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Econometric Modeling of Interdependent Discrete Choice with Applications to Market Structure

Author

Listed:
  • Andrew Chesher

    (Institute for Fiscal Studies and University College London)

  • Adam Rosen

    (Institute for Fiscal Studies and Duke University)

Abstract
This paper demonstrates the use of bounds analysis for empirical models of market structure that allow for multiple equilibria. From an econometric standpoint, these models feature systems of equalities and inequalities for the determination of multiple endogenous interdependent discrete choice variables. These models may be incomplete, delivering multiple values of outcomes at certain values of the latent variables and covariates, and incoherent, delivering no values. Alternative approaches to accommodating incompleteness and incoherence are considered in a unifying framework afforded by the Generalized Instrumental Variable models introduced in Chesher and Rosen (2017). Sharp identication regions for parameters of interest defined by systems of conditional moment equalities and inequalities are provided. Almost all empirical analysis of interdependent discrete choice uses models that include parametric specifications of the distribution of unobserved variables. The paper provides characterizations of identified sets and outer regions for structural functions and parameters allowing for any distribution of unobservables independent of exogenous variables. The methods are applied to the models and data of Mazzeo (2002) and Kline and Tamer (2016) in order to study the sensitivity of empirical results to restrictions on equilibrium selection and the distribution of unobservable payoff shifters, respectively. Confidence intervals for individual parameter components are provided using a recently developed inference approach from Belloni, Bugni, and Chernozhukov (2018). The relaxation of equilibrium selection and distributional restrictions in these applications is found to greatly increase the width of resulting confidence intervals, but nonetheless the models continue to sign strategic interaction parameters.

Suggested Citation

  • Andrew Chesher & Adam Rosen, 2020. "Econometric Modeling of Interdependent Discrete Choice with Applications to Market Structure," CeMMAP working papers CWP25/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:25/20
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    References listed on IDEAS

    as
    1. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes: coherence, completeness, and identification," CeMMAP working papers CWP21/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
    3. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2017. "Inference for subvectors and other functions of partially identified parameters in moment inequality models," Quantitative Economics, Econometric Society, vol. 8(1), pages 1-38, March.
    4. Andrew Chesher & Adam Rosen & Zahra Siddique, 2019. "Estimating Endogenous Effects on Ordinal Outcomes," CeMMAP working papers CWP66/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, vol. 42(6), pages 999-1012, November.
    6. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    7. Freyberger, Joachim & Horowitz, Joel L., 2015. "Identification and shape restrictions in nonparametric instrumental variables estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 41-53.
    8. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    9. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
    10. Blundell, Richard & Smith, Richard J., 1994. "Coherency and estimation in simultaneous models with censored or qualitative dependent variables," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 355-373.
    11. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    2. Lixiong Li & Désiré Kédagni & Ismaël Mourifié, 2024. "Discordant relaxations of misspecified models," Quantitative Economics, Econometric Society, vol. 15(2), pages 331-379, May.
    3. Lina Zhang & David T. Frazier & Don S. Poskitt & Xueyan Zhao, 2020. "Decomposing Identification Gains and Evaluating Instrument Identification Power for Partially Identified Average Treatment Effects," Monash Econometrics and Business Statistics Working Papers 34/20, Monash University, Department of Econometrics and Business Statistics.
    4. Chesher, Andrew & Kim, Dongwoo & Rosen, Adam M., 2023. "IV methods for Tobit models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1700-1724.
    5. , 2023. "Price Competition and Endogenous Product Choice in Networks: Evidence from the US airline Industry," Working Papers 950, Queen Mary University of London, School of Economics and Finance.
    6. Eleni Aristodemou & Adam M. Rosen, 2022. "A discrete choice model for partially ordered alternatives," Quantitative Economics, Econometric Society, vol. 13(3), pages 863-906, July.
    7. Christian Bontemps & Cristina Gualdani & Kevin Remmy, 2023. "Price Competition and Endogenous Product Choice in Networks: Evidence From the US Airline Industry," CRC TR 224 Discussion Paper Series crctr224_2023_400, University of Bonn and University of Mannheim, Germany.
    8. Eleni Aristodemou, 2021. "A discrete choice model for partially ordered alternatives," CeMMAP working papers CWP35/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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