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 and unobservable “modes. ” The form of model uncertainty our framework encompasses includes: simple i.i.d. model deviations; serially correlated model deviations; estimable regime-switching models; more complex structural uncertainty about very different models, for instance, backward- and forward-looking models; time-varying centralbank 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.” JEL Classification: E42, E52, E58

This paper specifies how to do policy simulations with alternative instrument-rate paths in DSGE models such as Ramses, the Riksbank’s main model for policy analysis and forecasting. The new element is that these alternative instrument-rate paths are anticipated by the private sector. Such simulations correspond to situations where the Riksbank transparently announces that it plans to implement a particular instrument-rate path and where this announcement is believed by the private sector. Previous methods have instead implemented alternative instrument-rate paths by adding unanticipated shocks to an instrument rule, as in the method of modest interventions by Leeper and Zha (2003). This corresponds to a very different situation where the Riksbank would nontransparently and secretly plan to implement deviations from an announced instrument rule. In actual simulations, such deviations are normally both serially correlated and large, which seems inconsistent with the assumption that they would remain unanticipated by the private sector. Simulations with anticipated instrument-rate paths seem more relevant for the transparent flexible inflation targeting that the Riksbank conducts. We provide an algorithm for the computation of policy simulations with arbitrary restrictions on

This paper specifies a new convenient algorithm to construct policy projections conditional on alternative anticipated policy-rate paths in linearized dynamic stochastic general equilibrium (DSGE) models, such as Ramses, the Riksbank’s main DSGE model. Such projections with anticipated policy-rate paths correspond to situations where the central bank transparently announces that it, conditional on current information, plans to implement a particular policyrate path and where this announced plan for the policy rate is believed and then anticipated by the private sector. The main idea of the algorithm is to include among the predetermined variables (the “state”of the economy) the vector of nonzero means of future shocks to a given policy rule that is required to satisfy the given anticipated policy-rate path.

We study the problem of a policymaker who seeks to set policy optimally in an economy where the true economic structure is unobserved, and he optimally learns from observations of the economy. This is a classic problem of learning and control, variants of which have been studied in the past, but seldom 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, computing 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 some simple examples to illustrate the role of learning and experimentation in an MJLQ framework.

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