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Control Function Corrections for Unobserved Factors in Differentiated Product Models


  • Amil Petrin

    () (GSB University of Chicago)

  • Kenneth Train


Unobserved factors in differentiated product models can generate severe bias in price elasticities. We develop a generalized control function method and specification test for this setting based on the nonparametric identification results from Petrin (2005), who shows the assumptions under which price functions can be inverted to obtain controls that condition on the part of the demand error that is not independent of price. Unlike using product-market controls, our approach does not require additive separability between observed and unobserved factors. We develop a ``hybrid'' approach that also loosens this restriction for that setting. We compare results across approaches on three data sets and demand specifications estimated elsewhere that span a range of markets and levels of aggregation, including automobiles (the original Berry, Levinsohn, and Pakes (1995) application), cable television, and margarine. The estimated elasticities are similar across the control function and product-market control approaches, and they both differ significantly from the uncorrected elasticity estimates, which are significantly biased up in every case

Suggested Citation

  • Amil Petrin & Kenneth Train, 2006. "Control Function Corrections for Unobserved Factors in Differentiated Product Models," 2006 Meeting Papers 856, Society for Economic Dynamics.
  • Handle: RePEc:red:sed006:856

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    References listed on IDEAS

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    More about this item


    endogenous prices; differentiated product models;

    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other


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