This paper de(=elops a theory of CU AN estimation for systems of nonlinear simultaneous equal/on.\ with additive disturbances. We first derive the Cramer-Rna lower bound for the variance ofa C UAN estimator. The method ofmaximum likelihood can be used fa generate an estimator that allain.< this bound. We show that minimum distance and instrumental ('ariables estimators cannot generally allain the Cramer-Rao bound. 1 The statistical theory of eVAN estimation is discl.!ssed by Rao (1973), pp.

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... 351. 2 Best eUAN estimators are discussed by Rao (1973), pp. 350-351. J This specification for simultaneous equations models is considered by Eisenpress and Greenstadt (1966. . A complete review ofthe theory ofeUAN estimation for systems oflinear simultaneous equations models i, presented by Malinvaud (1970), pp. 348-366, and Rcthenbcrg (B74, S«: Malinvaud (1970), pp. 675-678, for a discussion of maximum likelihood and twnimum distance estimators, and Brundy and Jorgenson (1971) for a discussion ofefficient instrumental variables estimators.