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Authorized for public release by the FOMC Secretariat on 02/09/2018

March 2, 2012
Simple Rules and Optimal Policies in Staff Models1
Christopher Erceg, Matteo Iacoviello, Michael Kiley, and David López-Salido
1. Introduction and summary
The staff regularly presents monetary policy prescriptions from simple rules and optimal control
simulations in Tealbook B. These prescriptions provide information on the implications of the
staff outlook for monetary policy through different lenses – with simple rules providing clear
benchmarks linking the federal funds rate to inflation and resource utilization, and optimal
control simulations illustrating how a commitment-based strategy can potentially improve
inflation and unemployment outcomes.
However, the factors that account for the different policy prescriptions of these alternative
strategies, as well as their relative performance in achieving ultimate policy goals, are not always
clear. Moreover, the Monetary Policy Strategies section of Tealbook B focuses exclusively on
the current baseline outlook. In this memo, we compare the performance of several simple
interest rate rules to the optimal policy across a range of scenarios, and highlight factors that
account both for their varying performance and somewhat differing policy prescriptions.
Our review suggests the following key results:


Simple policy rules with limited interest rate inertia, including the original Taylor (1993)
rule, the modified Taylor (1999) rule, and the outcome-based rule, do not approximate
optimal commitment strategies particularly well.
o Under current conditions, the optimal policy involves a commitment to keep
interest rates unusually low as the economy recovers so that unemployment
eventually falls below its natural rate and inflation rises somewhat above its 2
percent target; by contrast, the simple rules studied here imply a much sharper rise
in real interest rates as the economy recovers.
o Under initial conditions in which unemployment is close to the natural rate and
inflation is near 2 percent (“normal times”), we also find that these simple rules
do not approximate optimal policy well in response to both demand and supply
shocks. For example, the optimal policy succeeds better in restraining the
inflationary effect generated by an adverse supply shock through the conditional
commitment to keep policy tight for a protracted period.



The more aggressive response to the output gap in the Taylor (1999) rule relative to the
Taylor (1993) rule leads to somewhat better outcomes for resource utilization under the
modal outlook, and also in negative aggregate demand and supply shock scenarios.

1

 The authors thank James Clouse, William English, Jon Faust, Andrew Levin, Steve Meyer, David Reifschneider,
and David Wilcox for helpful comments and suggestions.

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However, a lower response to the output gap, as in the Taylor (1993) rule, leads to better
inflation developments in the event of the adverse supply shock.


Previous staff analysis suggests that some simple strategies can approximate optimal
commitment strategies in staff models. In particular, policies with features of flexibleprice level targeting – such as nominal income targeting – have desirable features in staff
models under a range of scenarios. In ongoing staff analysis, we are investigating the
degree to which simple commitment-based strategies can come close to the optimal
policy.

Section 2 of this memo compares the performance of simple interest rate rules to that of the
optimal policy under the current economic outlook. Section 3 discusses the optimal control and
simple rules under two scenarios: a recession scenario and an inflationary scenario. Section 4
focuses on the performance of these alternative strategies when the economy is initially
operating near full employment and the inflation rate is near target (that is, under normal
circumstances); a consideration of how policy strategies perform when the federal funds rate is
unconstrained at a more typical level well above zero highlights some of the special features of
current circumstances, where the zero lower bound is expected to bind for an extended period.
Finally, the last two sections of the memo provide an initial foray into issues that the staff plans
to investigate further. In particular, Section 5 briefly summarizes aspects of simple rules that
show promise in approximating (at least some features of) optimal commitment strategies, while
Section 6 briefly discusses the robustness of alternative strategies to mis-measurement of the
output gap, alternative models, and specifications of expectations.

2. Simple rules and optimal policy under the current economic outlook
FRB/US simulations
The left-hand column of Figure 1 presents outcomes for the federal funds rate, the
unemployment rate, and the headline PCE inflation rate under different policy strategies, using
the conditions expected in the January Tealbook as the underlying baseline, and assuming that
the dynamics of the economy match those of the FRB/US model under rational expectations.
The first set of strategies discussed here focuses on “optimal control” approaches. In the optimal
control simulations, policymakers are assumed to place equal weight on keeping PCE inflation
around 2 percent, on keeping the unemployment rate close to the staff’s estimate of the effective
NAIRU, and on minimizing changes in the federal funds rate. In the “discretion” case,
policymakers set policy on a period-by-period basis and are unwilling to promise unusual future
accommodation. Under “commitment,” policymakers are willing and able to credibly commit
(conditional on economic outcomes) to future policies that are potentially more expansionary
than usual in order to stimulate activity today. In both cases, policymakers are assumed to share
the baseline projection presented in the January Tealbook. As such, these policies condition on
all of the assumptions underlying the Tealbook projection: For example, these policies take into
account the effects of the staff’s baseline estimates for the impact of past and prospective balance
sheet actions on term premiums, economic activity, and inflation.

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Under the commitment strategy, optimal policy would involve holding the nominal federal funds
rate near its lower bound well into a projected economic recovery. Of course, this commitment
implies that the unemployment rate falls below its natural rate and inflation rises slightly above
its long-run objective value, outcomes that future Committees would prefer to act to avoid but
are assumed to accept as the price of delivering on the earlier conditional commitment. It is the
promise to remain accommodative and not prevent modestly above-target inflation and
moderately below-target unemployment in future periods that lowers current long-term interest
rates and thereby stimulates activity today. In contrast, “discretionary” optimal policies, which
do not constrain future actions, prescribe a considerably more rapid pace of tightening as the
economy recovers; this trajectory ensures that inflation rises at most only a bit above 2 percent
and that unemployment does not fall appreciably below its natural rate, but also results in
substantially poorer economic performance, on average, over the next decade.
We next compare these results under optimal policies with simulated outcomes when the funds
rate follows the prescriptions from three simple policy rules that appear regularly in Book B of
the Tealbook—the Taylor (1993) rule, the Taylor (1999) rule, and the outcome-based rule.2 As
was assumed in the case of optimal policy, the central bank enjoys complete credibility and
private agents fully understand the future economic implications of each rule. The Taylor (1999)
rule is identical to the original Taylor (1993) rule except that the former puts a higher weight (of
unity) on the output gap rather than 0.5 as in the original Taylor rule. Under the outcome-based
rule, the federal funds rate adjusts in response to the output gap and the change in the output gap,
as well as inflation. For both Taylor rules, we assume a modest degree of interest rate inertia by
setting the coefficient on the lagged nominal interest rate to 0.75, which is similar to that in the
outcome-based rule. Our results would not be noticeably different if we instead assumed a
completely non-inertial rule (that is, a coefficient of zero on the lag of the interest rate), as in the
original Taylor rule, though allowing for a modest degree of inertia does improve the
performance of the simple rules (relative to the optimal policy) slightly.3
As shown by the green lines in the left-hand column of Figure 1, outcomes under the Taylor
(1999) rule are substantially worse than those under the optimal commitment strategy (black
lines) though reasonably close to those under the discretion strategy (red-dashed lines). There
are two important differences between the Taylor (1999) rule and the optimal strategies. First,
the Taylor (1999) rule is somewhat less responsive to resource utilization, which appears to
account for the difference between the discretion strategy and the Taylor (1999) outcomes.
Second, the commitment strategy involves managing expectations regarding future policy
actions and remaining accommodative for a substantially longer period: These conditional
                                                            
2

The algebraic expressions for each rule appear in the Explanatory Notes attached at the end of each Tealbook B.
We ensure that each rule has the long-run steady-state equilibrium real interest rate that is consistent with the staff’s
January extended projection. The long-run equilibrium real interest rate is an important factor in the consideration
of alternative simple rules (as, for example, uncertainty about this concept can affect the performance of rules in
much the same way that uncertainty about the output gap does). This memo is focused on the role of responses to
resource utilization and inflation, and hence we do not consider the implications of uncertainty regarding the longrun equilibrium real interest rate.
3
With a coefficient of 0.75 on the lag of the interest rate, the current federal funds rate depends relatively little on
developments that occurred more than four or five quarters in the past, which accounts for why the implications are
very similar to the non-inertial rule. In contrast, as noted in Section 5, highly inertial rules (a coefficient on the lag
of the interest rate exceeding 0.9) can have markedly different implications.

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commitments lead to much better performance, on average, with only moderate overshooting of
inflation (above its goal) and unemployment (below its goal).
The Taylor (1993) strategy (the purple lines) involves raising the federal funds rate immediately,
leading to higher unemployment and inflation further below target over coming years. The
outcome-based rule also involves a somewhat earlier increase in the federal funds rate and hence
worse outcomes for both policy objectives—although the outcome-based rule is somewhat closer
to the Taylor (1999) rule, as it is more responsive to resource utilization than the Taylor (1993)
rule. Outcomes under both the Taylor (1993) and outcome-based strategies are further from
those under optimal policy than are outcomes under the Taylor (1999) strategy.4
SIGMA Simulations
The right-hand column of Figure 1 reports results for the same policy rules discussed above
based on simulations of the staff’s open economy model, SIGMA. SIGMA, like FRB/US,
assumes forward-looking behavior both in asset markets and in wage and price setting; however,
aggregate demand is more forward looking in SIGMA.
A comparison of the two columns reveals that the relative performance of the alternative
strategies for unemployment and inflation is broadly similar in the two models. In SIGMA, the
optimal rule is much more successful in reducing unemployment than any of the simple rules.
Given that SIGMA embeds a lower degree of intrinsic inflation persistence than FRB/US, the
optimal policy involves a larger initial increase in inflation (since it is less costly to bring
inflation back down), which lowers real interest rates and contributes to a faster recovery.
Among the simple rules, the Taylor (1999) rule performs a bit better than the outcome-based
rule. By contrast, the lack of relatively strong accommodation to slack in resource utilization
under the Taylor (1993) rule implies markedly higher real interest rates, lower inflation, and
higher unemployment.5

3. Performance of rules under two adverse scenarios
We now turn to an evaluation of how each policy rule would operate in both the FRB/US and
SIGMA models under two alternative scenarios. Such an analysis is critical to gauging the
robustness of the relative performance of the various rules under a range of conditions, and not
just under the baseline outlook (particularly as the economy may evolve in quite unexpected
ways). In the first scenario, adverse demand shocks lead to a moderately severe recession; in the
second scenario, adverse price shocks boost core PCE inflation significantly.
The adverse demand shocks under the recession scenario increase unemployment to around 11
percent in the FRB/US model under the Taylor (1999), Taylor (1993), and outcome-based rule
strategies, as can be seen in the left-hand column of Figure 2; as a result, the federal funds rate
remains at its effective lower bound until 2016 or later under each strategy, and core PCE prices
                                                            
4

Table 1 computes welfare losses for each of the alternative policy rules under the assumed quadratic loss function
described in Section 2.
5
The staff has not developed methods to compute optimal policy under discretion at the zero lower bound in the
SIGMA model.

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decline by ½ percent per year for several years starting in 2013. In the SIGMA model, the
different strategies lead to more distinct differences in outcomes: The Taylor (1999) rule
provides the most accommodation because of its strong response to resource utilization, whereas
the Taylor (1993) rule provides the least accommodation; as a result, unemployment and
inflation outcomes are closer to objective under the Taylor (1999) strategy than under the other
two simple rules, and performance is especially poor under the Taylor (1993) strategy.
In both models, the simple rules do not perform nearly as well as the optimal policy under
commitment. In the FRB/US model, optimal policy keeps the unemployment rate from rising
much above 10 percent and inflation remains above 1 percent; by contrast, the Taylor (1999) rule
allows for a sustained deflation and a much more protracted output contraction. In SIGMA,
optimal policy succeeds in boosting inflation well above target, promoting a much faster
recovery than under the Taylor (1999) rule. However, these outcomes are only achieved under
these commitment strategies by the promise to remain accommodative for a long period, which
involves promising to allow unemployment and inflation to notably overshoot their long-run
objectives later in the decade.
Figure 3 reports results in response to an adverse shift in inflation (that is, the scenario features
“supply” shocks to the Phillips curve). In both models, the optimal strategy is more
accommodative in the near-term than the simple rules. In fact, the optimal policy largely avoids
an increase in unemployment relative to the modal path, which is highly desirable in the current
environment in which unemployment is well above the natural rate. While the simple rules
imply a considerably earlier liftoff from the zero lower bound in response to the supply shock,
and a fairly rapid pace of tightening thereafter, the optimal policy takes more account of the
initially large unemployment gap. For example, the optimal policy keeps the federal funds rate
at zero through the end of 2014, while the modified Taylor (1999) rule prescribes a federal funds
rate of around 3 percent by that date.
In both models, the real federal funds rate is higher at longer horizons under optimal policy than
under the simple rules, which causes inflation to fall significantly below its 2 percent target by
2016. The longer-horizon commitment to tighten policy improves the near-term trade-off
between unemployment and inflation relative to the simple rules. Given the high initial level of
unemployment, this improved trade-off induces policymakers to pursue a highly accommodative
policy in the near-term. In SIGMA, inflation temporarily rises above 4 percent under the optimal
policy – noticeably higher than under the simple rules – but this cost is worth bearing to avoid
further increases in unemployment. In FRB/US the near-term trade off under the optimal policy
is so favorable that the near-term inflation rate is lower even under such an accommodative
monetary policy.

4. Simple rules and optimal policy under normal circumstances
We next consider the performance of the alternative rules when the economy is initially
operating near full employment, inflation is near target, and the nominal federal funds rate is
near its long-run value (that is, under more normal conditions). Such an analysis can help
distinguish between those features of optimal policies and simple rule strategies that are related
to the current zero-lower bound constraint, and those that are more general.

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The blue lines in Figure 4 show the effects of the recession scenario under the outcome-based
rule in each model. The shock is normalized to occur in year zero, and the panels show the
dynamic responses of nominal interest rates, unemployment, and inflation. In this scenario,
aggregate demand weakens enough to push the unemployment rate above 7 percent after two
years and inflation declines markedly.
The left-hand column presents results from the FRB/US model. Under the commitment strategy,
the federal funds rate is pushed to its effective lower bound for more than three years: As before,
a commitment strategy depends upon policymakers having a reputation to deliver on past
promises. In this case, the promise is to allow inflation to rise to 2½ percent later on so as to
keep unemployment closer to its natural rate in the near-term. The simulations shown here
highlight a result we emphasized earlier: The Taylor (1999) strategy is not as responsive to
resource utilization and does not mimic the commitments to remain accommodative once activity
has recovered that characterize the optimal commitment strategy in the FRB/US model. As a
result, the outcomes for inflation and unemployment are not as good. Finally, the Taylor (1993)
model delivers worse outcomes for unemployment, while inflation performance is little changed
relative to the other simple rules. In the SIGMA model, the relative performance of optimal
control and the simple rules is similar to FRB/US.6
Figure 5 reports results in response to an adverse shift in inflation (that is, shocks to the Phillips
curve). As discussed in the context of Figure 3, because the optimal policy promises to be less
accommodative at longer horizons than the simple rules, it is much more effective in restraining
inflation. For example, under optimal policy inflation averages only about 3 percent in the first
five years following the shock in FRB/US, compared with about 3½ percent under the Taylor
(1999) rule. Although it would be possible to achieve inflation outcomes similar to those
obtained under the optimal policy through a simple Taylor rule which reacted much more
aggressively to inflation, the outcomes for unemployment would be less palatable than under the
optimal rule. Thus, the optimal policy improves the inflation-unemployment tradeoff by
refraining from a large upfront tightening of policy, which would lead to a greater rise in
unemployment for any given inflation response, and instead makes the (conditional) commitment
to keep policy moderately tighter for a protracted period.
On balance, the promise to remain tighter in the future under the optimal policy leads to
considerable welfare improvement relative to the simple rules. Although there is some
difference in responses across the simple rules, each of them implies a relatively monotonic
convergence of inflation to target. Because the optimal policy is able to commit to a persistent
undershooting of inflation in the longer-run, it achieves a lower inflation rate in the near-term.

                                                            
6

In both models, the implications of the Taylor (1999) rule for unemployment and inflation are virtually identical to
those of the outcome-based rule. Our previous analysis conditioned on a modal path in which the economy began in
recession, and was expected to recover. In that environment, the outcome-based rule – because it reacts to GDP
growth, as well as the output gap and inflation – implied a more rapid tightening of policy rates than the modified
Taylor rule. The key difference in Figure 4 is that the public recognizes that the outcome-based rule implies a faster
decline in policy rates as the economy goes into recession than the modified Taylor (1999) rule; thus, although
policy rates are expected to rise more sharply as the economy recovers, the implications for longer-term real interest
rates turn out to be very similar under the two rules.

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5. Better approximating an optimal commitment strategy with a simple rule
Our simulation results underscore that a simple relatively non-inertial Taylor-style rule does not
approximate optimal policy under commitment particularly well, in line with a large academic
literature and related staff analysis.
Staff analyses have shown that simple strategies such as flexible price-level targeting – in which
policy aims to reverse past inflation shortfalls rather than let bygones be bygones – can
approximate optimal strategies under some conditions. Figure 6 illustrates how a form of
flexible-price level targeting – nominal income targeting – moves a step closer to the optimal
policy under the modal outlook (relative to the Taylor (1999) strategy) in both models. Under a
more inertial reaction (than implied by the 0.75 lag coefficient assumed above), a flexible pricelevel strategy would come even closer to the optimal policy, since the higher inertia means that
policy, in effect, takes greater account of past weakness in the economy. The relatively
favorable performance of a strategy like nominal income targeting also holds in scenarios
involving a recession or rise in inflation, of the type considered in previous sections.7
Although nominal income targeting may be beneficial in certain circumstances, such a strategy
may have potentially important shortcomings. Notably, as in the case of the optimal policy,
there is a significant commitment problem insofar as the benefits of an inertial nominal income
targeting rule in a zero lower bound situation are front-loaded, while the costs, in the form of
higher-than-desired inflation and lower-than-desired unemployment, are paid later.

6. Robustness of results to several key issues
Our analysis thus far has focused on a limited set of simulations using the FRB/US and SIGMA
models. The results are robust to some key considerations; that said, several issues clearly limit
their generality and deserve further investigation.
One possible concern is the robustness of the results to alternative views of how the economy
operates. One way of looking at this issue is to consider the robustness of these results to model
uncertainty. FRB/US and SIGMA represent distinctly different modeling approaches – one
being somewhat more data-based and the other placing a larger emphasis on behavioral
foundations for specific equations. Researchers have investigated issues similar to those we have
considered in a range of macroeconomic models, and, in general, have suggested conclusions
similar to ours. For example, Woodford (2011) discusses how the importance of commitment
strategies at the zero lower bound is a central aspect of optimal strategies (that is absent from the
simple rules we consider). Levin, Wieland, and Williams (1999) examined the performance of a
range of simple rules in four macroeconometric models (including FRB/US): They concluded
that, in general, policy strategies in which the federal funds rate responded with very persistent
accommodation or tightening in response to shocks (a feature sometimes called history                                                            
7

The nominal income interest rate rule and its performance in a range of scenarios similar to those examined here
was discussed in Michael Kiley, Christopher Erceg, and David López-Salido, “Alternative Monetary Policy
Frameworks,” memo sent to the Committee on October 6, 2011. In that memo, the lag on the interest rate in the
reaction function was set to 0.9, allowing nominal income targeting to come much closer to the optimal policy than
in Figure 6.

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dependence, and which characterizes commitment strategies) dominated rules without this
feature; they also showed that the Taylor (1993) and Taylor (1999) rules delivered, on average,
fairly similar performance in the situations they considered.
A further issue that is important in practice is the robustness of alternative strategies to mismeasurement of the output gap. Orphanides et al. (1999) showed that errors in output gap
measurement should lead policymakers to respond less to the output gap than they would in the
absence of such errors. Nonetheless, the best rules in their analysis had a greater short-run
responsiveness to the output gap than the inertial Taylor (1999) rule we considered. Moreover,
their analysis also suggested that it remained superior to respond to the level of the output gap,
rather than its change, for reasonable assumptions regarding output gap mis-measurement.
Similarly, Taylor and Williams (2011) summarized research on how mis-measurement of
resource utilization affects the performance of simple rules, and concluded that a high degree of
inertia and a sizable short-run response to resource utilization remains a feature of good rules in
the face of moderate mis-measurement of utilization. However, they also interpreted the
literature as supporting a potentially important role for responding to the change in resource
utilization (in addition to the level) when the risk of greatly mis-measuring slack is large.
Finally, a central reason why our analysis suggests an important role for strategies in which
policy accommodation remains highly persistent in response to current and past shortfalls in
demand (that is, history-dependence) in the current environment is that our models assume an
important role for expected future short-term interest rates in aggregate demand determination.
This echoes the finding in the related literature (for example, Levin et al (1999) and Woodford
(2011)): For example, Levin et al. (1999) emphasized how the central role for history
dependence arose because, in the range of models they considered, expected short-term interest
rates, through their effect on long-term interest rates, are the key channel through which
monetary policy strategies affect inflation and unemployment. Of course, the role of
expectations implies that all of the strategies we discuss rely on credible communication that
allows the public to understand the policy strategy. In the absence of such understanding, it is
likely that some of our key results would be weaker or could even be overturned: For example,
commitment strategies yield no benefits, and would even be costly, if the commitments had no
influence on long-term interest rates and aggregate demand; the benefits of such strategies would
also be smaller if expectations adjusted only very slowly to the announced strategy. At the
extreme, history-dependent strategies have been shown to perform very poorly in models in
which expectations regarding interest rates or inflation are purely backward looking, such as in
the widely analyzed simple model of Rudebusch and Svensson (1999).

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References
Taylor, John B. (1993). “Discretion versus Policy Rules in Practice,” Carnegie-Rochester
Conference Series on Public Policy, vol. 39 (December), pp. 195-214.
Taylor, John B. (1999). “A Historical Analysis of Monetary Policy Rules,” in John B. Taylor,
ed., Monetary Policy Rules. University of Chicago Press, pp. 319-341.
Levin, Andrew T., Volker Wieland and John Williams (1999). “Robustness of Simple Monetary
Policy Rules under Model Uncertainty,” in John B. Taylor, ed., Monetary Policy Rules.
University of Chicago Press, pp. 263-299.
Levin, Andrew T., Volker Wieland, John C. Williams (2003). “The Performance of ForecastBased Monetary Policy Rules under Model Uncertainty,” The American Economic Review, Vol.
93, No. 3 (Jun., 2003), pp. 622-645.
Orphanides, Athanasios, Richard D. Porter, David Reifschneider, Robert Tetlow, and
Federico Finan (2000). “Errors in the measurement of the output gap and the design of monetary
policy,” Journal of Economics and Business, vol. 52(1-2), pp. 117-141.
Svensson, Lars and Glenn Rudebusch (1999). “Policy Rules for Inflation Targeting,” in John B.
Taylor, ed., Monetary Policy Rules. University of Chicago Press, pp. 203-246.
Taylor, John and John Williams (2011). “Simple and Robust Rules for Monetary Policy,” in
B.M. Friedman and M. Woodford, eds., Handbook of Monetary Economics, vol. 3B, pp.829860.
Woodford, Michael (2011). “Optimal Monetary Stabilization Policy,” in B.M. Friedman and M.
Woodford, eds., Handbook of Monetary Economics, vol. 3B, 2011.

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Table 1: Welfare Losses under Alternative Rules

Welfare Losses at the Zero Lower Bound
FRB/US
Unemp. Loss Inflation Loss
Current Economic
Outlook

Commitment
Outcome‐based
Taylor 1993
Taylor 1999

Recession Scenario

Commitment
Outcome‐based
Taylor 1993
Taylor 1999

Adverse Price Shock

Commitment
Outcome‐based
Taylor 1993
Taylor 1999

51.7
77.3
87.8
67.6

29.4
105.8
92.0
90.1

Unemp. Loss Inflation Loss

61.2
97.4
119.4
78.5

Total Loss

1.4
9.4
11.6
4.6

Unemp. Loss Inflation Loss

227.7
315.4
304.0
299.4

SIGMA

22.4
68.4
83.8
126.7

54.8
87.5
99.9
72.9
Total Loss

261.0
422.4
397.1
391.0
Total Loss

85.6
167.4
204.5
206.6

Unemp. Loss Inflation Loss

21.6
77.8
130.5
63.8

14.8
6.5
21.9
2.9

Unemp. Loss Inflation Loss

51.9
309.5
461.6
215.2

16.0
26.3
62.2
11.2

Unemp. Loss Inflation Loss

57.0
114.8
195.7
87.7

64.0
44.1
28.4
67.2

Total Loss

38.4
84.8
152.9
67.2
Total Loss

69.5
336.5
524.8
227.1
Total Loss

123.4
159.8
224.7
155.8

Welfare Losses under normal circumstances
FRB/US
Unemp. Loss Inflation Loss
Recession Scenario

Commitment
Outcome‐based
Taylor 1993
Taylor 1999

Adverse Price Shock

Commitment
Outcome‐based
Taylor 1993
Taylor 1999

23.7
30.0
40.7
30.7

Total Loss

17.4
38.9
39.5
37.3

Unemp. Loss Inflation Loss

12.1
7.6
7.3
5.1

SIGMA

47.0
74.5
82.6
72.1

Total Loss

23.8
46.2
41.5
52.2

36.3
54.4
49.3
57.8

Unemp. Loss Inflation Loss

7.0
18.0
29.0
19.3

0.1
3.4
4.1
1.9

Unemp. Loss Inflation Loss

33.8
6.8
10.7
4.2

11.9
46.8
48.0
53.2

Total Loss

7.8
22.3
33.7
21.7

Total Loss

45.8
53.9
59.1
57.7

Welfare losses are, for unemployment, the sum of the squared deviations of unemployment from its natural rate; for inflation, the sum of the squared 
deviations of inflation from 2 percent. Total losses also include the sum of the squared quarter on quarter changes in the fed funds rate. The losses are 
calculated for each variable over a 15‐year horizon, and are discounted at 4 percent per annum.

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Figure 1: Outcomes for Different Rules, Modal Outlook
Nominal Fed Funds Rate, FRB/US
6

Nominal Fed Funds Rate, SIGMA
6

Commitment
Discretion
Outcome−based
Taylor 1993
Taylor 1999

5
4

5
4

3

3

2

2

1

1

0
2012

2014

2016

2018

2020

0
2012

Unemployment Rate, FRB/US
11

10

10

9

9

8

8

7

7

6

6

5

5
2014

2016

2018

2020

4
2012

Inflation (4−quarter), FRB/US
3.5

3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5
2014

2016
Year

2018

2018

2020

2014

2016

2018

2020

Inflation (4−quarter), SIGMA

3.5

0
2012

2016

Unemployment Rate, SIGMA

11

4
2012

2014

2020

0
2012

Page 11 of 16

2014

2016
Year

2018

2020

Authorized for public release by the FOMC Secretariat on 02/09/2018

Figure 2: Outcomes for Different Rules, Recession Scenario
Nominal Fed Funds Rate, FRB/US
8

Nominal Fed Funds Rate, SIGMA
8

Commitment
Outcome−based
Taylor 1993
Taylor 1999

6

6

4

4

2

2

0
2012

2014

2016

2018

2020

0
2012

Unemployment Rate, FRB/US
12

10

10

8

8

6

6

4

4
2014

2016

2018

2020

2012

Inflation (4−quarter), FRB/US
3

2

2

1

1

0

0

−1

−1
2014

2016
Year

2018

2018

2020

2014

2016

2018

2020

Inflation (4−quarter), SIGMA

3

2012

2016

Unemployment Rate, SIGMA

12

2012

2014

2020

Page 12 of 16

2012

2014

2016
Year

2018

2020

Authorized for public release by the FOMC Secretariat on 02/09/2018

Figure 3: Outcomes for Different Rules, Adverse Price Shock
Nominal Fed Funds Rate, FRB/US

Nominal Fed Funds Rate, SIGMA

6

6

5

5

4

4

3

3

2

Commitment

2

Outcome−based

1

Taylor 1993

1

Taylor 1999

0
2012

2014

2016

2018

2020

0
2012

Unemployment Rate, FRB/US
11

10

10

9

9

8

8

7

7

6

6

5

5
2014

2016

2018

2020

4
2012

Inflation (4−quarter), FRB/US
5

4

4

3

3

2

2

1

1

2014

2016
Year

2018

2018

2020

2014

2016

2018

2020

Inflation (4−quarter), SIGMA

5

0
2012

2016

Unemployment Rate, SIGMA

11

4
2012

2014

2020

0
2012

Page 13 of 16

2014

2016
Year

2018

2020

Authorized for public release by the FOMC Secretariat on 02/09/2018

Figure 4: Outcomes for Different Rules, Recession (Normal Conditions)
Nominal Fed Funds Rate, FRB/US
7

Nominal Fed Funds Rate, SIGMA
7

Commitment

6

6

Outcome−based
Taylor 1993

5

5

Taylor 1999

4

4

3

3

2

2

1

1

0

0

2

4

6

8

0

0

Unemployment Rate, FRB/US
8

7

7

6

6

5

5

4

4
2

4

6

8

0

Inflation (4−quarter), FRB/US
3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5

0

2

4
Year

6

6

8

2

4

6

8

Inflation (4−quarter), SIGMA

3

0

4

Unemployment Rate, SIGMA

8

0

2

8

0

Page 14 of 16

0

2

4
Year

6

8

Authorized for public release by the FOMC Secretariat on 02/09/2018

Figure 5: Outcomes for Different Rules, Price Shock (Normal Conditions)
Nominal Fed Funds Rate, FRB/US

Nominal Fed Funds Rate, SIGMA

8

8

7

7

6

6

5

5

4

4

Commitment
Outcome−based

3

3

Taylor 1993
Taylor 1999

2

0

2

4

6

8

2

0

Unemployment Rate, FRB/US
7.5

7

7

6.5

6.5

6

6

5.5

5.5

5

5

0

2

4

6

8

4.5

0

Inflation (4−quarter), FRB/US
5

4

4

3

3

2

2

1

1

0

2

4
Year

6

6

8

2

4

6

8

Inflation (4−quarter), SIGMA

5

0

4

Unemployment Rate, SIGMA

7.5

4.5

2

8

0

Page 15 of 16

0

2

4
Year

6

8

Authorized for public release by the FOMC Secretariat on 02/09/2018

Figure 6: Outcomes for Different Rules, Modal Outlook
Nominal Fed Funds Rate, FRB/US
6

Nominal Fed Funds Rate, SIGMA
6

Commitment
Taylor 1999
Nominal Income Targeting

5

5

4

4

3

3

2

2

1

1

0
2012

2014

2016

2018

2020

0
2012

Unemployment Rate, FRB/US
11

10

10

9

9

8

8

7

7

6

6

5

5
2014

2016

2018

2020

4
2012

Inflation (4−quarter), FRB/US
3.5

3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5
2014

2016
Year

2018

2018

2020

2014

2016

2018

2020

Inflation (4−quarter), SIGMA

3.5

0
2012

2016

Unemployment Rate, SIGMA

11

4
2012

2014

2020

0
2012

Page 16 of 16

2014

2016
Year

2018

2020


Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102