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Impossible inference in econometrics: theory and applications

Author

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  • Marinho Bertanha

    (Institute for Fiscal Studies)

  • Marcelo Moreira

    (Institute for Fiscal Studies and Fundação Getúlio Vargas)

Abstract

This paper studies models in which hypothesis tests have trivial power, that is, power smaller than size. This testing impossibility, or impossibility type A, arises when any alternative is not distinguishable from the null. We also study settings where it is impossible to have almost surely bounded confi dence sets for a parameter of interest. This second type of impossibility (type B) occurs under a condition weaker than the condition for type A impossibility: the parameter of interest must be nearly unidentifi ed. Our theoretical framework connects many existing publications on impossible inference that rely on different notions of topologies to show models are not distinguishable or nearly unidentifi ed. We also derive both types of impossibility using the weak topology induced by convergence in distribution. Impossibility in the weak topology is often easier to prove, it is applicable for many widely-used tests, and it is useful for robust hypothesis testing. We conclude by demonstrating impossible inference in multiple economic applications of models with discontinuity and time-series models.

Suggested Citation

  • Marinho Bertanha & Marcelo Moreira, 2019. "Impossible inference in econometrics: theory and applications," CeMMAP working papers CWP02/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:02/19
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    Cited by:

    1. Marcelo Moreira & Geert Ridder, 2019. "Efficiency loss of asymptotically efficient tests in an instrumental variables regression," CeMMAP working papers CWP03/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Bugni, Federico A. & Canay, Ivan A., 2021. "Testing continuity of a density via g-order statistics in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 221(1), pages 138-159.
    3. Marinho Bertanha & Andrew H. McCallum & Nathan Seegert, 2021. "Better Bunching, Nicer Notching," Papers 2101.01170, arXiv.org.
    4. Guido Imbens & Stefan Wager, 2019. "Optimized Regression Discontinuity Designs," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 264-278, May.
    5. Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf & Abdallah Zalghout, 2020. "Identification-Robust Inequality Analysis," Cahiers de recherche 03-2020, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    6. Bertanha, Marinho, 2020. "Regression discontinuity design with many thresholds," Journal of Econometrics, Elsevier, vol. 218(1), pages 216-241.
    7. Blaise Melly & Rafael Lalive, 2020. "Estimation, Inference, and Interpretation in the Regression Discontinuity Design," Diskussionsschriften dp2016, Universitaet Bern, Departement Volkswirtschaft.
    8. Marinho Bertanha & EunYi Chung, 2021. "Permutation Tests at Nonparametric Rates," Papers 2102.13638, arXiv.org.

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    More about this item

    Keywords

    hypothesis tests; confi dence intervals; weak identifi cation; regression discontinuity;
    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
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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