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Simulation-based estimation of Tobit model with random effects


  • Calzolari, Giorgio
  • Magazzini, Laura
  • Mealli, Fabrizia


The estimation of limited dependent variable panel data models usually involves objective functions in which integrals appear without a closed form solution: this is the case of the panel data Tobit model with random effects. Recently, simulation methods have shown to be useful in the inference process, as they offer methods to approximate such integrals (Laroque, Salanie, 1989; Gouri´eroux, Monfort, 1991, 1993; Hajivassiliou, McFadden, 1998; Mealli, Rampichini, 1999; Inkmann, 2000). Although the asymptotic performances of such methods are known and their application has been successfully undertaken, more precise ideas on their finite sample performance and computational efficiency is still needed. In this paper we propose to use the method of indirect inference, using different auxiliary models, and the simulated maximum likelihood to estimate these models. We use a panel data Tobit model with a simple correlation structure in the unobservables (i.e. a one-factor structure), but the model could be easily extended. Using both simulated and real data, we show the perfomances of the proposed methods in finite samples. The application on real data is concerned with a model of female labour supply.

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  • Calzolari, Giorgio & Magazzini, Laura & Mealli, Fabrizia, 2001. "Simulation-based estimation of Tobit model with random effects," MPRA Paper 22985, University Library of Munich, Germany, revised 2001.
  • Handle: RePEc:pra:mprapa:22985

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    References listed on IDEAS

    1. Inkmann, Joachim, 2000. "Misspecified heteroskedasticity in the panel probit model: A small sample comparison of GMM and SML estimators," Journal of Econometrics, Elsevier, vol. 97(2), pages 227-259, August.
    2. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
    3. Honore, Bo E., 1993. "Orthogonality conditions for Tobit models with fixed effects and lagged dependent variables," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 35-61, September.
    4. Honore, Bo E, 1992. "Trimmed LAD and Least Squares Estimation of Truncated and Censored Regression Models with Fixed Effects," Econometrica, Econometric Society, vol. 60(3), pages 533-565, May.
    5. repec:adr:anecst:y:1991:i:20-21:p:04 is not listed on IDEAS
    6. Giorgio Calzolari & F. Di Iorio & G. Fiorentini, 1999. "Indirect Estimation of Just-Identified Models with Control Variates," Econometrics Working Papers Archive quaderno46, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    7. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
    8. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    9. Gourieroux, Christian & Monfort, Alain, 1993. "Simulation-based inference : A survey with special reference to panel data models," Journal of Econometrics, Elsevier, vol. 59(1-2), pages 5-33, September.
    10. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 85-118, Suppl. De.
    11. G. S. Maddala, 1987. "Limited Dependent Variable Models Using Panel Data," Journal of Human Resources, University of Wisconsin Press, vol. 22(3), pages 307-338.
    12. Laroque, Guy & Salanie, Bernard, 1989. "Estimation of Multi-market Fix-Price Models: An Application of Pseudo Maximum Likelihood Methods," Econometrica, Econometric Society, vol. 57(4), pages 831-860, July.
    13. Mealli, Fabrizia & Rampichini, Carla, 1999. "Estimating binary multilevel models through indirect inference," Computational Statistics & Data Analysis, Elsevier, vol. 29(3), pages 313-324, January.
    14. James J. Heckman & Thomas E. Macurdy, 1980. "A Life Cycle Model of Female Labour Supply," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 47-74.
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    Cited by:

    1. Daniela Campus & Gianna Giannelli, 2016. "Is the Allocation of Time Gender Sensitive to Food Price Changes? An Investigation of Hours of Work in Uganda," Working Papers - Economics wp2016_16.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

    More about this item


    Tobit model; random effects; simulation based estimation; indirect estimation;

    JEL classification:

    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models


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