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The Discrete Choice Analytically Flexible (DCAF) Model of Demand for Differentiated Products

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  • Davis, Peter J

Abstract

In this paper I develop the Discrete Choice Analytically Flexible (DCAF) model of demand for differentiated products. DCAF relaxes the constraints imposed on the matrix of own- and cross-price elasticities of demand by popular analytic discrete choice models such as the Multinomial Logit (MNL) and Nested MNL models. At the same time, in contrast to models such as Probit (Hausman and Wise (1978)) and Random Coefficient-MNL (RC-MNL) models (Berry, Levinsohn and Pakes (1995)), DCAF does not require estimation via simulation; it is fully analytic. I show DCAF is a flexible functional form in the sense of Diewert (1974), thus ensuring that its parameters can be chosen to match a well defined class of possible own- and cross-price elasticities of demand. Under well defined constraints on the parameters, which may or may not be imposed in estimation, DCAF is shown to be a previously unexplored member of Mcfadden's(1978) class of Multivariate Extreme Value (MEV) discrete choice models. Hence, under testable parameter restrictions, DCAF is fully consistent with an underlying structural model of heterogeneous, utility maximizing, consumers. I provide a small monte-carlo study to illustrate use of the model and establish its properties. A full application of the model using data from the UK confectionary market is provided in the companion paper, Davis (2006).

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5880.

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Date of creation: Oct 2006
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Handle: RePEc:cpr:ceprdp:5880

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Keywords: demand; demand models; discrete choice; extreme value;

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  1. Davis, Peter, 2000. "Empirical models of demand for differentiated products," European Economic Review, Elsevier, vol. 44(4-6), pages 993-1005, May.
  2. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  3. Daniel McFadden, 1977. "Modelling the Choice of Residential Location," Cowles Foundation Discussion Papers 477, Cowles Foundation for Research in Economics, Yale University.
  4. Steven Berry & Oliver Linton & Ariel Pakes, 2002. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," Cowles Foundation Discussion Papers 1372, Cowles Foundation for Research in Economics, Yale University.
  5. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-26, June.
  6. Ivaldi, Marc & Verboven, Frank, 2001. "Quantifying the Effects from Horizontal Mergers in European Competition Policy," CEPR Discussion Papers 2697, C.E.P.R. Discussion Papers.
  7. Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. J. A. Hausman & D. A. Wise, 1976. "A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Working papers 173, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Austan Goolsbee & Amil Petrin, 2004. "The Consumer Gains from Direct Broadcast Satellites and the Competition with Cable TV," Econometrica, Econometric Society, vol. 72(2), pages 351-381, 03.
  10. Davis, Peter, 2002. "Estimating multi-way error components models with unbalanced data structures," Journal of Econometrics, Elsevier, vol. 106(1), pages 67-95, January.
  11. Peter Davis, 2006. "Spatial competition in retail markets: movie theaters," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 964-982, December.
  12. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
  13. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
  14. Aviv Nevo, 1998. "Measuring Market Power in the Ready-to-Eat Cereal Industry," NBER Working Papers 6387, National Bureau of Economic Research, Inc.
  15. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
  16. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
  17. Werden, Gregory J & Froeb, Luke M, 1994. "The Effects of Mergers in Differentiated Products Industries: Logit Demand and Merger Policy," Journal of Law, Economics and Organization, Oxford University Press, vol. 10(2), pages 407-26, October.
  18. Steven Berry & James Levinsohn & Ariel Pakes, 1995. "Voluntary Export Restraints on Automobiles: Evaluating a Strategic TradePolicy," NBER Working Papers 5235, National Bureau of Economic Research, Inc.
  19. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
  20. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1975. "Transcendental Logarithmic Utility Functions," American Economic Review, American Economic Association, vol. 65(3), pages 367-83, June.
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