We analyze the role of an exchange rate peg as a commitment mechanism to achieve inflation stability when multiple equilibria are possible. We show that there are ex ante large gains from choosing a more conservative regime not only in order to mitigate inflation bias from time inconsistency but also to avoid high inflation equilibria. In these circumstances, using a pegged exchange rate as an anti‐inflation commitment device can create a “trap” whereby the regime initially confers gains in anti‐inflation credibility but ultimately results in an exit occasioned by a big enough adverse real shock that creates large welfare losses to the economy.