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Large Market Asymptotics for Differentiated Product Demand Estimators With Economic Models of Supply


  • Timothy B. Armstrong


IO economists often estimate demand for differentiated products using data sets with a small number of large markets. This paper addresses the question of consistency and asymptotic distributions of instrumental variables estimates as the number of products increases in some commonly used models of demand under conditions on economic primitives. I show that, in a Bertrand–Nash equilibrium, product characteristics lose their identifying power as price instruments in the limit in certain cases, leading to inconsistent estimates. The reason is that product characteristic instruments achieve identification through correlation with markups, and, depending on the model of demand, the supply side can constrain markups to converge to a constant quickly relative to sampling error. I find that product characteristic instruments can yield consistent estimates in many of the cases I consider, but care must be taken in modeling demand and choosing instruments. A Monte Carlo study confirms that the asymptotic results are relevant in market sizes of practical importance.

Suggested Citation

  • Timothy B. Armstrong, 2016. "Large Market Asymptotics for Differentiated Product Demand Estimators With Economic Models of Supply," Econometrica, Econometric Society, vol. 84, pages 1961-1980, September.
  • Handle: RePEc:wly:emetrp:v:84:y:2016:i::p:1961-1980

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    Cited by:

    1. Laura Grigolon, 2017. "Blurred boundaries: a flexible approach for segmentation applied to the car market," Department of Economics Working Papers 2017-17, McMaster University.
    2. Christopher T. Conlon & Julie Holland Mortimer, 2018. "Empirical Properties of Diversion Ratios," Working Papers 18-16, New York University, Leonard N. Stern School of Business, Department of Economics.
    3. Givord, Pauline & Grislain-Letrémy, Céline & Naegele, Helene, 2018. "How do fuel taxes impact new car purchases? An evaluation using French consumer-level data," Energy Economics, Elsevier, vol. 74(C), pages 76-96.
    4. Susan J. Méndez, 2018. "Parallel trade of pharmaceuticals: The Danish market for statins," Health Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 333-356, February.
    5. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2019. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," NBER Working Papers 25827, National Bureau of Economic Research, Inc.
    6. Mogens Fosgerau & Julien Monardo & André de Palma, 2019. "The Inverse Product Differentiation Logit Model," Working Papers hal-02183411, HAL.
    7. Xavier D’Haultfœuille & Isis Durrmeyer & Philippe Février, 2019. "Automobile Prices in Market Equilibrium with Unobserved Price Discrimination," Review of Economic Studies, Oxford University Press, vol. 86(5), pages 1973-1998.
    8. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978, Cowles Foundation for Research in Economics, Yale University.
    9. Bernard Salanie & Frank A. Wolak, 2018. "Fast, "robust", and approximately correct: estimating mixed demand systems," CeMMAP working papers CWP64/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    11. Matthew Weinberg & Gloria Sheu & Nathan Miller, 2019. "Oligopolistic Price Leadership and Mergers: An Empirical Model of the U.S. Beer Industry," 2019 Meeting Papers 1210, Society for Economic Dynamics.
    12. Bartosz Olesiński, 2020. "The Analysis of the Tobacco Product Bans Using a Random Coefficients Logit Model," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(2), pages 113-144, June.
    13. Amit Gandhi & Jean-François Houde, 2019. "Measuring Substitution Patterns in Differentiated-Products Industries," NBER Working Papers 26375, National Bureau of Economic Research, Inc.
    14. Iaria, Alessandro & WANG, Ao, 2020. "Identification and Estimation of Demand for Bundles," CEPR Discussion Papers 14363, C.E.P.R. Discussion Papers.

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