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The Analysis of Models with Qualitative or Censored Dependent Variables

  • Thomas B. Fomby
  • Stanley R. Johnson
  • R. Carter Hill

Abstract

Traditionally economists have dealt with models designed to explain the variation in a dependent variable which could be assumed continuous and normally distributed. Economics, however, as a theory of choice, can be applied not only to questions about how much to produce or consume but also“whether” to produce or consume a certain item. More generally, individual economic units often must choose between a finite set of alternatives. Economists are interested in what factors are considered by the decision making unit and in quantifying their individual effects. Some examples of situations where such choices arise are:
  1. (i)

    a household must decide whether to buy or rent a suitable dwelling;

     
  2. (ii)

    a Senator must decide on whether to vote yes or no on a particular piece of legislation;

     
  3. (iii)

    a consumer must choose which of perhaps several shopping areas to visit and a mode of transportation;

     
  4. (iv)

    members of a household must decide whether to take part-time or fulltime employment, or whether or not to seek a second job; and

     
  5. (v)

    a person must decide whether or not to attend college.

     

Keywords

Logit Model Maximum Likelihood Estimator Probit Model Tobit Model Linear Probability Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Akin, J. S., Guilkey, D. R., and Sickles, R. (1979). A random coefficient probit model with an application to a study of migration. Journal of Econometrics, 11, 233–246.CrossRefGoogle Scholar
  2. Albright, R. L., Lerman, S. R., and Manski, C. F. (1977). Report on the development of an estimation program for the multinomial probit model. Prepared for the Federal Highway Administration.Google Scholar
  3. Amemiya, T. (1973). Regression analysis when the dependent variable is truncated normal. Econometrica, 42, 999–1012.CrossRefGoogle Scholar
  4. Amemiya, T. (1975). Qualitative response models. Annals of Economic and Social Measurement, 4, 363–372.Google Scholar
  5. Amemiya, T. (1978a). On a two-step estimator of a multivariate logit model. Journal of Econometrics, 8, 13–21.CrossRefGoogle Scholar
  6. Amemiya, T. (1978b). The estimation of a simultaneous equation generalized probit model. Econometrica, 46, 1193–1206.CrossRefGoogle Scholar
  7. Amemiya, T. (1979). The estimation of a simultaneous-equation tobit model. International Economic Review, 20, 169–182.CrossRefGoogle Scholar
  8. Amemiya, T. (1981). Qualitative response models: a survey. Journal of Economic Literature, 19, 1483–1536.Google Scholar
  9. Amemiya, T. and Powell, J. L. (1980). A comparison of the logit model and normal discriminant analysis when independent variables are binary. Technical Report No. 320, Institute for Mathematical Studies in the Social Sciences, Stanford Univ., Stanford, CA.Google Scholar
  10. Ashford, J. R. and Sowden, R. R. (1970). Multivariate probit analysis. Biometrics, 26, 535–456.CrossRefGoogle Scholar
  11. Daganzo, C. (1979). Multinomial Probit. New York: Academic Press.Google Scholar
  12. Dhrymes, P. J. (1978). Introductory Econometrics, New York: Springer-Verlag.CrossRefGoogle Scholar
  13. Domencich, T. and McFadden, D. (1975). Urban Travel Demand: A Behavioral Analysis. Amsterdam: North-Holland.Google Scholar
  14. Goldberger, A. S. (1981). Linear regression after selection. Journal of Econometrics, 15, 357–366.CrossRefGoogle Scholar
  15. Gourieroux, C, Laffont, J. J., and Monfort, A. (1980). Coherancy conditions in simultaneous linear equation models with endogenous switching regimes. Econometrica, 48, 675–695.CrossRefGoogle Scholar
  16. Gourieroux, C. and Monfort, A. (1981). Asymptotic properties of the maximum likelihood estimator in dichotomous logit models. Journal of Econometrics, 17, 83–98.CrossRefGoogle Scholar
  17. Greene, W. H. (1981a). On the asymptotic bias of the ordinary least squares estimator of the tobit model. Econometrica, 49, 505–514.CrossRefGoogle Scholar
  18. Greene, W. H. (1981b). Sample selection bias as a specification error. Econometrica, 49, 795–798.CrossRefGoogle Scholar
  19. Guilkey, D. K. and Schmidt, P. (1979). Some small sample properties of estimators and test statistics in the multivariate logit model. Journal of Econometrics, 10, 33–42.CrossRefGoogle Scholar
  20. Hauser, J. R. (1977). Testing the accuracy, usefulness and significance of probabilistic choice models: an information theoretic approach. Operations Research, 26, 406–421.CrossRefGoogle Scholar
  21. Hausman, J. A. and Wise, D. A. (1978). A conditional probit model for qualitative choice: discrete decisions recognizing interdependence and heterogeneous preferences. Econometrica, 46, 403–426.CrossRefGoogle Scholar
  22. Heckman, J. (1974). Shadow prices, market wages, and labor supply. Econometrica, 42, 679–694.CrossRefGoogle Scholar
  23. 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, 5, 475–492.Google Scholar
  24. Heckman, J. (1978). Dummy endogenous variables in a simultaneous equation system. Econometrica, 47, 153–161.CrossRefGoogle Scholar
  25. Heckman, J. (1979). Sample bias as specification error. Econometrica, 47, 153–162.CrossRefGoogle Scholar
  26. Hurd, M. (1979). Estimation in truncated samples when there is heteroscedasticity. Journal of Econometrics, 11, 247–258.CrossRefGoogle Scholar
  27. Judge, G. G., Griffiths, W. E., Hill, R. C, Lee, T. C. (1980). The Theory and Practice of Econometrics. New York: Wiley.Google Scholar
  28. Kahn, L. M. and Morimune, K. (1979). Unions and employment stability: a sequential logit approach. International Economic Review, 20, 217–235.CrossRefGoogle Scholar
  29. Kenny, L. W., Lee, L. F., Maddala, G. S., and Trost, R. P. (1979). Returns to college education: an investigation of self-selection bias based on project talent data. International Economic Review, 20, 775–790.CrossRefGoogle Scholar
  30. Lee, L. F. (1978a). Unionism and wage rates: a simultaneous equations model with qualitative and limited dependent variables. International Economic Review, 19, 415–434.CrossRefGoogle Scholar
  31. Lee, L. F. (1978b). On the estimation of probit choice model with censored dependent variables and Amemiya’s principle. Discussion Paper 78-99, Center For Economic Research, University of Minnesota, Minneapolis.Google Scholar
  32. Lee, L. F. (1979). Identification and estimation in binary choice models with limited (censored) dependent variables. Econometrica, 47, 977–996.CrossRefGoogle Scholar
  33. Lee, L. F. (1981). Fully recursive probability models and multivariate log-linear probability models for the analysis of qualitative data. Journal of Econometrics, 16, 51–70.CrossRefGoogle Scholar
  34. Lee, L. F. and Trost, R. P. (1978). Estimation of some limited dependent variable models with application to housing demand. Journal of Econometrics, 8, 357–382.CrossRefGoogle Scholar
  35. Lee, L. F., Maddala, G. S., and Trost, R. P. (1980). Asymptotic covariance matrices of two-stage probit and two-stage tobit methods for simultaneous equations models with selectivity. Econometrica, 48, 491–503.CrossRefGoogle Scholar
  36. Maddala, G. S. (1977). Econometrics. New York: McGraw-Hill.Google Scholar
  37. Maddala, G. S. (1983). Limited-Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press.Google Scholar
  38. Maddala, G. S. and Trost, R. S. (1981). Alternative formulations of the Nerlove-Press models. Journal of Econometrics, 16, 35–50.CrossRefGoogle Scholar
  39. Manski, C. F. and McFadden, D. (1981). Structural Analysis of Discrete Data with Econometric Applications. Cambridge: The MIT Press.Google Scholar
  40. McDonald, J. F. and Moffitt, R. A. (1980). The uses of tobit analysis. Review of Econo-mics and Statistics, 62, 318–321.CrossRefGoogle Scholar
  41. McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics. Edited by P. Zarembka. New York: Academic Press.Google Scholar
  42. McFadden, D. (1976a). Quantal choice analysis: a survey. Annals of Economic and Social Measurement, 5, 363–390.Google Scholar
  43. McFadden, D. (1976b). A comment on discriminant analysis “versus” logit analysis. Annals of Economic and Social Measurement, 5, 511–523.Google Scholar
  44. McFadden (1977). Quantitative methods for analyzing travel behavior of individuals: some recent developments. Co wies Foundation Discussion Paper No. 474, New Haven.Google Scholar
  45. McFadden (1978). Modelling the choice of residential location. In Spatial Interaction Theory and Residential Location. Edited by A. Karlquist, L. Lundquist, F. Snickars, and J. Weibull. North Holland, Amsterdam. Pp. 75–96.Google Scholar
  46. McKelvey, R. D. and Zavonia, W. (1975). A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology, 4, 103–120.CrossRefGoogle Scholar
  47. Morimune, K. (1979). Comparisons of normal and logistic models in the bivariate dichotomous analysis. Econometrica, 47, 957–975.CrossRefGoogle Scholar
  48. Nelson, F. and Olson, L. (1978). Spécification and estimation of a simultaneous-equation model with limited dependent variables. International Economic Review, 19, 695–710.CrossRefGoogle Scholar
  49. Nerlove, M. and Press, S. J. (1973). Univariate and multivariate log-linear and logistic models. Rand Corporation, R-1306-EDA/NIH, Santa Monica, CA.Google Scholar
  50. Nelson, F. D. (1981). A test for misspecification in the censored normal model. Econo-metrica, 49, 1317–1330.Google Scholar
  51. Olson, R. J. (1980a). Approximating a truncated regression with the method of moments. Econometrica, 48, 1099–1106.CrossRefGoogle Scholar
  52. Olson, R. J. (1980b). A least squares correction for selectivity bias. Econometrica, 48, 1815–1820.CrossRefGoogle Scholar
  53. Pindyck, R. S. and Rubinfield, D. L. (1976). Econometric Models and Economic Fore-casts. New York: McGraw-Hill.Google Scholar
  54. Poirier, D. J. and Ruud, P. A. (1981). On the appropriateness of endogenous switching. Journal of Econometrics, 16, 249–256.CrossRefGoogle Scholar
  55. Press, S. J. and Wilson, S. (1978). Choosing between logistic regression and discriminant analysis. Journal of the American Statistical Association, 73, 699–705.CrossRefGoogle Scholar
  56. Schmidt, P. (1978). Estimation of a simultaneous equations model with jointly dependent continuous and qualitative variables: the union-earnings question revisited. International Economic Review, 19, 453–466.CrossRefGoogle Scholar
  57. Schmidt, P. and Strauss, R. P. (1975a). Estimation of models with jointly dependent qualitative variables: a simultaneous logit approach. Econometrica, 43, 745–756.CrossRefGoogle Scholar
  58. Schmidt, P. and Strauss, R. P. (1975b). The prediction of occupation using multiple logit models. International Economic Review, 16, 471–486.CrossRefGoogle Scholar
  59. Tobin, J. (1958). Estimation of relationships for limited dependent variables. Econo-metrica, 26, 24–36.Google Scholar
  60. Wales, T. J. and Woodland, A. D. (1980). Sample selectivity and estimation of labor supply functions. International Economic Review, 21, 437–468.CrossRefGoogle Scholar
  61. Westin, R. B. (1974). Predictions from binary choice models. Journal of Econometrics, 2, 1–16.CrossRefGoogle Scholar
  62. Zellner, A. and Lee, T. H. (1965). Joint estimation of relationships involving discrete random variables. Econometrica, 33, 382–394.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Thomas B. Fomby
    • 1
  • Stanley R. Johnson
    • 2
  • R. Carter Hill
    • 3
  1. 1.Department of EconomicsSouthern Methodist UniversityDallasUSA
  2. 2.The Center for Agricultural and Rural DevelopmentIowa State UniversityAmesUSA
  3. 3.Department of EconomicsLouisiana State UniversityBaton RougeUSA

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