Monetary Policy with Model Uncertainty: Distribution Forecast Targeting


Lars E.O. Svensson
Princeton University, CEPR, and NBER

Noah Williams
University of Wisconsin and NBER

First draft: May 2005
This version: May 2007


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 allow forward-looking variables. 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 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.”

JEL Classification: E42, E52, E58
Keywords: Optimal policy, multiplicative uncertainty

Matlab programs

Programs by Satoru Shimizu, Lars E.O. Svensson, and Noah Williams
Last update: July 25, 2007

Matlab programs
to compute and analyze optimal policy in forward- or backward-looking Markov
jump- linear-quadratic systems with the algorithms of the paper are included
in a zip-file.

The main programs are opt_policy.m and
which compute optimal policy and the simulated distribution of impulse
responses under the optimal policy. They require that a user define a
model as a structured variable consisting of a collection of matrices.
Given a specification of appropriate matrices, set_up_model.m defines the structured variable appropriately.

Two examples of how to use the programs to reproduce the results in the DFT paper are given in the following:

  • kickoff_RS.m computes optimal policy and plots impulse responses in the Rudebusch-Svensson model as in Section 4.1 of the paper
  • kickoff_Linde.m computes optimal policy and plots impulse responses in the Linde model as in Section 4.2 of the paper
  • These programs also provide much more detail on the setup and structure of the models and algorithms.

    In a bit more detail, the other files consist of the following:

  • set_up_model.m: creates a structured variable, “model” given a specification of matrices.
  • opt_policy.m and opt_policy_light.m: compute the optimal policy. The two programs differ only in that opt_policy.m checks the dimensions of all matrices.
  • impul_res.m: computes the impulse response distribution.
  • plot_impul_res.m: plots the impulse response distribution.
  • Also included are two utility files from Lars Peter Hansen and Thomas J. Sargent that accompany their monograph
    Recursive Models of Dynamic Linear Economies

  •  olrp.m: solves standard discounted linear quadratic dynamic programming problems
  • doubleo.m: solves matrix Riccati equations using a doubling algorithm