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Instrumental variables interpretations of FIML and nonlinear FIML

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  • Calzolari, Giorgio
  • Sampoli, Letizia

Abstract

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.

Suggested Citation

  • Calzolari, Giorgio & Sampoli, Letizia, 1989. "Instrumental variables interpretations of FIML and nonlinear FIML," MPRA Paper 29024, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:29024
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    References listed on IDEAS

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    1. Hausman, Jerry A & Newey, Whitney K & Taylor, William E, 1987. "Efficient Estimation and Identification of Simultaneous Equation Models with Covariance Restrictions," Econometrica, Econometric Society, vol. 55(4), pages 849-874, July.
    2. 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.
    3. 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.
    4. Calzolari, Giorgio & Panattoni, Lorenzo & Weihs, Claus, 1987. "Computational efficiency of FIML estimation," Journal of Econometrics, Elsevier, vol. 36(3), pages 299-310, November.
    5. 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.
    6. 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.
    7. Amemiya, Takeshi, 1977. "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model," Econometrica, Econometric Society, vol. 45(4), pages 955-968, May.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Econometric models; simultaneous equations; full information maximum likelihood; iterative instrumental variables;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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