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A tobit model with garch errors

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Author Info

  • Gabriele Fiorentini

    ()
    (Universidad de Alicante)

  • Giorgio Calzolari

    (University of Florence)

Abstract

In the context of time series regression, we extend the standard Tobitmodel to allow for the possibility of conditional heteroskedastic error processes of the GARCH type.We discuss the likelihood function of the Tobit model in the presence of conditionally heteroskedastic errors.Expressing the exact likelihood function turns out to be infeasible, and we propose anapproximation by treating the model as being conditionally Gaussian. The performance of theestimator is investigated by means of Monte Carlo simulations. We find that, when the errorterms follow a GARCH process, the proposed estimator considerably outperforms the standardTobit quasi maximum likelihood estimator. The efficency loss due to the approximationof the likelihood is finally evaluated.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1997-13.pdf
File Function: Fisrt version / Primera version, 1997
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 1997-13.

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Length: 19 pages
Date of creation: Apr 1997
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:1997-13

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Keywords: Censored regressions; conditional heteroskedasticity;

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References

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  1. Pesaran, M.H. & Samiei, H., 1990. "Estimating Limited-Dependent Rational Expectations Models," Papers 18, California Los Angeles - Applied Econometrics.
  2. Pesaran, M.H. & Samiei, H., 1993. "Limited-Dependaent Rational Expectations Models with Future Expectations," Cambridge Working Papers in Economics 9321, Faculty of Economics, University of Cambridge.
  3. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
  4. Garcia, E.G., 1994. "A Devaluations Model for the EMS," Papers 9416, Centro de Estudios Monetarios Y Financieros-.
  5. Pesaran, M. Hashem & Samiei, Hossein, 1992. "Estimating limited-dependent rational expectations models with an application to exchange rate determination in a target zone," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 141-163.
  6. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
  7. Edin, P.A. & Vredin, A., 1991. "Devaluation Risk in Target Zones: Evidence from the Nordic Countries," Papers 1991g, Uppsala - Working Paper Series.
  8. Arabmazar, Abbas & Schmidt, Peter, 1982. "An Investigation of the Robustness of the Tobit Estimator to Non-Normality," Econometrica, Econometric Society, vol. 50(4), pages 1055-63, July.
  9. Hurd, Michael, 1979. "Estimation in truncated samples when there is heteroscedasticity," Journal of Econometrics, Elsevier, vol. 11(2-3), pages 247-258.
  10. Bertola, Giuseppe & Svensson, Lars E O, 1993. "Stochastic Devaluation Risk and the Empirical Fit of Target-Zone Models," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 689-712, July.
  11. Pesaran, M.H. & Ruge-Murcia, F.J., 1995. "A Discrete-Time Version of Target Zone Models with Jumps," Cahiers de recherche 9530, Universite de Montreal, Departement de sciences economiques.
  12. Hashem Pesaran, M. & Ruge-Murcia, Francisco J., 1996. "Limited-dependent rational expectations models with stochastic thresholds," Economics Letters, Elsevier, vol. 51(3), pages 267-276, June.
  13. Pesaran, M.H. & Samiei, H., 1991. "An Analysis of the determination of Dutsche Mark/French Franc Exchange rate in a Discrete-Time Target-Zone Model," Papers 38, California Los Angeles - Applied Econometrics.
  14. Arabmazar, Abbas & Schmidt, Peter, 1981. "Further evidence on the robustness of the Tobit estimator to heteroskedasticity," Journal of Econometrics, Elsevier, vol. 17(2), pages 253-258, November.
  15. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
  16. Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
  17. Calzolari, Giorgio, 2012. "Econometric notes," MPRA Paper 36765, University Library of Munich, Germany.
  18. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  19. Calzolari, Giorgio & Fiorentini, Gabriele, 1993. "Alternative covariance estimators of the standard Tobit model," Economics Letters, Elsevier, vol. 42(1), pages 5-13.
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Cited by:
  1. Juan José Echavarría & Luis Fernando Melo Velandia & Santiago Téllez & Mauricio Villamizar, 2013. "The Impact of Pre-announced Day-to-day Interventions on the Colombian Exchange Rate," BORRADORES DE ECONOMIA 010767, BANCO DE LA REPÚBLICA.
  2. Wei, Steven X., 2002. "A censored-GARCH model of asset returns with price limits," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 197-223, March.
  3. Hsieh, Ping-Hung & Yang, J. Jimmy, 2009. "A censored stochastic volatility approach to the estimation of price limit moves," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 337-351, March.
  4. Chen, Ho-Chyuan & Chang, Kuang-Liang & Yu, Shih-Ti, 2012. "Application of the Tobit model with autoregressive conditional heteroscedasticity for foreign exchange market interventions," Japan and the World Economy, Elsevier, vol. 24(4), pages 274-282.
  5. GIOT, Pierre & LAURENT, Sébastien & PETITJEAN, Mikael, . "Trading activity, realized volatility and jumps," CORE Discussion Papers RP -2223, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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