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.
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References
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.
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.
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.
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.
Brown, T. M., “Simplified Full Maximum Likelihood and Comparative Structural Estimates,” Econometrica, vol. 27, 1959, pp. 638–653.
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.
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.
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.
Court, R. H., “Utility Maximization and the Demand for New Zealand Meats,”Econometrica, vol. 35, 1967, pp. 424–446.
Cramer, H., Mathematical Methods of Statistics, Princeton, N.J., Princeton University Press, 1946.
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.
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.
Eisenpress, H., and J. Greenstadt, “The Estimation of Nonlinear Econometric Systems,” Econometrica, vol. 34, 1966, pp. 851–861.
Fisher, F. M., “Identifiability Criteria in Nonlinear Systems,” Econometrica, vol. 29, 1961, pp. 574–590.
Fisher, R. A., Statistical Methods for Research Workers, Edinburgh, Oliver and Boyd, 1954.
Haavelmo, T., “The Statistical Implications of a System of Simultaneous Equations,” Econometrica, vol. 11, 1943, pp. 1–12.
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.
Klein, L. R., A Textbook of Econometrics, Englewood Cliffs, N.J., Prentice-Hall, 1953.
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.
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.
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.
Mann, H. B., and A. Wald, “ On the Statistical Treatment of Linear Stochastic Difference Equations,”Econometrica, vol. 11, 1943, pp. 173–220.
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.
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.
Rao, C. R., Advanced Statistical Methods in Biometrie Research, New York, Wiley, 1952.
Rothenberg, T. J., and C. T. Leenders, “Efficient Estimation of Simultaneous Equation Systems,” Econometrica, vol. 32, 1964, pp. 57–76.
Sargan, J. D., “The Maximum Likelihood Estimation of Economic Relationships with Autoregressive Residuals,” Econometrica, vol. 29, 1961, pp. 414–426.
Tinbergen, J., “ Econometric Business Cycle Research,” Review of Economic Studies, vol. 7, 1940, pp. 73–90.
Tintner, G., “ Multiple Regression for Systems of Equations,” Econometrica, vol. 14, 1946, pp. 5–32.
Wold, H.,“ Statistical Estimation of Economic Relationships,” Econometrica, supplement, vol. 17, 1949, pp. 1–22.
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Dhrymes, P.J. (1974). Maximum Likelihood Methods. In: Econometrics. Springer Study Edition. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9383-2_7
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DOI: https://doi.org/10.1007/978-1-4613-9383-2_7
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