An Algorithm for FIML and 3SLS Estimation of Large Nonlinear Models

Abstract

THIS PAPER PRESENTS a numerical algorithm for computing full information maximum likelihood (FIML) and nonlinear three-stage least squares (3SLS) coefficient estimates for large nonlinear models. (The proposed algorithm will be denoted algorithm A.) Although the theory of FIML estimation has been available for thirty years [20], FIML estimation has long been regarded as impossible on large nonlinear models.2 The more recently proposed nonlinear 3SLS estimator [191 also poses difficulties for large models.3 Using the algorithm presented in this paper, FIML and 3SLS are now feasible alternatives for estimation of large nonlinear models. The principles behind algorithm A's efficiency can be summarized as follows. First, most of the algorithm's steps explicitly control the mean of each equation's residuals. Large changes in those means are avoided because the FIML and 3SLS estimation problems are extremely sensitive to the residuals' means. Second, the coefficients are grouped by equations and the groups are treated separately during most of each iteration. This focus on individual equations is effective because coefficients within the same equation are generally more