The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Logit, Probit and Tobit

  • Forrest D. Nelson
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1230

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

  1. Amemiya, T. 1973. Regression analysis when the dependent variable is truncated normal. Econometrica 41: 997–1016.CrossRefGoogle Scholar
  2. Amemiya, T. 1981. Qualitative response models: A survey. Journal of Economic Literature 19: 1483–1536.Google Scholar
  3. Amemiya, T. 1984. Tobit models: A survey. Journal of Econometrics 24: 3–61.CrossRefGoogle Scholar
  4. Arabmazar, A., and P. Schmidt. 1981. Further evidence on the robustness of the Tobit estimator to heteroscedasticity. Journal of Econometrics 17: 253–258.CrossRefGoogle Scholar
  5. Berkson, J. 1944. Application of the logistic function to bio-assay. Journal of the American Statistical Association 39: 357–365.Google Scholar
  6. Berkson, J. 1949. Maximum likelihood and minimum chi-square estimates of the logistic function. Journal of the American Statistical Association 44: 273–278.Google Scholar
  7. Bishop, Y., S. Fienberg, and P. Holland. 1975. Discrete multivariate analysis. Cambridge, MA: MIT Press.Google Scholar
  8. Bliss, C. 1934. The method of probits. Science 79: 38–39.CrossRefGoogle Scholar
  9. Cosslett, S. 1983. Distribution-free maximum likelihood estimator of the binary choice model. Econometrica 51: 765–782.CrossRefGoogle Scholar
  10. Farrell, M. 1954. The demand for motor cars in the United States. Journal of the Royal Statistical Society, Series A 117: 171–193.CrossRefGoogle Scholar
  11. Fechner, G. 1860. Elemente der Psychophysik. Leipzig: Breitkopf & Härtel.Google Scholar
  12. Finney, D. 1947. Probit analysis. Cambridge: Cambridge University Press.Google Scholar
  13. Gaddum, J. 1933. Reports on biological standards III. Methods of biological assay depending on a quantal response, Special report series medical research council, vol. 183. London: H.M. Stationery Office.Google Scholar
  14. Goldberger, A. 1964. Econometric theory. New York: Wiley.Google Scholar
  15. 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.Google Scholar
  16. Hausman, J., and D. Wise. 1977. Social experimentation, truncated distributions and efficient estimation. Econometrica 45: 319–339.Google Scholar
  17. Heckman, J. 1974. Shadow prices, market wages, and labor supply. Econometrica 42: 679–693.CrossRefGoogle Scholar
  18. Hurd, M. 1979. Estimation in truncated samples when there is heteroscedasticity. Journal of Econometrics 11: 247–258.CrossRefGoogle Scholar
  19. 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, MA: Harvard University Press.Google Scholar
  20. Luce, R. 1959. Individual choice behavior: A theoretical analysis. New York: Wiley.Google Scholar
  21. McFadden, D. 1974. Conditional logit analysis of qualitative choice behavior. In Frontiers in econometrics, ed. P. Zarembka. New York: Academic.Google Scholar
  22. McFadden, D. 1981. Econometric models of probabilistic choice. In Structural analysis of discrete data with econometric applications, ed. C. Manski and D. McFadden. Cambridge, MA: Harvard University Press.Google Scholar
  23. McKelvey, R., and W. Zavoina. 1975. A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology 4: 103–120.CrossRefGoogle Scholar
  24. Maddala, G.S. 1983. Limited dependent and qualitative variables in econometrics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  25. Manski, C. 1975. Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3: 205–228.CrossRefGoogle Scholar
  26. 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: Stanford University Press.Google Scholar
  27. Nelson, F. 1981. A test for misspecification in the censored-normal model. Econometrica 49: 1317–1329.CrossRefGoogle Scholar
  28. Olsen, R. 1978. A note on the uniqueness of the maximum likelihood estimator for the Tobit model. Econometrica 46: 1211–1215.CrossRefGoogle Scholar
  29. Powell, J. 1984. Least absolute deviations estimation for the censored regression model. Journal of Econometrics 25: 303–325.CrossRefGoogle Scholar
  30. Quandt, R. 1982. Econometric disequilibrium models. Econometric Reviews 1: 1–63.CrossRefGoogle Scholar
  31. Robinson, P. 1982. On the asymptotic properties of estimators of models containing limited dependent variables. Econometrica 50: 27–41.CrossRefGoogle Scholar
  32. Rosett, R. 1959. A statistical model of friction in economics. Econometrica 27: 263–267.CrossRefGoogle Scholar
  33. Rosett, R., and F.D. Nelson. 1975. Estimation of a two-limit probit regression model. Econometrica 43: 141–146.CrossRefGoogle Scholar
  34. Theil, H. 1969. A multinomial extension of the linear logit model. International Economic Review 10: 251–259.CrossRefGoogle Scholar
  35. Thurstone, L. 1927. A law of comparative judgement. Psychological Review 34: 273–286.CrossRefGoogle Scholar
  36. Tobin, J. 1955. The application of the multivariate probit analysis to economic survey data, Cowles foundation discussion paper, No. 1. New Haven.Google Scholar
  37. Tobin, J. 1958. Estimation of relationships for limited dependent variables. Econometrica 26: 24–36.CrossRefGoogle Scholar
  38. Urban, F. 1909. Die Psychophysichen Massmethoden als Grundlagen Empirischer Messungen. Archiv für die Gesammte Psychologie 15: 261–355.Google Scholar
  39. Zellner, A., and T. Lee. 1965. Joint estimation of relationships involving discrete random variables. Econometrica 33: 383–394.Google Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Forrest D. Nelson
    • 1
  1. 1.