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Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems

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Author Info
Steve Berry
Oliver B. Linton
Ariel Pakes

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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 estimator 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. We specialise our distribution theory to the Berry, Levinsohn, and Pakes (1995) random coeffcient logit model and a pure characteristic model. The required rates differ for these two frequently used demand models. A small Monte Carlo study shows that the difference in asymptotic properties of the two models are reflected in the models' small sample properties. These differences impact directly on the computational burden of the two models.

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Paper provided by Harvard - Institute of Economic Research in its series Harvard Institute of Economic Research Working Papers with number 1955.

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Date of creation: 2002
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Handle: RePEc:fth:harver:1955

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  2. Ariel Pakes & Steven Olley, 1994. "A Limit Theorem for a Smooth Class of Semiparametric Estimators," Cowles Foundation Discussion Papers 1066, Cowles Foundation, Yale University. [Downloadable!]
  3. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March. [Downloadable!] (restricted)
  4. Aviv Nevo, 1998. "Measuring Market Power in the Ready-to-Eat Cereal Industry," NBER Working Papers 6387, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Avner Shaked & John Sutton, 1990. "Multiproduct Firms and Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 45-62, Spring. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
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  7. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-37, July. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. 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.
  11. Steven Berry & James Levinsohn & Ariel Pakes, 2001. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Cowles Foundation Discussion Papers 1337, Cowles Foundation, Yale University. [Downloadable!]
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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. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  14. Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Blackwell Publishing, vol. 49(1), pages 3-13, January. [Downloadable!] (restricted)
  15. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July. [Downloadable!] (restricted)
  16. Hotz, V Joseph & Miller, Robert A, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Blackwell Publishing, vol. 60(3), pages 497-529, July. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Patrick Bayer & Christopher Timmins, 2003. "Estimating Equilibrium Models of Sorting across Locations," Working Papers 862, Economic Growth Center, Yale University. [Downloadable!]
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  2. Susan Athey & Guido Imbens, 2006. "Discrete Choice Models with Multiple Unobserved Choice Characteristics," Levine's Bibliography 122247000000001040, UCLA Department of Economics. [Downloadable!]
  3. Patrick Bayer & Robert McMillan, 2005. "Racial Sorting and Neighborhood Quality," NBER Working Papers 11813, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  4. Patrick Bayer & Fernando Ferreira & Robert McMillan, 2007. "A Unified Framework for Measuring Preferences for Schools and Neighborhoods," NBER Working Papers 13236, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Patrick Bayer & Robert McMillan & Kim Rueben, 2003. "An Equilibrium Model of Sorting in an Urban Housing Market: A Study of the Causes and Consequences of Residential Segregation," Working Papers 03-01, Center for Economic Studies, U.S. Census Bureau. [Downloadable!]
  6. Davis, Peter J, 2006. "The Discrete Choice Analytically Flexible (DCAF) Model of Demand for Differentiated Products," CEPR Discussion Papers 5880, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  7. Charles Romeo, 2007. "A Gibbs sampler for mixed logit analysis of differentiated product markets using aggregate data," Computational Economics, Springer, vol. 29(1), pages 33-68, February. [Downloadable!] (restricted)
  8. Maija Gao & Ari Hyytinen & Otto Toivanen, 2005. "Demand for Mobile Internet: Evidence from a Real-World Pricing Experiment," Discussion Papers 964, The Research Institute of the Finnish Economy. [Downloadable!]
  9. Irene Brambilla, 2005. "A Customs Union with Multinational Firms: The Automobile Market in Argentina and Brazil," NBER Working Papers 11745, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  10. John Yinger, 2009. "Hedonic Markets and Explicit Demands: Bid-Function Envelopes for Public Services, Neighborhood Amenities, and Commuting Costs," Center for Policy Research Working Papers 114, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
  11. Patrick Bayer & Robert McMillan & Kim Rueben, 2005. "Residential Segregation in General Equilibrium," NBER Working Papers 11095, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. Christos Genakos, 2004. "DIFFERENTIAL MERGER EFFECTS: The Case of the Personal Computer Industry," STICERD - Economics of Industry Papers 39, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  13. Patrick Bayer & Robert McMillan & Kim Rueben, 2003. "An Equilibrium Model of Sorting in an Urban Housing Market: The Causes and Consequences of Residential Segregation," Working Papers 860, Economic Growth Center, Yale University. [Downloadable!]
    Other versions:
  14. Reiss, Peter C. & Wolak, Frank A., 2003. "Structural Econometric Modeling: Rationales and Examples from Industrial Organization," Research Papers 1831, Stanford University, Graduate School of Business. [Downloadable!]
  15. Patrick Bayer & Robert McMillan & Kim Rueben, 2004. "An Equilibrium Model of Sorting in an Urban Housing Market," NBER Working Papers 10865, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  16. Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen Ryan, 2007. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients in Discrete Choice Models," Working Papers 36, Portuguese Competition Authority. [Downloadable!]
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