IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v20y2001i3p319-335.html
   My bibliography  Save this article

Recentered And Rescaled Instrumental Variable Estimation Of Tobit And Probit Models With Errors In Variables

Author

Listed:
  • Shigeru Iwata

Abstract

Since Durbin (1954) and Sargan (1958), instrumental variable (IV) method has long been one of the most popular procedures among economists and other social scientists to handle linear models with errors-in-variables. A direct application of this method to nonlinear errors-in-variables models, however, fails to yield consistent estimators. This article restricts attention to Tobit and Probit models and shows that simple recentering and rescaling of the observed dependent variable may restore consistency of the standard IV estimator if the true dependent variable and the IV's are jointly normally distributed. Although the required condition seems rarely to be satisfied by real data, our Monte Carlo experiment suggests that the proposed estimator may be quite robust to the possible deviation from normality.

Suggested Citation

  • Shigeru Iwata, 2001. "Recentered And Rescaled Instrumental Variable Estimation Of Tobit And Probit Models With Errors In Variables," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 319-335.
    • Handle: RePEc:taf:emetrv:v:20:y:2001:i:3:p:319-335
    DOI: 10.1081/ETC-100104937
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1081/ETC-100104937
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1081/ETC-100104937?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Stapleton, David C & Young, Douglas J, 1984. "Censored Normal Regression with Measurement Error on the Dependent Variable," Econometrica, Econometric Society, vol. 52(3), pages 737-760, May.
    3. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    4. Cheng Hsiao, 1991. "Identification and Estimation of Dichotomous Latent Variables Models Using Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(4), pages 717-731.
    5. Leamer, Edward E, 1978. "Least-Squares versus Instrumental Variables Estimation in a Simple Errors in Variables Model," Econometrica, Econometric Society, vol. 46(4), pages 961-968, July.
    6. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
    7. Chung, Ching-Fan & Goldberger, Arthur S, 1984. "Proportional Projections in Limited Dependent Variable Models," Econometrica, Econometric Society, vol. 52(2), pages 531-534, March.
    8. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    9. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    10. Hsiao, Cheng, 1989. "Consistent estimation for some nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 41(1), pages 159-185, May.
    11. Greene, William H., 1983. "Estimation of limited dependent variable models by ordinary least squares and the method of moments," Journal of Econometrics, Elsevier, vol. 21(2), pages 195-212, February.
    12. Iwata, Shigeru, 1992. "Instrumental variables estimation in errors-in-variables models when instruments are correlated with errors," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 297-322.
    13. Hsiao, C., 1992. "Nonlinear Latent Variable Models," Papers 9211, Southern California - Department of Economics.
    14. Greene, William H, 1981. "On the Asymptotic Bias of the Ordinary Least Squares Estimator of the Tobit Model," Econometrica, Econometric Society, vol. 49(2), pages 505-513, March.
    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. Joop Hartog & Luis Díaz-Serrano, 2007. "Earnings risk and demand for higher education: A cross-section test for Spain," Journal of Applied Economics, Universidad del CEMA, vol. 10, pages 1-28, May.
    2. Lee C. Adkins, 2008. "Small Sample Performance of Instrumental Variables Probit Estimators: A Monte Carlo Investigation," Economics Working Paper Series 0807, Oklahoma State University, Department of Economics and Legal Studies in Business.
    3. Lee C. Adkins, 2009. "An Instrumental Variables Probit Estimator Using Gretl," EHUCHAPS, in: Ignacio Díaz-Emparanza & Petr Mariel & María Victoria Esteban (ed.), Econometrics with gretl. Proceedings of the gretl Conference 2009, edition 1, chapter 4, pages 59-74, Universidad del País Vasco - Facultad de Ciencias Económicas y Empresariales.

    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. Song, Suyong, 2015. "Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 95-109.
    2. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    3. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    4. Wang, Liqun & Hsiao, Cheng, 2011. "Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 165(1), pages 30-44.
    5. Hong, Han & Tamer, Elie, 2003. "A simple estimator for nonlinear error in variable models," Journal of Econometrics, Elsevier, vol. 117(1), pages 1-19, November.
    6. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    7. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, April.
    8. Moschini, GianCarlo, 2001. "Production risk and the estimation of ex-ante cost functions," Journal of Econometrics, Elsevier, vol. 100(2), pages 357-380, February.
    9. Richard A. Ashley & Guo Li, 2013. "Re-Examining the Impact of Housing Wealth and Stock Wealth on Household Spending: Does Persistence in Wealth Changes Matter?," Working Papers e07-39, Virginia Polytechnic Institute and State University, Department of Economics.
    10. Jorge Gonz�lez, 2015. "Estimating income elasticities of leisure activities using cross-sectional categorized data," Documentos de Trabajo dt2015-02, Facultad de Ciencias Económicas y Empresariales, Universidad de Zaragoza.
    11. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers 41/12, Institute for Fiscal Studies.
    12. Xiaohong Chen & Han Hong & Denis Nekipelov, 2011. "Nonlinear Models of Measurement Errors," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 901-937, December.
    13. Duo Qin & Sophie Van Huellen & Qing-Chao Wang, 2015. "How Credible Are Shrinking Wage Elasticities of Married Women Labour Supply?," Econometrics, MDPI, vol. 4(1), pages 1-31, December.
    14. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information," CeMMAP working papers CWP18/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Jesse B. Tack & Rulon D. Pope & Jeffrey T. LaFrance & Ricardo H. Cavazos, 2015. "Modelling an aggregate agricultural panel with application to US farm input demands," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 42(3), pages 371-396.
    16. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    17. Li, Tong, 2000. "Estimation of nonlinear errors-in-variables models: a simulated minimum distance estimator," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 243-248, April.
    18. Li, Tong & Hsiao, Cheng, 2004. "Robust estimation of generalized linear models with measurement errors," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 51-65.
    19. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
    20. Duo Qin & Sophie van H¸llen & Qing-Chao Wang, 2014. "What Happens to Wage Elasticities When We Strip Playometrics? Revisiting Married Women Labour Supply Model," Working Papers 190, Department of Economics, SOAS University of London, UK.

    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:taf:emetrv:v:20:y:2001:i:3:p:319-335. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.