A Priori Inequality Restrictions and Bound Analysis in VAR Models

The aim of this paper is to use inequality restrictions on the parameters of a structural model to find bounds on impulse response functions which are valid for any structural representation satisfying those restrictions. Economic theories specify signs and bounds of the coefficients which are the same among alternative paradigms: parameters are either positive or negative and propensities are between zero and one. These restrictions can thus provide a core of well established a priori impositions on which one can derive an economically meaningful interpretation of the reduced form system. Unlike just and over-identifying restrictions, inequalities select a set of structural interpretations: for this reason inference on impulse responses is derived as a bound analysis. In the last section we introduce an objective method to compare alternative under-identifying restrictions expressed as inequalities.