Specification versus data fitting: SEM prediction and the Q-class estimator

We propose a new class of limited information estimators built upon an explicit trade-off between data fitting and a priori model specification. The estimators offer the researcher a continuum of estimators that range from an extreme emphasis on data fitting and robust reduced-form estimation to the other extreme of exact model specification and efficient estimation. The approach used to generate the estimators illustrates why ULS often outperforms 2SLS-PRRF even in the context of a correctly specified model, provides a new interpretation of 2SLS, and integrates Wonnacott and Wonnacott's least weighted variance estimators with other techniques. We apply the new class of estimators to Klein's Model I and generate forecasts. We find for this example that an emphasis on specification (as opposed to data fitting) produces better out-of-sample predictions.