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Local Semiparametric Efficiency Bounds Under Shape Restrictions

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  • Tripathi, Gautam

Abstract

Consider the model y = x′β0 + f*(z) + ε, where ε [d over =] N(0, σ02). We calculate the smallest asymptotic variance that n1/2 consistent regular (n1/2CR) estimators of β0 can have when the only information we possess about f* is that it has a certain shape. We focus on three particular cases: (i) when f* is homogeneous of degree r, (ii) when f* is concave, (iii) when f* is decreasing. Our results show that in the class of all n1/2CR estimators of β0, homogeneity of f* may lead to substantial asymptotic efficiency gains in estimating β0. In contrast, at least asymptotically, concavity and monotonicity of f* do not help in estimating β0 more efficiently, at least for n1/2CR estimators of β0.

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  • Tripathi, Gautam, 2000. "Local Semiparametric Efficiency Bounds Under Shape Restrictions," Econometric Theory, Cambridge University Press, vol. 16(5), pages 729-739, October.
    • Handle: RePEc:cup:etheor:v:16:y:2000:i:05:p:729-739_16
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    Cited by:

    1. Wolff, Hendrik & Heckelei, Thomas & Mittelhammer, Ronald C., 2004. "Imposing Monotonicity And Curvature On Flexible Functional Forms," 2004 Annual meeting, August 1-4, Denver, CO 20256, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Joris Pinkse & Karl Schurter, 2019. "Estimation of Auction Models with Shape Restrictions," Papers 1912.07466, arXiv.org.
    3. Kyungchul Song, 2009. "Point Decisions for Interval-Identified Parameters," PIER Working Paper Archive 09-036, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    4. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    5. Hendrik Wolff & Thomas Heckelei & Ron Mittelhammer, 2010. "Imposing Curvature and Monotonicity on Flexible Functional Forms: An Efficient Regional Approach," Computational Economics, Springer;Society for Computational Economics, vol. 36(4), pages 309-339, December.
    6. Ruixuan Liu & Zhengfei Yu, 2019. "Accelerated Failure Time Models with Log-concave Errors," Tsukuba Economics Working Papers 2019-003, Faculty of Humanities and Social Sciences, University of Tsukuba.

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