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Identification of a class of index models: A topological approach

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  • Mogens Fosgerau
  • Dennis Kristensen

Abstract

We establish nonparametric identification in a class of so-called index models using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions characterizing the model compared to existing strategies; in particular, it does not require any large support conditions on the regressors of our model. We apply the general identification result to additive random utility and competing risk models.

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  • Mogens Fosgerau & Dennis Kristensen, 2020. "Identification of a class of index models: A topological approach," Papers 2004.07900, arXiv.org.
    • Handle: RePEc:arx:papers:2004.07900
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    1. Lee, Sokbae & Lewbel, Arthur, 2013. "Nonparametric Identification Of Accelerated Failure Time Competing Risks Models," Econometric Theory, Cambridge University Press, vol. 29(5), pages 905-919, October.
    2. Bo E. Honoré & Adriana Lleras-Muney, 2006. "Bounds in Competing Risks Models and the War on Cancer," Econometrica, Econometric Society, vol. 74(6), pages 1675-1698, November.
    3. Jaap H. Abbring & Gerard J. Van Den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710, August.
    4. Daniel L. McFadden & Mogens Fosgerau, 2012. "A theory of the perturbed consumer with general budgets," NBER Working Papers 17953, National Bureau of Economic Research, Inc.
    5. Fosgerau, Mogens, 2006. "Investigating the distribution of the value of travel time savings," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 688-707, September.
    6. Steven T. Berry & Philip A. Haile, 2018. "Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure," Econometrica, Econometric Society, vol. 86(1), pages 289-315, January.
    7. Maddala,G. S., 1986. "Limited-Dependent and Qualitative Variables in Econometrics," Cambridge Books, Cambridge University Press, number 9780521338257.
    8. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    9. Fosgerau, Mogens & McFadden, Daniel & Bierlaire, Michel, 2010. "Choice probability generating functions," MPRA Paper 24214, University Library of Munich, Germany.
    10. Drew Fudenberg & Ryota Iijima & Tomasz Strzalecki, 2015. "Stochastic Choice and Revealed Perturbed Utility," Econometrica, Econometric Society, vol. 83, pages 2371-2409, November.
    11. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    12. Christophe Bontemps & Céline Nauges, 2016. "The Impact of Perceptions in Averting-decision Models: An Application of the Special Regressor Method to Drinking Water Choices," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 98(1), pages 297-313.
    13. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    14. Fosgerau, Mogens & Melo, Emerson & Shum, Matt, 2017. "Discrete Choice and Rational Inattention: a General Equivalence Result�," MPRA Paper 76605, University Library of Munich, Germany.
    15. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    16. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
    17. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
    18. Chiou, Yan-Yu & Chen, Mei-Yuan & Chen, Jau-er, 2018. "Nonparametric regression with multiple thresholds: Estimation and inference," Journal of Econometrics, Elsevier, vol. 206(2), pages 472-514.
    19. Roy Allen & John Rehbeck, 2019. "Identification With Additively Separable Heterogeneity," Econometrica, Econometric Society, vol. 87(3), pages 1021-1054, May.
    20. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    21. Yan-Yu Chiou & Mei-Yuan Chen & Jau-er Chen, 2017. "Nonparametric Regression with Multiple Thresholds: Estimation and Inference," Papers 1705.09418, arXiv.org, revised Feb 2018.
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    Cited by:

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    2. Sørensen, Jesper R.-V. & Fosgerau, Mogens, 2022. "How McFadden met Rockafellar and learned to do more with less," Journal of Mathematical Economics, Elsevier, vol. 100(C).

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