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

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Davis, Peter J

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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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Related research
Keywords: demand demand models discrete choice extreme value

Find related papers by JEL classification:
C0 - Mathematical and Quantitative Methods - - General
C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
D1 - Microeconomics - - Household Behavior
L0 - Industrial Organization - - General

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  2. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
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  8. Davis, Peter, 2002. "Estimating multi-way error components models with unbalanced data structures," Journal of Econometrics, Elsevier, vol. 106(1), pages 67-95, January. [Downloadable!] (restricted)
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  12. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-26, March. [Downloadable!] (restricted)
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  13. 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. [Downloadable!] (restricted)
  14. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  15. Daniel McFadden, 1977. "Modelling the Choice of Residential Location," Cowles Foundation Discussion Papers 477, Cowles Foundation, Yale University. [Downloadable!]
  16. Davis, Peter, 2000. "Empirical models of demand for differentiated products," European Economic Review, Elsevier, vol. 44(4-6), pages 993-1005, May. [Downloadable!] (restricted)
  17. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," Review of Economic Studies, Blackwell Publishing, vol. 71, pages 613-654, 07. [Downloadable!] (restricted)
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  18. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July. [Downloadable!] (restricted)
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