ARTICLE
ABSTRACT
The estimation of parameters of the tobit type models, that is models for a censored dependent variable, by the MLE method requires an assumption of the normal distribution of disturbances. Semiparametric methods are very useful, because allow to weaken these assumptions. In the paper, at first the tobit type I, II and III models are introduced, next some known in the literature semi-parametric methods for these models are presented. At the end of the paper there is shown the usefulness of semi-parametric methods to a verification of assumptions imposed on the distribution of disturbances.
REFERENCES
[1] Amemiya T. (1984), Tobit Models: A survey, Journal of Econometrics, vol. 24, s. 3-61.
[2] Andrews D., Schafgans M. (1998), Semiparametric Estimation of a Sample Selection Model, Review of Economic Studies, vol. 65, nr 224, s. 497-518.
[3] Bloomfield P., Steiger W.L. (1983), Least Absolute Deviations: Theory, Applications, and Algorithms, Progress in Probability and Statistics, vol. 6, Birkh¨auser Boston, Boston, Mass, USA.
[4] Chay K.Y., Honor´e B.E. (1998), Estimation of Semiparametric Regression Models, Journal of Human Resources, vol. 33, nr 1, s. 4-38.
[5] Chay K.Y., Powell J.L. (2001), Semiparametric Censored Regression Models, Journal of Economic Perspectives, vol. 15, nr 4, s. 29-42.
[6] Chen S. (1997), Semiparametric Estimation of the Type-3 Tobit Model, Journal of Econometrics, vol. 80, s. 1-34
[7] Chesher A., Irish M. (1987), Residual Analysis on the Grouped and Censored Normal Linear Model, Journal of Econometrics, vol. 34, s. 33-61.
[8] Gallant R., Nychka G. (1987), Semi-Nonparametric Maximum Likelihood Estimatnion, Econometrica, vol. 55, s. 363-390.
[9] Gruszczyński M. (2002), Modele i prognozy zmiennych jakościowych w finansach i bankowości, wyd. 2, Monografie i Opracowania 490, Oficyna Wydawnicza SGH, Warszawa.
[10] Hausman J.A. (1978), Specification Tests in Econometrics, Ecoonmetrica, vol. 46, s. 1251-1272.
[11] Heckman J. (1976), The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models, Annals of Economic and Social Measurement, nr 5/4, 1976, s. 475-492.
[12] Heckman J. (1979), Sample Selection Bias as a Specification Error, Econometrica, vol. 47, nr 1, s. 153-161.
[13] Heckman J. (1990), Varieties of Selection Bias, American Economic Review, 80, s. 313-318.
[14] Heckman J. (2003), Microdata, Heterogeneity and the Evaluation of Public Policy [w:] Nobel Lectures in Economic Sciences 1996 – 2000, T. Persson (ed.), World Scientific Publishing Co., Singapore, s. 255-322.
[15] Honor´e B.E., Kyriazidou E., Udry C. (1997), Estimation of Type 3 Tobit Models Using Symmetric Trimming and Pairwise Comperisions, Journal of Econometrics, vol. 76, s. 107-128.
[16] Honor´e B.E., Powell J.L. (1994), Pairwise Difference Estimators of Censored and Truncated Regression Models, Journal of Econometrics, vol. 64, nr 1–2, s. 241-278.
[17] Horowitz J.L., Neumann G.R. (1989), Specification Testing in Censored Regression Models: Parametric and Semiparametric Methods, Journal of Applied Econometrics, vol. 4, s. S61-S86.
[18] Johnston J. i DiNardo J. (1997), Econometric Methods, McGraw-Hill Companies, Inc., New York.
[19] Klein R.W., Spady R.H. (1993), An Efficient Semiparametric Estimator of Binary Response Models, Econometrica, vol. 61, nr 2, s. 387-421.
[20] Kostrzewska J. (2003), Model tobitowy jako szczególny przypadek cenzurowanego modelu regresji [w:] Przestrzenno-czasowe modelowanie i prognozowanie zjawisk gospodarczych, red. A. Zeliaś, Wyd. AE w Krakowie, Kraków, s. 397-404.
[21] Kostrzewska J. (2008), Zastosowanie wybranych modeli tobitowych do opisu tygodniowej liczby godzin pracy [w:] Taksonomia 15. Klasyfikacja i analiza danych – teoria i zastosowania, pod red. K. Jajugi i M. Walesiaka, Wyd. AE we Wrocławiu, Wrocław.
[22] Kostrzewska J. (2009), Truncated and Censored Dependent Variables and Their Models, referat wygłoszony na 15th Polish-Slovak-Ukrainian Scientific Seminar “Statistical Analysis of Socio-Economic Consequences of Transition Processes in Central-East European Countries”, Kraków, 21–24 października 2008 r.
[23] Kostrzewska J. (2011), Analiza porównawcza tygodniowego czasu pracy zamężnych kobiet pracujących na własny rachunek lub najemnie, [w:] Osiągnięcia i perspektywy modelowania i prognozowania zjawisk społeczno-gospodarczych, pod red. B. Pawełek, Wyd. UEK, Kraków, w druku.
[24] Kostrzewska J. (2011), Interpretacja w modelach tobitowych, Przegląd Statystyczny, tom 58, z. 3-4, s. 256-280.
[25] Lanot G., Walker I. (1998), The union/non-union wage differential: An application of semiparametric methods, Journal of Econometrics, vol. 84, nr 2, s. 327-349.
[26] Lee L.-F. (1994), Semiparametric Two-Stage Estimation of Sample-Selection Models Subject to Tobit-Type Selection Rules, Journal of Econometrics, vol. 61, s. 305-344.
[27] Maddala G.S. (1994), Limited-Dependent and Qualitative Variables in Econometrics, Cambridge University Press, Cambridge.
[28] Maddala G.S. (2006), Ekonometria, Wyd. Nauk. PWN, Warszawa.
[29] Manski C.F. (1989), Anatomy of the Selection Problem, The Journal of Human Resources, vol. 24, nr 3, s. 343-360.
[30] Martins M.F. (2001), Parametric and Semiparametric Estimation of Sample Selection Models: An Empirical Application to the Female Labour Force in Portugal, Journal of Applied Econometrics, vol. 16, nr 1, s. 23-39.
[31] Melenberg B., van Soest A. (1996), Parametric and Semi-Parametric Modelling on Vacation Expenditures, Journal of Applied Econometrics, vol. 11, s. 59-76.
[32] Nelson F.D. (1981), A Test for Misspecification in the Censored Normal Model, Econometrica, vol. 49, s. 1317-1329.
[33] Newey W.K. (1987), Specification Tests for Distributional Assumption in the Tobit Model, Journal of Econometrics, vol. 34, s. 125-145.
[34] Newey W.K. (1991), Efficient Estimation of Tobit Models under Conditional Symmetry [w:] Nonparametric and Semiparametric Estimation Methods in Econometrics and Statistics, pod red. W.A. Barnetta, J. Powella, G.E. Tauchena, Cambridge University Press, Cambridge.
[35] Newey W.K., Powell J.L., Walker J.R. (1990), Semiparametric Estimation of Selection Models: Some Empirical Results, The American Economic Review, vol.80, nr 2, s. 324-328.
[36] Pagan A.R., Ullah A. (1999), Nonparametric Econometrics, Cambridge University Press, Cambridge.
[37] Pagan A.R., Vella F. (1989), Diagnostic Tests for Models Based on Individual Data: A Survey, Journal of Applied Econometrics, vol. 4, s. S29-S59.
[38] Powell J.L. (1984), Least Absolute Deviations Estimation for the Censored Regression Model, Journal of Econometrics, vol. 25, nr 3, s. 303-325.
[39] Powell J.L. (1986), Censored Regression Quantiles, Journal of Econometrics, vol. 32, s. 143-155.
[40] Powell J.L. (1986), Symmetrically Trimmed Least Squares Estimation for Tobit Models, Econometrica, vol. 54, nr 6, s. 1435-1460.
[41] Powell J.L. (1994), Estimation of Semiparametric Models [w:] Handbook of Econometrics, vol. IV, red. R.F. Engle, D.L. McFadden, Elsevier Science Publishers B.V., s. 2444-2514.
[42] Powell J.L., Stock J.H., Stoker T.M. (1989), Semiparametric Estimation of Index Coefficients, Econometrica, vol. 57, nr 6, s. 1403-1430.
[43] Robinson P.M. (1987), Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form, Econometrica, vol. 55, s. 875-891.
[44] Schafgans M. (2004), Finite Sample Properties for the Semiparametric Estimation of the Intercept of a Censored Regression Model, Statistica Neerlandica, vol. 58, nr. 1, s. 35-56.
[45] Tobin J. (1958), Estimation of Relationships for Limited Dependent Variables, Econometrica, vol. 26, s. 24-36.
[46] Vella F. (1998), Estimating Models with Sample Selection Bias: A Survey, Journal of Human Resources, vol. 33, nr 1, s. 127-169.
[47] Verbeek M. (2001), A Guide to Modern Econometrics, John Wiley & Sons, Chichester.
