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A note on non-parametric estimation with predicted variables

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  • Stefan Sperlich

Abstract

This article gives the asymptotic properties of non-parametric kernel-based density and regression estimators when one of the variables is predicted. Such variables, also known as "constructed variables" or "generated predictors", occur quite frequently in econometric and applied economic analysis. The impact of using predicted rather than observed values on the properties of estimators has been extensively studied in the fully parametric context. The results derived here are applicable to the general situation in which the predictor is estimated using a consistent non-parametric method with standard convergence rates. Therefore, the presented results are, generally speaking, the asymptotics for semi-non-parametric two-step (or plug-in) estimation problems. The case of parametric estimation based on non-parametric predictors is also covered. Copyright © 2009 The Author(s). Journal compilation © Royal Economic Society 2009

Suggested Citation

  • Stefan Sperlich, 2009. "A note on non-parametric estimation with predicted variables," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 382-395, July.
    • Handle: RePEc:ect:emjrnl:v:12:y:2009:i:2:p:382-395
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    Cited by:

    1. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(4), pages 861-916, August.
    2. Ekpeno L. Effiong & Emmanuel E. Asuquo, 2017. "Migrants' Remittances, Governance and Heterogeneity," International Economic Journal, Taylor & Francis Journals, vol. 31(4), pages 535-554, October.
    3. Javier Alejo & Antonio F. Galvao & Julián Martinez-Iriarte & Gabriel Montes-Rojas, 2023. "Unconditional Quantile Partial Effects via Conditional Quantile Regression," Working Papers 217, Red Nacional de Investigadores en Economía (RedNIE).
    4. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    5. repec:hum:wpaper:sfb649dp2011-064 is not listed on IDEAS
    6. 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.
    7. Scholz, Michael & Sperlich, Stefan & Nielsen, Jens Perch, 2016. "Nonparametric long term prediction of stock returns with generated bond yields," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 82-96.
    8. 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.
    9. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "Carbon dioxide emissions and governance: A nonparametric analysis for the G-20," Energy Economics, Elsevier, vol. 40(C), pages 110-118.
    10. Grant, Charles & Padula, Mario, 2013. "Using bounds to investigate household debt repayment behaviour," Research in Economics, Elsevier, vol. 67(4), pages 336-354.
    11. repec:hum:wpaper:sfb649dp2014-043 is not listed on IDEAS
    12. 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.
    13. repec:hum:wpaper:sfb649dp2010-059 is not listed on IDEAS
    14. Haupt, Harry & Schnurbus, Joachim & Semmler, Willi, 2018. "Estimation of grouped, time-varying convergence in economic growth," Econometrics and Statistics, Elsevier, vol. 8(C), pages 141-158.
    15. 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.
    16. Elia Lapenta, 2022. "A Bootstrap Specification Test for Semiparametric Models with Generated Regressors," Papers 2212.11112, arXiv.org, revised Oct 2023.
    17. Ying-Ying Lee, 2018. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Papers 1811.00157, arXiv.org.
    18. Stefan Sperlich & Raoul Theler, 2015. "Modeling heterogeneity: a praise for varying-coefficient models in causal analysis," Computational Statistics, Springer, vol. 30(3), pages 693-718, September.
    19. Mochen Yang & Edward McFowland & Gordon Burtch & Gediminas Adomavicius, 2022. "Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem," INFORMS Joural on Data Science, INFORMS, vol. 1(2), pages 138-155, October.
    20. Patrick W Saart & Jiti Gao & Nam Hyun Kim, 2014. "Econometric Time Series Specification Testing in a Class of Multiplicative Error Models," Monash Econometrics and Business Statistics Working Papers 1/14, Monash University, Department of Econometrics and Business Statistics.
    21. Jinyong Hahn & Geert Ridder, 2013. "Asymptotic Variance of Semiparametric Estimators With Generated Regressors," Econometrica, Econometric Society, vol. 81(1), pages 315-340, January.
    22. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2010. "Nonparametric regression with nonparametrically generated covariates," SFB 649 Discussion Papers 2010-059, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    23. repec:grz:wpaper:2012-10 is not listed on IDEAS
    24. Jing Dai & Stefan Sperlich & Walter Zucchini, 2011. "Estimating and predicting the distribution of the number of visits to the medical doctor," MAGKS Papers on Economics 201148, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    25. 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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