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Nonparametric estimation and inference under shape restrictions

Author

Listed:
  • Joel L. Horowitz

    () (Institute for Fiscal Studies and Northwestern University)

  • Sokbae (Simon) Lee

    () (Institute for Fiscal Studies and Columbia University and IFS)

Abstract

Economic theory often provides shape restrictions on functions of interest in applications, such as monotonicity, convexity, non-increasing (non-decreasing) returns to scale, or the Slutsky inequality of consumer theory; but economic theory does not provide finite-dimensional parametric models. This motivates nonparametric estimation under shape restrictions. Nonparametric estimates are often very noisy. Shape restrictions stabilize nonparametric estimates without imposing arbitrary restrictions, such as additivity or a single-index structure, that may be inconsistent with economic theory and the data. This paper explains how to estimate and obtain an asymptotic uniform confidence band for a conditional mean function under possibly nonlinear shape restrictions, such as the Slutsky inequality. The results of Monte Carlo experiments illustrate the finite-sample performance of the method, and an empirical example illustrates its use in an application.

Suggested Citation

  • Joel L. Horowitz & Sokbae (Simon) Lee, 2015. "Nonparametric estimation and inference under shape restrictions," CeMMAP working papers CWP67/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:67/15
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    References listed on IDEAS

    as
    1. Jacho-Chávez, David & Lewbel, Arthur & Linton, Oliver, 2010. "Identification and nonparametric estimation of a transformed additively separable model," Journal of Econometrics, Elsevier, vol. 156(2), pages 392-407, June.
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    5. E. Mammen & C. Thomas‐Agnan, 1999. "Smoothing Splines and Shape Restrictions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 239-252, June.
    6. V. Chernozhukov & I. Fernández-Val & A. Galichon, 2009. "Improving point and interval estimators of monotone functions by rearrangement," Biometrika, Biometrika Trust, vol. 96(3), pages 559-575.
    7. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
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    9. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2013. "Testing functional inequalities," Journal of Econometrics, Elsevier, vol. 172(1), pages 14-32.
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    Cited by:

    1. Olivier Scaillet, 2016. "On ill‐posedness of nonparametric instrumental variable regression with convexity constraints," Econometrics Journal, Royal Economic Society, vol. 19(2), pages 232-236, June.
    2. repec:gnv:wpaper:unige:79975 is not listed on IDEAS
    3. Lee, Y-Y. & Bhattacharya, D., 2018. "Applied Welfare Analysis for Discrete Choice with Interval-data on Income," Cambridge Working Papers in Economics 1882, Faculty of Economics, University of Cambridge.
    4. Adams, Abigail, 2019. "Mutually Consistent Revealed Preference Demand Predictions," CEPR Discussion Papers 13580, C.E.P.R. Discussion Papers.
    5. repec:eee:econom:v:204:y:2018:i:1:p:119-130 is not listed on IDEAS

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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

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