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Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems

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  • Steve Berry
  • Oliver Linton
  • Ariel Pakes

Abstract

We provide an asymptotic distribution theory for a class of Generalized Method of Moments estimators that arise in the study of differentiated product markets when the number of observations is associated with the number of products within a given market. We allow for three sources of error: the sampling error in estimating market shares, the simulation error in approximating the shares predicted by the model, and the underlying model error. The limiting distribution of the parameter estgimator is normal provided the size of the consumer sample and the number of simulation draws grow at a large enough rate relative to the number of products. The required rates differ for two frequently used demand models, and a small Monte Carlo study shows that the difference in asymptotic properties of the two models are reflected in the models' small sample properties. The differences impact directly on the computational burden of the two models.

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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2000/400.

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Date of creation: Jul 2000
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Handle: RePEc:cep:stiecm:/2000/400

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Choice models; Method of Moments; Multinominal; Random Coefficients; Vertical Model;

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  1. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  3. Nevo, Aviv, 1999. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Competition Policy Center, Working Paper Series qt7cm5p858, Competition Policy Center, Institute for Business and Economic Research, UC Berkeley.
  4. Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Wiley Blackwell, vol. 49(1), pages 3-13, January.
  5. 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.
  6. V. Joseph Hotz & Robert A. Miller, 1992. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Working Papers 9202, Harris School of Public Policy Studies, University of Chicago.
  7. Andrews, Donald W.K., 1986. "Empirical process methods in econometrics," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 37, pages 2247-2294 Elsevier.
  8. 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.
  9. Avner Shaked & John Sutton, 1990. "Multiproduct Firms and Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 45-62, Spring.
  10. Pakes, Ariel & Olley, Steven, 1995. "A limit theorem for a smooth class of semiparametric estimators," Journal of Econometrics, Elsevier, vol. 65(1), pages 295-332, January.
  11. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
  12. Newey, W.K., 1989. "Efficient Instrumental Variables Estimation Of Nonlinear Models," Papers 341, Princeton, Department of Economics - Econometric Research Program.
  13. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
  14. Pakes, Ariel & Berry, Steven & Levinsohn, James A, 1993. "Applications and Limitations of Some Recent Advances in Empirical Industrial Organization: Price Indexes and the Analysis of Environmental Change," American Economic Review, American Economic Association, vol. 83(2), pages 241-46, May.
  15. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
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