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Nonlinear Latent Variable Models

  • Cheng Hsiao
Part of the Advanced Studies in Theoretical and Applied Econometrics book series (ASTA, volume 33)

Abstract

Models containing unobservable variables arise very often in economics, psychology, and other social sciences.1 They may arise because of measurement errors, or because behavioural responses are in part determined by unobservable characteristics of agents (e.g.,Chamberlain and Griliches [1975], Griliches [1974], [1977], [1979], Heckman [1981a, b], Robinson and Ferrara [1977], Train et al. [1987]). They may arise because the theoretical construction of the model depends on conceptual variables that are unobservable. The Friedman [1957] permanent income hypothesis, the Muth [1961] rational expectation hypothesis, and the hedonic approach towards consumer choice and the construction of price indexes (e.g., Court [1941], Gorman [1980], Griliches [1971], Lancaster [1966], Rosen [1974] and Tinbergen [1959]) are some of the examples.

Keywords

Instrumental Variable American Statistical Association Consistent Estimator Latent Variable Model Simultaneous Equation 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. Aigner, D.J., C. Hsiao, A. Kapteyn and T. Wansbeek [ 1984 ]: Latent Variable Models in Econometrics, in Handbook of Econometrics II, ed. by Z. Griliches and M.D. Intriligator, Amsterdam: North-Holland, 1322–1393.Google Scholar
  2. Amemiya, T. [ 1981 ]: Qualitative Response Models: A Survey, Technical report no. 338, Institute for Mathematical Studies in the Social Sciences, Stanford University.Google Scholar
  3. Amemiya, Y. [ 1985 ]: Instrumental Variable Estimator for the Nonlinear Errors-inVariables Model, Journal of Econometrics 28, 273–290.CrossRefGoogle Scholar
  4. Amemiya, Y. [ 1990 ]: Two-Stage Instrumental Variable Estimators for the Nonlinear Errors-in-Variables Model, Journal of Econometrics, 44, 311–332.CrossRefGoogle Scholar
  5. Amemiya, Y. and W. A. Fuller [ 1988 ]: Estimation for the Nonlinear Functional Relationship, The Annals of Statistics, 16, 147–160.CrossRefGoogle Scholar
  6. Anderson, T.W. [ 1976 ]: Estimation of Linear Functional Relationships: Approximate Distributions and Connections with Simultaneous Equations in Econometrics (with discussion), Journal of the Royal Statistical Society, B, 38, 1–36.Google Scholar
  7. Anderson, T.W. [ 1984 ]: Estimating Linear Statistical Relationships, 1982 Abraham Wald Memorial Lectures, Annals of Statistics, 12, 1–46.CrossRefGoogle Scholar
  8. Anderson, T.W. [ 1985 ]: An Introduction to Multivariate Analysis, 2nd ed. Wiley, New York.Google Scholar
  9. Anderson, T.W. and H. Rubin [ 1956 ]: Statistical Inference in Factor Analysis, in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probabilities, vol. V, Berkeley and Los Angeles: University of California Press, 111–156.Google Scholar
  10. Carroll, R.J. and L.A. Stefanski [ 1990 ]: Approximate Quasi-likelihood Estimation in Models with Surrogate Predictors, Journal of the American Statistical Association, 85, 652–633.CrossRefGoogle Scholar
  11. Chamberlain, G. and Z. Griliches [ 1975 ]: Unobservables with a Variance-Components Structure: Ability, Schooling and the Economic Success of Brothers, International Economic Review, 16, 422–450.CrossRefGoogle Scholar
  12. Court, L.M. [ 1941 ]: Entrepreneurial and Consumer Demand Theories for Commodity Spectra, Econometrica, 9, 135–62.CrossRefGoogle Scholar
  13. Efron, B. [ 1975 ]: The Efficiency of Logistic Regression Compared to Normal Discriminant Analysis, Journal of the American Statistical Association, 70, 892–898.CrossRefGoogle Scholar
  14. Friedman, M. [ 1957 ]: A Theory of the Consumption Function, Princeton: Princeton University Press.Google Scholar
  15. Fuller, W.A. [ 1987 ]: Measurement Error Models, Wiley: New York.CrossRefGoogle Scholar
  16. Gabrielson, A. [ 1978 ]: Consistency and Identifiability, Journal of Econometrics, 8, 26183.Google Scholar
  17. Geraci, V. [ 1976 ]: Identification of Simultaneous Equation Models with Measurement Error, Journal of Econometrics, 4, 263–283.CrossRefGoogle Scholar
  18. Geraci, V. [ 1977 ]: Estimation of Simultaneous Equation Models with Measurement Error, Econometrica, 45, 1243–1255.CrossRefGoogle Scholar
  19. Geraci, V. [ 1983 ]: Errors in Variables and the Individual Structural Equation, International Economic Review, 24, 217–236.CrossRefGoogle Scholar
  20. Goldberger, A.S. [ 1972 ]: Maximum Likelihood Estimation of Regressions Containing Unobservable Independent Variables, International Economic Review, 13, 1–15.CrossRefGoogle Scholar
  21. Gong, G. and F.J. Semaniego [ 1980 ]: Pseudo Maximum Likelihood Estimation: Theory and Applications, Annals of Statistics, 4, 861–869.Google Scholar
  22. Gorman, W.M. [ 1980 ]: A Possible Procedure for Analyzing Quality Differentials in the Egg Market, Review of Economic Studies, 47, 843–856.CrossRefGoogle Scholar
  23. Griliches, Z. [1971]: ed. Price Indexes and Quality Change, Cambridge, Mass: Harvard University Press.Google Scholar
  24. Griliches, Z. [ 1974 ]: Errors in Variables and Other Unobservables, Econometrica, 42, 971–998.CrossRefGoogle Scholar
  25. Griliches, Z. and J.A. Hausman [ 1984 ]: Errors—in—Variables in Panel Data, Journal of Econometrics, 31, 93–118.CrossRefGoogle Scholar
  26. Heckman, J.J. [ 1981a ]: Statistical Models for Discrete Data, in Structural Analysis of Discrete Data with Econometric Applications, ed. by C.F. Manski and D. McFadden, Cambridge, Mass., MIT Press, 114–178.Google Scholar
  27. Heckman, J.J. [ 1981b ]: The Incidental Parameters Problem and the Problem of Initial Conditions in Estimating a Discrete Time—Discrete Data Stochastic Process, in Structural Analysis of Discrete Data with Econometric Applications, ed. by C.F. Manski and D. McFadden, Cambridge, Mass: MIT Press, 179–195.Google Scholar
  28. Hsiao, C. [ 1976 ]: Identification and Estimation of Simultaneous equation Models with Measurement Error, International Economic Review 17, 319–339.CrossRefGoogle Scholar
  29. Hsiao, C. [ 1977 ]: Identification for a Linear Dynamic Simultaneous Error—Shock Model, International Economic Review 18, 181–194.CrossRefGoogle Scholar
  30. Hsiao, C. [ 1979 ]: Measurement Error in A Dynamic Simultaneous Equation Model with Stationary Disturbances, Econometrica 47, 475–494.CrossRefGoogle Scholar
  31. Hsiao, C. [ 1983 ]: Identification, in the Handbook of Econometrics, vol. I. ed.. by Z. Griliches and M. Intriligator, North—Holland: Amsterdam.Google Scholar
  32. Hsiao, C. [ 1989a ]: Consistent Estimation for Some Nonlinear Errors—in—Variables Models, Journal of Econometrics 41, 159–185.CrossRefGoogle Scholar
  33. Hsiao, C. [1989b]:Identification and Estimation of Dichotomous Latent Variables Models Using Panel Data, Working Paper, Center for Economic Research,Tilburg University.Google Scholar
  34. Hsiao, C. [ 1991 ]: Identification and Estimation of Latent Binary Choice Models Using Panel Data, Review of Economic Studies, 58, 717–731.CrossRefGoogle Scholar
  35. Hsiao, C. and P.M. Robinson [ 1978 ]: Efficient Estimation of a Dynamic Error—Shock Model, International Economic Review, 18, 467–480.CrossRefGoogle Scholar
  36. Hsiao, C. and G. Taylor [ 1991 ]:Some Remarks on Measurement Errors and the Identification of Panel Data Models, Statistica Neerlandica, 45, 187–194.CrossRefGoogle Scholar
  37. Jöreskog, K.G. and A.S. Goldberger [ 1975 ]: Estimation of a Model with Multiple Indicators and Multiple Causes of a Single Latent Variable, Journal of the American Statistical Association, 70, 631–639.CrossRefGoogle Scholar
  38. Lancaster, K.J. [ 1966 ]: A New Approach to Consumer Theory, Journal of Political Economy, 74, 132–157.CrossRefGoogle Scholar
  39. Lawley, D.N. and A.E. Maxwell [ 1971 ]: Factor Analysis as a Statistical Method, London: Butterworth and Company.Google Scholar
  40. Lawley, D.N. and A.E. Maxwell [ 1973 ]: Regression and Factor Analysis, Biometrika 60, 331–338.Google Scholar
  41. Learner, E.E. [ 1978 ]: Least—Squares versus Instrumental Variables Estimation in a Simple Errors in Variables Model, Econometrica, 46. 961–968.CrossRefGoogle Scholar
  42. Madansky, A. [ 1959 ]: The Fitting of Straight Lines When Both Variables are Subject to Error, Journal of the American Statistical Association, 54, 173–205CrossRefGoogle Scholar
  43. Maddala, G.S. [ 1983 ]: Limited Dependent and Qualitative Variables in Econometrics, Cambridge University Press: Cambridge.Google Scholar
  44. Maravall, A. [ 1979 ]: Identification in Dynamic Shock-Error Models, Berlin: Springer-Verlap.Google Scholar
  45. Maravall, A., and D.J. Aigner [ 1977 ]: Identification of the Dynamic Shock-Error Model: The Case of Dynamic Regression, in Latent Variables in Socio-Economic Models, ed. by D. Aigner and A. Goldberger, Amsterdam: North-Holland, 349–363.Google Scholar
  46. McFaddden, D. [ 1976 ]: Quantal Choice Analysis: A Survey, Annals of Economic and Social Measurement, 5, 363–390.Google Scholar
  47. McFaddden, D. [ 1981 ]: Econometric Models of Probabilistic Choice, in Structural Analysis of Discrete Data with Econometric Applications, ed. by C.F. Manski and D. McFadden, Cambridge: MIT Press.Google Scholar
  48. Muth, J.F. [ 1961 ]: Rational Expectations and the Theory of Price Movements, Econometrica, 29, 315–335.CrossRefGoogle Scholar
  49. Robinson, P.M. [ 1974 ]: Identification, Estimation and Large Sample Theory for Regressions Containing Unobservable Variables, International Economic Review, 15, 680–692.CrossRefGoogle Scholar
  50. Robinson, P.M. and M.C. Ferrara [ 1977 ]: The Estimation of a Model for an Unobservable Variable with Endogenous Causes, in D.J. Aigner and A.S. Goldberger, Eds., Latent Variables in Social-Economic Models, Amsterdam: North-Holland, 131–142.Google Scholar
  51. Rosen, S. [ 1974 ]: Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition, Journal of Political Economy, 82, 34–55.CrossRefGoogle Scholar
  52. Stefanski, L.A. [ 1985 ]: The Effects of Measurement Errors in Generalized Linear Models, Biometrika, 74, 385–391.Google Scholar
  53. Stefanski, L.A. and R.J. Carroll [ 1985 ]: Covariate Measurement Error in Logistic Regression, The Annals of Statistics, 13, 1335–1351.CrossRefGoogle Scholar
  54. Train, K., D. McFadden and A. Goett [ 1987 ]: The Incorporation of Attitudes in Econometric Models of Consumer Choice, Review of Economics and Statistics, 49, 383–391.CrossRefGoogle Scholar
  55. Villegas, C. [ 1969 ]: On the Least Squares Estimation of Nonlinear Relations, Annals of Mathematical Statistics, 40, 462–466.CrossRefGoogle Scholar
  56. Whittemore, A.S. and J.B. Keller [ 1988 ]: Approximations for Regression With Covariate Measurement Error, Journal of the American Statistical Association, 83, 1057–1072.CrossRefGoogle Scholar
  57. Wolter, K.M. and W.A. Fuller [ 1982a ]: Estimation of Nonlinear Errors-in-Variables Models, Annals of Statistics, 10, 539–548.CrossRefGoogle Scholar
  58. Wolter, K.M. and W.A. Fuller [ 1982b ]: Estimation of the Quadratic Errors-inVariables Model, Biometrika, 69, 175–182.Google Scholar
  59. Zellner, A. [ 1970 ]: Estimation of Regression Relationships Containing Unobservable Variables, International Economic Review, 11, 441–454.CrossRefGoogle Scholar

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© Kluwer Academic Publishers 1996

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  • Cheng Hsiao

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