A Defence of the FOMC - University of...
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A Defence of the FOMC
Martin Ellison and Thomas J. SargentOxford and NYU
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 1 / 27
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Sta¤ and FOMC forecasts
Sta¤ produce forecasts before each FOMC meeting
FOMC produces its own forecast twice a year after FOMC meeting
e.g. 1987Q3 forecasts:
Sta¤ FOMC
Current yearπU
3.5%6.3%
3.75%6.3%
Next yearπU
3.8%6.3%
4.0%6.25%
Information advantage is with FOMC
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 2 / 27
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Romer-Romer claim #1
Optimal predictions of ination and unemployment put zero weighton FOMC forecasts and unit weight on sta¤ forecasts
Regress outcomes on sta¤ forecasts Et and FOMC forecasts Êt :
πt+1 = �0.20(0.22)
+ 1.10(0.39)
Etπt+1 � 0.10(0.37)
Êtπt+1 R2 = 0.86
Ut+1 = 0.26(0.41)
+ 0.97(0.38)
EtUt+1 � 0.03(0.40)
ÊtUt+1 R2 = 0.79
Sta¤ forecast is better
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 3 / 27
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Romer-Romer claim #2
Sta¤ forecasts have smaller MSE than FOMC forecasts
MSE of Sta¤ forecast MSE of FOMC forecastπ 0.71 0.89U 0.54 0.57
Sta¤ forecast is closest to actual outcomes
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 4 / 27
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Romer-Romer claim #3
There is statistical and narrative evidence to suggest that di¤erencesbetween FOMC and sta¤ forecasts a¤ect actual policy outcomes
Regress Romer-Romer (2000) policy shocks on forecast di¤erences:
Mt = 0.04(0.06)
+ 0.31(0.20)
�Etπt+1 � Êtπt+1
�Mt = 0.04
(0.06)� 0.50(0.25)
�EtUt+1 � ÊtUt+1
�Monetary policy tightens when (i) FOMC ination forecast is aboveSta¤ forecast and (ii) when FOMC unemployment forecast is belowSta¤ forecast
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 5 / 27
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Romer-Romer conclusions (AER 2008)
the FOMC is not using the information in the sta¤ forecastse¤ectively
monetary policymakers may indeed act on information that is of littleor negative value
a more e¤ective division of labor within the Federal Reserve might befor the sta¤ to present policymakers with policy options and relatedforecast outcomes, and for policymakers to take those forecasts asgiven.
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 6 / 27
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A rst defence of the FOMC
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FOMC forecastGreenbook forecast
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Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 7 / 27
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A second defence of the FOMC
Romer and Romers criticism makes sense in a world with asingle-probability-density assumption and rational expectations
What if FOMC is actually responding in a reasonable way tospecication doubts?
FOMC forecasts may be worst case scenarios that are important for apolicymaker concerned that its model is only an approximation
Under this interpretation:I Sta¤ forecasts will be better predictors than FOMC forecastsI σ
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Hidden Markov models
Approximating model is a joint density f (x�, s�, x) over next periodsstate x� 2 X , next periods signal s�, and this periods state x 2 X
f (x�, s�, x) =Zf (x� jx )f (s� jx )f (x)dx
Assume x is only partially observable
f (x� js� ) = f (x�, s�)
f (s�)=
Rf (x� jx )f (s� jx )f (x)dxR
f (x�, s� jx )dx�
Policymaker distrusts f (x� jx ) and f (x)
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 9 / 27
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Robustness in hidden Markov models
Associated value function
W (f ) =Z �
U(x) +Z
βW̌ �(x�)f (x� jx )dx��f (x)dx
Distorted value function
Q(f ) = T2�U(x) +T1(βW̌ �(x�))(x)
�(f )
T1 is risk-sensitivity operator that induces worst-case distortion off (x� jx )T2 is risk-sensitivity operator that induces worst-case distortion off (x).
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 10 / 27
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Indirect utility functions
T1(W̌ �(x�))(x) � �θ1 logZexp
��W̌ �(x�)θ1
�f (x� jx )dx�
T2Z (x) � �θ2 logZexp
��Z (x)θ2
�f (x)dx
T2 is an object that occurs in work on ambiguity aversion
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 11 / 27
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Hidden Markov model for monetary policy
Primiceri (QJE 2006) model with unobserved NAIRU.
πt+1 = πt + γ0(Ut � uNt ) + γ1(Ut�1 � uNt�1) + cπwt+1(Ut+1 � uNt+1) = ρ1(Ut � uNt ) + ρ2(Ut�1 � uNt�1) + Vt + cUwt+1
Vt is a policy variable
NAIRU believed to follow an AR(1) process
uNt+1 = (1� γ)u� + γuNt + cU �wt+1
Objective for policymaker
�.5∞
∑t=0
βt�(πt � π�)2 + λ(Ut � kuNt )2 + φ(Vt � Vt�1)2
�
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 12 / 27
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Estimation process for policymaker
Policymaker has joint estimation and decision process
State space form:
yt+1 = A11yt + A12zt + B1at + C1wt+1zt+1 = A21yt + A22zt + B2at + C2wt+1st+1 = D1yt +D2zt +Hat + Gwt+1
This is a Kalman lter problem
yt+1 = A11yt + A12 žt + B1at + C1wt+1 + A12(zt � žt )žt+1 = A21yt + A22 žt + B2at +K2(∆t )Gwt+1 +K2(∆t )D2(zt � žt )
∆t+1 = C (∆t )
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 13 / 27
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Robust decision process
A form of certainty equivalence holds in this class of models.
Robust policy solves deterministic problem:
maxaminu
"Ũ(y , ž , z � ž , a) + θ2 u
0∆�1u2
+minṽ
�βW (y �, ž�,∆�, z�) + θ1 ṽ
0 ṽ2
� #s.t.
y � = A11y + A12 ž + B1a+ C1ṽ + A12u
z� = A21y + A22 ž + B2a+ C2ṽ + A22u
ž� = A21y + A22 ž + B2a+K2(∆)ṽ +K2(∆)D2u∆� = C (∆)
θ1 is preference to guard against forecast errors
θ2 is preference to guard against tracking errors
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 14 / 27
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Optimal policy
Optimal robust policy is simple linear feedback rule
a = ��Fy Fz
� � yž
�ṽ = �
�Ky Kz
� � yž
�u = �
�Ly Lz
� � yž
�
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 15 / 27
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Forecasts
Modied model
y � = A11y + A12 ž + B1a+ C1ṽ + A12u
Forecasts under the approximating model
E [y � jy , ž ] = (A11 � B1Fy )y + (A12 � B1Fz )ž
Forecasts under the worst-case model
Ê [y � jy , ž ] = (A11 � B1Fy � C1Ky � A12Ly )y+ (A12 � B1Fz � C1Kz � A12Lz )ž
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 16 / 27
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Numerical example
Primiceri (QJE 2006) empirical estimates
πt+1 = πt � 1.02(Ut � uNt ) + 0.903(Ut�1 � uNt�1) + cπwt+1(Ut+1 � uNt+1) = 1.756(Ut � uNt )� 0.779(Ut�1 � uNt�1) + Vt + cUwt+1
�.5∞
∑t=00.99t
�(πt � 2)2 + (Ut � 0.2uNt )2 + 475(Vt � Vt�1)2
�NAIRU process
uNt+1 = 0.05u� + 0.95uNt + cU �wt+1
Preferences for robustness
maxaminu
"Ũ(y , ž , z � ž , a) + 200u 0∆�1u2
+minṽ
�βW (y �, ž�,∆�, z�) + 200 ṽ
0 ṽ2
� #
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 17 / 27
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Example forecasts
0 10 20-5
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15Inflation
0 10 20-2
0
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12Unemployment
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 18 / 27
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Romer-Romer claim #1
Optimal predictions of ination and unemployment essentially putzero weight on FOMC forecasts and unit weight on sta¤ forecasts
Regress outcomes on sta¤ forecasts Et and FOMC forecasts Êt :
πt+1 = �0.83(0.44)
+ 1.22(0.42)
Etπt+1 � 0.16(0.24)
Êtπt+1 R2 = 0.38
Ut+1 = 0.52(1.28)
+ 1.02(0.45)
EtUt+1 � 0.15(0.26)
ÊtUt+1 R2 = 0.17
Sta¤ forecast being better can be rationalised
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 19 / 27
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Romer-Romer claim #2
Sta¤ forecasts have smaller MSE than FOMC forecasts
MSE of Sta¤ forecast MSE of FOMC forecastπ 2.80 3.36U 3.34 4.26
Sta¤ forecast being closest to actual outcomes can be rationalised
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 20 / 27
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Romer-Romer claim #3
There is statistical and narrative evidence to suggest that di¤erencesbetween FOMC and sta¤ forecasts a¤ect actual policy outcomes
Regress policy shocks on forecast di¤erences:
Mt = �0.07(0.02)
+ 0.023(0.009)
�Etπt+1 � Êtπt+1
�Mt = �0.05
(0.02)� 0.030(0.015)
�EtUt+1 � ÊtUt+1
�Can rationalise that monetary policy tightens when (i) FOMCination forecast is above Sta¤ forecast and (ii) when FOMCunemployment forecast is below Sta¤ forecast
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 21 / 27
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Estimation
Our model has the potential to explain the di¤erent forecasts of theSta¤ and the FOMC. Whether the model actually explains forecastdi¤erences is a question of estimation
Romer and Romer report that FOMC is:1 on average 13 basis points pessimistic on ination forecasts2 on average 6 basis points optimistic on unemployment forecasts
Can robustness rationalise these through parameters θ1 and θ2?
Set other parameters at Primiceri (2006) estimated values.
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 22 / 27
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Neurotic breakdown
θ1
0 100 200 300 400 5000
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1000
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2000
2500
θ2
Model breaks down if θ1 or θ2 too small
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 23 / 27
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Average ination forecast di¤erence
FOMC is 13 basis points pessimistic on ination forecasts
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θ1
0.2
0.30.4
0.60.8
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500
1000
1500
2000
2500
θ2
Can be explained by many combinations of θ1 and θ2
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 24 / 27
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Average unemployment forecast di¤erence
FOMC is 6 basis points optimistic on unemployment forecasts.θ1
-0.12
-0.1
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-0.04
-0.0
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0
0.04
0.04 0.120.12
0 100 200 300 400 5000
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1000
1500
2000
2500
θ2
Optimisim requires high θ1 and low θ2
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 25 / 27
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Average unemployment forecast di¤erence
Suggests FOMC care more about tracking errors (θ2) than forecastingerrors (θ1)
Forecasting is tracking ... Most of the focus in policy discussionconcerns todays state vector ... Further out is normally slow meanreversion ... Through experience, forecasters learned that the nearrandom walk model works best
(President James Bullard, 2009)
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 26 / 27
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Conclusions
Di¤erences between Sta¤ and FOMC forecasts consistent with arational response of FOMC to model misspecication
Average forecast di¤erences are consistent with FOMC forecastsbeing worst case scenarios
Worst case is pessimistic for ination and optimistic forunemployment if FOMC cares more about tracking than forecasting
Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 27 / 27