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Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems

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  • Steve Berry
  • Oliver B. 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: 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, Wiley-Blackwell.

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Bibliographic Info

Article provided by Oxford University Press in its journal The Review of Economic Studies.

Volume (Year): 71 (2004)
Issue (Month): 3 ()
Pages: 613-654

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Handle: RePEc:oup:restud:v:71:y:2004:i:3:p:613-654

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  1. Newey, W.K., 1989. "Efficient Instrumental Variables Estimation Of Nonlinear Models," Papers, Princeton, Department of Economics - Econometric Research Program 341, Princeton, Department of Economics - Econometric Research Program.
  2. Pakes, Ariel & Olley, Steven, 1995. "A limit theorem for a smooth class of semiparametric estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 65(1), pages 295-332, January.
  3. Aviv Nevo, 2003. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Microeconomics, EconWPA 0303006, EconWPA.
  4. Steven Berry & James Levinsohn & Ariel Pakes, 1998. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," NBER Working Papers 6481, National Bureau of Economic Research, Inc.
  5. Shaked, Avner & Sutton, John, 1982. "Relaxing Price Competition through Product Differentiation," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 49(1), pages 3-13, January.
  6. Hotz, V Joseph & Miller, Robert A, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 60(3), pages 497-529, July.
  7. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, Elsevier, vol. 34(3), pages 305-334, March.
  8. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
  9. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 63(4), pages 841-90, July.
  10. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  11. 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, American Economic Association, vol. 83(2), pages 241-46, May.
  12. J. A. Hausman & D. A. Wise, 1976. "A Conditional Profit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 173, Massachusetts Institute of Technology (MIT), Department of Economics.
  13. Donald W.K. Andrews, 1993. "Empirical Process Methods in Econometrics," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1059, Cowles Foundation for Research in Economics, Yale University.
  14. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, Econometric Society, vol. 57(5), pages 1027-57, September.
  15. Avner Shaked & John Sutton, 1990. "Multiproduct Firms and Market Structure," RAND Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 21(1), pages 45-62, Spring.
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