We examine the challenge faced by a government aiming to implement a gradual reduction in inflation by entrusting monetary policy to an independent central bank with limited credibility. Expanding upon the framework established by Barro and Gordon (1983b) , we demonstrate that an optimal policy for minimizing the sacrifice ratio of disinflation involves a gradual disinflationary process coupled with the announcement of intermediate targets. The speed at which disinflation occurs strikes a balance between the objective of enhancing credibility and the associated costs of unexpected inflation. Our theoretical framework provides an explanation for the disinflationary experiences observed in Chile and Colombia during the 1990s, wherein these countries established new monetary institutions and steadily achieved single-digit inflation levels through the annual announcement of decreasing inflation targets. We argue that the use of intermediate targets played a pivotal role in their design, facilitating the establishment of credibility with lower output costs.
