IDEAS home Printed from https://ideas.repec.org/p/keo/dpaper/2019-006.html
   My bibliography  Save this paper

Doubly Robust-type Estimation of Population Moments and Parameters in Biased Sampling

Author

Listed:
  • Takahiro Hoshino

    (Faculty of Ecoomics, Keio University)

  • Yuya Shimizu

    (Graduate School of Economics, Keio University)

Abstract

We propose an estimation method of population moments or population parameters in "biased sampling data" in which for some units of data, not only the variable of interest but also the covariates, have missing observations and the proportion of "missingness" is unknown. We use auxiliary information such as the distribution of covariates or their moments in random sampling data in order to correct the bias. Moreover, with additional assumptions, we can correct the bias even if we have only the moment information of covariates. The main contribution of this paper is the development of a doubly robust-type estimator for biased sampling data. This method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified. We prove the consistency and semi-parametric efficiency of the doubly robust estimator. Both the simulation and empirical application results demonstrate that the proposed estimation method is more robust than existing methods.

Suggested Citation

  • Takahiro Hoshino & Yuya Shimizu, 2019. "Doubly Robust-type Estimation of Population Moments and Parameters in Biased Sampling," Keio-IES Discussion Paper Series 2019-006, Institute for Economics Studies, Keio University.
    • Handle: RePEc:keo:dpaper:2019-006
    as

    Download full text from publisher

    File URL: https://ies.keio.ac.jp/upload/pdf/en/DP2019-006.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liang H. & Wang S. & Robins J.M. & Carroll R.J., 2004. "Estimation in Partially Linear Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 357-367, January.
    2. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    3. Qin J. & Leung D. & Shao J., 2002. "Estimation With Survey Data Under Nonignorable Nonresponse or Informative Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 193-200, March.
    4. Keisuke Hirano & Guido W. Imbens & Geert Ridder & Donald B. Rubin, 2001. "Combining Panel Data Sets with Attrition and Refreshment Samples," Econometrica, Econometric Society, vol. 69(6), pages 1645-1659, November.
    5. Wang, Lu & Rotnitzky, Andrea & Lin, Xihong, 2010. "Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1135-1146.
    6. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    7. Takahiro Hoshino, 2007. "Doubly Robust-Type Estimation for Covariate Adjustment in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 535-549, December.
    8. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    9. Nevo, Aviv, 2003. "Using Weights to Adjust for Sample Selection When Auxiliary Information Is Available," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 43-52, January.
    10. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    11. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    2. repec:hal:spmain:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    3. Simon Calmar Andersen & Louise Beuchert & Phillip Heiler & Helena Skyt Nielsen, 2023. "A Guide to Impact Evaluation under Sample Selection and Missing Data: Teacher's Aides and Adolescent Mental Health," Papers 2308.04963, arXiv.org.
    4. Joachim Inkmann, 2010. "Estimating Firm Size Elasticities of Product and Process R&D," Economica, London School of Economics and Political Science, vol. 77(306), pages 384-402, April.
    5. Katrin Hussinger, 2008. "R&D and subsidies at the firm level: an application of parametric and semiparametric two-step selection models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(6), pages 729-747.
    6. Nevo, Aviv, 2003. "Using Weights to Adjust for Sample Selection When Auxiliary Information Is Available," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 43-52, January.
    7. repec:spo:wpmain:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    8. Marcel Das & Vera Toepoel & Arthur van Soest, 2011. "Nonparametric Tests of Panel Conditioning and Attrition Bias in Panel Surveys," Sociological Methods & Research, , vol. 40(1), pages 32-56, February.
    9. Schafgans, Marcia M. A., 2000. "Gender wage differences in Malaysia: parametric and semiparametric estimation," Journal of Development Economics, Elsevier, vol. 63(2), pages 351-378, December.
    10. Nicoletti, Cheti, 2008. "Multiple sample selection in the estimation of intergenerational occupational mobility," ISER Working Paper Series 2008-20, Institute for Social and Economic Research.
    11. Martin Huber, 2014. "Treatment Evaluation in the Presence of Sample Selection," Econometric Reviews, Taylor & Francis Journals, vol. 33(8), pages 869-905, November.
    12. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 1053-1079.
    13. Rene Segers & Philip Hans Franses, 2014. "Panel design effects on response rates and response quality," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(1), pages 1-24, February.
    14. repec:spo:wpecon:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    15. Liu, Ruixuan & Yu, Zhengfei, 2022. "Sample selection models with monotone control functions," Journal of Econometrics, Elsevier, vol. 226(2), pages 321-342.
    16. James J. Heckman, 2005. "Micro Data, Heterogeneity and the Evaluation of Public Policy Part 2," The American Economist, Sage Publications, vol. 49(1), pages 16-44, March.
    17. Rahul Singh, 2021. "Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection," Papers 2111.05277, arXiv.org.
    18. repec:hal:wpspec:info:hdl:2441/3vl5fe4i569nbr005tctlc8ll5 is not listed on IDEAS
    19. Gayle, George-Levi & Viauroux, Christelle, 2007. "Root-N consistent semiparametric estimators of a dynamic panel-sample-selection model," Journal of Econometrics, Elsevier, vol. 141(1), pages 179-212, November.
    20. Chen, Qixuan & Paik, Myunghee Cho & Kim, Minjin & Wang, Cuiling, 2016. "Using link-preserving imputation for logistic partially linear models with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 174-185.
    21. E. Santarelli & H. T. Tran, 2013. "Diversification Strategies and Firm Performance: A Sample Selection Approach," Working Papers wp896, Dipartimento Scienze Economiche, Universita' di Bologna.
    22. Masayuki Hirukawa & Di Liu & Irina Murtazashvili & Artem Prokhorov, 2023. "DS-HECK: double-lasso estimation of Heckman selection model," Empirical Economics, Springer, vol. 64(6), pages 3167-3195, June.
    23. Timothy Reese & Majid Mojirsheibani, 2017. "On the $$L_p$$ L p norms of kernel regression estimators for incomplete data with applications to classification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 81-112, March.
    24. Emre Ekinci, 2009. "Dealing with Attrition When Refreshment Samples are Available: An Application to the Turkish Household Labor Force Survey," 2009 Meeting Papers 353, Society for Economic Dynamics.

    More about this item

    Keywords

    Auxiliary information; Biased sampling; Missing data; Propensity score; Doubly robust estimator;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:keo:dpaper:2019-006. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Institute for Economics Studies, Keio University (email available below). General contact details of provider: https://edirc.repec.org/data/iekeijp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.