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Semiparametric Estimation With Generated Covariates

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  • Mammen, Enno
  • Rothe, Christoph
  • Schienle, Melanie

Abstract

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g. estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a non-standard problem due to the presence of generated covariates. We give conditions under which estimators are root-n consistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.
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  • Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(05), pages 1140-1177, October.
  • Handle: RePEc:cup:etheor:v:32:y:2016:i:05:p:1140-1177_00
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    Cited by:

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    2. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(04), pages 861-916, August.
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    4. Patrick Cheridito & Ulrich Horst & Michael Kupper & Traian A. Pirvu, 2016. "Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 174-195, February.
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    6. Raffaele Fiocco, 2012. "Competition and regulation with product differentiation," Journal of Regulatory Economics, Springer, vol. 42(3), pages 287-307, December.
    7. Fabio A. Miessi Sanches & Daniel Silva Junior, Sorawoot Srisuma, 2015. "Minimum Distance Estimation of Search Costs using Price Distribution," Working Papers, Department of Economics 2015_31, University of São Paulo (FEA-USP).
    8. Bocart, Fabian Y.R.P. & Hafner, Christian M., 2012. "Econometric analysis of volatile art markets," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3091-3104.
    9. Enno Mammen & Christoph Rothe & Melanie Schienle, 2012. "Generated Covariates in Nonparametric Estimation: A Short Review," SFB 649 Discussion Papers SFB649DP2012-042, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(05), pages 1140-1177, October.
    11. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    12. Nikolaus Hautsch & Julia Schaumburg & Melanie Schienle, 2015. "Financial Network Systemic Risk Contributions," Review of Finance, European Finance Association, vol. 19(2), pages 685-738.
    13. Ying-Ying Lee, 2015. "Efficient propensity score regression estimators of multi-valued treatment effects for the treated," Economics Series Working Papers 738, University of Oxford, Department of Economics.
    14. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    15. Alena MyÅ¡iÄ ková & Song Song & Piotr Majer & Peter N.C. Mohr & Hauke R. Heekeren & Wolfgang K. Härdle, 2011. "Risk Patterns and Correlated Brain Activities. Multidimensional statistical analysis of fMRI data with application to risk patterns," SFB 649 Discussion Papers SFB649DP2011-085, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Dorothee Schneider, 2011. "The Labor Share: A Review of Theory and Evidence," SFB 649 Discussion Papers SFB649DP2011-069, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    17. Rothe, Christoph, 2016. "The Value of Knowing the Propensity Score for Estimating Average Treatment Effects," IZA Discussion Papers 9989, Institute for the Study of Labor (IZA).
    18. Debopam Bhattacharya & Pascaline Dupas & Shin Kanaya, 2013. "Estimating the Impact of Means-tested Subsidies under Treatment Externalities with Application to Anti-Malarial Bednets," CREATES Research Papers 2013-06, Department of Economics and Business Economics, Aarhus University.
    19. Lu, Xun & White, Habert, 2015. "Testing For Treatment Dependence Of Effects Of A Continuous Treatment," Econometric Theory, Cambridge University Press, vol. 31(05), pages 1016-1053, October.
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    21. Gregor Heyne & Michael Kupper & Christoph Mainberger, 2011. "Minimal Supersolutions of BSDEs with Lower Semicontinuous Generators," SFB 649 Discussion Papers SFB649DP2011-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    22. Ulrich Horst & Michael Kupper & Andrea Macrina & Christoph Mainberger, 2011. "Continuous Equilibrium under Base Preferences and Attainable Initial Endowments," SFB 649 Discussion Papers SFB649DP2011-082, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    23. Gao, Jiti & Kim, Nam Hyun & Saart, Patrick W., 2015. "A misspecification test for multiplicative error models of non-negative time series processes," Journal of Econometrics, Elsevier, vol. 189(2), pages 346-359.
    24. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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