Abstract: Modern macroeconomic identification increasingly sharpens inference by combining multiple economically motivated restrictions. However, more restrictions are not a free lunch: conclusions based on them depend crucially on their credibility. This paper develops a robust Bayesian framework for modeling partial credibility in set-identified models. Because the likelihood does not update the unidentified structural component, qualitative prior information on policy-relevant functionals can be imposed by reweighting baseline structural draws. Prior classes become linear restrictions on the weights, so posterior bounds are computed by linear programs. The framework links marginal-prior correction and full ambiguity robust Bayes inference, while allowing intermediate prior classes based on tail, moment, sign, or shape restrictions. The method shows that in oil-market SVARs, demand dominance is robust, while the near-irrelevance of supply shocks requires stringent elasticity-prior discipline. In monetary-policy SVARs, restrictions on policy statistics discipline inference about multipliers and policy implications.

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