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On the Consistency of Non-Linear FIML

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Abstract

Examples are given which show that:(i) normality is not Necessary for the consistency of the quasi maximum likelihood estimator in the nonlinear simultaneous equations model (nonlinear FIML) even when there are major departures from linearity; and (ii) the lemma which is used extensively by Amemiya [2] in the theoretical development of the properties of nonlinear FIML under the assumption of normality is, as presently stated, incorrect.

Suggested Citation

  • Phillips, Peter C.B., 1980. "On the Consistency of Non-Linear FIML," Cowles Foundation Discussion Papers 573, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:573
    Note: CFP 549.
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    References listed on IDEAS

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    1. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
    2. Gallant, A. Ronald, 1977. "Three-stage least-squares estimation for a system of simultaneous, nonlinear, implicit equations," Journal of Econometrics, Elsevier, vol. 5(1), pages 71-88, January.
    3. Fair, Ray C. & Parke, William R., 1980. "Full-information estimates of a nonlinear macroeconometric model," Journal of Econometrics, Elsevier, vol. 13(3), pages 269-291, August.
    4. Gallant, A Ronald & Holly, Alberto, 1980. "Statistical Inference in an Implicit, Nonlinear, Simultaneous Equation Model in the Context of Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 48(3), pages 697-720, April.
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    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. Agabriel, Jacques & Lherm, Michel & Mosnier, Claire & Reynaud, Arnaud & Thomas, Alban, 2009. "Estimating a Production Function under Production and Output Price Risks: An Application to Beef Cattle in France," TSE Working Papers 09-046, Toulouse School of Economics (TSE).
    4. B. Bhaskara Rao & Artur Tamazian, 2011. "A simultaneous equations model of finance and growth: FIML estimates for India," Applied Economics, Taylor & Francis Journals, vol. 43(25), pages 3699-3708.
    5. Ericsson, Neil R. & Campos, Julia & Tran, Hong-Anh, 1990. "Pc-Give and David Hendry'S Econometric Methodology," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 10(1), April.
    6. J. Campos, 1986. "Instrumental Variables Estimation of Dynamic Simultaneous Systems with ARMA Errors," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 125-138.
    7. Tripathi, Janhavi Shankar, 2023. "Trade-growth nexus: A study of G20 countries using simultaneous equations model with dynamic policy simulations," Journal of Policy Modeling, Elsevier, vol. 45(4), pages 806-816.
    8. Hall, Anthony David & Pagan, Adrian Rodney, 1981. "The LIML and Related Estimators of an Equation with Moving Average Disturbances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 719-730, October.

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