IDEAS home Printed from
   My bibliography  Save this article

Semiparametric estimation of a bivariate Tobit model


  • Chen, Songnian
  • Zhou, Xianbo


The existing semiparametric estimation literature has mainly focused on univariate Tobit models and no semiparametric estimation has been considered for bivariate Tobit models. In this paper, we consider semiparametric estimation of the bivariate Tobit model proposed by Amemiya (1974), under the independence condition without imposing any parametric restriction on the error distribution. Our estimator is shown to be consistent and asymptotically normal, and simulation results show that our estimator performs well in finite samples. It is also worth noting that while Amemiya’s (1974) instrumental variables estimator (IV) requires the normality assumption, our semiparametric estimator actually outperforms his IV estimator even when normality holds. Our approach can be extended to higher dimensional multivariate Tobit models.

Suggested Citation

  • Chen, Songnian & Zhou, Xianbo, 2011. "Semiparametric estimation of a bivariate Tobit model," Journal of Econometrics, Elsevier, vol. 165(2), pages 266-274.
  • Handle: RePEc:eee:econom:v:165:y:2011:i:2:p:266-274 DOI: 10.1016/j.jeconom.2011.07.005

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

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

    References listed on IDEAS

    1. Yannis M. Ioannides & Vassilis A. Hajivassiliou, 2007. "Unemployment and liquidity constraints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 479-510.
    2. Lee, Lung-Fei, 1992. "Semiparametic Nonlinear Least-Squares Estimation of Truncated Regression Models," Econometric Theory, Cambridge University Press, vol. 8(01), pages 52-94, March.
    3. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    4. Nelson, Forrest & Olson, Lawrence, 1978. "Specification and Estimation of a Simultaneous-Equation Model with Limited Dependent Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 695-709, October.
    5. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
    6. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    7. Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, vol. 42(6), pages 999-1012, November.
    8. Honore, Bo E. & Powell, James L., 1994. "Pairwise difference estimators of censored and truncated regression models," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 241-278.
    9. Wales, T J & Woodland, A D, 1980. "Sample Selectivity and the Estimation of Labor Supply Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(2), pages 437-468, June.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Zhou, Xianbo & Pan, Zhewen, 2015. "Two-step semiparametric estimation of the Type-3 Tobit model," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 96-105.

    More about this item


    Access and download statistics


    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:eee:econom:v:165:y:2011:i:2:p:266-274. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.