Two Modified FIML Estimators for use in Small Samples

Full-information maximum likelihood (FIML) estimation becomes impossible if the number of variables in a linear model without identities exceeds the number of observations. Two modified FIML estimators, K-FIML and S-FIML, are proposed. Both have less restrictive sample sizes than FIML does. The S-FIML requires a sample size that is the minimum possible for any full information estimator. The 2 models differ in maximizing the FIML likelihood function over different subsets of the parameters. K-FIML and S-FIML have advantages in possible efficiency gains, easy generalizations to nonlinear models, and the ability to estimate models with constraints across equations. K-FIML offers a computational advantage if maximizing the FIML likelihood function over the entire coefficient vector is expensive. Both S-FIML and K-FIML are more suitable than other estimation techniques in small samples. Both are appropriate when dealing with constraints across equations that force ad hoc modification of a 2SLS estimation strategy.