," CEPR Discussion Papers 8584, C.E.P.R. Discussion Papers.
  9. 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.

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