IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2019-07.html
   My bibliography  Save this paper

On the construction of confidence intervals for ratios of expectations

Author

Listed:
  • Alexis Derumigny

    (CREST)

  • Lucas Girard

    (CREST)

  • Yannick Guyonvarch

    (CREST)

Abstract

In econometrics, many parameters of interest can be written as ratios of expectations. The main approach to construct confidence intervals for such parameters is the delta method. However, this asymptotic procedure yields intervals that may not be relevant for small sample sizes or, more generally, in a sequence-of-model framework that allows the expectation in the denominator to decrease to 0 with the sample size. In this setting, we prove a generalization of the delta method for ratios of expectations and the consistency of the nonparametric percentile bootstrap. We also investigate finite-sample inference and show a partial impossibility result: nonasymptotic uniform confidence intervals can be built for ratios of expectations but not at every level. Based on this, we propose an easy-to-compute index to appraise the reliability of the intervals based on the delta method. Simulations and an application illustrate our results and the practical usefulness of our rule of thumb.

Suggested Citation

  • Alexis Derumigny & Lucas Girard & Yannick Guyonvarch, 2019. "On the construction of confidence intervals for ratios of expectations," Working Papers 2019-07, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2019-07
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2019-07.pdf
    File Function: CREST working paper version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    2. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    2. Khalaf, Lynda & Saphores, Jean-Daniel & Bilodeau, Jean-Francois, 2003. "Simulation-based exact jump tests in models with conditional heteroskedasticity," Journal of Economic Dynamics and Control, Elsevier, vol. 28(3), pages 531-553, December.
    3. Jean-Thomas Bernard & Ba Chu & Lynda Khalaf & Marcel Voia, 2019. "Non-Standard Confidence Sets for Ratios and Tipping Points with Applications to Dynamic Panel Data," Annals of Economics and Statistics, GENES, issue 134, pages 79-108.
    4. Doko Tchatoka, Firmin & Dufour, Jean-Marie, 2020. "Exogeneity tests, incomplete models, weak identification and non-Gaussian distributions: Invariance and finite-sample distributional theory," Journal of Econometrics, Elsevier, vol. 218(2), pages 390-418.
    5. Pamela Jakiela & Edward Miguel & Vera Velde, 2015. "You’ve earned it: estimating the impact of human capital on social preferences," Experimental Economics, Springer;Economic Science Association, vol. 18(3), pages 385-407, September.
    6. Firmin Doko Tchatoka & Qazi Haque, 2024. "Revisiting the Macroeconomic Effects of Monetary Policy Shocks," The Economic Record, The Economic Society of Australia, vol. 100(329), pages 234-259, June.
    7. DUFOUR, Jean-Marie & JASIAK, Joanna, 1998. "Finite-Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors," Cahiers de recherche 9812, Universite de Montreal, Departement de sciences economiques.
    8. Daniel J. Lewis, 2022. "Robust Inference in Models Identified via Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 104(3), pages 510-524, May.
    9. Gergely Ganics & Atsushi Inoue & Barbara Rossi, 2021. "Confidence Intervals for Bias and Size Distortion in IV and Local Projections-IV Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 307-324, January.
    10. Keisuke Hirano & Jack R. Porter, 2015. "Location Properties of Point Estimators in Linear Instrumental Variables and Related Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 720-733, December.
    11. Bekker, Paul A. & Lawford, Steve, 2008. "Symmetry-based inference in an instrumental variable setting," Journal of Econometrics, Elsevier, vol. 142(1), pages 28-49, January.
    12. Marmer, Vadim & Yu, Zhengfei, 2015. "Efficient Inference in the Classical IV Regression Model with Weak Identification: Asymptotic Power Against Arbitrarily Large Deviations from the Null Hypothesis," Microeconomics.ca working papers vadim_marmer-2015-17, Vancouver School of Economics, revised 02 Sep 2015.
    13. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    14. Bertille Antoine & Pascal Lavergne, 2020. "Identification-Robust Nonparametric Interference in a Linear IV Model," Discussion Papers dp20-03, Department of Economics, Simon Fraser University.
    15. Russell Davidson & James G. MacKinnon, 2008. "Bootstrap inference in a linear equation estimated by instrumental variables," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 443-477, November.
    16. Doko Tchatoka, Firmin Sabro & Dufour, Jean-Marie, 2008. "Instrument endogeneity and identification-robust tests: some analytical results," MPRA Paper 29613, University Library of Munich, Germany.
    17. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc.
    18. Russell Davidson & James G. MacKinnon, 2014. "Bootstrap Confidence Sets with Weak Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 651-675, August.
    19. Moreira, Humberto Ataíde & Moreira, Marcelo J., 2013. "Contributions to the Theory of Optimal Tests," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 747, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    20. Marina-Selini Katsaiti & Mrittika Shamsuddin, 2016. "Weight discrimination in the German labour market," Applied Economics, Taylor & Francis Journals, vol. 48(43), pages 4167-4182, September.

    More about this item

    Keywords

    delta method; confidence regions; uniformly valid inference; sequence of models; nonparametric percentile bootstrap.;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2019-07. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.