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Central banks target CPI inflation; independent central banks are concerned about their balance sheet and the level of their capital. The first fact makes it difficult for a central bank to implement the optimal escape from a liquidity trap, because it undermines a commitment to overshoot the inflation target. We show that the second fact provides a solution. Capital concerns provide a mechanism for an independent central bank to commit to inflate ex post. The optimal policy can take the form of a currency depreciation combined with a crawling peg, a policy advocated by Svensson as the "Foolproof Way" to escape from a liquidity trap. (JEL E31, E52, E58, E62)

We study the problem of a policymaker who seeks to set policy optimally in an economy where the true economic structure is unobserved, and policymakers optimally learn from their observations of the economy. This is a classic problem of learning and control, variants of which have been studied in the past, but little with forward-looking variables which are a key component of modern policy-relevant models. As in most Bayesian learning problems, the optimal policy typically includes an experimentation component reflecting the endogeneity of information. We develop algorithms to solve numerically for the Bayesian optimal policy (BOP). However the BOP is only feasible in relatively small models, and thus we also consider a simpler specification we term adaptive optimal policy (AOP) which allows policymakers to update their beliefs but shortcuts the experimentation motive. In our setting, the AOP is significantly easier to compute, and in many cases provides a good approximation to the BOP. We provide a simple example to illustrate the role of learning and experimentation in an MJLQ framework.

We examine optimal and other monetary policies in a linear-quadratic setup with a relatively general form of model uncertainty, so-called Markov jump-linear-quadratic systems extended to include forward-looking variables. The form of model uncertainty our framework encompasses includes : simple i.i.d. model deviations; serially correlated model deviations; estimable regimeswitching models; more complex structural uncertainty about very different models, for instance, backward- and forward-looking models; time-varying central-bank judgment about the state of model uncertainty; and so forth. We provide an algorithm for finding the optimal policy as well as solutions for arbitrary policy functions. This allows us to compute and plot consistent distribution forecasts "fan charts" of target variables and instruments. Our methods hence extend certainty equivalence and "mean forecast targeting" to more general certainty non-equivalence and "distribution forecast targeting."