Reduced form estimation and prediction from uncertain structural models: a generic approach

Abstract This paper proposes a direct hierarchical model for the analysis of the reduced forms (RF) of the classical linear simultaneous equations models (SEM). The mean of the prior p.d.f. on RF coefficients is partially assessed with the aid of the traditionally exact a priori restrictions. Its variance may be partially specified to reflect degrees of model uncertainty and reliability of inferences that are asymptotically valid. Bayes or ‘maximum joint probability’ estimates are derived for both the RF and the ‘structural’ parameters. One variant of the RF estimator is shown to have desirable limiting and finite sample properties. It performs well in an empirical example which incorporates some elements of the two real-life problems of concern to us: simultaneous presence of different types of misspecification and small sample sizes.

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