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Goodness-of-fit tests based on series estimators in nonparametric instrumental regression

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  • Breunig, Christoph
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    Abstract

    This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or nonparametric specification as well as a test of exogeneity of the vector of regressors. The tests are asymptotically normally distributed under correct specification and consistent against any alternative model. Under a sequence of local alternative hypotheses, the asymptotic distribution of the tests is derived. Moreover, uniform consistency is established over a class of alternatives whose distance to the null hypothesis shrinks appropriately as the sample size increases.

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    File URL: https://ub-madoc.bib.uni-mannheim.de/32111/1/Breunig_13%2D12.pdf
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    Bibliographic Info

    Paper provided by University of Mannheim, Department of Economics in its series Working Papers with number 12-13.

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    Date of creation: 2012
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    Handle: RePEc:mnh:wpaper:32111

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    1. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(03), pages 472-496, June.
    2. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    3. Xiaohong Chen & Markus Reiss, 2007. "On rate optimality for ill-posed inverse problems in econometrics," CeMMAP working papers CWP20/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
    5. Serge Darolles & Jean-Pierre Florens & Eric Renault, 2000. "Nonparametric Instrumental Regression," Working Papers 2000-17, Centre de Recherche en Economie et Statistique.
    6. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
    7. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, 03.
    8. Horowitz, Joel L., 2012. "Specification testing in nonparametric instrumental variable estimation," Journal of Econometrics, Elsevier, vol. 167(2), pages 383-396.
    9. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    10. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Patrick Gagliardini & Olivier Scaillet, 2007. "A Specification Test For Nonparametric Instrumental Variable Regression," Swiss Finance Institute Research Paper Series 9602, Swiss Finance Institute.
    12. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
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