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Edgeworth approximations for semiparametric instrumental variable estimators and test statistics

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  • Linton, Oliver

Abstract

We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable considered in Newey (1990) as well as to the distribution of a Wald statistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and [a version of] nearest neighbour estimates as special cases. Our expansions are valid to order n �2є for some 0

Suggested Citation

  • Linton, Oliver, 2000. "Edgeworth approximations for semiparametric instrumental variable estimators and test statistics," LSE Research Online Documents on Economics 2156, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2156
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    References listed on IDEAS

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    19. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
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    Cited by:

    1. Matsushita, Yukitoshi & Otsu, Taisuke, 2020. "Likelihood inference on semiparametric models with generated regressors," LSE Research Online Documents on Economics 102696, London School of Economics and Political Science, LSE Library.
    2. Paul Rilstone, 2021. "Higher-Order Stochastic Expansions and Approximate Moments for Non-linear Models with Heterogeneous Observations," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 99-120, December.
    3. Carrasco, Marine & Kotchoni, Rachidi, 2017. "Efficient Estimation Using The Characteristic Function," Econometric Theory, Cambridge University Press, vol. 33(2), pages 479-526, April.
    4. Kundhi, Gubhinder & Rilstone, Paul, 2012. "Edgeworth expansions for GEL estimators," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 118-146.
    5. Juan Carlos Escanciano, 2010. "The Integrated Instrumental Variables Estimator: Exploiting Nonlinearities for Identification of Linear Models," CAEPR Working Papers 2010-001, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    6. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    7. Chen, Songnian & Zhang, Hanghui, 2015. "Binary quantile regression with local polynomial smoothing," Journal of Econometrics, Elsevier, vol. 189(1), pages 24-40.

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    More about this item

    Keywords

    Bandwidth selection; Edgeworth approximation; instrumental variables; kernel estimation; local polynomials;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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