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A Curious Result on Exact FIML and Instrumental Variables


  • Calzolari, Giorgio
  • Sampoli, Letizia


The iterative application of an instrumental variable method to a system of simultaneous equations may exactly produce FIML, upon convergence. Instruments achieving this target do not need to be either uncorrelated with the error terms or correlated as much as possible with the replaced explanatory variables. This curious mathematical result, which contradicts some common wisdom and intuition, is proved in our paper. Our proof also provides a unified scheme that covers the available traditional instrumental variable interpretations of FIML, whether the model is linear or nonlinear, and whether covariance restrictions are or are not imposed.

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  • Calzolari, Giorgio & Sampoli, Letizia, 1993. "A Curious Result on Exact FIML and Instrumental Variables," Econometric Theory, Cambridge University Press, vol. 9(02), pages 296-309, April.
  • Handle: RePEc:cup:etheor:v:9:y:1993:i:02:p:296-309_00

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    References listed on IDEAS

    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
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    4. Heckman, James J. & Singer, Burton, 1984. "Econometric duration analysis," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 63-132.
    5. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
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    Cited by:

    1. Calzolari, Giorgio, 1992. "Stima delle equazioni simultanee non-lineari: una rassegna
      [Estimation of nonlinear simultaneous equations: a survey]
      ," MPRA Paper 24123, University Library of Munich, Germany, revised 1992.
    2. Calzolari, Giorgio, 2012. "Econometric notes," MPRA Paper 36765, University Library of Munich, Germany.
    3. Calzolari, Giorgio & Fiorentini, Gabriele, 1994. "Conditional heteroskedasticity in nonlinear simultaneous equations," MPRA Paper 24428, University Library of Munich, Germany.
    4. Giorgio Calzolari, 2015. "Indirect estimation and econometrics exams: how to live a round life," Econometrics Working Papers Archive 2015_01, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    5. Giorgio Calzolari & Laura Magazzini, 2011. "Moment Conditions and Neglected Endogeneity in Panel Data Models," Working Papers 02/2011, University of Verona, Department of Economics.

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