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Identifying the Average Treatment Effect in a Two Threshold Model

Author

Listed:
  • Arthur Lewbel

    (Boston College)

  • Thomas Tao Yang

    (Boston College)

Abstract

Assume individuals are treated if a latent variable, containing a continuous instrument, lies between two thresholds. We place no functional form restrictions on the latent errors. Here unconfoundedness does not hold and identification at infinity is not possible. Yet we still show nonparametric point identification of the average treatment effect. We provide an associated root-n consistent estimator. We apply our model to reinvestigate the inverted-U relationship between competition and innovation, estimating the impact of moderate competitiveness on innovation without the distributional assumptions required by previous analyses. We find no evidence of an inverted-U in US data.

Suggested Citation

  • Arthur Lewbel & Thomas Tao Yang, 2013. "Identifying the Average Treatment Effect in a Two Threshold Model," Boston College Working Papers in Economics 825, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:825
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    References listed on IDEAS

    as
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    19. Arthur Lewbel, 2012. "An Overview of the Special Regressor Method," Boston College Working Papers in Economics 810, Boston College Department of Economics.
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    21. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Viewpoint: Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics, Canadian Economics Association, vol. 45(3), pages 809-829, August.
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    More about this item

    Keywords

    Average treatment effect; Ordered choice model; Special regressor; Semiparametric; Competition and innovation; Identification.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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