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The Econometrics of Shape Restrictions


  • Denis Chetverikov

    () (Department of Economics, University of California, Los Angeles, California 90095, USA)

  • Andres Santos

    () (Department of Economics, University of California, Los Angeles, California 90095, USA)

  • Azeem M. Shaikh

    () (Department of Economics, University of Chicago, Chicago, Illinois 60637, USA)


We review recent developments in the econometrics of shape restrictions and their role in applied work. Our objectives are threefold. First, we aim to emphasize the diversity of applications in which shape restrictions have played a fruitful role. Second, we intend to provide practitioners with an intuitive understanding of how shape restrictions impact the distribution of estimators and test statistics. Third, we aim to provide an overview of new advances in the theory of estimation and inference under shape restrictions. Throughout the review, we outline open questions and interesting directions for future research.

Suggested Citation

  • Denis Chetverikov & Andres Santos & Azeem M. Shaikh, 2018. "The Econometrics of Shape Restrictions," Annual Review of Economics, Annual Reviews, vol. 10(1), pages 31-63, August.
  • Handle: RePEc:anr:reveco:v:10:y:2018:p:31-63
    DOI: 10.1146/annurev-economics-080217-053417

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    Cited by:

    1. Matthew A. Masten & Alexandre Poirier, 2018. "Interpreting Quantile Independence," Papers 1804.10957,
    2. Xi Chen & Victor Chernozhukov & Iv'an Fern'andez-Val & Scott Kostyshak & Ye Luo, 2018. "Shape-Enforcing Operators for Point and Interval Estimators," Papers 1809.01038,, revised Oct 2019.


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