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Nonparametric identification of endogenous and heterogeneous aggregate demand models: complements, bundles and the market level

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  • Fabian Dunker
  • Stefan Hoderlein
  • Hiroaki Kaido
Abstract
This paper studies nonparametric identification in market level demand models for differentiated products. We generalize common models by allowing for the distribution of heterogeneity parameters (random coefficients) to have a nonparametric distribution across the population and give conditions under which the density of the random coefficients is identified. We show that key identifying restrictions are provided by (i) a set of moment conditions generated by instrumental variables together with an inversion of aggregate demand in unobserved product characteristics; and (ii) an integral transform (Radon transform) that maps the random coefficient density to the aggregate demand. This feature is shown to be common across a wide class of models, and we illustrate this by studying leading demand models. Our examples include demand models based on the multinomial choice (Berry, Levinsohn, Pakes, 1995), the choice of bundles of goods that can be substitutes or complements, and the choice of goods consumed in multiple units.

Suggested Citation

  • Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2015. "Nonparametric identification of endogenous and heterogeneous aggregate demand models: complements, bundles and the market level," CeMMAP working papers 51/15, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:51/15
    DOI: 10.1920/wp.cem.2015.5115
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    1. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    2. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random coefficients in static games of complete information," CeMMAP working papers CWP12/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    11. Dunker, Fabian & Florens, Jean-Pierre & Hohage, Thorsten & Johannes, Jan & Mammen, Enno, 2014. "Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression," Journal of Econometrics, Elsevier, vol. 178(P3), pages 444-455.
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    Cited by:

    1. Rui Wang, 2023. "Testing and Identifying Substitution and Complementarity Patterns," Papers 2304.00678, arXiv.org.
    2. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2017. "Nonparametric identification of random coefficients in endogenous and heterogeneous aggregate demand models," CeMMAP working papers 11/17, Institute for Fiscal Studies.
    3. Roy Allen & John Rehbeck, 2020. "Identification of Random Coefficient Latent Utility Models," Papers 2003.00276, arXiv.org.
    4. Fabian Dunker, 2015. "Adaptive estimation for some nonparametric instrumental variable models," Papers 1511.03977, arXiv.org, revised Aug 2021.

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