Abstract
Two convenient classifications for variables which are not amenable to treatment by the principal tool of econometrics, regression analysis, are quantal responses and limited responses. In the quantal response (all or nothing) category are dichotomous, qualitative and categorical outcomes, and the methods of analysis identified as probit and logit are appropriate for these variables. Illustrative applications include decisions to own or rent, choice of travel mode, and choice of professions. The limited response category covers variables which take on mixtures of discrete and continuous outcomes, and the prototypical model and analysis technique is identified as tobit. Examples are samples with both zero and positive expenditures on durable goods, and models of markets with price ceilings including data with both limit and non-limit prices. While the tobit model evolved out of the probit model and the limited and quantal response methods share many properties and characteristics, they are sufficiently different to make separate treatment more convenient.
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Bibliography
Amemiya, T. 1973. Regression analysis when the dependent variable is truncated normal. Econometrica 41, 997–1016.
Amemiya, T. 1981. Qualitative response models: a survey. Journal of Economic Literature 19, 1483–536.
Amemiya, T. 1984. Tobit models: a survey. Journal of Econometrics 24, 3–61.
Arabmazar, A. and Schmidt, P. 1981. Further evidence on the robustness of the Tobit estimator to heteroscedasticity. Journal of Econometrics 17, 253–8.
Berkson, J. 1944. Application of the logistic function to bio-assay. Journal of the American Statistical Association 39, 357–65.
Berkson, J. 1949. Maximum likelihood and minimum chi-square estimates of the logistic function. Journal of the American Statistical Association 44, 273–8.
Bishop, Y., Fienberg, S. and Holland, P. 1975. Discrete Multivariate Analysis. Cambridge, Mass.: MIT Press.
Bliss, C. 1934. The method of probits. Science 79, 38–9.
Cosslett, S. 1983. Distribution-free maximum likelihood estimator of the binary choice model. Econometrica 51, 765–82.
Farrell, M. 1954. The demand for motor cars in the United States. Journal of the Royal Statistical Society, Series A117, 171–93.
Fechner, G. 1860. Elemente der Psychophysik. Leipzig: Breitkopf & Härtel.
Finney, D. 1947. Probit Analysis. Cambridge: Cambridge University Press.
Gaddum, J. 1933. Reports on biological standards III. Methods of biological assay depending on a quantal response. Special Report Series Medical Research Council No. 183, London.
Goldberger, A. 1964. Economic Theory. New York: Wiley.
Goldberger, A. 1983. Abnormal selection bias. In Studies in Econometrics: Time Series and Multivariate Statistics, ed. S. Karlin, T. Amemiya and L.A. Goodman, New York: Academic Press.
Hausman, J. and Wise, D. 1977. Social experimentation, truncated distributions and efficient estimation. Econometrica 45, 319–39.
Heckman, J. 1974. Shadow prices, market wages, and labor supply. Econometrica 42, 679–93.
Hurd, M. 1979. Estimation in truncated samples when there is heteroscedasticity. Journal of Econometrics 11, 247–58.
Lee, L.F. 1981. Simultaneous equations models with discrete and censored variables. In Structural Analysis of Discrete Data with Econometric Applications, ed. C. Manski and D. McFadden, Cambridge, Mass.: Harvard University Press.
Luce, R. 1959. Individiaul Choice Behavior: a Theoretical Analysis. New York: Wiley.
McFadden, D. 1974. Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics, ed. P. Zarembka, New York: Academic Press.
McFadden, D. 1981. Econometric models of probabilistic choice. In Structural Analysis of Discrete Data with Econometric Applications, ed. C. Manski and D. McFadden, Cambridge, Mass.: Harvard University Press.
McKelvey, R. and Zavoina, W. 1975. A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology 4, 103–120.
Maddala, G.S. 1983. Limited Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press.
Manski, C. 1975. Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3, 205–28.
Marschak, J. 1960. Binary-choice constraints and random utility indicators. In Mathematical Methods in the Social Sciences, ed. K. Arrow, S. Karlin and P. Suppes, Stanford: University Press.
Nelson, F. 1981. A test for misspecification in the censored-normal model. Econometrica 49, 1317–29.
Olsen, R. 1978. A note on the uniqueness of the maximum likelihood estimator for the Tobit model. Econometrica 46, 1211–15.
Powell, J. 1984. Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25, 303–25.
Quandt, R. 1982. Econometric disequilibrium models. Econometric Review 1, 1–63.
Robinson, P. 1982. On the asymptotic properties of estimators of models containing limited dependent variables. Econometrica 50, 27–41.
Rosett, R. 1959. A statistical model of friction in economics. Econometrica 27, 263–7.
Rosett, R. and Nelson, F.D. 1975. Estimation of a two-limit probit regression model. Econometrica 43, 141–6.
Theil, H. 1969. A multinomial extension of the linear logit model. International Economic Review 10, 251–9.
Thurstone, L. 1927. A law of comparative judgement. Psychological Review 34, 273–86.
Tobin, J. 1955. The application of the multivariate probit analysis to economic survey data. Cowles Foundation Discussion Paper No. 1, New Haven.
Tobin, J. 1958. Estimation of relationships for limited dependent variables. Econometrica 26, 24–36.
Urban, F. 1909. Die Psychophysichen Massmethoden als Grundlagen Empirischer Messungen. Archiv für die Gesammte Psychologie 15, 261–355.
Zellner, A. and Lee, T. 1965. Joint estimation of relationships involving discrete random variables. Econometrica 33, 383–94.
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Nelson, F.D. (1990). Logit, Probit and Tobit. In: Eatwell, J., Milgate, M., Newman, P. (eds) Econometrics. The New Palgrave. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-20570-7_19
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DOI: https://doi.org/10.1007/978-1-349-20570-7_19
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