Structural Sign Patterns and Reduced Form Restrictions

This paper reconsiders the degree to which the sign patterns of hypothesized structural arrays limit the possible outcomes for the sign pattern of the corresponding estimated reduced form. The conditions under which any structural restrictions would apply were believed to be very narrow, rarely found to apply, and virtually never investigated. As a result, current practice does not test the structural hypothesis in terms of the comparison of the estimated reduced form and the permissible reduced form sign patterns. This paper shows that such tests are always possible. Namely, that the sign patterns of the hypothesized structural arrays always limit the sign patterns that can be taken on by the estimated reduced form. Given this, it is always possible to falsify a structural hypothesis based only upon the sign pattern proposed. Necessary conditions, algorithmic principles, and examples are provided to illustrate the analytic principle and the means of its application.