Abstract: Modern tools for macroeconomic policy evaluation and causal inference often rely on sufficient statistics, which are non-linear functions of impulse responses. This paper extends these methods to the case where we are only able to set identify dynamic causal effects within a VAR framework. I examine the complications that arise when applying non-linear transformations—such as regressions in the impulse response space—under set identification, and I propose a robust Bayes approach to address these issues. Further, by expressing parameters of interest as functions of the VAR’s orthogonal reduced form, I introduce a novel class of identification strategies sharpening the identification of dynamic causal effects.

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