IDEAS home Printed from https://ideas.repec.org/a/oup/restud/v80y2013i1p343-364.html
   My bibliography  Save this article

Discrete Choice Non-Response

Author

Listed:
  • Esmeralda A. Ramalho
  • Richard J. Smith

Abstract

Missing values are endemic in the data sets available to econometricians. This paper suggests a semiparametrically efficient likelihood-based approach to deal with general non-ignorable missing data problems for discrete choice models. Our concern is when the dependent variable and/or covariates are unobserved for some sampling units. A supplementary random sample of observations on all covariates may be available. The key insight of this paper is the recognition of non-response as a modification of choice-based (CB) samples. Semiparametrically efficient generalized method of moments (GMM) estimation appropriate for CB samples is then adapted for the non-response framework considered in this paper. Simulation results for various GMM estimators proposed here are very encouraging. Copyright , Oxford University Press.

Suggested Citation

  • Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(1), pages 343-364.
    • Handle: RePEc:oup:restud:v:80:y:2013:i:1:p:343-364
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/restud/rds018
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Imbens, Guido W, 1992. "An Efficient Method of Moments Estimator for Discrete Choice Models with Choice-Based Sampling," Econometrica, Econometric Society, vol. 60(5), pages 1187-1214, September.
    2. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
    3. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    4. Ramalho, Esmeralda A., 2007. "Binary models with misclassification in the variable of interest and nonignorable nonresponse," Economics Letters, Elsevier, vol. 96(1), pages 70-76, July.
    5. Judith K. Hellerstein & Guido W. Imbens, 1999. "Imposing Moment Restrictions From Auxiliary Data By Weighting," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 1-14, February.
    6. John Fitzgerald & Peter Gottschalk & Robert Moffitt, 1998. "An Analysis of Sample Attrition in Panel Data: The Michigan Panel Study of Income Dynamics," Journal of Human Resources, University of Wisconsin Press, vol. 33(2), pages 251-299.
    7. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    8. repec:bla:obuest:v:64:y:2002:i:s1:p:653-676 is not listed on IDEAS
    9. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    10. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    11. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    12. Horowitz, Joel L. & Manski, Charles F., 1998. "Censoring of outcomes and regressors due to survey nonresponse: Identification and estimation using weights and imputations," Journal of Econometrics, Elsevier, vol. 84(1), pages 37-58, May.
    13. Lancaster, Tony & Imbens, Guido, 1996. "Case-control studies with contaminated controls," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 145-160.
    14. repec:bla:obuest:v:64:y:2002:i:0:p:653-76 is not listed on IDEAS
    15. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
    16. Mark B. Stewart, 1983. "On Least Squares Estimation when the Dependent Variable is Grouped," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 737-753.
    17. Guido W. Imbens & Tony Lancaster, 1994. "Combining Micro and Macro Data in Microeconometric Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 655-680.
    18. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(2), pages 451-470, April.
    19. Ramalho, Esmeralda A., 2002. "Regression models for choice-based samples with misclassification in the response variable," Journal of Econometrics, Elsevier, vol. 106(1), pages 171-201, January.
    20. Molinari, Francesca, 2010. "Missing Treatments," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 82-95.
    21. J. F. Lawless & J. D. Kalbfleisch & C. J. Wild, 1999. "Semiparametric methods for response‐selective and missing data problems in regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 413-438, April.
    22. 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.
    23. Gong Tang, 2003. "Analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 90(4), pages 747-764, December.
    24. Imbens, Guido W. & Lancaster, Tony, 1996. "Efficient estimation and stratified sampling," Journal of Econometrics, Elsevier, vol. 74(2), pages 289-318, October.
    25. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
    26. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    27. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    28. Esmeralda Ramalho, 2004. "Covariate Measurement Error in Endogenous Stratified Samples," Economics Working Papers 2_2004, University of Évora, Department of Economics (Portugal).
    29. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
    30. Guido W. Imbens, 1997. "One-Step Estimators for Over-Identified Generalized Method of Moments Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 359-383.
    31. Imbens, Guido W, 1992. "An Efficient Method of Moments Estimator for Discrete Choice Models with Choice-Based Sampling," Econometrica, Econometric Society, vol. 60(5), pages 1187-1214, September.
    32. Guido W. Imbens, 2004. "Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 4-29, February.
    33. Gang Li & Jing Qin, 1998. "Semiparametric likelihood‐based inference for biased and truncated data when the total sample size is known," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 243-254.
    34. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-1988, November.
    35. Chris Skinner & Nigel Stuttard & Gabriele Beissel‐Durrant & James Jenkins, 2002. "The Measurement of Low Pay in the UK Labour Force Survey," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(supplemen), pages 653-676, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Melvin Stephens & Takashi Unayama, 2019. "Estimating the Impacts of Program Benefits: Using Instrumental Variables with Underreported and Imputed Data," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 468-475, July.
    2. Breunig, Christoph & Mammen, Enno & Simoni, Anna, 2018. "Nonparametric estimation in case of endogenous selection," Journal of Econometrics, Elsevier, vol. 202(2), pages 268-285.
    3. Jesús M. Carro & Matilde P. Machado & Ricardo Mora, 2023. "The role of mothers on female labour force participation: an approach using historical parish records," Empirical Economics, Springer, vol. 65(3), pages 1345-1384, September.
    4. Breunig, Christoph & Haan, Peter, 2021. "Nonparametric regression with selectively missing covariates," Journal of Econometrics, Elsevier, vol. 223(1), pages 28-52.
    5. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2019. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201905, University of Kansas, Department of Economics, revised Mar 2019.
    6. Breunig, Christoph, 2017. "Testing missing at random using instrumental variables," SFB 649 Discussion Papers 2017-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    7. Lukáš Lafférs & Bernhard Schmidpeter, 2021. "Early child development and parents' labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(2), pages 190-208, March.
    8. repec:hum:wpaper:sfb649dp2015-016 is not listed on IDEAS
    9. Christoph Breunig & Peter Haan, 2018. "Nonparametric Regression with Selectively Missing Covariates," Papers 1810.00411, arXiv.org, revised Oct 2020.
    10. Machado, Matilde & Carro, Jesus & Mora, Ricardo, 2014. "Transmission of preferences and beliefs about female labor market participation: direct evidence on the role of mothers," CEPR Discussion Papers 10218, C.E.P.R. Discussion Papers.
    11. repec:hum:wpaper:sfb649dp2017-007 is not listed on IDEAS
    12. Breunig, Christoph, 2015. "Testing missing at random using instrumental variables," SFB 649 Discussion Papers 2015-016, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. d'Haultfoeuille, Xavier, 2010. "A new instrumental method for dealing with endogenous selection," Journal of Econometrics, Elsevier, vol. 154(1), pages 1-15, January.
    14. Breunig, Christoph & Kummer, Michael & Ohnemus, Jörg & Viete, Steffen, 2016. "IT outsourcing and firm productivity: Eliminating bias from selective missingness in the dependent variable," ZEW Discussion Papers 16-092, ZEW - Leibniz Centre for European Economic Research.
    15. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2020. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202004, University of Kansas, Department of Economics, revised Feb 2020.
    16. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    17. Richard Dorsett & Richard Hendra & Philip K. Robins, 2018. "Using Administrative Data to Explore the Effect of Survey Nonresponse in the UK Employment Retention and Advancement Demonstration," Evaluation Review, , vol. 42(5-6), pages 491-514, October.
    18. Laurent Davezies & Xavier d'Haultfoeuille, 2013. "Endogenous Attrition in Panels," Working Papers 2013-17, Center for Research in Economics and Statistics.

    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. Esmerelda A. Ramalho & Richard Smith, 2003. "Discrete choice non-response," CeMMAP working papers 07/03, Institute for Fiscal Studies.
    2. 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.
    3. Esmeralda A. Ramalho & Joaquim J. S. Ramalho, 2006. "Two‐Step Empirical Likelihood Estimation Under Stratified Sampling When Aggregate Information Is Available," Manchester School, University of Manchester, vol. 74(5), pages 577-592, September.
    4. Ramalho, Esmeralda A., 2002. "Regression models for choice-based samples with misclassification in the response variable," Journal of Econometrics, Elsevier, vol. 106(1), pages 171-201, January.
    5. Ramalho Esmeralda A., 2010. "Covariate Measurement Error: Bias Reduction under Response-Based Sampling," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-34, September.
    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. Esmeralda Ramalho, 2004. "Covariate Measurement Error in Endogenous Stratified Samples," Economics Working Papers 2_2004, University of Évora, Department of Economics (Portugal).
    8. Prokhorov, Artem & Schmidt, Peter, 2009. "GMM redundancy results for general missing data problems," Journal of Econometrics, Elsevier, vol. 151(1), pages 47-55, July.
    9. Kyungchul Song, 2009. "Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling," PIER Working Paper Archive 09-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    10. Inkmann, J., 2005. "Inverse Probability Weighted Generalised Empirical Likelihood Estimators : Firm Size and R&D Revisited," Other publications TiSEM c39cff1f-16c1-4446-a83f-c, Tilburg University, School of Economics and Management.
    11. Esmeralda Ramalho & Joaquim Ramalho, 2006. "Bias-Corrected Moment-Based Estimators for Parametric Models Under Endogenous Stratified Sampling," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 475-496.
    12. Nail Kashaev, 2022. "Estimation of Parametric Binary Outcome Models with Degenerate Pure Choice-Based Data with Application to COVID-19-Positive Tests from British Columbia," University of Western Ontario, Departmental Research Report Series 20225, University of Western Ontario, Department of Economics.
    13. Bhattacharya, Debopam, 2005. "Asymptotic inference from multi-stage samples," Journal of Econometrics, Elsevier, vol. 126(1), pages 145-171, May.
    14. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition, and stratification," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 1(2), pages 117-139, August.
    15. Richard Smith, 2005. "Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura," CeMMAP working papers CWP13/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. d'Haultfoeuille, Xavier, 2010. "A new instrumental method for dealing with endogenous selection," Journal of Econometrics, Elsevier, vol. 154(1), pages 1-15, January.
    17. 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.
    18. Devereux, Paul J. & Tripathi, Gautam, 2009. "Optimally combining censored and uncensored datasets," Journal of Econometrics, Elsevier, vol. 151(1), pages 17-32, July.
    19. Butler, J. S., 2000. "Efficiency results of MLE and GMM estimation with sampling weights," Journal of Econometrics, Elsevier, vol. 96(1), pages 25-37, May.
    20. Ramalho, Esmeralda A., 2007. "Binary models with misclassification in the variable of interest and nonignorable nonresponse," Economics Letters, Elsevier, vol. 96(1), pages 70-76, July.

    More about this item

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    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:oup:restud:v:80:y:2013:i:1:p:343-364. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/restud .

    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.