Abstract Proponents of inflation targeting (IT) claim that it increases the credibility of central banks, which in turn should result in smaller sacrifice ratios (SRs) – that is, the ratio of output losses to the change in trend inflation during disinflations. We show that IT does indeed reduce SRs, but only if the disinflation is long: in a four‐year‐long disinflation, our estimates suggest that IT reduces SRs by at least 60%. In fast disinflations, IT does not affect SRs. These results suggest that IT and fast disinflations are substitute alternatives in enhancing the credibility of disinflationary processes and reducing their costs.