Calzolari, Giorgio and Sampoli, Letizia (1989): Instrumental variables interpretations of FIML and nonlinear FIML.
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FIML estimates of a simultaneous equation econometric model can be obtained by iterating to convergence an instrumental variables formula that is perfectly consistent with the intuitive textbook-type interpretation of efficient instruments: instruments for an equation must be uncorrelated with the error term of the equation, but at the same time must have the highest correlation with the explanatory variables. However, if our purpose is to obtain FIML from iterating to convergence some full information instrumental variables, the intuitive textbook-type interpretation of the efficient instruments is not necessarily helpful, and can be too restrictive. The purpose of this paper is to show that, in the full information framework, there is a much wider flexibility in the choice of the instruments. Against intuition, instruments may be not purged enough of correlation with the error term: for example, the instruments for the endogenous variables or functions of endogenous variables included in one equation do not need to be purged of the residuals of equations that are correlated with the given one. Viceversa, instruments can be purged too much: for example, if there are zero covariance restrictions, instruments may be purged also of the estimated residuals of equations uncorrelated with the given one.
|Item Type:||MPRA Paper|
|Original Title:||Instrumental variables interpretations of FIML and nonlinear FIML|
|Keywords:||Econometric models, simultaneous equations, full information maximum likelihood, iterative instrumental variables|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling
C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables
|Depositing User:||Giorgio Calzolari|
|Date Deposited:||13. Mar 2011 23:34|
|Last Modified:||01. Aug 2015 11:27|
Amemiya, T. (1977): "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares in the General Nonlinear Simultaneous Equation Model", Econometrica 45, 955-968.
Amemiya, T. (1982): "Correction to a Lemma", Econometrica 50, 1325-1328.
Brundy, J. M., and D. W. Jorgenson (1971): "Efficient Estimation of Simultaneous Equations by Instrumental Variables", The Review of Economics and Statistics 53, 207-224.
Calzolari, G., L. Panattoni, and C. Weihs (1987): "Computational Efficiency of FIML Estimation", Journal of Econometrics 36, 299-310.
Dagenais, M. G. (1978): "The Computation of FIML Estimates as Iterative Generalized Least Squares Estimates in Linear and Nonlinear Simultaneous Equations Models", Econometrica 46, 1351-1362.
Durbin, J. (1963): "Maximum Likelihood Estimation of the Parameters of a System of Simultaneous Regression Equations". London School of Economics: discussion paper presented at The European Meeting of the Econometric Society, Copenhagen.
Fomby, T. B., R. C. Hill, and S. R. Johnson (1984): Advanced Econometric Methods. New York: Springer-Verlag.
Friedmann, R. (1985): "Multivariate Predictions from Structural Econometric Models with Covariance Restrictions". University of Bielefeld: discussion paper presented at The Fifth International Symposium on Forecasting, Montreal.
Hausman, J. A. (1974): "Full Information Instrumental Variables Estimation of Simultaneous Equations Systems·, Annals of Economic and Social Measurement 3, 641-652.
Hausman, J. A. (1975): "An Instrumental Variable Approach to Full Information Estimators for Linear and Certain Nonlinear Econometric Models", Econometrica 43, 727-738.
Hausman, J, A. (1983): "Specification and Estimation of Simultaneous Equation Models', in Handbook of Econometrics, ed. by Z. Griliches and M. D. Intriligator. Amsterdam, North-Holland Publishing Company, Vol.l, 391-448.
Hausman, J. A., W. K. Newey, and W. E. Taylor (1987): "Efficient Estimation and Identification of Simultaneous Equation Models with Covariance Restrictions". Econometrica 55. 849-874.
Koopmans, T. C., H. Rubin, and R. B. Leipnik (1950): "Measuring the Equation Systems of Dynamic Economics", in Statistical Inference in Dynamic Economic Models, ed. by T. C. Knopmans. New York: John Wiley & Sons, Cowles Commission Monograph No. 10, 53-237.
Maddala, G. S. (1981): "Statistical Inference in Relation to the Size of the Model", in Large-Scale Macro-Econometric Models, ed. by J. Kmenta and J. B. Ramsey. Amsterdam: North-Holland Publishing Company, 191-218.
Rothenberg.T.J. (1973). Efficient Estimation with A Priori Information, Cowles Foundation Monograph 23. New Haven: Yale Unlversity Press.