Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Econometric Methods

Ed. by Giacomini, Raffaella / Li, Tong

Mathematical Citation Quotient (MCQ) 2018: 0.06

See all formats and pricing
More options …

Uniformity and the Delta Method

Maximilian KasyORCID iD: https://orcid.org/0000-0002-8679-5179
Published Online: 2018-07-31 | DOI: https://doi.org/10.1515/jem-2018-0001


When are asymptotic approximations using the delta-method uniformly valid? We provide sufficient conditions as well as closely related necessary conditions for uniform negligibility of the remainder of such approximations. These conditions are easily verified by empirical practitioners and permit to identify settings and parameter regions where pointwise asymptotic approximations perform poorly. Our framework allows for a unified and transparent discussion of uniformity issues in various sub-fields of statistics and econometrics. Our conditions involve uniform bounds on the remainder of a first-order approximation for the function of interest.

Keywords: asymptotic theory; delta method; uniformity


  • Andrews, D., M. Moreira, and J. Stock. 2006. “Optimal Two-sided Invariant Similar Tests for Instrumental Variables Regression.” Econometrica 74 (3): 715–752.CrossrefGoogle Scholar

  • Andrews, I., and A. Mikusheva. 2014. “A Geometric Approach to Weakly Identified Econometric Models.” MIT Working Paper.Google Scholar

  • Belloni, A., V. Chernozhukov, I. Fernández-Val, and C. Hansen. 2013. “Program Evaluation with High-dimensional Data.” arXiv preprint arXiv:1311.2645.Google Scholar

  • Guggenberger, P. 2010. “The Impact of a Hausman Pretest on the Asymptotic Size of a Hypothesis Test.” Econometric Theory 26 (2): 369.Web of ScienceCrossrefGoogle Scholar

  • Hahn, J., and G. Ridder. 2014. “Non-standard Tests Through a Composite Null and Alternative in Point-identified Parameters.” Journal of Econometric Methods 4 (1): 1–28.Google Scholar

  • Imbens, G. W., and C. F. Manski. 2004. “Confidence Intervals for Partially Identified Parameters.” Econometrica 72 (6): 1845–1857.CrossrefWeb of ScienceGoogle Scholar

  • Le Cam, L., and G. L. Yang. 2012. Asymptotics in Statistics: Some Basic Concepts. New York: Springer.Google Scholar

  • Leeb, H., and B. M. Pötscher. 2005. “Model Selection and Inference: Facts and Fiction.” Econometric Theory 21 (1): 21–59.Google Scholar

  • Mikusheva, A. 2007. “Uniform Inference in Autoregressive Models.” Econometrica 75 (5): 1411–1452.Web of ScienceCrossrefGoogle Scholar

  • Moreira, M. 2003. “A Conditional Likelihood Ratio Test for Structural Models.” Econometrica 71 (4): 1027–1048.CrossrefGoogle Scholar

  • Phillips, P. C. B. 2012. “Folklore Theorems, Implicit Maps, and Indirect Inference.” Econometrica 80 (1): 425–454.CrossrefWeb of ScienceGoogle Scholar

  • Rudin, W. 1991. Principles of Mathematical Analysis. New York: McGraw-Hill.Google Scholar

  • Staiger, D., and J. Stock. 1997. “Instrumental Variables Regression with Weak Instruments.” Econometrica 65 (3): 557–586.CrossrefGoogle Scholar

  • Stock, J., and M. Watson. 1996. Confidence Sets in Regressions with Highly Serially Correlated Regressors. manuscript, Harvard University.Google Scholar

  • van der Vaart, A. 2000. Asymptotic Statistics. Cambridge: Cambridge University Press.Google Scholar

  • van der Vaart, A., and J. A. Wellner. 1996. Weak Convergence. New York: Springer.Google Scholar

About the article

Published Online: 2018-07-31

Citation Information: Journal of Econometric Methods, Volume 8, Issue 1, 20180001, ISSN (Online) 2156-6674, DOI: https://doi.org/10.1515/jem-2018-0001.

Export Citation

©2019 Walter de Gruyter GmbH, Berlin/Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Atsushi Inoue and Lutz Kilian
SSRN Electronic Journal , 2019

Comments (0)

Please log in or register to comment.
Log in