On the computational competitiveness of full-information maximum-likelihood and three-stage least-squares in the estimation of nonlinear, simultaneous-equations models

Abstract While full-information maximum-likehood (FIML) estimation has long been considered an important theoretical econometric estimation technique, computational considerations have greatly restricted its use in practice. Recent advances in numerical analysis and in computational software, however, have combined to provide algorithms capable of carrying out the FIML calculations quite efficiently relative to past standards. This paper compares the computational competitiveness of FIML with its most popular competitor, 3SLS, in the estimation of a variety of linear and non-linear (in parameters and variables) models. The nonlinear full-information maximum-likelihood (NLFIML) estimator is described and a computationally efficient approximation, TRUNFIML, is defined. Nonlinear three-stage least-squares (NL3SLS) is accomplished by the method of Jorgenson-Laffont. Comparisons are made on the basis of numbers of iterations to convergence, number of function evaluations, and total computer CPU time required, this latter figure being most relevant to a comparison of computational effort and cost.

[1]  H. Theil,et al.  Three-Stage Least Squares: Simultaneous Estimation of Simultaneous Equations , 1962 .

[2]  G. Stewart.  Introduction to matrix computations , 1973 .

[3]  E. Malinvaud,et al.  Statistical Methods of Econometrics. by E. Malinvaud , 1972 .

[4]  David A. Belsley.  Estimation of Systems of Simultaneous Equations, and Computational Specifications of GREMLIN , 1974 .

[5]  J. J. Moré,et al.  Quasi-Newton Methods, Motivation and Theory , 1974 .

[6]  J. G. Cragg.  On the Relative Small-Sample Properties of Several Structural-Equation Estimators , 1967 .

[7]  Dale W. Jorgenson,et al.  EFFICIENT ESTIMATION OF NONLINEAR SIMULTANEOUS EQUATIONS WITH ADDITIVE DISTURBANCES , 2022 .

[8]  J. G. Cragg.  On the Sensitivity of Simultaneous-Equations Estimators to the Stochastic Assumptions of the Models , 1966 .

[9]  R. Fair.  Efficient estimation of simultaneous equations with auto-regressive errors by instrumental variables , 1972 .

[10]  Robert Summers,et al.  A Capital-Intensive Approach to the Small Sample Properties of Various Simultaneous Equation Estimators , 1965 .

[11]  Virginia Klema,et al.  The Singular Value Analysis in Matrix Computation , 1974 .

[12]  W. Dent.  Computation of the exact likelihood function of an arima process , 1977 .

[13]  Alston S. Householder,et al.  Handbook for Automatic Computation , 1960, Comput. J..

[14]  Yonathan Bard,et al.  Comparison of Gradient Methods for the Solution of Nonlinear Parameter Estimation Problems , 1970 .

[15]  Takeshi Amemiya,et al.  The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model , 1977 .

[16]  R. L. Basmann.  A GENERALIZED CLASSICAL METHOD OF LINEAR ESTIMATION OF COEFFICIENTS IN A STRUCTURAL EQUATION , 1957 .

[17]  John Greenstadt,et al.  The Estimation of Nonlinear Econometric Systems , 1966 .

[18]  J. H. Wilkinson.  The algebraic eigenvalue problem , 1966 .

[19]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[20]  P. Newbold.  The exact likelihood function for a mixed autoregressive-moving average process , 1974 .

[21]  D. Cochrane,et al.  Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms , 1949 .

[22]  Forrest D. Nelson,et al.  On a General Computer Algorithm for the Analysis of Models with Limited Dependent Variables , 1974 .

[23]  G. Golub.  MATRIX DECOMPOSITIONS AND STATISTICAL CALCULATIONS , 1969 .

[24]  Denis Sargan,et al.  The maximun likelihood estimation of economic relationships with autoregressive residuals , 1961 .

[25]  Bronwyn H Hall,et al.  Estimation and Inference in Nonlinear Structural Models , 1974 .

[26]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[27]  D. Hendry.  The structure of simultaneous equations estimators , 1976 .

[28]  W. M. Mikhail,et al.  A Comparative Monte Carlo Study of the Properties , 1975 .

[29]  H. Theil,et al.  Economic Forecasts and Policy. , 1959 .

[30]  G. Chow,et al.  On the Computation of Full-Information Maximum Likelihood Estimates for Nonlinear Equation Systems , 1973 .