Bjø nland, Hilde Ch is iane; C oss, Jamie; Hölz, Jonas
Wo king Pape
Re- isi ing he ela ionship be ween oil p ices and
mone a y policy
Wo king Pape , No. 4/2025
P o ided in Coope a ion wi h:
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Sugges ed Ci a ion: Bjø nland, Hilde Ch is iane; C oss, Jamie; Hölz, Jonas (2025) : Re- isi ing
he ela ionship be ween oil p ices and mone a y policy, Wo king Pape , No. 4/2025, ISBN
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Wo king Pape
Re- isi ing he Rela ionship Be ween Oil P ices and
Mone a y Policy
No ges Bank Resea ch
Au ho s
:
Hilde C. B
jø nland
Jamie L. C oss
Jonas Hölz
K
eywo ds:
P oxy
-SVAR, Mone a y Policy
Ins umen , Oil P ice Ins umen ,
Coun e ac ual Analysis, Mone a y
Policy ade-o s
4 | 2025
No ges Bank Wo king Pape
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ISSN 1502-8143 (online)
ISBN 978-82-8379-357-4 (online)
Re- isi ing he Rela ionship Be ween Oil P ices
and Mone a y Policy∗
Hilde C. Bjø nland†Jamie L. C oss‡Jonas Hölz §
Ma ch 15, 2025
Abs ac
This pape examines how cen al banks espond o supply-side shocks and
in es iga es he ade-o s hey ace in s abilizing in la ion and ou pu . To do
so we de elop a dual ex e nal ins umen p oxy s uc u al ec o au o eg es-
si e (SVAR) model o disen angle he mac oeconomic e ec s o oil supply
news and mone a y policy shocks. Ou iden i ica ion s a egy, which com-
bines mul iple ex e nal ins umen s wi h sign es ic ions, enables a sha p
dis inc ion be ween s uc u al shocks, allowing us o analyze hei dynamic
e ec s and cons uc policy coun e ac uals o di e en cen al bank objec-
i es. We ind ha bo h oil supply and mone a y policy shocks signi ican ly
in luence U.S. ou pu and in la ion. Mo eo e , while mone a y policy can
mi iga e some o he ou pu losses caused by oil p ice shocks, i canno ully
o se hei in la iona y e ec s. Finally, we es ima e ha he Fede al Re-
se e’s his o ical esponse aligns closely wi h a policy ha places wice as
much weigh on in la ion s abiliza ion han on ou pu s abiliza ion.
JEL classi ica ion codes: C32, E31, E43, Q41, Q43
Keywo ds: P oxy-SVAR, Mone a y Policy Ins umen , Oil P ice Ins u-
men , Coun e ac ual Analysis, Mone a y Policy ade-o s
∗This pape should no be epo ed as ep esen ing he iews o No ges Bank. The iews exp essed a e hose
o he au ho s and do no necessa ily e lec hose o No ges Bank. We hank Knu A e Aas ei , Ch is iane
Baumeis e , Chenghan Hou, Sil ia Mi anda-Ag ippino, Lo enzo Mo i, Ma hew Read, Lei Ande s Tho s ud,
Benjamin Wong, an anonymous e e ee o ou No ges Bank Wo king Pape , and con e ence pa icipan s a he
SNDE 2024 Symposium in Pado a, he Dolomi i Mac o Mee ing 2024 in Kas el u h and he Midwes Econome ics
G oup Con e ence 2024 in Lexing on o use ul commen s and sugges ions. This pape is pa o he esea ch
ac i i ies a he Cen e o Applied Mac o and commodi y P ices (CAMP) a he BI No wegian Business School.
†BI No wegian Business School and No ges Bank. Email: hilde.c.b[email p o ec ed]
‡Melbou ne Business School, Uni e si y o Melbou ne. Email: j.c [email protected]
§BI No wegian Business School. Email: [email p o ec ed]
1 In oduc ion
Pe iods o commodi y p ice ola ili y ha e long posed challenges o mone a y
policymake s, aising ques ions abou he ex en o which cen al banks should
in e ene o mi iga e hei economic consequences. The ecen su ge in in la ion
ollowing he COVID-19 pandemic and he Russia-Uk aine wa has eigni ed in-
e es in his issue, d awing compa isons o he high-in la ion episodes o he 1970s
and 1980s. These his o ical pa allels highligh an endu ing mac oeconomic ques-
ion: wha cons i u es an op imal cen al bank esponse o supply shocks?
A cen al issue in his discussion is he ade-o be ween in la ion s abiliza-
ion and sus aining economic ac i i y ha cen al banks ace when esponding
o supply shocks. This ques ion has been a he co e o mac oeconomic esea ch
since he seminal wo k o Be nanke e al. (1997), who a gued ha he dep h o
oil-induced ecessions is la gely a consequence o he cen al bank’s eac ion a he
han he shock i sel . Howe e , subsequen s udies, including Hamil on and He -
e a (2004), He e a and Pesa en o (2009), Kilian and Lewis (2011) and Bjø nland
e al. (2018), ha e challenged his iew, demons a ing ha mone a y policy e ec-
i eness depends on he unde lying model amewo k, he design o coun e ac ual
exe cises and b oade economic condi ions, including he p e ailing policy egime.
Empi ical challenges in disen angling he e ec s o mone a y policy om o he
mac oeconomic dis u bances ha e long hinde ed p og ess in esol ing his deba e.
Howe e , ecen ad ancemen s in mul i a ia e ime-se ies modeling ha e imp o ed
shock iden i ica ion echniques, while he de elopmen o mo e obus coun e ac-
ual analysis o e s he po en ial o a mo e p ecise assessmen o how mone a y
policy in luences economic ou comes ollowing supply shocks.
Agains his backd op, ou s udy employs s a e-o - he-a econome ic ech-
niques o eassess his long-s anding ques ion, o e ing new insigh s in o he ade-
o s cen al banks ace in na iga ing supply-side shocks. Speci ically, we employ
a dual ex e nal ins umen p oxy s uc u al ec o au o eg essi e (SVAR) model
ha allows us o join ly iden i y mone a y policy shocks and oil supply news shocks
wi hin he SVAR. This builds on he p oxy SVAR li e a u e (S ock and Wa son,
2012; Me ens and Ra n, 2013) and ecen ex ensions ha allow o mul iple in-
s umen s (Pi e and Pods awski, 2018; A ias e al., 2021; B aun and B üggemann,
1
2022; Giacomini e al., 2022; Angelini e al., 2024).
P ecise shock iden i ica ion in s uc u al analysis equi es ca e ully chosen in-
s umen s. To cons uc he mone a y policy ins umen , we ollow he me hodol-
ogy o Baue and Swanson (2023a) wi h wo adjus men s: ex ending hei analysis
h ough he COVID-19 pe iod and by adding oil p ices in o he se o mac oe-
conomic a iables used o o hogonalize he shock se ies. This la e enhances
obus ness, pa icula ly in pe iods o s ong oil-ma ke -policy in e ac ion. Fo oil
supply news shocks, we adap he ins umen om Känzig (2021), which iden i-
ies shocks ia oil u u es p ice mo emen s a ound OPEC mee ings. To ensu e
obus ness, we also es some ecen al e na i e oil supply measu es (Baumeis e
and Hamil on (2019); Degaspe i (2023)).
While we expec he wo ex e nal ins umen s o exhibi low co ela ion, B uns
e al. (2024) highligh ha e en weakly co ela ed ins umen s can in oduce un-
in ended co ela ions be ween iden i ied shocks, dis o ing impulse esponse es i-
ma es. To mi iga e his isk, we impose s uc u ed co ela ion es ic ions ha
ensu e each ins umen is mo e s ongly co ela ed wi h i s in ended shock han
wi h he al e na i e, ein o cing iden i ica ion. This app oach enhances obus ness
in P oxy SVAR amewo ks, whe e explici ly accoun ing o co ela ion is c ucial.
A cen al inno a ion o ou pape is he applica ion o he McKay and Wol
(2023) amewo k o cons uc ing mone a y policy coun e ac uals in a way ha
is obus o he Lucas c i ique. In pa icula , a he han elying on a pa ame ic
s uc u al model, we use empi ical es ima es o policy shock ansmission o in e
al e na i e policy pa hs. This allows us o quan i y he ade-o s policymake s ace
when esponding o oil shocks, de e mining how di e en policy p io i ies—such
as g ea e emphasis on in la ion s abiliza ion e sus ou pu s abiliza ion—a ec
economic ou comes.
We ha e h ee main indings. Fi s , we show ha , consis en wi h many s ud-
ies, bo h oil supply shocks and mone a y policy shocks signi ican ly in luence in-
la ion and economic ou pu , wi h hei ela i e impo ance shi ing o e ime.
Second, coun e ac ual analyses indica e ha al hough mone a y policy can e-
duce ou pu losses, i canno ully neu alize he in la iona y p essu es c ea ed by
oil p ice shocks. This unde sco es he pe sis en in luence o oil p ice mo emen s
on mac oeconomic ou comes, e en unde op imal policy in e en ions, challenging
2
he conclusions o Be nanke e al. (1997). In pa icula , by highligh ing he in in-
sic s ag la iona y dynamics o oil supply news shocks, ou analysis unde sco es he
need o a nuanced unde s anding o how oil supply shocks in e ac wi h b oade
mac oeconomic condi ions, ega dless o mone a y policy in e en ion. Thi d, ou
analysis unde sco es he ade-o s cen al banks ace when esponding o oil p ice
shocks. P io i izing in la ion con ol leads o igh e policy and g ea e ou pu
losses, while emphasizing ou pu s abiliza ion esul s in mo e accommoda i e poli-
cies bu highe in la ion. In ac , we show ha baseline policy pa h closely mi o s
a scena io whe e in la ion is weigh ed 2.5 imes mo e han ou pu , e lec ing a
p agma ic balance be ween hese compe ing objec i es in he ace o oil-d i en
dis up ions.
Rela ed Li e a u e. This pape con ibu es o he empi ical li e a u e on
he ole o mone a y policy in ansmi ing oil p ice shocks o he eal economy,
c. . Be nanke e al. (1997) o a seminal pape showing ha sys ema ic mone a y
policy esponses we e a p ima y d i e o ecessions ollowing majo oil p ice shocks
and Hamil on and He e a (2004), He e a and Pesa en o (2009), Kilian and Lewis
(2011) and Bjø nland e al. (2018) ha challenge his iew. Mo e ecen analysis,
such as Miyamo o e al. (2024), ha e ocused on he impac o oil supply shocks
on he mac oeconomy du ing he ze o lowe bound pe iod, while Cas elnuo o
e al. (2024) s udy he ansmission mechanism o a ious commodi y ma ke
shocks. Mo e ela ed is he pape by Gaglia done and Ge le (2023), ha analyze
he ade-o s in mone a y policy esponses using a calib a ed quan i a i e New-
Keynesian model. We complemen Gaglia done and Ge le (2023) by analysing
he in la iona y p essu es o oil p ice shocks and he ade-o s in mone a y policy
esponses using a p oxy SVAR model. Ou amewo k allows o an empi ical
assessmen o he ela i e impac s o oil and mone a y shocks o e ime, as well
as he s udy o op imal mone a y policy using an empi ical model.
F om a me hodological iewpoin , ou s udy ela es o he li e a u e ha uses
mul iple ex e nal ins umen s o iden i y di e en s uc u al shocks wi hin SVAR
amewo ks. This line o wo k began wi h Me ens and Ra n (2013), who in o-
duced a amewo k o mul i-shock iden i ica ion, assuming a ecu si e o de ing
o he wo shocks iden i ied. Pi e and Pods awski (2018) ex end his app oach
by in oducing he idea o mul iple con amina ed ins umen s, bu wo ked in a
3
equen is se ing. A ias e al. (2021) and Giacomini e al. (2022) ex end he
mul i-shock iden i ica ion amewo k o Bayesian me hods. Ou s udy builds on
Pi e and Pods awski (2018) by employing a equen is app oach, bu augmen ed
o allow o wo ins umen s o dis inc ly iden i y oil supply and mone a y policy
shocks. Subsequen ly, he use o coun e ac uals is also new o his pape .
Finally, in applying mul iple high- equency iden i ied shocks as ex e nal in-
s umen s, his pape ela es o he high- equency iden i ica ion li e a u e, see
e.g. Ku ne (2001), Gü kaynak e al. (2005), Ge le and Ka adi (2015), Al a illa
e al. (2019), Mi anda-Ag ippino and Ricco (2021), Acos a (2022) and Baue and
Swanson (2023a) o examples o how o iden i y mone a y policy shocks and
Känzig (2021), Degaspe i (2023) and Miyamo o e al. (2024) o oil supply shocks.
We con ibu e by ex ending he mone a y policy ins umen ela ed o Baue and
Swanson’s amewo k o include da a h ough he COVID pe iod and by obus-
i ying he ins umen by accoun ing o co-mo emen s be ween oil p ice changes
and mone a y policy shocks.
The pape is o ganized as ollows. Sec ion 2 ou lines he econome ic ame-
wo k, including he iden i ica ion and cons uc ion o he shocks. Sec ion 3 p esen s
ou main empi ical esul s ega ding he e ec s o he oil and mone a y policy
shocks, while Sec ion 4 s udies op imal policy esponses. Sec ion 5 p esen s se -
e al obus ness checks be o e we conclude in Sec ion 6.
2 The Econome ic F amewo k
The ec o au o eg ession (VAR) model o o de pcan be exp essed in i s educed-
o m ep esen a ion as:
y “b`Bx `u ,(1)
whe e y is an nˆ1 ec o o endogenous a iables, bis an nˆ1 ec o o
in e cep s, and B“ pB1,...,Bpq ep esen s he coe icien ma ices, wi h Bi“
A´1
0Ai o i“1, . . . , p. He e, A0is an in e ible nˆnma ix wi h posi i e
diagonal elemen s, and Aia e nˆnma ices cap u ing he au o eg essi e dynamics
4
o he model. The ec o x “ py1
´1,...,y1
´pq1agg ega es he lagged alues o he
endogenous a iables, and he educed- o m shocks u a e ela ed o he s uc u al
shocks ϵ ia he linea mapping:
u “Sϵ .(2)
The nˆnimpac ma ix S“A´1
0is in e ible and can be pa i ioned as
S“ S1,S2s, whe e S1is an nˆkma ix co esponding o he s uc u al shocks
o in e es , and S2is an nˆ pn´kqma ix co esponding o he emaining shocks.
The s uc u al shocks ϵ a e assumed o be unco ela ed, sa is ying:
Epϵ ϵ1
q “ In,Epϵ ϵ1
sq “ 0n o ‰s. (3)
2.1 Iden i ica ion ia Ex e nal Ins umen s
In he con ex o P oxy S uc u al VARs (P oxy SVARs), ex e nal ins umen s
m “ pm1 , . . . , mk q1a e used o iden i y a subse o kďns uc u al shocks,
co esponding o he S1ma ix. These ins umen s mus sa is y ele ance and
exogenei y condi ions.
The s uc u al shocks can be decomposed as:
ϵ “”ϵ1
1 ϵ1
2 ı1
,(4)
whe e ϵ1 is a k-dimensional ec o ep esen ing he s uc u al shocks o in e -
es , and ϵ2 is an pn´kq-dimensional ec o ep esen ing he emaining shocks.
Co espondingly, he nˆnco a iance ma ix Φis decomposed as:
Φ“”Φ1Φ2ı,(5)
whe e Φ1is a kˆkco a iance ma ix cap u ing he co ela ion be ween he k
ins umen al a iables and he s uc u al shocks o in e es , and Φ2is an pn´kqˆk
ma ix o co ela ions wi h he emaining shocks. The goal is o iden i y he
s uc u al shocks ϵ1 using he ins umen al a iables in m . Gi en ha Epm ϵ1
q “
Φ, he combina ion o Equa ions (4) and (5) yields:
5
policy e en s, while he ex ended and adjus ed se ies in ed aligns closely wi h
he o iginal ins umen bu p o ides addi ional in o ma ion o ecen pe iods.10
The lowe panel illus a es he oil supply news shocks, cap u ing signi ican luc-
ua ions du ing no able oil ma ke e en s such as geopoli ical ensions o global
supply dis up ions, c. . Känzig (2021).
3 The e ec o oil supply news and mone a y
policy shocks
Below we p o ide some de ails abou he VAR es ima ion and ins umen alidi y,
be o e examining he e ec s o he oil supply news shocks and he mone a y policy
shocks h ough impulse esponses and his o ical decomposi ion.
3.1 VAR es ima ion and ins umen alidi y
The P oxy-SVAR is es ima ed a a mon hly equency o e he sample pe iod om
Ma ch 1984 o Ap il 2023. We include 12 lags and a cons an in he es ima ion.
Pa ame e unce ain y is simula ed using he wild boo s ap me hod. To con ol
o he sequence o ex eme obse a ions du ing he COVID-19 pandemic, espe-
cially h oughou he i s mon hs o he pandemic, we ollow Lenza and P imice i
(2022) and include dummies o Ma ch, Ap il, and May 2020.11
When ex e nal ins umen s a e weakly co ela ed wi h he shocks hey aim
o cap u e, s anda d in e ence in SVARs may be un eliable, necessi a ing he use
o weak-ins umen obus in e ence me hods. Ins umen s eng h is ypically
e alua ed using he F-s a is ic om he i s -s age eg ession, whe e he esiduals
10The ins umen cap u es no able mone a y policy e en s, such as he 2008 Financial C isis,
du ing which he Fede al Rese e implemen ed apid a e cu s and uncon en ional policies like
quan i a i e easing, e lec ed in heigh ened ola ili y a ound 2008-2009 in he blue se ies. Sim-
ila ly, he ex ended ed se ies shows dis inc spikes a ound 2020, co esponding o he Fede al
Rese e’s eme gency mone a y esponses o he COVID-19 pandemic.
11While Lenza and P imice i (2022) model he e oskedas ici y in a Bayesian amewo k, ou
app oach ollows a equen is es ima ion s a egy, inco po a ing dummy a iables o he ini ial
mon hs o he pandemic. This aligns wi h he logic o he Pandemic P io app oach bu wi hin
a equen is se ing.
12
o he a ge a iable om he VAR—in his case, he oil p ice and ede al unds
a e—a e eg essed on he ex e nal ins umen .
We o mally assess ins umen s eng h in Appendix Table 1, which epo s
he i s -s age eg ession esul s. Bo h he oil supply news and mone a y policy
ins umen s exhibi i s -s age F-s a is ics exceeding 10 o hei espec i e a ge
a iables, a h eshold widely used in he li e a u e o mi iga e conce ns abou weak
iden i ica ion.12 These esul s sugges ha weak-ins umen conce ns a e unlikely
o be a signi ican issue in ou se ing.
3.2 Impulse esponses o oil and mone a y policy shocks
We analyse he e ec s o he shocks h ough impulse esponses, be o e ocusing
on his o ical decomposi ions. The oil supply news shock is scaled o inc ease he
eal p ice o oil by 10%, while he mone a y policy shock aises he ede al unds
a e by 25 basis poin s on impac . The co esponding impulse esponse unc ions
(IRFs) and con idence in e als o bo h shocks a e epo ed in Figu e 2.
We i s examine a con ac iona y oil supply news shock, which is cons uc ed
o inc ease he eal p ice o oil. The impulse esponses sugges a s ag la iona y e -
ec on he economy. This shock leads o a g adual decline in indus ial p oduc ion
by 1% a i s peak, occu ing a ound 20 mon hs a e he shock. Addi ionally, U.S.
consume p ices inc ease signi ican ly, wi h a peak inc ease o a ound 0.5% a e 10
mon hs. The ede al unds a e ises o e he i s 20 mon hs, indica ing ha he
cen al bank igh ens mone a y policy in esponse o ising in la ion. These ind-
ings align wi h Gaglia done and Ge le (2023), who epo simila bu s onge
esponses in he igh ening o he ede al unds a e ollowing an oil supply shock.
The inc ease in eal oil p ices leads o a pe sis en ise in he commodi y p ice
index o e he whole ho izon, peaking a a ound 3% be o e g adually e e ing
o he s eady s a e. The IRFs a e simila o hose in Känzig (2021), wi h mino
di e ences due o a ying a iable selec ions.13
12See Olea e al. (2020) and e e ences he ein o a discussion on he h eshold le el and he
implica ions o weak ins umen in e ence.
13Some ecen s udies, i.e., Bjø nland and Sk e ing (2024) and Hanson and He e a (2024)
ha e epo ed mo e posi i e esponses in manu ac u ing p oduc ion o job ealloca ion o oil
shocks du ing he shale oil boom, in pa icula in oil p oducing s a es. Ou indings sugges ha
he impac on agg ega e U.S. indus ial p oduc ion du ing ou ull sample s ill emains nega i e.
13
(a) Oil Supply News Shock
(b) Mone a y Policy Shock
Figu e 2: Impulse Responses o oil supply news and mone a y policy shocks
No es: The o oil supply news and mone a y policy shocks, a e no malized o inc ease oil p ices
by 10% and he ede al unds a e by 25 bps, espec i ely. The solid line ep esen s he median
es ima e, wi h da k and ligh -shaded a eas indica ing he 68% and 95% con idence in e als,
espec i ely, ob ained ia he wild boo s ap me hod.
The mone a y policy shock, no malized o inc ease he ede al unds a e by
25 basis poin s on impac , leads o a decline in indus ial p oduc ion, wi h a peak
14
educ ion o 0.8% a e wo yea s. The p ice le el also dec eases, eaching a max-
imum decline o 0.5% ollowing he policy igh ening, be o e g adually e u ning
o he s eady s a e. Real oil p ices and commodi y p ices all immedia ely a e
he shock, bu hey g adually e e o hei ini ial le els o e he i s wo yea s.
Addi ionally, he excess bond p emium ises by app oxima ely 25 basis poin s on
impac . Ou indings b oadly align wi h hose o Baue and Swanson (2023a),
al hough sligh di e ences a ise due o ou a iable selec ion and sample pe iod.
We epo somewha la ge e ec s, in pa icula o indus ial p oduc ion, han
ypically ound in high- equency mone a y policy shock s udies, such as Ge le
and Ka adi (2015), which ely on non-o hogonalized shock measu es. Ou la ge
es ima es p ima ily e lec ou use o o hogonalized mone a y policy shocks, which
emo e biases associa ed wi h endogenous policy esponses, hus yielding s onge
es ima ed e ec s.14
3.3 His o ical Decomposi ion
To assess he in luence o mone a y policy and oil supply shocks on luc ua ions in
indus ial p oduc ion and consume p ices o e he ull sample pe iod, we compu e
he his o ical decomposi ion, p esen ed in Figu e 3. O e all, he con ibu ion o oil
supply shocks o indus ial p oduc ion (uppe panel) has emained ela i ely s able
o e ime bu has played a mo e p ominen ole in ce ain pe iods. No ably, oil
shocks had a nega i e impac du ing he pe iods leading up o he global inancial
c isis and p io o he co id pandemic. We also see ha pe iods o con ac iona y
mone a y policy, such as he a e hikes in he ea ly 2000s and 2022, coincide
wi h declines in indus ial ou pu , highligh ing he sec o ’s sensi i i y o policy
adjus men s.
Tu ning o in la ion in he lowe panel o Figu e 3, we see ha oil shocks
consis en ly con ibu e o inc ease in la ion o e ime. No ably, du ing he ecen
in la ion su ge, oil shocks accoun ed o a la ge sha e o he inc ease, peaking in
ea ly 2022. As oil p ices declined a e wa d, he con ibu ion o hese shocks o
in la ion simila ly eceded, highligh ing he esponsi eness o p ices o changes in
14O hogonaliza ion gene ally p oduces la ge es ima es by explici ly emo ing biases due o
mone a y policy esponding endogenously o economic condi ions (Baue and Swanson (2023a),
see Figu e 3 and ela ed discussion; see also Mi anda-Ag ippino and Ricco (2021)).
15
(a) Indus ial P oduc ion
(b) Consume P ice Index
Figu e 3: His o ical decomposi ion o U.S. IP ( op) and U.S. CPI (bo om)
No es: The his o ical decomposi ions o Indus ial P oduc ion and he Consume P ice Index
due o mone a y policy (MP) and oil shocks. The decomposi ion is compu ed om he s ochas ic
componen o he es ima ed model. The a iables en e he model in logs, bu o p esen a ion,
we epo hei yea -o e -yea changes. The decomposi ions a e exp essed as de ia ions om
hei espec i e sample means and escaled acco dingly. G ay ba s indica e NBER ecession
pe iods.
oil ma ke s. Mone a y policy shocks ha e also played a signi ican ole in d i ing
changes in consume p ices, pa icula ly in he mos ecen pe iod. The Fede al
Rese e’s ini ially accommoda i e s ance, cha ac e ized by s able in e es a es,
con ibu ed posi i ely o he ise in in la ion. Howe e , he subsequen in e es
16
a e hikes om 2022 began exe ing a nega i e in luence on in la ion om 2023.15
4 Mone a y policy esponses
Ha ing examined he e ec s o oil supply news shocks and mone a y policy shocks,
we now u n o analyzing policy esponses h ough coun e ac ual scena ios. Ou
app oach builds on he me hodologies o Sims and Zha (2006) and McKay and Wol
(2023). Finally, o assess op imal policy ade-o s, we build on he amewo k o
McKay and Wol (2023), ocusing on he balance be ween in la ion con ol and
ou pu s abiliza ion in esponse o oil-d i en dis u bances. 16
4.1 Coun e ac ual scena ios
We i s conduc a coun e ac ual scena io analysis in which he Fede al Funds
Ra e emains unchanged in esponse o oil p ice shocks, allowing us o isola e he
di ec economic e ec s o oil p ice shocks wi hou mone a y policy adjus men s.
To comp ehensi ely assess he ole o sys ema ic mone a y policy, we cons uc
wo coun e ac ual scena ios based on al e na i e me hodologies: he i s ollows
Sims and Zha (2006), and he second builds on he amewo k p oposed by McKay
and Wol (2023).
The Sims and Zha (2006) app oach in oduces a sequence o mone a y policy
shocks ha neu alize he e ec o oil shocks on he Fede al Funds Ra e pe iod-
by-pe iod.17 Because hese adjus men s a e imposed sequen ially and ex pos ,
p i a e-sec o expec a ions a e no aligned ex an e wi h he coun e ac ual policy
egime, aising conce ns highligh ed by he Lucas C i ique, c. ., Lucas (1976).
In con as , he me hodology p oposed by McKay and Wol (2023) cons uc s
policy coun e ac uals h ough a linea combina ion o mul iple mone a y policy
15Be ghol e al. (2024) ha e a gued ha his o ical decomposi ion can be poo ly iden i ied
as he de e minis ic componen o VAR models ends o be imp ecisely es ima ed. To check
obus ness o his, we ollow one o hei ecommenda ions and use demeaned da a and e-
es ima e ou SVAR model. Ou his o ical decomposi ion emains quali a i ely obus , hough
mone a y policy e ec s on in la ion appea mo e p onounced, in pa icula pos -GFC.
16A simila app oach o assess op imal policy esponses has been p oposed by Ba nichon and
Mes e s (2023), bu ou analysis is mo e closely aligned wi h he me hodology o McKay and
Wol .
17A de ailed desc ip ion o his me hod is p o ided in Appendix B.
17
Figu e 4: Coun e ac ual Impulse Responses
No es: Coun e ac ual impulse esponses o oil supply news shocks, unde coun e ac ual Fede al
Funds Ra e pa hs. The solid black line ep esen s he median es ima e, wi h da k and ligh -
shaded a eas indica ing he 68% and 95% con idence in e als, espec i ely, ob ained ia he
wild boo s ap me hod. The coun e ac uals om he Sims & Zha and he McKay & Wol
me hods a e in he solid ed line and dashed ed line, espec i ely.
shocks implemen ed simul aneously a ime 0, a he han sequen ially ac oss pe i-
ods. The key a ionale o employing mul iple shocks is ha sys ema ic mone a y
policy esponses ypically equi e simul aneous adjus men s o in e es a es a
mul iple u u e ho izons. A single mone a y policy shock gene ally canno achie e
dis inc adjus men s a se e al u u e poin s in ime. By combining mone a y pol-
icy shocks wi h di e en pe sis ence and dynamic esponse pa e ns, we can closely
eplica e, a he ini ial da e, he ull sys ema ic mone a y policy esponse ac oss
mul iple ho izons. C ucially, his simul aneous adjus men aligns p i a e-sec o
expec a ions immedia ely wi h he coun e ac ual policy egime, di ec ly add ess-
ing he conce ns aised by he Lucas C i ique, which a ise when adjus men s a e
implemen ed sequen ially and ex pos .
Speci ically, we combine wo dis inc mone a y policy shocks o app oxima e
his sys ema ic policy esponse. Fi s , we use ou o hogonalized mone a y pol-
icy shock (desc ibed in Sec ion 2.4), which cap u es immedia e adjus men s and
o wa d-guidance componen s. Second, we employ he mone a y policy shock om
Rome and Rome (2004), which p ima ily cap u es sho - e m disc e iona y pol-
18
icy adjus men s.18 By combining shocks ha di e in pe sis ence and dynamic
implica ions, we can eplica e he sys ema ic mone a y policy esponse closely a
he ini ial da e, aligning p i a e-sec o expec a ions immedia ely wi h he e ised
policy s ance and hus add essing he conce ns highligh ed by he Lucas (1976).19
The coun e ac ual impulse esponses a e p esen ed in Figu e 4. While some
mino di e ences a ise be ween he wo me hodologies (Sims and Zha: ed do ed;
McKay and Wol : ed dashed), hese di e ences a e small and no s a is ically
signi ican . Bo h app oaches indica e ha oil p ice shocks induce s ag la iona y
e ec s e en in he absence o a sys ema ic mone a y policy esponse. Speci ically,
he con ac ion in indus ial p oduc ion is sligh ly mi iga ed—by app oxima ely
0.10 pe cen age poin s on a e age o e he i s 12 mon hs—while in la iona y
p essu es a e ampli ied, wi h a peak inc ease o abou 0.15 pe cen age poin s a e
15 mon hs ela i e o he baseline.
These indings unde sco e ha bo h oil p ice and mone a y policy shocks play a
signi ican ole in shaping in la ion and economic ac i i y. In line wi h Gaglia done
and Ge le (2023), who examine he ole o mone a y policy in ecen in la iona y
cycles using a DSGE amewo k, ou esul s sugges ha while mone a y policy
can dampen he s ag la iona y e ec s o oil supply shocks, i canno ully elim-
ina e in la iona y p essu es. This highligh s he s uc u al cons ain s aced by
cen al banks in esponding o oil-d i en in la ion, pa icula ly when a emp ing
o balance p ice s abili y wi h ou pu s abiliza ion.
4.2 Op imal Policy Response
The ade-o iden i ied in ou coun e ac ual analysis—whe e e aining om mon-
e a y policy in e en ion mi iga es ou pu declines bu exace ba es in la iona y
p essu es—unde sco es a key challenge o policymake s. Designing an op imal e-
sponse equi es weighing he ela i e impo ance o in la ion s abili y e sus ou pu
s abiliza ion, pa icula ly in he ace o supply-side shocks. A s onge ocus on
in la ion con ol necessi a es a mo e con ac iona y s ance, which push ou pu u -
18The ex ended Rome and Rome shock se ies was e ie ed om Acos a (2022) and is a ail-
able on he au ho ’s websi e.
19See Appendix B.2 o addi ional me hodological de ails, including he de i a ion o shock
weigh s (Equa ion 28).
19
he down, while p io i izing ou pu s abiliza ion calls o a mo e accommoda i e
app oach, p olonging in la iona y p essu es.
To cons uc an op imal policy esponse we ollow McKay and Wol (2023) who
base he esponses on policy coun e ac uals. In pa icula , hey demons a e ha
he e ec s o al e na i e policy ules can be in e ed di ec ly om empi ical es i-
ma es o policy shock ansmission, wi hou equi ing a ully speci ied s uc u al
model. Applying hei me hod, we iden i y he sequence o policy in e en ions
ha bes aligns wi h a policymake ’s objec i es, ensu ing he coun e ac ual e-
sponse emains obus o he Lucas c i ique.
A cen al esul in McKay and Wol (2023) is ha op imal policy can be de i ed
by conside ing how di e en ypes o policy shocks in luence he economy. Thei
amewo k highligh s ha , i he e ec s o bo h con empo aneous and an icipa ed
policy shocks a e known, i is possible o cons uc coun e ac ual policy pa hs ha
eplica e he in ended s abiliza ion objec i es. Following his logic, we cha ac e ize
he op imal policy esponse o an oil supply shock by selec ing he combina ion o
policy in e en ions ha achie es he bes ade-o be ween in la ion and ou pu
s abiliza ion. Ra he han es ima ing a ule-based policy unc ion, we compu e he
equi ed sequence o policy shocks ha implemen he desi ed ou come, ensu ing
consis ency wi h he empi ical e idence on policy ansmission.20 In p ac ice, his
me hod allows us o assess how di e en policy p io i ies shape he esponse o
oil supply-side dis u bances. A mo e con ac iona y s ance, o example, educes
in la ion pe sis ence bu ampli ies ou pu declines, whe eas a mo e accommoda i e
app oach mi iga es ou pu losses a he cos o highe in la ion.
Figu e 5 illus a es he esul ing op imal policy pa hs o a 10% oil p ice shock
unde h ee di e en weigh ing scena ios. The i s assigns equal impo ance o
ou pu and in la ion ("Equal weigh ed", dashed-do ed g een), he second p io i-
izes in la ion s abiliza ion ("In la ion a ge ing", dashed ed), and he hi d em-
phasizes ou pu s abiliza ion ("Ou pu a ge ing", do ed ed). The op imal policy
esponse a ies signi ican ly depending on he ela i e weigh s assigned o ou pu
and in la ion s abiliza ion . Fi s , when he policymake assigns equal impo ance
o ou pu and in la ion, he policy en ails a mode a e easing o he ede al unds
a e—on he o de o 7 basis poin s—which helps cushion he decline in indus ial
20See Appendix B.3 o a de ailed desc ip ion o he me hod.
20
Figu e 5: Op imal Policy Response Pa hs
No es: The igu e illus a es op imal policy esponses o a 10% oil p ice shock unde h ee loss
unc ion objec i es:equally-weigh ed (dashed-do ed g een), in la ion- a ge ing (dashed ed), and
ou pu - a ge ing (do ed ed). The solid black line is he median es ima e om he main model
speci ica ion, wi h shaded a eas indica ing 68% (da k blue) and 95% (ligh blue) con idence
in e als om he wild boo s ap me hod. The “Bes App oxima ion” (dashed black line wi h
ma ke s) desc ibed in he ex , iden i ies he weigh ing scena io ha mos closely eplica es he
baseline esponse.
p oduc ion bu allows o sligh ly highe in la ion in he sho un compa ed o
he baseline.
In con as , p io i izing in la ion s abiliza ion (in la ion a ge ing) esul s in
a mo e o ce ul igh ening o o e 35 basis poin s; al hough i nea ly o se s he
immedia e in la iona y e ec o he oil shock, indus ial p oduc ion con ac s by
nea ly wice as much as in he equal-weigh ed scena io. Finally, when he emphasis
is placed on ou pu s abiliza ion (ou pu a ge ing), he policy esponse ea u es a
sizable a e cu o abou 20 basis poin s, mi iga ing he loss in indus ial p oduc ion
bu signi ican ly ampli ying in la iona y p essu es o e a longe ho izon.
These di e ences unde sco e he ade-o s cen al banks ace when esponding
o oil p ice shocks. P io i izing in la ion s abiliza ion en ails deepe ou pu losses,
whe eas emphasizing ou pu s abiliza ion in ensi ies in la ion. No ably, he peak
de ia ion in he policy a e ac oss he scena ios exceeds 60 basis poin s, e lec ing
he ange o ou comes d i en by di e en policy p io i ies.
21
—Appendix—
A Da a
A.1 Ins umen S eng h
Real Oil Fed Funds Indus ial Consume P ice Commodi y P ice Excess Bond
P ice Ra e P oduc ion Index Index P emia
Oil P ice Ins umen
β0.009*** 0.008* -0.001 0.001*** 0.001** -0.011*
F17.349 3.181 0.433 10.469 4.684 2.867
R20.036 0.007 0.001 0.022 0.0101 0.006
Mone a y Policy Ins umen
β0.017 0.422˚˚˚ -0.008 -0.001 -0.022 0.386˚˚
F 0.056 10.216 1.469 0.808 1.309 4.577
R20.001 0.022 0.003 0.002 0.003 0.009
No es: The models es ima ed a e ˆu “α`βimi
`η , whe e ˆu is he esidual om he VAR
equa ion co esponding o each a iable in he able, and mi
is he p oxy o ei he he oil supply
news shock o he mone a y policy shock. The null hypo hesis es s whe he βi“0. S a is ical
signi icance is based on he asymp o ic dis ibu ion o he OLS es ima o .
Table 1: Tes s on he S eng h o he Ins umen s
28
A.2 Da a Desc ip ion
Va iable Desc ip ion Sou ce
Baseline a iables
Real Oil P ice WTI spo c ude oil p ice
(WTISPLC) de la ed by
U.S. CPI (CPIAUCSL)
FRED
Fed Funds Ra e Fede al Funds E ec i e
Ra e (FEDFUNDS)
FRED
U.S. Indus ial P oduc ion U.S. Indus ial P oduc ion:
To al Index (INDPRO)
FRED
U.S. CPI U.S. Consume P ice Index
o All U ban Consume s
(CPIAUCSL)
FRED
Commodi y P ice Index U.S. Spo ma ke p ice in-
dex: All commodi ies
Commodi y Re-
sea ch Bu eau
(CRB)
Excess Bond P emia Excess bond p emia om
Gilch is and Zak ajšek
(2012)
Fede al Rese e
Table 2: Da a Desc ip ion and Da a Sou ces
29
B Me hodology
B.1 Coun e ac ual cons uc ion ollowing Sims & Zha
To analyze he ole o sys ema ic mone a y policy in he ansmission o oil supply
news shocks, we cons uc a coun e ac ual scena io in which he Fede al Funds
Ra e (FFR) emains unchanged ollowing an oil supply news shock. This app oach
ollows he me hodology o Sims and Zha (2006), which neu alizes he mone a y
policy esponse by applying a sequence o exogenous mone a y policy shocks a
each ho izon.
The educed- o m VAR ep esen a ion o ou model in Equa ion 1 can be
s a ed as:
y “b`
p
ÿ
i“1
Biy ´i`u ,(12)
while he companion o m o he VAR in Equa ion (12) is gi en by:
Z “FZ ´1` ,(13)
whe e:
Z “
»
—
—
—
—
—
—
—
–
y
y ´1
y ´2
.
.
.
y ´p`1
i
i
i
i
i
i
i
i
l
,F“
»
—
—
—
—
—
—
—
–
B1B2. . . Bp´1Bp
I0. . . 0 0
0I. . . 0 0
.
.
..
.
.....
.
..
.
.
0 0 . . . I0
i
i
i
i
i
i
i
i
l
, “
»
—
—
—
—
—
—
—
–
u
0
0
.
.
.
0
i
i
i
i
i
i
i
i
l
.
The impulse esponse unc ions (IRFs) o a s uc u al shock a e compu ed
ecu si ely as:
BZ `s
Bε1
“BZ `s
Bu1
¨Bu
Bε1
“ΨsA´1
0“Θs,(14)
whe e Ψsis he (non-o hogonalized) IRF ma ix a ho izon s, ob ained using
he i s n ows o Fs, wi h Ψs“e1
1Fse1.
30
Following an oil supply news shock, he coun e ac ual impulse esponse unc-
ion mus neu alize he impac on he Fede al Funds Ra e a each impulse ho izon
s. Gi en he a iable o de ing in ou model, whe e oil p ices a e o de ed i s and
he Fede al Funds Ra e is he second a iable, we de ine a selec ion ec o eF F R,
which ex ac s he in e es a e componen :
θF F R,j,s “e1
F F RΘsε .(15)
To cons uc he coun e ac ual, we in oduce a sequence o mone a y policy
shocks εm,c
ha o se s he impac o he oil supply news shock on in e es a es:
e1
F F R ´Θsε `Θsεm,c
¯“0.(16)
Sol ing o εm,c
, we ob ain:
εm,c
“ ´ pe1
F F RΘseF F Rq´1e1
F F RΘsε .(17)
The emaining sequence o coun e ac ual shocks is compu ed ecu si ely:
εm,c
`s“θF F R,j,s `řS´1
m“0e1
F F RFmA´1
0eF F Rεm,c
`m
e1
F F RA´1
0eF F R
.(18)
Thus, he coun e ac ual impulse esponse unc ion o any a iable i o he oil
supply news shock is:
θc
i,j,s “θi,j,s `
S´1
ÿ
m“0
e1
iFmA´1
0eF F Rεm,c
`m.(19)
31
B.2 Coun e ac ual cons uc ion ollowing McKay & Wol
The second me hod we use o cons uc coun e ac uals ollows he app oach o
McKay and Wol (2023). Gene ally, assume ha he economy can be desc ibed
by he ollowing sys em o equa ions:
Hww`Hxx`Hzz`Hεε“0(20)
Axx`Azz`ν“0(21)
whe e wand xa e ec o s o endogenous a iables, wi h he c ucial dis inc-
ion ha he a iables in xa e obse able o he econome ician— ep esen ing
he mac oeconomic a iables o in e es —while wis unobse able. The ec o z
con ains he policy ins umen , in ou case he Fede al Funds Ra e, while ε ep e-
sen s he exogenous s uc u al non-policy shock, speci ically he oil supply shock
in ou model. The linea mappings Hw,Hx,Hz,Hεudesc ibe he non-policy
block o he economy, independen o he baseline policy ule in Equa ion 21,
whe e Ax,Azua e he coe icien s o he policy ule and νcon ains he ull se
o policy-shocks o he p e ailing ule ac oss all ho izons. To de i e and cons uc
coun e ac ual impulse esponse unc ions o he economy unde al e na i e policy
unc ions, i is necessa y ha he policy ule in Equa ion 21 induces a unique equi-
lib ium. The coun e ac ual policy ule unde an al e na i e policy speci ica ion
can hen be exp essed as:
˜
Axx˜
A`˜
Azz˜
A“0,(22)
whe e ˜
Axand ˜
Aza e he coe icien s associa ed wi h he al e na i e policy ule,
and x˜
Apεqand z˜
Apεq ep esen he dynamic esponses unde his new ule o
he non-policy shock ε, which we seek o cons uc . I is also equi ed ha he
al e na i e policy ule in Equa ion 22 induces a unique equilib ium.
The cons uc ion o coun e ac ual scena ios unde al e na i e policy ules e-
qui es wo key inpu s:
•The dynamic causal e ec s o he non-policy shock εunde he baseline ule,
deno ed as xApεq,zApεqu
•The dynamic causal e ec s o he policy shocks νon he policy ins umen
32
zand he mac oeconomic obse ables o in e es x
The impulse esponses unde he baseline policy ule can be exp essed as:
ΘA”«Ωx,ε,A Ωx,ν,A
Ωz,ε,A Ωz,ν,A ,(23)
whe e Ωx,ε,A and Ωz,ε,A con ain he impulse esponses o mac oeconomic a i-
ables o in e es and he policy ins umen o he non-policy shock ε, while Ωx,ν,A
and Ωz,ν,A con ain he esponses o he policy shocks ν.
Gi en ha he econome ician knows he policy shock causal e ec s Ωx,ν,A,Ωz,ν,Au
and he esponse o he a iables xApεq,zApεqu o he shock ε, he coun e ac ual
policy esponses x˜
Apεq,z˜
Apεqu unde a coun e ac ual policy ule ˜
Ax,˜
Azucan
be eco e ed as:
x˜
Apεq “ xApε, ˜νq ” xApεq ` Ωx,ν,A ˆ˜ν(24)
z˜
Apεq “ zApε, ˜νq ” zApεq ` Ωz,ν,A ˆ˜ν(25)
whe e ˜νsol es he sys em:
˜
Ax xApεq ` Ωx,ν,A ˆ˜νs ` ˜
Az zApεq ` Ωz,ν,A ˆ˜νs “ 0.(26)
Thus, gi en he comple e se o policy shock pe u ba ions, i is always possible
o cons uc a da e-0 policy shock ec o ν ha eplica es he equilib ium pa h o
zunde he coun e ac ual policy ule. Since he non-policy block o he economy
is in luenced by mone a y policy solely h ough he expec ed pa h o he policy
ins umen , he esul ing equilib ium alloca ions unde he coun e ac ual ule
align exac ly wi h hose ob ained unde he app op ia ely adjus ed baseline ule.
Howe e , in p ac ice, an exac eplica ion o he equilib ium pa h unde he
coun e ac ual ule is no always easible. The lowe -dimensional s uc u e o he
iden i ied policy shocks ypically ende s he sys em o equa ions go e ning he
coun e ac ual adjus men unde de e mined o in easible. As a esul , esea che s
mus app oxima e he coun e ac ual ule as closely as possible by selec ing op imal
weigh s νwon he da e-0 iden i ied policy shocks in ν. The na u al app oach is
o sol e an op imiza ion p oblem ha minimizes he de ia ion om he desi ed
33
coun e ac ual pa h while emaining wi hin he span o he empi ically iden i ied
policy shocks:
min
νw›››˜
AxpxApϵq ` Ωx,ν,A ˆνwq ` ˜
AzpzApϵq ` Ωz,ν,A ˆνwq›››.(27)
The solu ion o he minimiza ion p oblem is gi en as:
νw“ ´ ”`˜
AxΩx,ν,A `˜
AzΩz,ν,A˘
1
`˜
AxΩx,ν,A `˜
AzΩz,ν,A˘ı´1
ˆ”`˜
AxΩx,ν,A `˜
AzΩz,ν,A˘
1
`˜
AxxApεq ` ˜
AzzApεq˘ı.
(28)
This solu ion allows o he cons uc ion o coun e ac ual impulse esponses ha
app oxima e he in ended al e na i e policy coun e ac ual as closely as possible,
gi en he a ailable se o iden i ied policy shock pa hs. Since all shocks a e da ed a
“0, he cons uc ed coun e ac ual pa hs emain obus o he Lucas c i ique. In
gene al, he accu acy o he coun e ac ual app oxima ion imp o es as he numbe
o iden i ied policy pa hs inc eases. As we a e in e es ed in o se ing he Fede al
Funds Ra e esponse, we implemen a ule22 ha can be hough o as simila o
a e a ge ing. In ou empi ical applica ion, xincludes he a iables o in e es ,
U.S. CPI and U.S. indus ial p oduc ion, while z ep esen s he Fede al Funds
Ra e as he policy ins umen . The non-policy shock, ε, co esponds o he oil
supply news shock, see Sec ion 2.5, whe eas νconsis s o he wo mone a y policy
shocks desc ibed in Sec ion 4.1.
22This depends on he applica ion he econome ician has in mind; o he op ions include he
implemen a ion o a Taylo - ype ule, ou pu a ge ing, o o he policy ules.
34
B.3 Op imal policy cons uc ion ollowing McKay & Wol
In his sec ion, we ou line he me hodology used o de i e op imal policy esponses,
ollowing he no a ion and app oach o McKay and Wol (2023). While Ba nichon
and Mes e s (2023) de elop a simila amewo k o op imal policy assessmen ,
ou analysis is mo e closely aligned wi h McKay and Wol (2023), pa icula ly in
ocusing on he ade-o be ween in la ion and ou pu s abiliza ion. The cen al
idea is o de e mine he policy ule ha minimizes a gi en policymake ’s loss
unc ion, subjec o he cons ain s imposed by he economic sys em. Assume
ha he policymake seeks o minimize he ollowing quad a ic loss unc ion:
L“1
2
nx
ÿ
i“1
λixi
1Wxi(29)
whe e λi ep esen s he weigh s assigned o di e en policy objec i es, xicon-
ains he mac oeconomic a iables o in e es and W“diagp1, β, β2, ...qallows
o discoun ing. A necessa y condi ion o sol ing he policymake ’s op imiza ion
p oblem is ha , gi en any non-policy exogenous shock ε, he e exis s a unique
solu ion o choosing he policy a iable z o minimize he loss unc ion, subjec
o he non-policy cons ain in Equa ion 20.
Wi h his condi ion in place, he goal is o de i e he dynamic esponse pa hs
xApεq,zApεqunde he op imal policy ule Ax,Az, which akes he o m:
A˚
x“ pλ1Ω1
x1,ν,AW, λ2Ω1
x2,ν,AW, ..., λnxΩ1
xnx,ν,AWq(30)
A˚
z“0(31)
Wi h hese policy coe icien s, he coun e ac ual impulse esponse pa hs unde
he op imal policy ule can be cha ac e ized as in P oposi ion 1 23, ollowing he
s uc u e o Equa ion 24:
x“xpεq ` Ωx,ν,A ˆν˚(32)
whe e he minimiza ion p oblem o he loss unc ion in Equa ion 29 leads o
23Fo he p oo o equi alence, see McKay and Wol (2023).
35
he op imali y condi ion:
nx
ÿ
i“1
λiΩxi,ν,AW xi“0(33)
Thus, he op imal policy coun e ac ual is gi en by:
ν˚“ ´ ”Ω1
x,ν,AλW Ωx,ν,Aı´1ˆ”Ω1
x,ν,AλW xApεqı.(34)
The same in o ma ion ha enables he cons uc ion o alid coun e ac uals
o a bi a y policy ules also allows o he cha ac e iza ion o op imal policy
ules. The in ui ion emains unchanged: since we ha e knowledge o he causal
e ec s o all possible policy pe u ba ions νon he policymake ’s a ge a iables
x, we can de e mine he ull se o ou comes ha can be achie ed h ough policy
ac ions. Op imal policy co esponds o he poin wi hin his implemen able se
ha minimizes he policymake ’s loss unc ion. As be o e, whe he his op imum
is eached ia a sys ema ic policy ule o h ough shocks o an al e na i e ule is
inconsequen ial.
36
B.4 Op imal policy - su ace analysis
This sec ion p esen s a su ace analysis o op imal policy esponses based on a g id
sea ch o e he policymake ’s p e e ences o in la ion and ou pu s abiliza ion.
The p ocedu e uses impulse esponse unc ions (IRFs) es ima ed om he baseline
model as inpu s, cap u ing he his o ical dynamics o a 10% oil p ice shock and 25
bps inc ease in he ede al unds a e. The op imal policy is compu ed by minimiz-
ing a weigh ed loss unc ion, whe e weigh s on in la ion and ou pu de ia ions a e
sys ema ically a ied. The h ee-dimensional su aces in Figu e 6 illus a e how
U.S. Consume P ices (le ), U.S. Indus ial P oduc ion (cen e ), and he Fede al
Funds Ra e ( igh ) e ol e o e ime (ho izon al axis) as p e e ences shi om in-
la ion p io i iza ion o ou pu p io i iza ion ( on - o-back axis). Wa me colo s
indica e la ge esponses, while coole colo s signal smalle esponses.
Figu e 6: Su ace Plo : Op imal Policy Response Pa hs
No es: These h ee-dimensional su aces show how he dynamic esponses o U.S. Consume
P ices (le ), U.S. Indus ial P oduc ion (cen e ), and he Fede al Funds Ra e ( igh ) e ol e
o e ime (ho izon al axis) as he policy-make ’s p e e ences shi om in la ion p io i iza ion o
ou pu p io i iza ion ( on - o-back axis). Wa me colo s (i.e., yellow) indica e la ge esponses,
while coole colo s (i.e., blue) signal smalle esponses. The black-dashed line co esponds o he
“bes app oxima ion” pa h discussed in he main ex , e lec ing he weigh ing o in la ion and
ou pu s abiliza ion ha mos closely eplica es he baseline esponse.
37
