Calzolari, Giorgio and Sampoli, Letizia (1989): Instrumental variables interpretations of FIML and nonlinear FIML.

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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 textbooktype 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 textbooktype 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 
Language:  English 
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 
Item ID:  29024 
Depositing User:  Giorgio Calzolari 
Date Deposited:  13 Mar 2011 23:34 
Last Modified:  06 Oct 2019 09:53 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/29024 