Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems

52 Pages Posted: 21 May 2002

See all articles by Steven Berry

Steven Berry

Yale University - Department of Economics; National Bureau of Economic Research (NBER); Yale University - Cowles Foundation

Oliver B. Linton

University of Cambridge

Ariel Pakes

National Bureau of Economic Research (NBER); Harvard University - Department of Economics

Date Written: May 2002

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 coefficient 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.

Keywords: Choice Models, Method of Moments, Random Coefficients, Product Differentiation

JEL Classification: C13, C15, C35, D43, L13

Suggested Citation

Berry, Steven T. and Linton, Oliver B. and Pakes, Ariel, Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems (May 2002). Cowles Foundation Discussion Paper No. 1372; Harvard Institute of Economics Research Paper No. 1955. Available at SSRN: https://ssrn.com/abstract=313007

Steven T. Berry (Contact Author)

Yale University - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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Yale University - Cowles Foundation

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Oliver B. Linton

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom

Ariel Pakes

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Harvard University - Department of Economics ( email )

Littauer Center
Room 117
Cambridge, MA 02138
United States
617-495-5320 (Phone)
617-495-8570 (Fax)

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