A Defence of the FOMC - University of...

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A Defence of the FOMC Martin Ellison and Thomas J. Sargent Oxford and NYU Martin Ellison and Thomas J. Sargent A Defence of the FOMC 1 / 27

Transcript of A Defence of the FOMC - University of...

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • A rst defence of the FOMC

    1980 1985 1990 1995 20000

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    4

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    14

    Infla

    tion

    Q1 forecast for current year

    FOMC forecastGreenbook forecast

    1980 1985 1990 1995 20000

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    4

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    12

    14Q3 forecast for current year

    1980 1985 1990 1995 20000

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    14Q3 forecast for following year

    1980 1985 1990 1995 20000

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    4

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    14

    Une

    mpl

    oym

    ent

    1980 1985 1990 1995 20000

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    4

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    1980 1985 1990 1995 20000

    2

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    14

    Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 7 / 27

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • Example forecasts

    0 10 20-5

    0

    5

    10

    15Inflation

    0 10 20-2

    0

    2

    4

    6

    8

    10

    12Unemployment

    Martin Ellison and Thomas J. Sargent ()A Defence of the FOMC 18 / 27

  • 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

  • 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

  • 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

  • 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

  • Neurotic breakdown

    θ1

    0 100 200 300 400 5000

    500

    1000

    1500

    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

  • Average ination forecast di¤erence

    FOMC is 13 basis points pessimistic on ination forecasts

    .

    θ1

    0.2

    0.30.4

    0.60.8

    0 100 200 300 400 5000

    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

  • Average unemployment forecast di¤erence

    FOMC is 6 basis points optimistic on unemployment forecasts.θ1

    -0.12

    -0.1

    2

    -0.04

    -0.0

    4

    0

    0

    0.04

    0.04 0.120.12

    0 100 200 300 400 5000

    500

    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

  • 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

  • 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