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Nonparametric estimation and inference under shape restrictions

Author

Listed:
  • Joel L. Horowitz
  • Sokbae (Simon) Lee
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, 2016. "Nonparametric estimation and inference under shape restrictions," CeMMAP working papers 29/16, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:29/16
    DOI: 10.1920/wp.cem.2016.2916
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    References listed on IDEAS

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    Cited by:

    1. Lee, Ying-Ying & Bhattacharya, Debopam, 2019. "Applied welfare analysis for discrete choice with interval-data on income," Journal of Econometrics, Elsevier, vol. 211(2), pages 361-387.
    2. Harold D. Chiang & Kengo Kato & Yuya Sasaki & Takuya Ura, 2021. "Linear programming approach to nonparametric inference under shape restrictions: with an application to regression kink designs," Papers 2102.06586, arXiv.org.
    3. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Sep 2021.
    4. Eric Auerbach, 2019. "Identification and Estimation of a Partially Linear Regression Model using Network Data," Papers 1903.09679, arXiv.org, revised Jun 2021.
    5. Zheng Fang & Juwon Seo, 2021. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Econometrica, Econometric Society, vol. 89(5), pages 2439-2458, September.
    6. David T. Frazier & Bonsoo Koo, 2020. "Indirect Inference for Locally Stationary Models," Monash Econometrics and Business Statistics Working Papers 30/20, Monash University, Department of Econometrics and Business Statistics.
    7. Adams-Prassl, Abigail, 2019. "Mutually Consistent Revealed Preference Demand Predictions," CEPR Discussion Papers 13580, C.E.P.R. Discussion Papers.
    8. 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.
    9. Botosaru, Irene, 2020. "Nonparametric analysis of a duration model with stochastic unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 217(1), pages 112-139.
    10. Yu Zhu, 2020. "Inference in nonparametric/semiparametric moment equality models with shape restrictions," Quantitative Economics, Econometric Society, vol. 11(2), pages 609-636, May.
    11. Freyberger, Joachim & Rai, Yoshiyasu, 2018. "Uniform confidence bands: Characterization and optimality," Journal of Econometrics, Elsevier, vol. 204(1), pages 119-130.
    12. Yu-Chang Chen & Haitian Xie, 2022. "Personalized Subsidy Rules," Papers 2202.13545, arXiv.org, revised Mar 2022.
    13. repec:gnv:wpaper:unige:79975 is not listed on IDEAS
    14. Koohyun Kwon & Soonwoo Kwon, 2020. "Adaptive Inference in Multivariate Nonparametric Regression Models Under Monotonicity," Papers 2011.14219, arXiv.org.
    15. Frazier, David T. & Koo, Bonsoo, 2021. "Indirect inference for locally stationary models," Journal of Econometrics, Elsevier, vol. 223(1), pages 1-27.
    16. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.

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    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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