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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: sampling error in estimating market shares, simulation error in approximating the shares predicted by the model, and the underlying model error. It is shown that the estimators are CAN 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 consider the implications of the results for the Berry, Levinsohn and Pakes (1995) random coefficient logit model and the pure characteristics model analysed in Berry and Pakes (2002). The required rates differ for these two frequently used demand models. A small Monte Carlo study shows that the differences in asymptotic properties of the two models are reflected, in quite a striking way, in the models' small sample properties. Moreover the limit distributions provide a good approximation to the actual Monte Carlo distribution of the parameter estimates. The results have important implications for the computational burden of the two models. Copyright 2004 The Review of Economic Studies Ltd.

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Article provided by Blackwell Publishing in its journal The Review of Economic Studies.

Volume (Year): 71 (2004)
Issue (Month): (07)
Pages: 613-654
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Handle: RePEc:bla:restud:v:71:y:2004:i::p:613-654

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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. 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)
  2. 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)
  3. 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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  4. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-37, July. [Downloadable!] (restricted)
  5. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-42, March.
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  6. 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)
  7. 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)
  8. 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.
  9. 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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  10. 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!]
  11. 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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  12. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  13. 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)
  14. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March. [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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Cited by:
(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 & Kim Rueben, 2005. "Residential Segregation in General Equilibrium," NBER Working Papers 11095, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. 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!]
  5. Patrick Bayer & Robert McMillan, 2005. "Racial Sorting and Neighborhood Quality," NBER Working Papers 11813, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. 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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  7. 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!]
  8. 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!]
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  9. 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!]
  10. 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)
  11. 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)
  12. 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)
  13. 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!]
  14. 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!]
  15. 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)
  16. 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!]
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