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Testing for Monotonicity in Unobservables under Unconfoundedness

Author

Listed:
  • Stefan Hoderlein

    (Boston College)

  • Liangjun Su

    (Singapore Management University)

  • Halbert White

    (University of California)

  • Thomas Tao Yang

    (Australian National University)

Abstract

Monotonicity in a scalar unobservable is a common assumption when modeling heterogeneity in structural models. Among other things, it allows one to recover the underlying structural function from certain conditional quantiles of observables. Nevertheless, monotonicity is a strong assumption and in some economic applications unlikely to hold, e.g., random coefficient models. Its failure can have substantive adverse consequences, in particular inconsistency of any estimator that is based on it. Having a test for this hypothesis is hence desirable. This paper provides such a test for cross-section data. We show how to exploit an exclusion restriction together with a conditional independence assumption, which in the binary treatment literature is commonly called unconfoundedness, to construct a test. Our statistic is asymptotically normal under local alternatives and consistent against global alternatives. Monte Carlo experiments show that a suitable bootstrap procedure yields tests with reasonable level behavior and useful power. We apply our test to study the role of unobserved ability in determining Black-White wage differences and to study whether Engel curves are monotonically driven by a scalar unobservable.

Suggested Citation

  • Stefan Hoderlein & Liangjun Su & Halbert White & Thomas Tao Yang, 2016. "Testing for Monotonicity in Unobservables under Unconfoundedness," Working Papers 03-2016, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:03-2016
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    File URL: http://ink.library.smu.edu.sg/soe_research/1785/
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    Citations

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    Cited by:

    1. Babii, Andrii & Florens, Jean-Pierre, 2017. "Are unobservables separable?," TSE Working Papers 17-802, Toulouse School of Economics (TSE).
    2. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    3. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.
    4. Tatiana Komarova & Javier Hidalgo, 2019. "Testing nonparametric shape restrictions," Papers 1909.01675, arXiv.org, revised Jun 2020.

    More about this item

    Keywords

    Control variables; Conditional exogeneity; Endogenous variables; Monotonicity; Nonparametrics; Nonseparable; Specification test; Unobserved heterogeneity;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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