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Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems

  • Steve Berry
  • Oliver B. Linton
  • Ariel Pakes

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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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. Ariel Pakes & Steven Olley, 1994. "A Limit Theorem for a Smooth Class of Semiparametric Estimators," Cowles Foundation Discussion Papers 1066, Cowles Foundation for Research in Economics, Yale University.
  2. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 497-529.
  3. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-37, July.
  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. Aviv Nevo, 1998. "Measuring Market Power in the Ready-to-Eat Cereal Industry," NBER Working Papers 6387, National Bureau of Economic Research, Inc.
  6. 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.
  7. 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.
  8. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  9. 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.
  10. Avner Shaked & John Sutton, 1990. "Multiproduct Firms and Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 21(1), pages 45-62, Spring.
  11. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
  12. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  13. 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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