IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/22598.html
   My bibliography  Save this paper

Estimating variances and covariances in a censored regression model

Author

Listed:
  • Calzolari, Giorgio
  • Fiorentini, Gabriele

Abstract

When the coefficients of a Tobit model are estimated by maximum likelihood their covariance matrix is typically, even if not necessarily, associated with the algorithm employed to maximize the likelihood. Covariance estimators used in practice are derived by: (1) the Hessian (observed information), (2) the matrix of outer products of the first derivatives of the log-likelihood (OPG version), (3) the expected Hessian (estimated information), (4) a mixture of 1 and 2 (White's QML covariance matrix). Significant differences among these estirnates are are usually interpreted as an indication of misspecification. From our Monte Carlo study this seems not to be true, unless the sample size is really very large. Even in absence of misspecification, large differences are encountered in small samples, and the sign of the differences is almost systematic. This suggests that the choice of the covariance estimator is not neutral and the results of hypotheses testing may be strongly affected by such a choice.

Suggested Citation

  • Calzolari, Giorgio & Fiorentini, Gabriele, 1993. "Estimating variances and covariances in a censored regression model," MPRA Paper 22598, University Library of Munich, Germany, revised 1993.
    • Handle: RePEc:pra:mprapa:22598
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/22598/1/MPRA_paper_22598.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Lee, Lung-fei, 1994. "Rational expectations in limited dependent variable models," Economics Letters, Elsevier, vol. 46(2), pages 97-104, October.
    4. Edin, Per-Anders & Vredin, Anders, 1993. "Devaluation Risk in Target Zones: Evidence from the Nordic Countries," Economic Journal, Royal Economic Society, vol. 103(416), pages 161-175, January.
    5. Giorgio Calzolari & Gabriele Fiorentini, 1998. "A tobit model with garch errors," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 85-104.
    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. Giuseppe Bertola & Lars E. O. Svensson, 1993. "Stochastic Devaluation Risk and the Empirical Fit of Target-Zone Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 689-712.
    8. Calzolari, Giorgio & Fiorentini, Gabriele, 1993. "Alternative covariance estimators of the standard Tobit model," Economics Letters, Elsevier, vol. 42(1), pages 5-13.
    9. 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..
    10. 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.
    11. 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.
    12. Pesaran, M.H. & Samiei, H., 1990. "Estimating Limited-Dependent Rational Expectations Models," Papers 18, California Los Angeles - Applied Econometrics.
    13. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    14. Garcia, E.G., 1994. "A Devaluations Model for the EMS," Papers 9416, Centro de Estudios Monetarios Y Financieros-.
    15. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 63-84, Suppl. De.
    16. Hurd, Michael, 1979. "Estimation in truncated samples when there is heteroscedasticity," Journal of Econometrics, Elsevier, vol. 11(2-3), pages 247-258.
    17. 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.
    Full references (including those not matched with items on IDEAS)

    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. Giorgio Calzolari & Gabriele Fiorentini, 1998. "A tobit model with garch errors," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 85-104.
    2. Campos, M. Isabel & Herrera, Julio & Jimenez-Ridruejo, Zenon, 1999. "Censured Exchange Rates in a Discrete Time Target Zones Model: The Spanish Peseta/Deutsche Mark Case," ERSA conference papers ersa99pa183, European Regional Science Association.
    3. M. Hashem Pesaran & Francisco J. Ruge-Murcia, 1996. "Limited-dependent rational expectations models with jumps," Discussion Paper / Institute for Empirical Macroeconomics 111, Federal Reserve Bank of Minneapolis.
    4. M. Isabel Campos & Zenón Jiménez-Ridruejo, 2000. "Were The Peseta Exchange Rate Crises Forecastable During Target Zone Period?," Working Papers 00-07, Asociación Española de Economía y Finanzas Internacionales.
    5. Francisco J. Ruge-Murcia, 2000. "Uncovering financial markets' beliefs about inflation targets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 483-512.
    6. M. Isabel Campos & Zenon Jimenez-Ridruejo, 2003. "Were the peseta exchange rate crises forecastable during target zone period?," Applied Economics, Taylor & Francis Journals, vol. 35(9), pages 1087-1099.
    7. M. Isabel Campos & Zenón Jiménez-Ridruejo, "undated". "Were the Peseta Exchange Rate Crises Forecastable During Target Zone Period?," Working Papers on International Economics and Finance 00-07, FEDEA.
    8. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    9. 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.
    10. Broto, Carmen, 2006. "Using auxiliary residuals to detect conditional heteroscedasticity in inflation," DES - Working Papers. Statistics and Econometrics. WS ws060402, Universidad Carlos III de Madrid. Departamento de Estadística.
    11. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    12. Giorgio Calzolari, 2015. "Indirect estimation and econometrics exams: how to live a round life," Econometrics Working Papers Archive 2015_01, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    13. Sentana, Enrique & Calzolari, Giorgio & Fiorentini, Gabriele, 2008. "Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks," Journal of Econometrics, Elsevier, vol. 146(1), pages 10-25, September.
    14. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    15. Drew Creal & Siem Jan Koopman & André Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
    16. Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation of Conditionally Heteroskedastic Factor Models," Working Papers wp2004_0409, CEMFI.
    17. Lee, Lung-fei, 1999. "Estimation of dynamic and ARCH Tobit models," Journal of Econometrics, Elsevier, vol. 92(2), pages 355-390, October.
    18. 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.
    19. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    20. repec:rim:rimwps:40-07 is not listed on IDEAS
    21. Wocken, Meike & Kneib, Thomas, 2012. "Tobit regression to estimate impact of EU market intervention in dairy sector," 123rd Seminar, February 23-24, 2012, Dublin, Ireland 122528, European Association of Agricultural Economists.

    More about this item

    Keywords

    Tobit model; maximum likelihood; hessian matrix; outer products matrix; covariance estimators;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

    Statistics

    Access and download statistics

    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:pra:mprapa:22598. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.