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Tests of Additive Derivative Constraints

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  • Thomas M. Stoker

Abstract

This paper proposes nonparametric tests of additive constraints on the first and second derivatives of a model E(y|x) = g(x), where the true function g is unknown. Such constraints are illustrated by the economic restrictions of homogeneity and symmetry, and the functional form restrictions of additivity and linearity. The proposed tests are based on estimates of regression coefficients, that statistically characterize the departures from the constraint exhibited by the data. The coefficients are based on weighted-average derivatives, that are reformulated in terms of derivatives of the density of x. Coefficient estimators are proposed that use nonparametric kernel estimators of the density and its derivatives. These statistics are shown to be √N consistent and asymptotically normal, and thus are comparable to estimators based on a (correctly specified) parametric model of g(x).

Suggested Citation

  • Thomas M. Stoker, 1989. "Tests of Additive Derivative Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(4), pages 535-552.
    • Handle: RePEc:oup:restud:v:56:y:1989:i:4:p:535-552.
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    File URL: http://hdl.handle.net/10.2307/2297499
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    Citations

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    Cited by:

    1. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
    2. Dette, Holger & Hoderlein, Stefan & Neumeyer, Natalie, 2016. "Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness," Journal of Econometrics, Elsevier, vol. 191(1), pages 129-144.
    3. Bas Donkers & Marcia M Schafgans, 2005. "A method of moments estimator for semiparametric index models," STICERD - Econometrics Paper Series 493, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. White, Halbert & Hong, Yongmiao, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series qt9qz123ng, Department of Economics, UC San Diego.
    5. Yukitoshi Matsushita & Taisuke Otsu, 2018. "Likelihood Inference on Semiparametric Models: Average Derivative and Treatment Effect," The Japanese Economic Review, Japanese Economic Association, vol. 69(2), pages 133-155, June.
    6. Hoderlein, Stefan, 2011. "How many consumers are rational?," Journal of Econometrics, Elsevier, vol. 164(2), pages 294-309, October.
    7. Escanciano, Juan Carlos & Song, Kyungchul, 2010. "Testing single-index restrictions with a focus on average derivatives," Journal of Econometrics, Elsevier, vol. 156(2), pages 377-391, June.
    8. Prakasa Rao, B. L. S., 1995. "Consistent estimation of density-weighted average derivative by orthogonal series method," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 205-212, February.

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