We develop a new automatically-computable test for super exogeneity, using a variant of general-to-specific modeling. Based on the recent developments of impulse saturation applied to marginal models under the null that no impulses matter, we select the significant impulses for testing in the conditional. Since zero-mean changes are relatively undetectable in both VARs and conditional equations, we focus on location shifts, although we also discuss variance changes. The approximate analyti...