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A Simulation Study on FIML Covariance Matrix

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  • Calzolari, Giorgio
  • Panattoni, Lorenzo

Abstract

In econometric models, estimates of the asymptotic covariance matrix of FIML coefficients are traditionally computed in several different ways: with a generalized least squares type matrix; using the Hessian of the concentrated log-likelihood; using the outer product of the first derivatives of the log-likelihoods; with some suitable joint use of Hessian and outer product. The different alternative estimators are asymptotically equivalent in case of correct model's specification, but may produce large differences in the numerical application to small samples. The behaviour of the different estimators of the covariance matrix in standardizing or normalizing FIML estimated coefficients in the small samples is investigated in this paper. Monte Carlo experiments are performed on several small-medium size models, and some systematic behaviours are evidenced.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 28804.

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Date of creation: 03 Sep 1984
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Handle: RePEc:pra:mprapa:28804

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Keywords: Econometric models; simultaneous equations; FIML; maximum likelihood; covariance matrix; Hessian; outer product;

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References

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  1. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
  2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 1-25, January.
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  4. Hall, Alastair, 1987. "The Information Matrix Test for the Linear Model," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(2), pages 257-63, April.
  5. Calzolari, Giorgio & Panattoni, Lorenzo, 1983. "Hessian and approximated Hessian matrices in maximum likelihood estimation: a Monte Carlo study," MPRA Paper 28847, University Library of Munich, Germany.
  6. Calzolari, Giorgio, 1983. "Asymptotic distribution of power spectra and peak frequencies in the stochastic response of econometric models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 5(1), pages 235-247, February.
  7. Morimune, Kimio, 1983. "Approximate Distributions of k-Class Estimators When the Degree of Overidentifiability Is Large Compared with the Sample Size," Econometrica, Econometric Society, Econometric Society, vol. 51(3), pages 821-41, May.
  8. Brundy, James M & Jorgenson, Dale W, 1971. "Efficient Estimation of Simultaneous Equations by Instrumental Variables," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 207-24, August.
  9. Anderson, T W & Kunitomo, Naoto & Sawa, Takamitsu, 1982. "Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1009-27, July.
  10. Hatanaka, Michio, 1978. "On the efficient estimation methods for the macro-economic models nonlinear in variables," Journal of Econometrics, Elsevier, Elsevier, vol. 8(3), pages 323-356, December.
  11. Hendry, D F, 1971. "Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(2), pages 257-72, June.
  12. Parke, William R, 1982. "An Algorithm for FIML and 3SLS Estimation of Large Nonlinear Models," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 81-95, January.
  13. James M. Brundy & Dale W. Jorgenson, 1971. "Efficient estimation of simultaneous equations by instrumental variables," Working Papers in Applied Economic Theory, Federal Reserve Bank of San Francisco 3, Federal Reserve Bank of San Francisco.
  14. Jerry A. Hausman, 1974. "Full Information Instrumental Variables Estimation of Simultaneous Equations Systems," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 91-102 National Bureau of Economic Research, Inc.
  15. E.K. Berndt & B.H. Hall & R.E. Hall, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 103-116 National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Calzolari, Giorgio & Panattoni, Lorenzo, 1987. "Finite sample performance of the robust Wald test in simultaneous equation systems," MPRA Paper 22557, University Library of Munich, Germany.
  2. Weihs, Claus & Calzolari, Giorgio & Panattoni, Lorenzo, 1986. "The behavior of trust-region methods in FIML estimation," MPRA Paper 24122, University Library of Munich, Germany, revised 1987.

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