AbstractOptimal estimation is necessary for empirical modelling, but can be summarized in an estimator generating equation (EGE). The EGE reduces a vast literature on estimating individual equations and linear simultaneous systems to a single, simple expression based on the ‘score’, namely, the first derivative of the log‐likelihood function for full information maximum likelihood (FIML). The EGE also reveals how to generate new estimators and whether any given estimator is consistent and/or efficient. Consequently, the computation of maximum likelihood estimators is related to the properties of numerical optimization algorithms: estimators are numerical algorithms for approximating the solution of the score, classified by their choice of initial values, numbers of iterations and approximations to the Hessian of FIML. Different statistical approximations must be distinguished from alternative numerical optimization methods, which implement FIML, but some estimators are just different optimization algorithms, emphasizing the inter‐dependence between computational considerations based on numerical analyses and on statistical analyses.