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The Distribution of FIML in the Leading Case

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  • Phillips, P C B

Abstract

In a recent article (1984a) Phillips showed that the distribution of the limited information maximum likelihood (LIML) estimator of the coefficients of the endogenous variables in a single structural equation is multivariate Cauchy in the leading (totally unidentified) case. The purpose of the present note is to show that the same result holds for the full information maximum likelihood (FIML) estimator. Our proof relies on the theory of invariant measures on a Stiefel manifold. This approach provides a major simplification of the derivation of the LIML result given in the earlier article and extends to the FIML case without difficulty. We start by illustrating its use for LIML.

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Bibliographic Info

Article provided by Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association in its journal International Economic Review.

Volume (Year): 27 (1986)
Issue (Month): 1 (February)
Pages: 239-43

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Handle: RePEc:ier:iecrev:v:27:y:1986:i:1:p:239-43

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  1. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516 Elsevier.
  2. Peter C.B. Phillips, 1983. "The Exact Distribution of Exogenous Variable Coefficient Estimators," Cowles Foundation Discussion Papers 681, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January.
  2. Peter C.B. Phillips, 1991. "Unidentified Components in Reduced Rank Regression Estimation of ECM's," Cowles Foundation Discussion Papers 1003, Cowles Foundation for Research in Economics, Yale University.
  3. Peter C. B. Phillips, 2005. "A Remark on Bimodality and Weak Instrumentation in Structural Equation Estimation," Cowles Foundation Discussion Papers 1540, Cowles Foundation for Research in Economics, Yale University.

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