Forecasting and Policy Making (Paper) - Center for Financial Studies

where it is assumed that the policy maker observes potential output ¯yt and sets the y ∗ t accordingly.
Contrary to the simple rules discussed above, the optimal control policy implies a direct interest
rate response to all state variables, including zt, which stands for many variables that affect output
and inflation. The forecast-based rule incorporates an indirect response to all state variables via the
inflation and output forecasts, but the functional form of this rule imposes additional restrictions on the
coefficients relative to the optimal control policy. The optimal control coefficients ˜ φπ, ˜ φy and ˜ φz are
nonlinear functions of the structural model and loss function parameters (κ,γ,α,σ,δ,θ1,θ2,θ3,β,λ).
These coefficients are generally different from the response parameters in the simple rules, that is
(φπ,φy) and (φπ,h,φy,k). Forecasts of future inflation and output deviations from the central bank’s
targets—conditional on the central bank’s model and information set—are used in optimizing the path
of the central bank interest rate.
No central bank has publicly announced that it strictly implements an optimal control policy and
communicated the preference and model parameters needed for the policy calculation. Svensson
(1999, 2003) has proposed to mimic the optimal control policy by pursuing a so-called forecast tar-
geting rule. This rule is expressed in forecasts of the target variables output and inflation, rather than
directly implementable interest rate prescriptions. In his terminology the loss function with inflation
and the output gap in equation (1) is referred to as flexible inflation targeting. He breaks the opti-
mization problem in two steps. First, he derives the first-order conditions with respect to output and
inflation conditional on the Phillips curve, equation (4), that determines the economic tradeoff be-
tween these two target variables. In the second step, the other model equations are used to derive the
interest rate setting. This interest rate setting is equivalent to the optimal control policy defined by
equation (7). Svensson (2003) shows that the optimality condition corresponds to,
E[πt+j+1 − π ∗ |It] = λ
βκ (βE[(yt+j+1 − y ∗ t+j+1) − (yt+j − y ∗ t+j)|It]), j ≥ 0. (8)
for the case when zt is exogenous. This relationship between output and inflation forecasts provides an
implicit definition of the optimal control policy. With regard to its practical implementation, Svensson
(2003) recommends that ”the central bank staff construct the ”feasible” set of forecasts and instru-
ment plans. The decision-making body ... then selects the combination of forecasts that ”look best”
...., the best compromise between stabilizing the inflation gap and the output gap. ” This recommenda-
tion is similar but not identical to another often-used description of inflation forecast targeting, which
states that central banks should set policy such that the implied inflation forecast is equal to the central
bank’s target at some given, constant horizon.
Having presented several different approaches to the use of forecasts in policy design, namely sim-
ple outcome-based rules, simple forecast-based rules, optimal control policies and forecast targeting
rules, we close by noting an equivalence result that is obtained under restrictive conditions. Specifi-
cally, if the parameters γ and δ are set to zero, the other endogenous variable(s) denoted by zt do not
affect inflation or output. Thus, the optimal control policy takes the form of a simple outcome-based
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