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Econometrics pp 314-357 | Cite as

Maximum Likelihood Methods

  • Phoebus J. Dhrymes
Part of the Springer Study Edition book series (SSE)

Abstract

In dealing with the problem of estimating the parameters of a structural system of equations, we had not, in previous chapters, explicitly stated the form of the density of the random terms appearing in the system. Indeed, the estimation aspects of classical least squares techniques and their generalization to systems of equations are distribution free, so that no explicit assumption need be made with respect to the distribution of the error terms. On the other hand, in considering various tests of significance on 2SLS or 3SLS estimated parameters of a structural system, we have occasionally found it convenient to assert (joint) normality of the structural error terms. Under this assumption, the derivation of the asymptotic distribution of such estimators is simplified considerably.

Keywords

Likelihood Function Maximum Likelihood Estimator Maximum Likelihood Method Full Information Maximum Likelihood Moment Matrix 
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. 1.
    Anderson, T. W., “Estimation of the Parameters of a Single Equation by the Limited Information Maximum Likelihood Method,” Chapter 9 in Statistical Inference in Dynamic Economic Models, T. C. Koopmans (Ed.). Cowles Foundation for Research in Economics, Monograph No. 10, New York, Wiley, 1950.Google Scholar
  2. 2.
    Anderson, T. W., and H. Rubin, “ Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations,” Annals of Mathematical Statistics, vol. 20, 1949, pp. 46–63.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Anderson, T. W., and H. Rubin, “The Asymptotic Properties of Estimates of the Parameters of a Single Equation in a Complete System of Stochastic Equations,” Annals of Mathematical Statistics, vol. 20, 1950. pp. 570–582.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bellman, R., A Survey of the Boundedness, Stability, and Asymptotic Behavior of Solutions to Linear and Nonlinear Differential and Difference Equations. Contract NC ori-105 Task-order V, Washington, D.C., Office of Naval Research, Dept. of the Navy, 1949.Google Scholar
  5. 5.
    Brown, T. M., “Simplified Full Maximum Likelihood and Comparative Structural Estimates,” Econometrica, vol. 27, 1959, pp. 638–653.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Chernoff, H., and N. Divinsky, “The Computation of Maximum Likelihood Estimates of Linear Structural Equations,” in Studies in Econometric Methods, W. C. Hood and T. C. Koopmans (Eds.), New York, Wiley, 1953.Google Scholar
  7. 7.
    Chernoff, H., and H. Rubin, “Asymptotic Properties of Limited Information Estimates Under Generalized Conditions,” in Studies in Econometric Methods, W. C. Hood and T. C. Koopmans (Eds.), New York, Wiley, 1953.Google Scholar
  8. 8.
    Chow, G. C., “Two Methods of Computing Full Information Maximum Likelihood Estimates in Simultaneous Stochastic Equations,” International Economic Review, vol. 9, 1968, pp. 100–112.MATHCrossRefGoogle Scholar
  9. 9.
    Court, R. H., “Utility Maximization and the Demand for New Zealand Meats,”Econometrica, vol. 35, 1967, pp. 424–446.CrossRefGoogle Scholar
  10. 10.
    Cramer, H., Mathematical Methods of Statistics, Princeton, N.J., Princeton University Press, 1946.MATHGoogle Scholar
  11. 11.
    Durbin, J., “Maximum Likelihood Estimation of the Parameters of a System of Simultaneous Regression Equations.” Paper presented at the meetings of the Econometric Society, Copenhagen, 1963.Google Scholar
  12. 12.
    Eisenpress, H., “Note on the Computation of Full Information Maximum Likelihood Estimates of Coefficients of a Simultaneous System,” Econometrica, vol. 30, 1962, pp. 343–348.CrossRefGoogle Scholar
  13. 13.
    Eisenpress, H., and J. Greenstadt, “The Estimation of Nonlinear Econometric Systems,” Econometrica, vol. 34, 1966, pp. 851–861.MATHCrossRefGoogle Scholar
  14. 14.
    Fisher, F. M., “Identifiability Criteria in Nonlinear Systems,” Econometrica, vol. 29, 1961, pp. 574–590.MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Fisher, R. A., Statistical Methods for Research Workers, Edinburgh, Oliver and Boyd, 1954.Google Scholar
  16. 16.
    Haavelmo, T., “The Statistical Implications of a System of Simultaneous Equations,” Econometrica, vol. 11, 1943, pp. 1–12.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Hood, W. C., and T. C. Koopmans (Eds.), Studies in Econometric Methods, Cowles Foundation for Research in Economics, Monograph No. 14, New York, Wiley, 1953.Google Scholar
  18. 18.
    Klein, L. R., A Textbook of Econometrics, Englewood Cliffs, N.J., Prentice-Hall, 1953.Google Scholar
  19. 19.
    Koopmans, T. C., “The Equivalence of Maximum Likelihood and Least Squares Estimates of Regression Coefficients,” Chapter 7 in Statistical Inference in Dynamic Economic Models. T. C. Koopmans (Ed.) Cowles Foundation for Research in Economics, Monograph No. 10, New York, Wiley, 1950.Google Scholar
  20. 20.
    Koopmans, T. C., and W. C. Hood, “The Estimation of Simultaneous Economic Relationships,” in Studies in Econometric Methods, W. C. Hood and T. C. Koopmans (Eds.), New York, Wiley, 1953.Google Scholar
  21. 21.
    Koopmans, T. C., H. Rubin, and R. B. Leipnik, “Measuring the Equation Systems of Dynamic Economics,” Chapter 2 in Statistical Inference in Dynamic Economic Models, T. C. Koopmans (Ed.), New York, Wiley, 1950.Google Scholar
  22. 22.
    Mann, H. B., and A. Wald, “ On the Statistical Treatment of Linear Stochastic Difference Equations,”Econometrica, vol. 11, 1943, pp. 173–220.MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Marschak, J., “Economic Interdependence and Statistical Analysis,” in Studies in Mathematical Economics and Econometrics, in Memory of Henry Schultz, O. Lange, F. Mclntyre, and T. O. Yntema (Eds.), Chicago, University of Chicago Press, 1942.Google Scholar
  24. 24.
    Meyer, J. R., and H. L. Miller, Jr., “Some Comments on the ’Simultaneous Equations Approach,” Review of Economics and Statistics, vol. 36, 1954, pp. 88–92.CrossRefGoogle Scholar
  25. 25.
    Rao, C. R., Advanced Statistical Methods in Biometrie Research, New York, Wiley, 1952.Google Scholar
  26. 26.
    Rothenberg, T. J., and C. T. Leenders, “Efficient Estimation of Simultaneous Equation Systems,” Econometrica, vol. 32, 1964, pp. 57–76.MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    Sargan, J. D., “The Maximum Likelihood Estimation of Economic Relationships with Autoregressive Residuals,” Econometrica, vol. 29, 1961, pp. 414–426.MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Tinbergen, J., “ Econometric Business Cycle Research,” Review of Economic Studies, vol. 7, 1940, pp. 73–90.CrossRefGoogle Scholar
  29. 29.
    Tintner, G., “ Multiple Regression for Systems of Equations,” Econometrica, vol. 14, 1946, pp. 5–32.MathSciNetMATHCrossRefGoogle Scholar
  30. 30.
    Wold, H.,“ Statistical Estimation of Economic Relationships,” Econometrica, supplement, vol. 17, 1949, pp. 1–22.Google Scholar

Copyright information

© Springer-Verlag New York Inc 1974

Authors and Affiliations

  • Phoebus J. Dhrymes
    • 1
  1. 1.Columbia UniversityUSA

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