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Simple Estimators for Invertible Index Models

Author

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  • Hyungtaik Ahn
  • Hidehiko Ichimura
  • James L. Powell
  • Paul A. Ruud

Abstract

This article considers estimation of the unknown linear index coefficients of a model in which a number of nonparametrically identified reduced form parameters are assumed to be smooth and invertible function of one or more linear indices. The results extend the previous literature by allowing the number of reduced form parameters to exceed the number of indices (i.e., the indices are “overdetermined” by the reduced form parameters. The estimator of the unknown index coefficients (up to scale) is the eigenvector of a matrix (defined in terms of a first-step nonparametric estimator of the reduced form parameters) corresponding to its smallest (in magnitude) eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal, and under additional restrictions an efficient choice of a “weight matrix” is derived in the overdetermined case.

Suggested Citation

  • Hyungtaik Ahn & Hidehiko Ichimura & James L. Powell & Paul A. Ruud, 2018. "Simple Estimators for Invertible Index Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 1-10, January.
    • Handle: RePEc:taf:jnlbes:v:36:y:2018:i:1:p:1-10
    DOI: 10.1080/07350015.2017.1379405
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    References listed on IDEAS

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    Cited by:

    1. Matias D. Cattaneo & Max H. Farrell & Michael Jansson & Ricardo Masini, 2022. "Higher-order Refinements of Small Bandwidth Asymptotics for Density-Weighted Average Derivative Estimators," Papers 2301.00277, arXiv.org, revised Feb 2024.
    2. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2019. "Inference on Semiparametric Multinomial Response Models," Boston College Working Papers in Economics 980, Boston College Department of Economics.
    3. Allen, Roy, 2022. "Injectivity and the law of demand," Economics Letters, Elsevier, vol. 215(C).
    4. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Discrete Choice Models for Bundles," Discussion Papers Series 625, School of Economics, University of Queensland, Australia.
    5. Lewbel, Arthur & Lin, Xirong, 2022. "Identification of semiparametric model coefficients, with an application to collective households," Journal of Econometrics, Elsevier, vol. 226(2), pages 205-223.
    6. Aradillas-López, Andrés, 2021. "Computing semiparametric efficiency bounds in discrete choice models with strategic-interactions and rational expectations," Journal of Econometrics, Elsevier, vol. 221(1), pages 25-42.
    7. Shakeeb Khan & Xiaoying Lan & Elie Tamer & Qingsong Yao, 2021. "Estimating High Dimensional Monotone Index Models by Iterative Convex Optimization1," Papers 2110.04388, arXiv.org, revised Feb 2023.
    8. Wayne Yuan Gao & Ming Li, 2020. "Robust Semiparametric Estimation in Panel Multinomial Choice Models," Papers 2009.00085, arXiv.org.
    9. Irene Botosaru & Chris Muris, 2022. "Identification of time-varying counterfactual parameters in nonlinear panel models," Papers 2212.09193, arXiv.org, revised Nov 2023.
    10. Qingsong Yao, 2023. "Stochastic Learning of Semiparametric Monotone Index Models with Large Sample Size," Papers 2309.06693, arXiv.org, revised Oct 2023.

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