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We study the link between central bank independence and episodes of unusually high inflation—what we call inflation tail risks—and highlight the perils of weakening central bank independence. Using a novel historical dataset of central bank independence for 17 Latin American, our empirical analysis finds that, in addition to the well-established negative association between central bank independence and inflation, high central bank independence is associated with reductions in the likelihood of high inflation episodes, as shown by linear probability models and quantile regressions. Moreover, a dynamic quantile regression approach shows that the benefits of central bank independence in terms of reducing high inflation accumulate over time. Finally, using alternative measures of central bank independence, we find that the lessons stemming from Latin America's experience extend to emerging markets more broadly.