Calzolari, Giorgio and Panattoni, Lorenzo (1984): A Simulation Study on FIML Covariance Matrix. Published in: paper presented at the European Meeting of the Econometric Society. Universidad Autonoma de Madrid, September 37. (3 September 1984): pp. 144.

PDF
MPRA_paper_28804.pdf Download (956kB)  Preview 
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 loglikelihood; using the outer product of the first derivatives of the loglikelihoods; 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 smallmedium size models, and some systematic behaviours are evidenced.
Item Type:  MPRA Paper 

Original Title:  A Simulation Study on FIML Covariance Matrix 
Language:  English 
Keywords:  Econometric models; simultaneous equations; FIML; maximum likelihood; covariance matrix; Hessian; outer product 
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:  28804 
Depositing User:  Giorgio Calzolari 
Date Deposited:  11 Feb 2011 18:18 
Last Modified:  07 Oct 2019 17:53 
References:  Amemiya, T. (1977), "The Maximum Likelihood and the Nonlinear ThreeStage Least Squares in the General Nonlinear Simultaneous Equation Model", Econometrica 45, 955968. Anderson, T.W., N. Kunitomo, and T.Sawa (1982), "Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator", Econometrica 50, 10091027. Artus, P., G. Laroque, and G.Michel (1982), "Estimation of a Quarterly Model with Quantity Rationing". Paris: INSEE, discussion paper presented at the European Meeting of the Econometric Society, Dublin. Berndt, E. K, Hall. B. H.. Hall, R.E., Hausman, J. A.: Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement 3. 653665 (1974). Brundy,J.M. and D.W.Jorgenson (1971), "Efficient Estimation of Simultaneous Equations by Instrumental Variables", The Review of Economics and Statistics 53, 207224. Calzolari, G. (1983), "Asymptotic Distribution of Power Spectra and Peak Frequencies in the Stochastic Response of Econometric Models", Journal of Economic Dynamics and Control 5, 235247. Calzolari,G., and L.Panattoni (1983), "Hessian and Approximated Hessian Matrices in Maximum Likelihood Estimation : A Monte Carlo Study". Pisa: Centro Scientifico IBM, discussion paper presented at the European Meeting of the Econometric Society, Pisa. Chernoff, H., and N. Divinsky (1953), "The Computation of MaximumLikelihood Estimates of Linear Structural Equations", in Studies in Econometric Method, ed. by W. C. Hood and T. C. Koopmans. New York: John Wiley & Sons, Inc., Cowles Commission Monograph No. 14, 236302. Dagenais, M. G. (1978), The computation of FIMLestimates as iterative generalized leastsquares estimates in linear and nonlinear simultaneous equation models. Econometrica 46, 13511362. Dhrymes, P. J. (1970), Econometrics: Statistical Foundations and Applications. New York: Harper & Row. Eisenpress, H. and J. Greenstadt (1966), "The Estimation of Nonlinear Econometric Systems". Econometrica 34, 85186l. Gourieroux, C., A. Monfort, and A. Trognon (1984), "Pseudo Maximum Likelihood Methods: Theory". Econometrica 52, 681700. Hall, A.R. (1983), "The lnformation Matrix Test for the Linear Model". R. University of Warwick: discussion paper presented at the European Meeting of the Econometric Society, Pisa. Hatanaka, M. (1978), "On the Efficient Estimation Methods for the MacroEconomic Models Nonlinear in Variables", Journal of Econometrics 8, 323356. Hausman, J. A. (1974), "Full Information Instrumental Variables Estimation of Simultaneous Equations Systems", Annals of Economic and Social Measurement 3, 641652. Hendry, D. F. (1971), "Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process", International Economic Review 12, 257272. Klein, L. R. (1969), "Estimation of lnterdependent Systems in Macroeconometrics", Econometrica 37, 171192. Kmenta, J. (1971), Elements of Econometrics. New York: The Macmillan Company. Morimune, K. (1983), "Approximate Distriburion of kclass Estimators when the Degree of Overidentifiability is Large Compared with the Sample Size", Econometrica 51, 821 841. Parke, W. R.: An algorithm for FIML and 3SLS estimation of large nonlinear models. Econometrica 50, 8195 (1982). Rothenberg,T.J. and C.T.Leenders (1964), "Efficient Estimation of Simultaneous Equation Systems", Econometrica 32, 5716. Rothenberg.T.J. (1973). Efficient Estimation with A Priori Information, Cowles Foundation Monograph 23. New Haven: Yale Unlversity Press. Sitzia, B., and M. Tivegna (1975), "Un Modello Aggregato dell'Economia Italiana 19521971", in Contributi alla Ricerca Economica No.4. Roma: Banca d'ltalia, 195223. White, H. (1982), Maximum Likelihood Estimation of Misspecified Models, Econometrica 50, 125. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/28804 