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Discussion of “Simple Estimators for Invertible Index Models” by H. Ahn, H. Ichimura, J. Powell, and P. Ruud

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  • S. Khan
  • E. Tamer

Abstract

This is an interesting article that considers the question of inference on unknown linear index coefficients in a general class of models where reduced form parameters are invertible function of one or more linear index. Interpretable sufficient conditions such as monotonicity and or smoothness for the invertibility condition are provided. The results generalize some work in the previous literature by allowing the number of reduced form parameters to exceed the number of indices. The identification and estimation expand on the approach taken in previous work by the authors. Examples include Ahn, Powell, and Ichimura (2004) for monotone single-index regression models to a multi-index setting and extended by Blundell and Powell (2004) and Powell and Ruud (2008) to models with endogenous regressors and multinomial response, respectively. A key property of the inference approach taken is that the estimator of the unknown index coefficients (up to scale) is computationally simple to obtain (relative to other estimators in the literature) in that it is closed form. Specifically, unifying an approach for all models considered in this article, the authors propose an estimator, which is the eigenvector of a matrix (defined in terms of a preliminary estimator of the reduced form parameters) corresponding to its smallest eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal.

Suggested Citation

  • S. Khan & E. Tamer, 2018. "Discussion of “Simple Estimators for Invertible Index Models” by H. Ahn, H. Ichimura, J. Powell, and P. Ruud," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 11-15, January.
  • Handle: RePEc:taf:jnlbes:v:36:y:2018:i:1:p:11-15
    DOI: 10.1080/07350015.2017.1392312
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    Cited by:

    1. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2020. "Inference on Semiparametric Multinomial Response Models," Discussion Papers Series 627, School of Economics, University of Queensland, Australia.
    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.

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