Instrumental variables interpretations of FIML and nonlinear FIML
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.
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- James M. Brundy & Dale W. Jorgenson, 1971. "Efficient estimation of simultaneous equations by instrumental variables," Working Papers in Applied Economic Theory 3, Federal Reserve Bank of San Francisco.
- Hausman, Jerry A & Newey, Whitney K & Taylor, William E, 1987.
"Efficient Estimation and Identification of Simultaneous Equation Models with Covariance Restrictions,"
Econometric Society, vol. 55(4), pages 849-874, July.
- J. Hausman & W. Newey & W. Taylor, 1983. "Efficient Estimation and Identification of Simultaneous Equation Models with Covariance Restrictions," Working papers 331, Massachusetts Institute of Technology (MIT), Department of Economics.
- Jerry A. Hausman & Whitney K. Newey & William E. Taylor, 1985. "Efficient Estimation and Identification of Simultaneous Equation Models with Covariance Restrictions," Working papers 369, Massachusetts Institute of Technology (MIT), Department of Economics.
- Calzolari, Giorgio & Panattoni, Lorenzo & Weihs, Claus, 1987. "Computational efficiency of FIML estimation," Journal of Econometrics, Elsevier, vol. 36(3), pages 299-310, November.
- Dagenais, Marcel G, 1978. "The Computation of FIML Estimates as Iterative Generalized Least Squares Estimates in Linear and Nonlinear Simultaneous Equations Models," Econometrica, Econometric Society, vol. 46(6), pages 1351-1362, November.
- Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448 Elsevier.
- Hausman, Jerry A, 1975. "An Instrumental Variable Approach to Full Information Estimators for Linear and Certain Nonlinear Econometric Models," Econometrica, Econometric Society, vol. 43(4), pages 727-738, July.
- Jerry A. Hausman, 1974. "Full Information Instrumental Variables Estimation of Simultaneous Equations Systems," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 641-652 National Bureau of Economic Research, Inc.
- Brundy, James M & Jorgenson, Dale W, 1971. "Efficient Estimation of Simultaneous Equations by Instrumental Variables," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 207-224, August.
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