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A tobit model with garch errors

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  • Giorgio Calzolari
  • Gabriele Fiorentini

Abstract

In the context of time series regression, we extend the standard Tobit model 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 an approximation by treating the model as being conditionally Gaussian. The performance of the estimator is investigated by means of Monte Carlo simulations. We find that, when the error terms follow a GARCH process, the proposed estimator considerably outperforms the standard Tobit quasi maximum likelihood estimator. The efficiency loss due to the approximation of the likelihood is finally evaluated.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 17 (1998)
Issue (Month): 1 ()
Pages: 85-104

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Handle: RePEc:taf:emetrv:v:17:y:1998:i:1:p:85-104

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Related research

Keywords: censored regressions; conditional heteroskedasticity; Monte Carlo simulations;

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References

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  1. Calzolari, Giorgio & Fiorentini, Gabriele, 1993. "Alternative covariance estimators of the standard Tobit model," Economics Letters, Elsevier, vol. 42(1), pages 5-13.
  2. Edin, P.A. & Vredin, A., 1991. "Devaluation Risk in Target Zones: Evidence from the Nordic Countries," Papers 1991g, Uppsala - Working Paper Series.
  3. 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.
  4. Pesaran, M.H. & Samiei, H., 1990. "Estimating Limited-Dependent Rational Expectations Models," Papers 18, California Los Angeles - Applied Econometrics.
  5. 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.
  6. Pesaran, M. Hashem & Samiei, Hossein, 1995. "Limited-dependent rational expectations models with future expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 19(8), pages 1325-1353, November.
  7. Pesaran, H.M. & Ruge-Murcia, F.J., 1995. "A Discrete-Time Version of Target Zone Models with Jumps," Cambridge Working Papers in Economics 9513, Faculty of Economics, University of Cambridge.
  8. 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.
  9. 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.
  10. Hurd, Michael, 1979. "Estimation in truncated samples when there is heteroscedasticity," Journal of Econometrics, Elsevier, vol. 11(2-3), pages 247-258.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Calzolari, Giorgio, 2012. "Econometric notes," MPRA Paper 36765, University Library of Munich, Germany.
  16. Garcia, E.G., 1994. "A Devaluations Model for the EMS," Papers 9416, Centro de Estudios Monetarios Y Financieros-.
  17. 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.
  18. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
  19. 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..
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. 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).
  5. 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.

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