Facul ad de Economía y Emp esa
Depa amen o del Análisis Económico
In o ma ion ic ions and policy in DSGE models
Pablo Aguila a
Ph.D Thesis
Ad iso : Jesús Vázquez
Bilbao, Ap il 2021
aDepa amen o del Análisis Económico, Facul ad de Economía y Emp esa, Uni e sidad del País Vasco (UPV/EHU), A .
Lehendaka i Agui e 83, 48015 Bilbao (Spain)
∗This esea ch was pa ially suppo ed by he p e-doc o al schola ship om he Uni e si y o he Basque Coun y (UPV/EHU),
he Spanish Minis y o Economy and Compe i ion unde g an s numbe s ECO2013-43773P and ECO2016-78749-P, and he
Basque Go e nmen (Spain) unde g an s numbe s IT-793-13 and IT-1336-19. Addi ional suppo unding was p o ided by he
Bank o Spain.
1
(cc)2021 PABLO ALBERTO AGUILAR GARCIA (cc by-nc-nd 4.0)
Acknowledgmen s
I would like o ake his oppo uni y o since ely hank hesis ad iso , P o esso Jesús
Vázquez, who has made his hesis posible, om you I had always a close guidance, en-
cou agemen , ca e o he de ails and g ea ad ise -no only in he ma e o his hesis. I
also wan o hank P o esso Luca Pensie oso, o hos ing me du ing my pe iod in Lou ain
and ollowing his hesis all hese yea s and o he membe s o he ju y.
This has been a long jou ny and I would like o sha e my g a i ude o all o you ha ha e
helped along, especially o Ra Wou e s, S ephan Fa h, Samuel Hu ado, Albe o U asun,
and o he es o colleagues om he di e en s places whe e I ha e been, Málaga, Bilbao,
Lou ain, F ank u and Mad id.
Finally I wan o exp ess my g a i ude o Me cedes, my wi e, o accompying me all hese
yea s and o my amily, ha has always encou age me pu sue my ca ee .
2
Con en s
I Adap i e lea ning wi h e m s uc u e in o ma ion 9
1 In oduc ion 9
2 An AL model wi h e m s uc u e 12
2.1 TheDSGEmodel........................................... 12
2.2 The e ms uc u eex ension .................................... 13
2.3 Adap i e lea ning wi h e m s uc u e in o ma ion . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Es ima ion esul s 19
3.1 Da aandes ima ionapp oach.................................... 19
3.2 Pos e io es ima es.......................................... 22
3.3 Model i ............................................... 27
3.4 Va iancedecomposi ion ....................................... 29
3.5 Te mp emiumes ima es....................................... 30
4 The empi ical alidi y o he PLM 35
5 Conclusions 41
II Lea ning wi h ELMo: in la ion expec a ions and mone a y pol-
icy ules 47
1 In oduc ion 47
2 A DSGE model wi h mul i-pe iod expec a ions o he Eu o A ea 52
2.1 Es ima ion .............................................. 53
2.2 The e olu ion o expec a ions: cycle and end . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.3 In e na ionalcompa ison....................................... 56
3 Mone a y policy unde lea ning: T ansi ional e ec s 58
3.1 T ansi ionalexce cise......................................... 58
3.2 Resul s................................................. 59
4 Conclusions 63
3
III The impo ance o da a e isions 66
1 In oduc ion 66
2 Da a e isions 69
2.1 Theconcep o da a e isions.................................... 69
2.2 Reg ession analysis o da a e isions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3 Real- ime da a wi hin a DSGE model 76
3.1 An explici speci ica ion o he e isions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2 Thenewse o equa ions....................................... 79
3.2.1 TheEule equa ion...................................... 79
3.2.2 Mone a ypolicy ule..................................... 81
4 Da a and es ima ion p ocedu e 83
5 Es ima ion esul s 84
5.1 Pa ame e es ima es ......................................... 84
5.2 Second-momen s a is ics ...................................... 86
5.3 Va iancedecomposi ion ....................................... 87
6 Conclusions 87
IV Bo owe -based measu es in a DSGE model 105
1 In oduc ion 105
2 Mac op uden ial policies in he 3D model 108
2.1 Bo owe -based measu es: Modelling s a egy . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.2 Calib a ionins eadys a e...................................... 111
2.3 E ec s o a ying household le e age in he 3D model . . . . . . . . . . . . . . . . . . . . . . 114
3 Rela ing LTV and LTI policies a loan o igina ion o he dynamic model 119
3.1 LTV (LTI) limi s and i s e ec s on a e age c edi s anda ds a loan o igina ion . . . . . . . . 120
3.2 Linking c edi s anda ds a loan o igina ion o ou s anding loans . . . . . . . . . . . . . . . . 124
3.3 Policysimula ion........................................... 126
4 Conclusions 132
4
Gene al in oduc ion
In his hesis I explo e key aspec s o gene al equilib ium models widely used in Cen al Banks,
bo h in e ms o heo e ical assump ions and p ac ical implica ions o policy make s. This
documen is di ided in ou chap e s. In he i s wo chap e s I s udy an al e na i e o he
a ional expec a ion assump ion and i s implica ions in he unde s anding o he business
cycle, while in he las wo chap e s I explo e policy ques ions ela ed o he use o hese
models in policy.
Gene al equilib ium models adi ionally used in he design o mone a y policy s a om
he p emise ha agen s o m hei expec a ions abou he economy in a a ional manne .
Unde a ional expec a ions, agen s ha e ull in o ma ion abou he ue economic model, and
use i acco dingly o o m hei p edic ions. In pa icula , agen s a e capable o unde s anding
he na u e o mac oeconomic shocks and hei du a ion, and ha e he abili y o consis en ly
inco po a e news abou he expec ed e olu ion o he economy o changes in mone a y policy
in o hei expec a ions. The heo y o a ional expec a ions has been embedded no only
in o eal business cycle models, bu also in o mo e ealis ic New Keynesian models, including
many o he DSGE models ha a e used o policy pu poses in cen al banks. Howe e ,
in eali y, agen s a e unlikely o ha e pe ec abili y o obse e and p ocess in an e icien
manne all a ailable in o ma ion. Thus, on many occasions, he na u e o he dis u bances, o
hei ansmission channels, a e only impe ec ly known by he agen s o pa ially igno ed.
Al e na i es o his hypo hesis ha e been la gely deba ed in he li e a u e, he i s wo
chap e s explo e di e en aspec s o he adap i e lea ning app oach as an al e na i e o
a ional expec a ions hypo hesis, while he las wo chap e explo e modelling implica ions
in he policy use o DSGE models.
Mo e p ecisely, he i s chap e assesses he impo ance o e m s uc u e and su ey da a
in o ma ion o he adap i e lea ning li e a u e and he capabili y o mac o- inancial DSGE
models wi h lea ning expec a ions o es ima e a measu e o he e m p emium associa ed
5
wi h he 10-yea US T easu y bond yield. The in oduc ion o su ey da a adds a sou ce
o discipline in expec a ions unde adap i e lea ning, which o he wise, a e o en c i icized
o a bi a y. In his con ex , his chap e inds ha adding e m s uc u e in o ma ion in
agen ’s o ecas ing models imp o es he o e all i and does a g ea job in ma ching he
expec a ions epo ed in he SPF ac oss all o wa d-looking a iables o he DSGE model.
The a ionale o his inding is ha he SPF o ecas s a e based on eal- ime da a and
he e m sp ead in o ma ion included in ou small o ecas ing models is also a ailable in
eal ime. These wo pieces o eal- ime da a—SPF and he yield cu e— may he e o e
sha e impo an in o ma ion in o ecas ing he economic ou look. This is consis en wi h he
p e ious inding ha he e m s uc u e con ains use ul in o ma ion o o ecas ing eal- ime
mac oeconomic da a. The second pa o he chap e ex ends his model up o 10-yea s o
es ima e a measu e o he e m p emium associa ed wi h he 10-yea US T easu y bond yield
om he medium-scale DSGE model unde AL, showing ha he inclusion o bo h e m
s uc u e and su ey da a imp o es he es ima ion o he bond e m p emium, in line wi h
he om no-a bi age a ine e m s uc u e models.
The second chap e looks a he ancho ing o in la ion expec a ions in he Eu o A ea and
he pe o mance o al e na i e mone a y policy ules using a DSGE model wi h adap i e
lea ning. The app oach used allows a dis inc ion o be d awn be ween which po ion o he
low in la ion phenomenon migh be due o empo a y ac o s and which migh be conside ed
pe manen . The esul s o he analysis o he eu o a ea sugges ha agen s pe cei e he
in la ion a e’s ecen depa u e om he mone a y policy objec i e o be p edominan ly
empo a y, al hough he de ia ions om a ge a e ma ked by a conside able deg ee o pe -
sis ence. Ano he ele an aspec is he impac o a p olonged pe iod o low in la ion in he
e ec i eness o mone a y policy, and mo e impo an ly, unde he p esence o he e ec i e
lowe bound. The second pa o he chap e s udies he p ope ies o he mone a y pol-
icy egime unde he cu en expec a ions and s udies he ansi ional e ec s caused by he
change in in la ion expec a ions o al e na i e egimes such as asymme ic in la ion a ge ing
6
and p ice-le el a ge ing, now popula in he academic deba e. The esul s show ha while
cu en expec a ions a e cu bing he e ec i eness o mone a y policy unde he p esence o
he ze o lowe bound, al e na i e ules such asymme ic in la ion a ge ing ules ( ha e-
spond s onge when in la ion is below end) a e bene icial o he economy. In addi ion, his
chap e s a es he implica ions in he ansi ion om one mone a y policy ule o ano he ,
showing ha changing he ule is no e y e ec i e un il agen s ha e had ime o lea n abou
i . The he announcemen o he new ule has he maximum e ec agen s obse e hei im-
plemen a ion and lea n abou i , which equi es ime, which is e y di e en om wha he
s anda d a ional expec a ions models, whe e he announcemen pe ec ly ancho s agen s’
expec a ions and has immedia e e ec s in he economy.
The hi d chap e de o es o he impo ance o eal- ime da a and da a e isions in he
business cycle analysis. The main mac oeconomic se ies a e egula ly e ised ela i e o hei
eal- ime elease o inco po a e new in o ma ion, which o en, a e signi ican and, i igno ed,
may lead o a bias in he s udy o he business cycle. This chap e p o ides a de ailed analysis
o he s a is ical p ope ies o da a e isions o he eu o a ea and s udies he app op ia e
modeling o eal- ime da a and i s e ision in DSGE models o business cycle analysis. The
i s pa o he chap e p o ides s udies he s a is ical p ope ies o da a e isions in he eu o
a ea, showing ha he se ies o GDP, consump ion and in la ion a e p edic able ( hey a e
co ela ed wi h he ini ial announcemen ) and ha e high ola ili y, sugges ing ha hey a e
no well-beha ed and s udies he app op ia e cha ac e iza ion o he da a e ision p ocesses
o i s la e inclusion in DSGE models. The second pa o he pape de ails how o include
eal- ime da a and i s e ision in a DSGE model, by assuming ha decisions ela ed o GDP,
Consump ion and in la ion a e based on he ini ial announcemen , and acknowledging ha
hey a e subjec o e isions. This app oach deli e s wo impo an esul s: i s , i con i ms
he empi ical indings om he educed- o m analysis and second, da a e isions become an
impo an sou ce in he business cycle decomposi ion analysis. In he case o he Eu o A ea,
hey accoun o one hi d o he ou pu a iabili y, leading o he conclusion ha DSGE
7
models omi ing eal- ime da a and da a e isions migh be igno ing impo an sou ces o
agg ega e luc ua ions.
Finally he ou h chap e has an impo an policy iewpoin , by assessing quan i a i ely
he ansmissions o mac op uden ial policies in he economy. Mac op uden ial policies a e an
impo an oolki o cen al banks nowadays, his includes bo owe -based mac op uden ial
measu es such as limi s on loan- o- alue and loan- o-income which hei assessmen has been
adi ionally in pa ial equilib ium models. By combining he model wi h in o ma ion on he
dis ibu ion o loan- o- alue and loan- o-income a ios con ained in he loan da a, his pape
acks he impac o bo owe -based measu es om hei impac on c edi condi ions a loan
o igina ion o he long- e m mac oeconomic e ec s on GDP, c edi , eal es a e in es men
as well as mo gage de aul s and mo gage sp eads. The assessmen e eals ha bo owe -
based measu es ha e sizable e ec s on c edi amoun s and can educe long- un de aul s.
I s assessmen is ne e heless limi ed o long- e m e ec s, gi en limi a ion in he ela i ely
simple way he eal es a e ma ke is modeled. I opens up ex ension possibili ies o de elop
addi ional models o shed ligh on he de ailed wo king o he eal es a e ma ke by ocusing
on addi ional sou ces o shocks and he ole played by expec a ions o eal es a e p ices.
8
Pa I
Adap i e lea ning wi h e m s uc u e
in o ma ion
1 In oduc ion
Since he pionee ing publica ions by Ma ce and Sa gen (1989) and E ans and Honkapohja
(2001) a g owing body o li e a u e (including P es on, 2005; Milani, 2007, 2008, 2011; Eu-
sepi and P es on, 2011; Slobodyan and Wou e s, 2012a,b) has conside ed adap i e lea ning
(AL) as an al e na i e o he a ional expec a ions (RE) assump ion in cha ac e izing highly
pe sis en mac oeconomic dynamics. Recen pape s (Sinha 2015, 2016) ocus on some impli-
ca ions o AL in he yield cu e, bu he e a e s ill a ew pape s (e.g. Aguila and Vázquez,
2019) ha analyze how e m s uc u e in o ma ion may in e ac wi h bo h lea ning and
mac oeconomic dynamics.
This pape conside s he Eule -equa ion app oach o AL sugges ed in Slobodyan and
Wou e s (2012a) o unde s and he con ibu ion o e m s uc u e in o ma ion in dealing
wi h he incomple e knowledge issue add essed in he ela ed AL li e a u e.1,2Te m s uc u e
Wi h Jesús Vázquez (UPV/EHU)
1The e a e wo main app oaches o AL in he ecen li e a u e. The Eule -equa ion app oach ocuses on
sho -sigh ed agen s, o whom op imal cu en decisions a e based on jus one-pe iod-ahead expec a ions
ha show up in he s anda d Eule equa ions (e.g. Milani, 2007; Slobodyan and Wou e s, 2012a,b), while
he o he app oach ocuses on long-sigh ed agen s (e.g. P es on, 2005; Eusepi and P es on, 2011; Sinha,
2015; and Sinha; 2016), aking in o accoun in ini e-ho izon o ecas s d i en by hei in e empo al decision
p oblem. This dis inc ion can be c ucial because he second app oach esul s in a much s onge sou ce
o pe sis en dynamics (see Eusepi and P es on, 2011). By including he e m s uc u e o in e es a es,
ou app oach ce ainly goes beyond he one-pe iod-ahead expec a ions, bu s ill ollows he Eule -equa ion
app oach.
2Mo e gene ally, he Eule -equa ion app oach alls unde he b oad class o a es ic ed pe cep ions equilib-
ium, whe e agen s use a small misspeci ied model bu o m hei belie s op imally gi en he misspeci ica ion
(Sa gen , 1991; Hommes and So ge , 1998; Milani, 2007; Honkapohja, Mi a, and E ans, 2013). O he pape s
(Adam, 2005; O phanides and Williams, 2005; B anch and E ans, 2006; Hommes and Zhu, 2014, O meño
and Molná , 2015) also p o ide suppo o he use o small o ecas ing models on se e al g ounds, including
hei o ecas pe o mance, hei use ulness o acili a ing coo dina ion, and hei abili y o app oxima e he
Su ey o P o essional Fo ecas e s well.
9
de ia ion o ou pu om i s unde lying neu al p oduc i i y p ocess), and sp{4}
= {4}
−
deno es he e m sp ead associa ed wi h he 1-yea ma u i y yield.11
2.3 Adap i e lea ning wi h e m s uc u e in o ma ion
This sec ion p o ides a b ie explana ion o how AL expec a ion o ma ion wo ks.12 A DSGE
model can be ep esen ed in ma ix o m as ollows:
A0
y −1
w −1
+A1
y
w
+A2E y +j+B0 = 0,
whe e y is he ec o o endogenous a iables a ime , E y +jcon ains mul i-pe iod-ahead
expec a ions, and w is a ec o including eigh exogenous shocks and he lagged inno a ions,
−1, o he p ice- and wage-ma kup shocks since hey a e modeled as ARMA(1, 1) p ocesses.
Agen s a e assumed o ha e a limi ed iew o he economy unde AL. Thei so-called “pe -
cei ed law o mo ion” (PLM) p ocesses—i.e. hei small o ecas ing models— a e gene ally
de ined as ollows:
y +j=X β{j}
−1+u +j, o j = 1,2, ..., n,
whe e yis he ec o con aining he o wa d-looking a iables o he model, Xis he ma ix
o eg esso s, β{j}is he ec o o upda ing pa ame e s, which includes an in e cep , and uis
a ec o o e o s. These e o s a e linea combina ions o he ue model inno a ions. The
a iance-co a iance ma ices, Σ=E[u +juT
+j], a e he e o e non-diagonal. Agen s a e u he
assumed o use simple econome ic ools unde AL. In pa icula , hey use a linea leas
squa es p ojec ion scheme in which he pa ame e s a e upda ed o o m hei expec a ions
o each o wa d-looking a iable: E y +j=X β{j}
−1. The upda ing pa ame e ec o , β,
which esul s om s acking all he ec o s β{j}, is u he assumed o ollow an au o eg essi e
11As in SlW, all bu a ew o he s uc u al shocks ollow AR(1) p ocesses. The p ice- and wage-ma kup
shocks ollow ARMA(1,1) p ocesses, and he AR(1) p oduc i i y shock allows o an in e ac ion wi h he
go e nmen spending shock.
12Fo a de ailed explana ion see Slobodyan and Wou e s (2012a,b).
16
p ocess whe e agen s’ belie s a e upda ed h ough a Kalman il e as desc ibed below. This
upda ing expec a ion p ocess can be ep esen ed as in SlW by he equa ion: β −¯
β=
F(β −1−¯
β) + , whe e Fis a diagonal ma ix wi h he lea ning pa ame e |ρ|≤ 1on he
main diagonal and a e i.i.d. e o s wi h a iance-co a iance ma ix V. This s anda d AL
app oach assumes ha agen s do no ake in o accoun he ac ha hei belie coe icien s
will be e ised in he u u e (e.g. Sinha (2016) and Eusepi and P es on (2011, 2018)). This
assump ion can be a ionalized by using an an icipa ed u ili y app oach pu o wa d in K eps
(1998) and Sa gen (1999).13
No ice ha each expec a ional ho izon is es ima ed sepa a ely in ou AL app oach. This
is in clea con as o he main ained belie s hypo hesis sugges ed in P es on (2005)—an
app oach also ollowed in Eusepi and P es on (2011) and Sinha (2015, 2016)— which no
only imposes an in ini e o ecas ho izon, bu also conside s i e a ed o ecas s used unde
he MSV app oach. Ne e heless, ou app oach sha es wi h o he AL app oaches he use o
o ecas ing models based on linea leas squa es p ojec ions, which implies ha he law o
i e a ed expec a ions holds: E (E +hy +j) = E y +j, o any j > h > 0(see Sa gen (1987,
chap e X, pp. 223-229) o a o mal discussion), and his is consis en wi h he law o
i e a ed expec a ions assumed in he de i a ion o he log pu e e sion o he EH, equa ion
(2), abo e.
Once he expec a ions o he o wa d-looking a iables,E y +j, a e compu ed hey a e
plugged in o he ma ix ep esen a ion o he DSGE model o ob ain a backwa d-looking
ep esen a ion o he model as ollows
y
w
=µ +T
y −1
w −1
+R ,
whe e he ime- a ying ma ices µ ,T and R a e nonlinea unc ions o s uc u al pa ame e s
13The an icipa ed u ili y app oach assumes ha agen s do no ake in o accoun u u e upda es o belie s
when making cu en decisions bu a e o he wise ully op imal. This is in con as o he Bayesian belie
app oach, which akes belie upda es in o accoun .
17
(en e ing in o ma ices A0,A1,A2and B0) oge he wi h he lea ning coe icien s, β. This
ep esen a ion o he model is called he ac ual law o mo ion (ALM).
The s anda d Kalman- il e upda ing and ansi ion equa ions o he belie coe icien s
and hei co esponding co a iance ma ix a e gi en by
β | =β | −1+R | −1X −1Σ+XT
−1R−1
| −1X −1−1y −X −1β | −1,
whe e (β +1| −¯
β) = F(β | −¯
β).β | −1is he es ima e o βusing he in o ma ion up o ime
−1(bu u he conside ing he au o eg essi e p ocess ollowed by β), R | −1is he mean
squa ed e o associa ed wi h β | −1. The e o e, he upda ed lea ning ec o β | is equal o
he p e ious one, β | −1, plus a co ec ion e m ha depends on he p e ious o ecas e o ,
y −X −1β | −1. The mean squa ed e o , R | , associa ed wi h his upda ed es ima e is
gi en by
R | =R | −1−R | −1X −1Σ+XT
−1R−1
| −1X −1−1XT
−1R−1
| −1,
wi h R +1| =FR | FT+V.
The ini ializa ion o his Kalman il e o he belie coe icien s equi es he speci ica ion
o β1|0=β,R1|0,Σ, and V. We ollow Slobodyan and Wou e s (2012a), whe e all hese
exp essions a e de i ed om he co ela ions be ween he model a iables implied by he RE
equilib ium e alua ed a he co esponding s uc u al pa ame e ec o .
A PLM wi h e m s uc u e in o ma ion
The baseline small o ecas ing models assumed in SlW a e simple AR(2) p ocesses. Tha is,
he PLM o each o wa d-looking a iable o he DSGE model is desc ibed by
E y +j=θ{j}
y, −1+β{j}
y,1, −1y +β{j}
y,2, −1y −1,(5)
whe e he in e cep o he PLM, θ{j}
y, −1, cap u es he low equency mo emen s o he co e-
sponding o wa d-looking a iable, E y +j, and he coe icien s β{j}
y,1, −1and β{j}
y,2, −1 oge he
18
measu e he pe sis ence o belie s.
We analyze he impo ance o in oducing TS in o ma ion by simply augmen ing hese
PLM wi h he e m sp ead sp{4}
:
E y +j=θ{j}
y, −1+β{j}
y,1, −1y +β{j}
y,2, −1y −1+β{j}
y,3, −1sp{4}
,(6)
whe e he coe icien β{j}
y,3, −1cap u es agen s’ eac ion o he e m sp ead in o ma ion while
o ecas ing E y +j.
This small modi ica ion in he PLM enables us o clea ly iden i y he con ibu ion o
TS in o ma ion beyond ha p o ided by cu en and lagged alues o he o wa d-looking
a iables conside ed in SlW.14
3 Es ima ion esul s
We begin his sec ion by desc ibing he da a and he es ima ion app oach, hen p oceed o
discuss he model i , es ima ion esul s, a compa ison o ac ual and simula ed momen s, he
a iance decomposi ion o shocks, and he es ima e o he smoo hed AL e m p emium.
3.1 Da a and es ima ion app oach
We es ima e he AL model ex ended wi h TS o he al e na i e speci ica ions o he PLM
using US da a o wo sample pe iods: The whole sample pe iod unning om 1965:4 un il
2009:1 and a subsample om 1981:4 un il 2009:1. The se o obse able a iables used o
he whole sample pe iod es ima ion is he same one used by Slobodyan and Wou e s (2012a)
(i.e. he qua e ly se ies o he in la ion a e, he Fed unds a e, he log o hou s wo ked,
he qua e ly log di e ences in eal consump ion, eal in es men , eal wages, and eal GDP)
14Aguila and Vázquez (2019) also conside TS in o ma ion bu hey de ia e much u he om he PLM
assumed in SlW by conside ing only he e m sp ead in he PLM. The app oach ollowed he e makes i easie
o iden i y he con ibu ion made by adding TS in o ma ion o e and abo e he in o ma ion p o ided by AR
p ocesses.
19
plus he 1-yea ze o-coupon T easu y yield (i.e. a se o eigh obse able a iables).15
The es ima ion o he sho e sample pe iod ex ends he se o obse ables conside ed in
he whole sample pe iod o include six obse able o ecas s epo ed in he SPF. Mo e p e-
cisely, we conside he SPF o ecas s a ailable, which ha e coun e pa s in o wa d-looking
a iables in he DSGE model: 1-qua e -ahead o ecas s o in la ion, 1-qua e -ahead o e-
cas s o he consump ion and in es men g ow h a es, and 1-, 2- and 3-qua e -ahead o e-
cas s o he sho - e m nominal in e es a e16,17 Analyzing his sho e sample pe iod, bu
wi h a la ge numbe o obse ables, enables us o assess he impo ance o TS in o ma ion in
disciplining model expec a ions by i ing SPF o ecas s as well as assessing he obus ness o
esul s by s udying a sample pe iod ea u ing bo h milde agg ega e luc ua ions ( he G ea
Mode a ion) and an in la ion down end, which is in sha p con as wi h he s ag la ion in
he 1970s and ea ly 1980s p esen in he i s -hal o he whole sample pe iod.
15The ze o-coupon T easu y bond yields come om he Gü kaynak, Sack and W igh (2007) da a se
a ailable on he esea ch da a websi e o he Boa d o Go e no s o he Fede al Rese e.
16Del Neg o and Eusepi (2011) pionee he use o SPF expec a ion da a o discipline RE in DSGE models.
A ew mo e ecen pape s (O meño and Molna , 2015; Aguila and Vázquez, 2018) also use SPF da a o
discipline AL expec a ions in DSGE models.
17SPF o ecas s we e downloaded om he websi e o he Fede al Rese e Bank o Philadelphia. In la ion
o ecas s a e epo ed back o he la e 1960’s, bu he es o he o ecas ime se ies s a s a 1981:3. Thus,
da a a ailabili y pa ially de e mines he choice o he i s pe iod in he sho sample. Mo eo e , he ini ial
qua e o he sho sample oughly coincides wi h he s a o a success ul disin la ion pe iod.
20
The measu emen equa ion is
X =
dlGDP
dlCONS
dlINV
dlWAG
dlP
lHou s
FEDFUNDS
1−yea TB yield
dlCONSSPF
+1
dlINV SP F
+1
dlPSPF
SPF{1}
SPF {2}
SPF {3}
=
γ
γ
γ
γ
π
l
{4}
γSPF
c
γSPF
i
πSPF
SPF
SPF
SPF
+
y −y −1
c −c −1
i −i −1
w −w −1
π
l
{4}
E (c +1 −c −1) + c,
E (i +1 −i −1) + i,
E π +j+π,
E ( +1) + {1}
,
E ( +2) + {2}
,
E ( +2) + {3}
,
,(7)
whe e land dl ep esen he log and he log di e ence, espec i ely. γ= 100(γ−1) is he
common qua e ly end g ow h a e o eal GDP, eal consump ion, eal in es men , and
eal wages. ¯
l,π, and {4}a e he s eady-s a e le els o hou s wo ked, in la ion, he ede al
unds a e, and he 1-yea (4-qua e ) bond yield, espec i ely. The supe sc ip s SPF and
{j}in he las six ows o he measu emen equa ion deno e ac ual o ecas s om he SPF
and he co esponding o ecas ho izon o j= 1,2,3; espec i ely. As in O meño and Molná
(2015), he measu emen e o s, , showing he de ia ions o model expec a ions om he
ac ual o ecas s epo ed in he SPF, a e assumed o be i.i.d. p ocesses. We also allow o
di e ences in end g ow h a es ac oss SPF (consump ion and in es men ) o ecas s as well
as di e ences be ween he s eady-s a e le els o ac ual and SPF o ecas da a.
The measu emen equa ion (7) educes o he i s eigh equa ions when he al e na i e
21
e sions o he AL model a e es ima ed o he whole sample pe iod, whe eas he comple e
sys em (7) is used o he sho sample pe iod when SPF da a is conside ed in he es ima ion
p ocedu e.
We ollow a Bayesian es ima ion p ocedu e. Fi s , he log pos e io unc ion is maximized
by combining p io in o ma ion on he pa ame e s wi h he likelihood o he da a. The p io
assump ions a e exac ly he same as in Slobodyan and Wou e s (2012a). In addi ion, we
conside loose p io s o he pa ame e s cha ac e izing bo h he 1-yea yield dynamics and
he measu emen e o p ocesses. The Me opolis-Has ings algo i hm is used o gene a e he
pos e io dis ibu ion and o compu e he log densi y o he model.18
3.2 Pos e io es ima es
Ou es ima ed AL model wi h TS (hence o h called he SlW-TS model) only di e s om
ha o Slobodyan and Wou e s (2012a) (hence o h called he SlW model) in he speci ica ion
o he small o ecas ing models.
Table 1 shows he es ima ion esul s o he a ious PLM speci ica ions and he a ious
samples conside ed. Ou sample pe iod is almos iden ical o he one conside ed in SlW.
Thus, he i s column o Table 1 shows he es ima ion esul s o he SlW model o he whole
sample pe iod 1966:1-2009:1 using hei o iginal se o se en obse able a iables, whe eas he
second and hi d columns epo he es ima ion esul s using he PLM o SlW and he PLM
augmen ed wi h TS in o ma ion (SlW-TS) as desc ibed by equa ions (5) and (6), espec i ely.
The emaining wo columns show he es ima ion esul s o he wo PLM speci ica ions o
he sho sample pe iod unning om 1981:4 un il 2009:1, whe e he SPF ime se ies a e also
included in he se o obse ables as desc ibed in he measu emen equa ion (7).19
Fo each model es ima ed, Table 1 i s ly epo s he numbe o obse able ime se ies,
18The DSGE models a e es ima ed using Dyna e codes kindly p o ided by Se gey Slobodyan and Ra
Wou e s wi h a ew modi ica ions o accommoda e he p esence o TS in o ma ion in bo h he s uc u al
model and he small o ecas ing models, as desc ibed abo e.
19Fo he sho sample pe iod, we ind ha simple speci ica ions o he wo PLM buil on AR(1) p ocesses—
i.e. imposing β{j}
y,2, −1= 0 in equa ions (5) and (6)— imp o e he model i . The es ima ion esul s epo ed
o he sho sample pe iod a e based on hese simple speci ica ions.
22
and he model i based on he log da a densi y. The emaining ows show he pos e io mean
and he co esponding 90 pe cen in e al o he pos e io dis ibu ion—in pa en heses— o
ou g oups o selec ed pa ame e s. The i s and second g oups con ain he pa ame e s o
eal and nominal igidi ies, espec i ely. The hi d g oup con ains he pa ame e s which
desc ibe he ARMA coe icien s cha ac e izing p ice and wage ma kup shocks. Finally, he
ou h g oup con ains he policy ule pa ame e s.20
A compa ison o column 1 in Table 1 wi h he igu es epo ed in Slobodyan and Wou e s
(2012a, Table 1, p. 74) shows a simila i and almos iden ical pa ame e es ima es. This
sugges s ha including o igno ing a ew qua e ly obse a ions and assuming a loga i hmic
u ili y unc ion has no impac on he es ima ion esul s.
The consequences o conside ing he 1-yea T easu y bill
A compa ison o columns 1 and 2 shows ha including he 1-yea T easu y bill as an ob-
se able in he SlW model dec eases he impo ance o a ew sou ces o endogenous igidi y,
such as Cal o p ice and wage pa ame e s, p ice and wage indexa ion pa ame e s, and he
pa ame e ea u ing he capi al u iliza ion adjus ing cos , ψ. The a ionale o his dec ease
in a ew sou ces o endogenous pe sis ence is ha conside ing he EH o he e m s uc u e
(equa ion (3)) b ings wi h i addi ional pe sis ence in ( he expec ed pa h o ) he sho - e m
a e ha is ansmi ed o o he agg ega e a iables. Mo eo e , he e is a la ge inc ease in
pe sis ence d i en by he inc ease in he AR coe icien s ha desc ibe he p ocesses o p ice
and wage ma kup shocks.
20All pa ame e es ima es a e epo ed in a supplemen a y appendix a ailable om he au ho s upon
eques .
23
Table 1. Selec ed pa ame e es ima es
Wi hou SPF da a (1965:4-2009:1) Wi h SPF da a (1981:4-2009:1)
SlW SlW SlW-TS SlW SlW-TS
Numbe o obse ables 7 8 8 14 14
log da a densi y -984.930 -1092.600 -1057.596 -1070.311 -853.960
Pa ame e s associa ed wi h eal igidi ies
habi o ma ion 0.787 0.851 0.759 0.631 0.630
(h)(0.742,0.833) (0.842,0.878) (0.745,0.788) (0.607,0.643) (0.611,0.643)
cos o adjus ing capi al 4.846 7.975 4.616 4.219 5.294
(ϕ)(3.257,6.491) (7.946,8.014) (4.579,4.646) (4.192,4.258) (5.168,5.323)
capi al u iliza ion adjus ing cos 0.611 0.151 0.092 0.163 0.050
(ψ)(0.424,0.819) (0.149,0.180) (0.085,0.100) (0.153,0.171) (0.046,0.053)
Pa ame e s associa ed wi h nominal igidi ies
p ice Cal o p obabili y 0.612 0.472 0.545 0.617 0.715
(ξp)(0.544,0.684) (0.459,0.487) (0.524,0.554) (0.598,0.630) (0.702,0.730)
wage Cal o p obabili y 0.774 0.565 0.464 0.495 0.259
(ξw)(0.721,0.831) (0.549,0.589) (0.456,0.482) (0.485,0.511) (0.245,0.268)
p ice indexa ion 0.372 0.178 0.377 0.896 0.820
(ιp)(0.169,0.566) (0.151,0.192) (0.325,0.401) (0.884,0.928) (0.796,0.863)
wage indexa ion 0.386 0.185 0.470 0.218 0.400
(ιw)(0.203,0.582) (0.107,0.229) (0.410,0.486) (0.195,0.237) (0.337,0.437)
24
Table 1. (Con inued)
Wi hou SPF da a (1965:4-2009:1) Wi h SPF da a (1981:4-2009:1)
SlW SlW SlW-TS SlW SlW-TS
Pa ame e s associa ed wi h p ice and wage ma kups
ma kup p ice AR coe . 0.457 0.880 0.875 0.609 0.575
(ρp)(0.130,0.786) (0.860,0.904) (0.875,0.911) (0.584,0.690) (0.558,0.602)
ma kup wage AR coe . 0.554 0.838 0.918 0.843 0.938
(ρw)(0.287,0.827) (0.827,0.853) (0.909,0.928) (0.833,0.858) (0.929,0.950)
ma kup p ice MA coe . 0.476 0.608 0.693 0.590 0.747
(µp)(0.224,0.742) (0.591,0.635) (0.676,0.711) (0.547,0.638) (0.741,0.769)
ma kup wage MA coe . 0.494 0.325 0.477 0.556 0.450
(µw)(0.209,0.793) (0.309,0.368) (0.454,0.517) (0.543,0.569) (0.422,0.487)
Policy ule pa ame e s
ine ia 0.880 0.884 0.886 0.834 0.835
(ρ )(0.85,0.92) (0.881,0.907) (0.878,0.896) (0.808,0.845) (0.819,0.849)
in la ion 1.692 1.662 1.617 2.373 1.854
( π)(1.384,2.01) (1.659,1.683) (1.570,1.643) (2.291,2.394) (1.762,1.888)
ou pu 0.101 0.075 0.038 0.080 0.082
( y)(0.043,0.159) (0.065,0.095) (0.033,0.047) (0.068,0.089) (0.075,0.092)
ou pu g ow h 0.118 0.122 0.144 0.075 0.040
( ∆y)(0.087,0.150) (0.104,0.131) (0.132,0.154) (0.068,0.090) (0.036,0.053)
e m sp ead - 0.255 0.140 0.112 0.155
( sp )- (0.218,0.284) (0.118,0.159) (0.086,0.145) (0.129,0.174)
No es: Pa ame e no a ion and 90% in e als o he pos e io dis ibu ion in pa en heses.
25
200 basis poin s a ound 1984 o one o he AL measu es, bu he disc epancy be ween he
ACM and DB e m p emia is much la ge o he same pe iod ( oughly 450 basis poin s!).
Ano he subs an ial disc epancy appea s a ound he 2001-2002 ecession, when he di e ences
be ween he DB e m p emium and any o he e m p emium ake alues close o 5%, whe eas
he di e ences be ween any pai o he es o he e m p emium measu es a e a ound 1%
in all cases. These disc epancies ac oss models a e no , howe e , explained by i ing e o s
implied by he al e na i e models, as all models end o i he yield da a e y well (as indeed
ou AL-DSGE model does (see Figu e 2 below)). In spi e o la ge disc epancies o a ew
pe iods, he di e ences be ween al e na i e e m p emia a e in gene al less han 100 basis
poin s.
Focusing on he compa ison be ween he AL and ACM e m p emia, i can be obse ed
ha he luc ua ions in he ACM e m p emium a e sligh ly milde han hose in he AL e m
p emium: The s anda d de ia ions o hese wo e m p emium measu es a e 1.13 and 1.38,
espec i ely (1.28 when he ACM e m p emium is no included in he se o obse ables).
Mo eo e , bo h AL and ACM measu es exhibi an upwa d end du ing he S ag la ion pe iod
and a downwa d end du ing he disin la ion pe iod, which implies ha he wo measu es a e
con empo aneously co ela ed (0.86 wi h he ACM measu e in he se o obse ables and 0.65
wi hou i ). They also exhibi a high deg ee o pe sis ence ( he i s -o de au oco ela ion
coe icien is 0.96 o he ACM e m p emium and oughly 0.93 o he wo AL e m p emia).
Fu he mo e, he co ela ions be ween he ACM and AL and he cyclical measu e o GDP
ob ained om he Hod ick and P esco il e (Hod ick and P esco , 1997) show a weak
coun e cyclicali y (-0.30, and -0.26, espec i ely) somewha in line wi h he indings in he
ela ed li e a u e (e.g. in Campbell and Coch ane, 1999; Coch ane and Piazzesi, 2005; Baue ,
Rudebusch and Wu, 2014). This co ela ion is a li le lowe a -0.17 when he ACM e m
p emium is emo ed om he se o obse ables.
32
Figu e 1. 10-yea e m p emia
No e: The annualized AL e m p emia shown in his igu e a e compu ed as h {40}− +ξ{40}
i×4.
Figu e 2 shows he ac ual igu e and he o ecas o he 10-yea yield based on he AL-
DSGE model oge he wi h he es ima ed a e age o he expec ed pa h o he sho - e m a e
o e 10 yea s (i.e. he es ima ed 10-yea yield implied by he EH o he e m s uc u e). I
is clea ha he es ima ed 10-yea yield implied by he EH unde AL shows g ea a iabili y
o e he sample pe iod, bu i also shows a ela i ely small a iabili y in he ea ly 1980s when
he 10-yea yield shows he win-peak luc ua ions, which esul s in he la ge luc ua ions o
he es ima ed AL e m p emium shown in Figu e 1.
Figu e 2. Ac ual and o ecas 10-yea yields, and he es ima ed a e age o he expec ed
pa h o he sho - e m a e o e 10 yea s
The ela i ely small a iabili y o he expec a ions o he sho - e m a e in he ea ly
1980’s is con i med in Figu e 3, whe e he belie coe icien s associa ed wi h a ew o wa d-
33
looking a iables a e shown. Thus, he bo om le g aph in Figu e 3 shows ha he a e age
o he sho - e m belie coe icien s o he 1- 2- and 3-qua e ahead AL expec a ions does
no cap u e he high a iabili y o he ede al unds a e in he ea ly 1980s.
Figu e 3 also shows ha he e m sp ead coe icien s associa ed wi h he PLM o he
al e na i e o wa d-looking a iables exhibi g ea a iabili y in gene al, cap u ing a s ong
eac ion by agen s o he sp ead while o ecas ing key mac oeconomic a iables. This is ue
in pa icula o in es men belie s, o which he e m sp ead coe icien inc eases a ound
ecessions (in he mid and la e 1970s, ea ly 1980s, he 2001-2002 pe iod, and be o e he G ea
Recession).
Figu e 3. Time a ia ion o belie coe icien s
No e: The coe icien s shown o he sho - e m in e es a e a e he a e ages o he co esponding belie coe icien s o he
1- 2- and 3-qua e ahead AL expec a ions.
An analysis o he con empo aneous c oss-co ela ions be ween he h ee ypes o belie
coe icien (i.e. he in e cep , he sum o he AR coe icien s, and he e m sp ead coe icien )
34
also shows an in e es ing inding: The e is a s ong co ela ion be ween he e m sp ead
belie coe icien and he co esponding PLM’s in e cep o eal a iables (consump ion and
in es men ), indica ing ha he a iabili y in he agen ’s eac ion o he e m sp ead is
somewha linked o he pe cep ion on he low- equency mo emen s o consump ion and
in es men . Thus, he es ima ed co ela ion be ween he in e cep and he e m sp ead
coe icien is nega i e a -0.73 o consump ion belie s, and posi i e a 0.79 o in es men
belie s. Simila ly, we also ind a s ong nega i e co ela ion be ween he in e cep and he sum
o he AR coe icien s o consump ion (-0.71), in la ion (-0.85), and sho - e m a e (-0.77)
belie s indica ing ha bo h ypes o belie coe icien also compe e o cap u e expec a ions
abou he low- equency mo emen s o hese a iables.
4 The empi ical alidi y o he PLM
This sec ion analyzes he empi ical alidi y o he PLM implied by he wo speci ica ion
op ions in o de o assess he con ibu ion o TS in o ma ion o bo h imp o e model i and
ma ch SPF o ecas s.
Table 4 shows he RMSE s a is ics om he PLM o ecas s o he o wa d-looking a i-
ables ha ha e obse able coun e pa s. We also include he 1-yea yield implied by he pu e
EH (i.e. he one-yea yield implied by (2) whe e he e m p emium is es ic ed o ze o).
To assess he PLM (i.e. pe cei ed law o mo ion) pe o mance u he , we also epo he
RMSE o he ALM (i.e. ac ual law o mo ion) o he obse able a iables. No ice ha
hese s a is ics a e all based on in-sample o ecas s. ALM o ecas e o s a e also minimized
in he es ima ion p ocedu e, so hey p o ide a minimum bound agains which he PLM pe -
o mance can be assessed. Fu he mo e, since he log ma ginal densi y is a unc ion o he
ALM o ecas e o s, he RMSE s a is ics compu ed o al e na i e a iables p o ide aluable
in o ma ion abou he sou ces o he imp o emen in he model i based on he log ma ginal
densi y implied by in oducing TS in o ma ion in o he PLM.
Table 4 has h ee panels. The i s wo show he RMSE s a is ics associa ed wi h he
35
ALM and he PLM o he whole sample— oge he wi h he PLM s a is ics associa ed wi h
speci ic pe iods such as he S ag la ion pe iod (1966:1-1981:4), he disin la ion pe iod (1982:1-
2009:1), and he con ac ion pe iods as da ed by he NBER business cycle commi ee— o
he DSGE model es ima ed unde he wo speci ica ions o he PLM (equa ions (5) and (6)).
The i s wo panels also show he RMSE s a is ics o he wo PLM speci ica ions using
he i s announcemen s ( eal- ime da a) ins ead o he ac ual ( e ised) da a used in he
es ima ion p ocedu e. To acili a e discussion, we also epo he RMSE s a is ics ob ained
om he es ima ion in he Slobodyan and Wou e s (2012a) model (i.e. mu ing he TS pa
o he model and emo ing he 1-yea yield om he se o obse ables) in he hi d panel.
Se e al impo an conclusions eme ge om Table 4. Fi s , he RMSE s a is ics associa ed
wi h he ALM a e lowe o he lea ning speci ica ion ha includes TS in o ma ion ac oss
all h ee eal a iables (i.e. he g ow h a es o consump ion, in es men and he eal wage),
whe eas he i o he nominal a iables is simila o he wo AL speci ica ions. A compa ison
o hese s a is ics wi h hose epo ed in he hi d panel sugges s ha including he 1-yea
yield as an obse able a iable and cha ac e izing he 1-yea yield in he model ha e only
a sligh e ec on he model i ac oss a iables, wi h a small imp o emen in he i o
consump ion, in es men , and in la ion. Second, he RMSE s a is ics associa ed wi h he
PLM a e also lowe o he lea ning speci ica ion wi h TS in o ma ion ac oss all a iables bu
he 1-yea yield. This ou pe o mance by he PLM wi h TS is ai ly obus ac oss al e na i e
subsample pe iods: The accele a ing in la ion pe iod (1966:1-1981:4), he down end in la ion
pe iod (1982:1-2009:1), and he pe iods o economic con ac ion. In e es ingly, he PLM
associa ed wi h he SlW speci ica ion does a much be e job in o ecas ing he 1-yea yield
in he disin la ion pe iod han in he S ag la ion pe iod, bu he opposi e is ue o he PLM
wi h TS in o ma ion. Finally, he ou pe o mance by he PLM wi h TS ex ends o he case
whe e he RMSE s a is ics a e compu ed wi h eal- ime da a as a e e ence ins ead o he
ac ual e ised da a used in he es o he able. This sugges s ha by helping o imp o e
he o ecas s o he i s announcemen s o mac oeconomic da a, he yield cu e (which is
36
obse ed in eal ime) p o ides use ul in o ma ion o cha ac e izing agen s’ expec a ions
abo e and beyond ha included in e ised mac oeconomic da a.22
Table 4. RMSE compa ison o PLM o ecas s (1966:1-2009:1)
SlW-TS ∆c∆in ∆w π {4}
ALM 0.686 1.757 0.669 0.257 0.234 0.208
PLM 0.779 1.819 2.450 0.282 0.266 1.024
PLM (pe iod 66:1-81:4) 0.823 2.145 2.682 0.379 0.365 0.484
PLM (pe iod 82:1-09:1) 0.753 1.601 2.306 0.206 0.186 1.232
PLM (con ac ion pe iods) 1.353 2.889 2.181 0.305 0.391 0.411
PLM ( eal- ime da a) 0.775 4.320 – 0.325 – –
SlW
ALM 0.726 1.792 0.763 0.256 0.232 0.209
PLM 1.335 2.001 2.650 0.300 0.268 0.930
PLM (pe iod 66:1-81:4) 1.227 2.201 2.601 0.369 0.354 1.439
PLM (pe iod 82:1-09:1) 1.394 1.876 2.679 0.252 0.202 0.409
PLM (con ac ion pe iods) 1.827 3.121 2.099 0.297 0.358 0.439
PLM ( eal- ime da a) 1.335 4.478 – 0.348 – –
SlW wi h 7 obse ables
ALM 0.700 1.784 0.657 0.260 – –
PLM 0.705 1.812 0.673 0.281 – –
As poin ed ou by Slobodyan and Wou e s (2012a), a sound pe o mance by he expec-
a ion models in e ms o RMSE may help ob ain a good o e all i o he model, bu i
p o ides only indi ec e idence on he empi ical alidi y o hose expec a ions. Nex , we as-
sess he o ecas ing pe o mance o he wo PLM speci ica ions s udied in his pape agains
22See C ousho e (2011) o an ou s anding e iew o he li e a u e on eal- ime mac oeconomic da a and
he analysis o da a e isions.
37
he o ecas s epo ed in he SPF. Speci ically, he SPF epo s p i a e sec o qua e ly ex-
pec a ions on consump ion, in es men , GDP de la o in la ion, and he sho - e m in e es
a e (3-mon h TB yield) om la e 1981 onwa d.23 Table 5 shows he RMSE compa ison o
PLM o ecas s wi h SPF da a a he han he ac ual da a used in he es ima ion p ocedu e.
Clea ly, he PLM o ecas s including TS in o ma ion do a much be e job in ma ching he
expec a ions epo ed in he SPF ac oss all o wa d a iables han he PLM o ecas s wi h-
ou TS in o ma ion. The a ionale o his inding is ha he SPF o ecas s a e based on
eal- ime da a and he e m sp ead in o ma ion included in ou PLM speci ica ion is also
a ailable in eal ime, whe eas he PLM o ecas s unde he SlW speci ica ion a e based only
on ex-pos e ised da a. The wo pieces o eal- ime da a (SPF and he yield cu e) may
hus sha e impo an in o ma ion a ailable in eal ime. This inding is consis en wi h ou
p e ious inding ha TS in o ma ion p o ides use ul in o ma ion o ma ching o ecas s on
eal- ime mac oeconomic da a. These indings sugges ha he use o SPF da a may help o
discipline model expec a ions and imp o e he empi ical i o model expec a ions.
Table 5. RMSE compa ison o PLM o ecas s w. . . SPF da a
Es ima ion pe iod: 1966:1-2009:1
Compa ison pe iod : 1982:1-2009:1
∆c∆in π
SlW-TS 0.363 1.240 0.442 1.007
SlW 1.358 2.106 1.206 1.580
The p e ious sec ion looks a he implica ions o he pa ame e s es ima ed o conside ing
SPF da a in he es ima ion p ocedu e, as desc ibed in he measu emen equa ion (7), o he
23Al hough SPF expec a ions on in la ion a e a ailable o 1968 onwa d, we decided o ocus on he pe iod
s a ing in he i s qua e o 1982, when SPF expec a ions became a ailable o all o wa d-looking a iables
conside ed in his analysis. 1982:1 also oughly coincides wi h he ime when he a e o in la ion s a ed o
go down. Fu he mo e, no e ha we conside he SPF o ecas s o he 3-mon h TB a e as a good p oxy o
he expec a ions o he ede al unds a e because he ac ual ime se ies o hese wo sho - e m a es a e
almos pe ec ly co ela ed.
38
sho sample pe iod cha ac e ized by he G ea Mode a ion. Table 6 shows he co esponding
RMSE s a is ics o PLM o ecas s ob ained om he model es ima ed o he sho sample
pe iod. As a e e ence, he i s panel in his able shows he RMSE s a is ics o he SPF
o ecas s. The emaining wo panels show he RMSE s a is ics o he wo speci ica ions o he
small o ecas ing models associa ed wi h he ALM and he PLM. The numbe s in pa en heses
below he RMSE s a is ics associa ed wi h he PLM o ecas s indica e he pe cen age changes
in he co esponding RMSE-s a is ics when model expec a ions a e disciplined wi h SPF da a
(i.e. he pe cen age changes be ween he igu es epo ed in he ow labeled as “PLM (pe iod
82:1-09:1)” in Table 4 and he co esponding igu es in Table 6).
Table 6. RMSE compa ison o PLM o ecas s (1982:1-2009:1)
∆c∆in ∆w π {4}
SPF 0.589 1.699 – 0.229 0.161 –
SlW-TS
ALM 0.754 1.636 0.854 0.213 0.166 0.176
PLM 0.667 2.222 5.246 0.215 0.201 0.493
(-11%) (39%) (127%) (4%) (8%) (-60%)
SlW
ALM 0.667 1.517 1.017 0.246 0.155 0.154
PLM 0.660 2.044 3.628 0.217 0.263 0.455
(-53%) (9%) (35%) (-14%) (30%) (11%)
In e es ingly, he o ecas s based on he ALM om he wo AL speci ica ions a e as good
as hose epo ed in he SPF when SPF is conside ed in he se o obse ables. I is also
impo an o highligh ha he AL speci ica ion wi h TS esul s in simila RMSE s a is ics
e en when SPF is no used in he se o obse ables, as shown in Table 4. In e es ingly,
including SPF in he es ima ion p ocedu e esul s in a g ea e imp o emen in he o ecas s
39
o hose a iables ha pe o m wo s when SPF da a is no used. Thus, he imp o emen
in he consump ion g ow h o ecas is g ea e o he SlW speci ica ion (a educ ion in he
RMSE o 53%) han o he speci ica ion ha includes TS in o ma ion (a educ ion o 11%).
Mo eo e , he pe o mance o he PLM wi h TS in o ma ion is lowe o he es o he
a iables, excep o he 1-yea yield, when SPF is included in he se o obse ables.24 Thus,
including SPF da a imp o es he PLM o ecas s o he 1-yea yield when he PLM conside s
TS in o ma ion ( he e is a 60% educ ion in he RMSE). Howe e , he opposi e occu s ( he e
is an inc ease o 11%) o he o ecas ing models based on he SlW o mula ion.
In line wi h he esul s shown in Table 5 o he DSGE models es ima ed using he whole
sample pe iod, Table 7 clea ly shows ha he PLM o ecas s ha include TS in o ma ion
(SlW-TS) do a be e job han he SlW speci ica ion in ma ching he expec a ions epo ed in
he SPF ac oss mos o wa d a iables when he wo AL speci ica ions a e es ima ed using he
sho e sample (1982:1-2009:1) and SPF da a is included in he es ima ion p ocedu e. The
igu es in pa en heses show he pe cen age changes in he RMSE-s a is ics when SPF da a a e
conside ed in he se o obse ables (i.e. he pe cen age changes be ween he igu es epo ed
in Table 5 and he co esponding igu es in Table 7). As expec ed, he o ecas s om he wo
PLM speci ica ions become close o he SPF o ecas s when hose o ecas s a e used in he
es ima ion p ocedu e o discipline model expec a ions. Mo eo e , he imp o emen in he
wo PLM speci ica ions is in e sely ela ed o hei ela i e abili y o ma ch SPF o ecas s
when hese o ecas s a e no used as obse ables in he es ima ion p ocedu e (shown in
Table 5). Pu di e en ly, he need o discipline expec a ions is g ea ly educed o he eal
o wa d-looking a iables (and o a lesse ex en o he nominal a iables) by including TS
in o ma ion in he small o ecas ing models.
24This de e io a ion obse ed o some a iables may be due o he ac ha lea ning equi es ime and
in o ma ion. Tha is, he RMSE-s a is ics compu ed o he pe iod 1982:1-2009:1 using he whole sample
pe iod in he es ima ion p ocedu e ( hose epo ed in Table 4) may be somewha supe io o hose RMSE-
s a is ics compu ed o he pe iod 1982:1-2009:1 using he es ima es o his sho e pe iod ( epo ed in Table
6) because he AL p ocesses associa ed wi h he o me ake in o accoun in o ma ion p eda ing 1982.
40
Table 7. RMSE compa ison o PLM o ecas s w. . . SPF da a
Compa ison pe iod : 1982:1-2009:1 ∆c∆in π
SlW-TS 0.301 1.024 0.179 0.293
(-17%) (-17%) (-60%) (-71%)
SlW 0.374 1.180 0.175 0.338
(-72%) (-44%) (-85%) (-79%)
5 Conclusions
This pape conside s an es ima ed DSGE model wi h adap i e lea ning (AL) in which he
o ecas ing models o agen s include e m s uc u e in o ma ion. Mo e p ecisely, we ex end
he AL model o Slobodyan and Wou e s (2012a) by in oducing he e m s uc u e o in e es
a es and hen including e m s uc u e in o ma ion obse ed in addi ion o he cu en and
lagged alues o he o wa d-looking a iables.
The es ima ion esul s show ha including e m s uc u e in o ma ion in he agen s’ o e-
cas ing models esul s in an imp o emen in model i . Mo eo e , he lea ning speci ica ion
augmen ed wi h e m s uc u e in o ma ion imp o es he pe o mance o AL in o ecas ing
ac ual e ised mac oeconomic da a used in he es ima ion p ocedu e as well as eal- ime (i.e.
he i s announcemen s o ) mac oeconomic da a. The la e inding sugges s ha he yield
cu e con ains impo an in o ma ion a ailable in eal ime, which is e y use ul in o ecas ing
agg ega e a iables abo e and beyond ha p o ided by e ised mac oeconomic da a. In line
wi h hese indings, ou es ima ion esul s also show ha e m s uc u e in o ma ion helps
AL expec a ions o ma ch he o ecas s o agg ega e a iables epo ed in he Su ey o P o-
essional Fo ecas e s, which a e o med using in o ma ion a ailable in eal ime. The e o e,
e m s uc u e in o ma ion u he con ibu es o he empi ical alidi y o AL.
41
below i s p e ious igu es. Fo he 2009-2019 pe iod, he a e o change o co e in la ion
was 1.1%, 0.6 pp down on he phase p io o he global inancial c isis. And u he o he
ou b eak o COVID-19, his disin la iona y p ocess has ended o become mo e acu e. Such a
p olonged pe iod o mode a e in la ion migh be due ei he o empo a y causes, albei wi h
high pe sis ence, o , al e na i ely, o mo e s uc u al easons. The i s g oup o explana o y
ac o s, namely he empo a y ones, would include elemen s such as he decline in ene gy
p ices o he du able p esence o e his pe iod o a high deg ee o slack bo h in he Eu o A ea
and global economies. The s uc u al causes in luencing long- e m in la ion mo emen s ela e
o changes in ce ain undamen als o he economy. These include mos no ably sec o al
composi ion (wi h an inc ease in he weigh o he se ices sec o 1), globaliza ion (which
would gi e ise o a g ea e in e connec edness o in la ion a es ac oss di e en economies,
agains he backd op o he p og essi e inco po a ion in o global ade o coun ies wi h lowe
p oduc ion cos s) and changes in consump ion pa e ns linked o popula ion aging.
A s able pa h o in la ion expec a ions consis en wi h he p ice s abili y objec i e smoo hs
mone a y policy implemen a ion, leading gene ally o a educ ion in he ola ili y o he
economic cycle. Howe e , he p olonga ion o e ime o he cu en low-in la ion phase
has gi en ise o a deba e on some deancho ing o in la ion expec a ions in ela ion o he
cen al bank’s medium- e m objec i e, and po en ial eedback be ween ac ual in la ion and
expec a ions. As a esul , he diminished pace o p ice changes would be exe ing a downwa d
impac on economic agen s’ in la ion expec a ions, which would in u n a ec ac ual in la ion
in he same di ec ion.
Mos models adi ionally used in mone a y policy design s a om he p emise ha
agen s o m expec a ions abou he economy a ionally.2This hypo hesis implies ha , in he
shaping o hei expec a ions, agen s obse e and p ocess e icien ly all a ailable in o ma ion.
1In pa icula , he e is a g owing body o e idence indica ing ha se ices p ices a e adjus ing wi h less
equency han in o he sec o s o he economy. See, o example, Bouakez, H., Ca dia, E. and Ruge-Mu cia,
F. (2014), and Ál a ez e al. (2006).
2Fo example, some o he gene al equilib ium models ha a e commonly used by he New Yo k Fed-
e al Rese e (FRBNY DSGE) o he Eu opean Cen al Bank (EAGLE), mainly o conduc ing simula ion
exe cises, a e based on a ional expec a ions.
48
In pa icula , agen s a e able o unde s and he na u e o mac oeconomic shocks and hei
du a ion, and ha e he capaci y o consis en ly inco po a e news on mone a y policy changes
o on expec ed de elopmen s in he economy in o hei expec a ions. Howe e , in eali y, i is
unlikely ha agen s a e able o obse e and p ocess all a ailable in o ma ion.3On nume ous
occasions, he na u e o shocks and hei ansmission channels a e only impe ec ly known
by agen s and a e di icul o iden i y. Al e na i es o his hypo hesis ha e been la gely
deba ed in he li e a u e.4In his pape we explo e he al e na i e o adap i e lea ning
expec a ions. This al e na i e assumes ha agen s’ expec a ions abou u u e e en s a e
pa ly and p og essi ely upda ed wi h he in o ma ion hey ecei e abou de elopmen s in he
main mac oeconomic agg ega es. I is u he assumed ha , when shaping hei expec a ions,
agen s use a limi ed amoun o in o ma ion, which hey inco po a e e e y pe iod upon he
a i al o new in o ma ion.
The model used in he pape is an Ex ended Lea ning Model (ELMo) e sion o Sme s
and Wou e s (SW, 2007) as in Aguila and Vazquez (2019) es ima ed o he EA. The model
builds on he DSGE o Sme s and Wou e s (2007) unde he assump ion o adap i e lea ning
expec a ions and he inco po a ion o he e m s uc u e o in e es a es h ough mul iple
Eule equa ions associa ed wi h he di e en bond ma u i ies. The ex ended model esul s in
mul i-pe iod-ahead expec a ions appea ing in he di e en Eule equa ions. Mo e p ecisely,
in his e sion o he model, agen s o m expec a ions on in la ion (and consump ion) om
one qua e up o i e yea s. The model, es ima ed o he Eu o A ea as a whole o he
pe iod om 1999 Q1 o 2019 Q4, combines mac oeconomic in o ma ion, (consump ion and
in la ion, among o he s) wi h inancial in o ma ion ela ing o he yield cu e. The inclusion
o he yield cu e enables inancial-ma ke in o ma ion on he u u e cou se o he economy
3The empi ical li e a u e gene ally inds de ia ions in su ey-based da a om a ional expec a ions. As
i is explained in Coibion e al. (2018), su eys o expec a ions e eal ha he e a e biases ac oss di e en
demog aphic g oups, and ha , o example, pe cei ed in la ion is a ec ed by each agen ’s consump ion baske ,
e en i he e is a commi men om a cen al bank.
4Since he pionee ing publica ions by Ma ce and Sa gen (1989) and E ans and Honkapohja (2001) a
g owing li e a u e (including P es on, 2005; Milani, 2007, 2008, 2011; Eusepi and P es on, 2011; Slobodyan
and Wou e s, 2012) , see he discussion in his ega d in Aguila and Vazquez (2019) and Vazquez and Aguila
(2021).
49
o be inco po a ed.5Acco dingly, his speci ica ion allows a mo e comple e cha ac e iza ion
o expec a ions, by combining mac oeconomic and inancial in o ma ion.
This pape ocuses on he na u e o he de ia ions om he in la ion objec i e h ough
a lea ning scheme, his allows us o unde s and o wha ex en agen s pe cei e cu en
de ia ions in he in la ion a e as empo a y o pe manen and shed some ligh on he
(de)ancho ing o in la ion expec a ions in he EA. The ecen conclusions in he li e a u e
ela ed o he EA poin in wo di ec ions. On he one hand, Na oli and Sigalo i (2018) look
a co-mo emen s be ween sho - and long- e m in la ion expec a ions and ind highe co -
ela ion and nega i e shocks a ec ing sho - un belie s ha impac long- un expec a ions,
sugges ing a isk o de-ancho ing in he long- un. On he o he hand, G ishchenko e al
(2019) s udy he beha io o su ey da a o he US and EA in a dynamic ac o model,
inding ha he expec a ions emain ancho ed in bo h economies.
Ano he aspec ele an is he p esence o he E ec i e Lowe Bound (ELB) du ing a
p olonged pe iod o low in la ion and poo economic ac i i y. The p esence o he ELB
cu es he abili y o he cen al bank o implemen i s mone a y policy and has he isk o
making low in la ion episodes longe han in i s absence. Al e na i es o educe he equency
and du a ion o ELB episodes wi h espec o he cu en amewo k a e now in he deba e
in Be nanke (2017), and Me ens and Williams (2019) among o he s. These pape s show
ha al e na i es o he cu en amewo k such as, In la ion Ta ge ing (IT) and P ice-le el
Ta ge ing (PLT), wi h he addi ion o an asymme ic e sion o each: Asymme ic In la ion
Ta ge ing (AsIT) and Tempo a y P ice-le el Ta ge ing (TPLT), educe he p esence o ELB
episodes, howe e , hese esul s hinge on he assump ion ha he new ule is c edible.
The e is a bunch o pape s s udying he in e ac ion be ween mone a y policy and ex-
pec a ions unde adap i e lea ning. E ans e al. (2008) a gue ha agg essi e iscal policy
measu es may educe he se e i y o liquidi y aps. E ans and Honkapohja (2005) s udy
5In pa icula , he b eakdown o nominal in e es a es in o he eal, isk- ee in e es a e, in la ion
expec a ions and a isk componen enables he ela ionship be ween he implied yield on a bond and he
in la ion a e o be exploi ed
50
he abili y o agg essi e money supply ules o o e come ELB episodes. In Honkapohja and
Mi a (2020), p ice-le el a ge ing is a po en ool by means o escaping liquidi y aps, e en
i he p ice-le el a ge ing policy is impe ec ly c edible. Findings in Eusepi and P es on
(2011, 2018) sugges ha ac i e iscal heo y may help s abilize in la ion in economies wi h
in e es a e pegs and lea ning agen s. Me ens and Ra n (2014) simula e an economy wi h
lea ning agen s and a one- ime ELB episode and show ha he lea ning economy can escape
he ELB when expec a ions a e no oo pessimis ic. In his ma e his pape goes u he
and s udies he ansi ional e ec s o new policy ules o in la ion expec a ions.
The esul s show ha cu en expec a ions a e shaping he e ec s o mone a y policy. An
asymme ic in la ion a ge ing ule, wi h a s onge esponse o in la ion when i is below i s
end, seems o be a obus al e na i e ha p o ides imp o emen s o e s anda d in la ion
a ge ing, in e ms o educing he p esence o ELB episodes, howe e he e is one impo an
conside a ion: changing he ule is no e y e ec i e un il agen s ha e had ime o lea n abou
i : in his model, he announcemen o he new ule has no e ec on agen s’ expec a ions;
ins ead, hey only upda e hem as hey see he cen al bank beha ing in a di e en way and
lea n abou i , which equi es ime. This is e y di e en om wha we obse e in models
wi h a ional expec a ions, whe e he announcemen pe ec ly ancho s agen s’ expec a ions
and has immedia e e ec s in he economy.
The pape is s uc u ed as ollows. Sec ion 2 in oduces he DSGE model wi h mul i-
pe iod expec a ions es ima ed o he EA. Sec ion 3 s udies he de e minan s o in la ion
expec a ions in he EA since i s c ea ion. Sec ion 4 analyses he ansi ional e ec s o al e -
na i es o he cu en mone a y policy amewo k, and sec ion 5 concludes.
51
2 A DSGE model wi h mul i-pe iod expec a ions o he
Eu o A ea
The model builds on he SW model and i s AL ex ensions s udied by Slobodyan and Wou e s
(2012) and Aguila and Vázquez (2019). This s anda d medium-scale es ima ed DSGE model
con ains bo h nominal and eal ic ions a ec ing he choices o households and i ms. The
assump ion o adap i e lea ning implies ha expec a ions a e based on a limi ed in o ma ion
se , meaning ha agen s use small o ecas ing models in o ming hei belie s abou u u e
ealiza ions o o wa d-looking a iables, in his case by using simple au o eg essi e models,
and ha hey adap he coe icien s o hese o ecas ing models by a simple Kalman il e
upda ing p ocedu e. In addi ion, he ex ension o he model o accoun o he e m s uc u e
o in e es a es h ough he Eule equa ion esul s in o a mul i-pe iod o ecas ing model,
wi h expec a ions abou he key mac oeconomic a iables anging om one qua e o i e
yea s ahead.
Mo e speci ically, he expec a ions- o ma ion mechanism o consump ion, in es men and
in la ion in he model es s, in each pe iod, on simple lea ning ules ha ake in o consid-
e a ion he la es obse ed alue and he size o he p e ious e o o ecas s o upda e he
lea ning coe icien s. In he conc e e case o in la ion, he ule o upda ing expec a ions is
as ollows:
E π +i=αi, −1+βπi, −1π −1,
whe e π −1is he de ia ion om a ge obse ed in he las qua e and βπi, −1measu es
he deg ee o ansmission o he obse ed de ia ion o expec a ions i(deno ing a numbe )
qua e s ahead. Tha is o say, unde his ule agen s inco po a e he la es a ailable in o -
ma ion on he de ia ion by in la ion om a ge in o hei in la ion expec a ions a di e en
ho izons (up o 5 yea s) a ge . Mo eo e , his lea ning ule cap u es h ough αi, −1 he pos-
sibili y ha de ia ions om he in la ion objec i e may ha e long-las ing e ec s on in la ion
52
expec a ions o e a o ecas ho izon o i qua e s. Th ee possible alues a e conside ed in he
analysis o i: one, ou and 20 qua e s.
The g ea e he pe sis ence o he de ia ions pe cei ed by agen s (π −1) is, o a gi en
ho izon i, he g ea e βπi, −1will be and, he e o e, he highe he pass- h ough o hese de-
ia ions o expec a ions. By way o illus a ion, a pe cei ed alue o βπi, −1equals o 0.5
means ha agen s expec he la es obse ed de ia ion om a ge o hal e in i qua e .
Al e na i ely, a uni alue o his coe icien would mean ha agen s expec he de ia ion
o hold in ull o e he nex i qua e s. Mo eo e , i agen s we e o belie e ha de ia ions
om a ge a e pe manen , which would be an amoun o a change in he in la ion a ge ,
hen he coe icien αi, −1would be obse ed o be o he han ze o.
Tes ing he ancho ing o expec a ions
Unde his simple expec a ions- o ma ion amewo k, i is possible o es ima e bo h lea ning
coe icien s and, on he basis he eo , o analyze he deg ee o empo a iness associa ed wi h
he de ia ions om in la ion assigned by agen s in cons uc ing hei expec a ions. Unde a
scena io o ully c edible mone a y policy, agen s would no pe cei e pe manen de ia ions
om a ge αi, −1= 0 and empo a y de ia ions would diminish o e he cou se o he o ecas
ho izon (βπ1> βπ4> βπ20 ).
2.1 Es ima ion
The DSGE model is es ima ed o he sample pe iod om 1999Q1:2019Q4, using he qua e ly
se ies o he in la ion a e, he sho e m in e es a e, he log o hou s wo ked, and he
qua e ly log di e ences o eal consump ion, eal in es men , eal wages, and eal GDP wi h
he addi ion o he 1, 3 and 5-yea go e nmen benchma k bond yields. The measu emen
equa ion is
53
X =
dlGDP
dlCONS
dlINV
dlWAG
dlP
lHou s
ECB a e
1−yea TB yield
1−3yea TB yield
1−5yea TB yield
=
γ
γ
γ
γ
π
l
{4}
{12}
{20}
+
y −y −1
c −c −1
i −i −1
w −w −1
π
l
{4}
{12}
{20}
,(9)
whe e land dl ep esen he log and he log di e ence, espec i ely. γ= 100(γ−1) is
he common qua e ly end g ow h a e o eal GDP, eal consump ion, eal in es men ,
and eal wages. ¯
l,π, and {j}a e he s eady-s a e le els o hou s wo ked, in la ion, he
ECB in e es a e, and he 1,3,5-yea (ie. o j equal o 4,12,20 qua e s) bond yields,
espec i ely.
We ollow a Bayesian es ima ion p ocedu e. Fi s , he log pos e io unc ion is maximized
by combining p io in o ma ion on he pa ame e s wi h he likelihood o he da a. The p io
assump ions a e exac ly he same as in Slobodyan and Wou e s (2012). In addi ion, we
conside loose p io s o he pa ame e s cha ac e izing bo h he 1,3,5-yea yield dynamics
and he measu emen e o p ocesses. The Me opolis-Has ings algo i hm is used o gene a e
he pos e io dis ibu ion and o compu e he log densi y o he model. We epo he key
pa ame e es ima es in he model in Appendix A.1.
2.2 The e olu ion o expec a ions: cycle and end
Figu e 1 shows, o he di e en ho izons analyzed, he es ima ed coe icien s o he Eu o
A ea o he pe iod 1999-2019. As migh be expec ed, he alue o he coe icien s indica es
54
ha , excep o some isola ed pe iod, he weigh assigned by agen s o pas in la ion in
hei o ma ion o expec a ions abou p ice g ow h diminishes as he ime ho izon inc eases
(βπ1> βπ4> βπ20 ). The alue o he coe icien a one qua e (βπ1) is close o uni y,
sugges ing ha agen s expec , a h ee mon hs, ha he de ia ions o in la ion om a ge
will hold unchanged. Mo eo e , his coe icien has been highly s able since he s a o
Economic and Mone a y Union. In he case o medium- e m expec a ions, i.e. ou and 20
qua e s ahead (βπ4and βπ20 ), he es ima es sugges ha agen s educe, as he ime ho izon
inc eases, he weigh hey assign in hei lea ning ule o he la es obse ed igu e. The
cou se o bo h coe icien s shows a posi i e co ela ion wi h he beha io o ac ual in la ion,
indica ing ha , in pe iods wi h highe in la ion a es (2001-2002 and 2007-2008), agen s
es ima e ha de ia ions ha e a highe pe sis ence. This inding sugges s ha p ices show a
di e en deg ee o adjus men acco ding o he le el o he in la ion a e h ough he cycle.6
In any e en , acco ding o he model, in he longe un in la ion would e u n, in he absence
o esh shocks, o he medium- e m mone a y policy objec i e, since he alue es ima ed o
(αi, −1) is e y close o ze o a any o ecas ho izon.7
6One possible explana ion is he g ea e ease wi h which i ms can, in pe iods o excess demand, aise
p ices ins ead o inc easing p oduc i e capaci y. Con e sely, in pe iods o low demand, hey can op o educe
hei capaci y empo a ily. See Bobeica and Sokol (2019).
7The cha depic s he coe icien es ima ed when i= 20 qua e s. In p ac ice, he es ima ed alue when i
is equal o 1 o 4 is e y simila , which can be explained by he ac ha agen s ha e he same in o ma ion o
es ima e he long- e m de ia ion by in la ion om a ge i espec i e o he ho izon i a which hey o mula e
hei sho o medium- e m expec a ions.
55
Figu e 1. In la ion expec a ions coe icien ’s e olu ion
2.3 In e na ional compa ison
When compa ing wi h he es ima es om Aguila and Vazquez (2019) o he Uni ed S a es
(US), see igu e 2 below, he deg ee o pe sis ence o in la ion o e he pas 20 yea s on
a e age can be seen o be less in he US han in he Eu o A ea. Tha migh be indica i e o
less nominal igidi ies in he US economy. A shock o in la ion will be mo e o less pe sis en
depending on a se ies o ac o s which include, among o he s, he deg ee o wage ine ia
(depending on he deg ee o which wages a e linked o he o e all p ice index), p ice-se ing
igidi ies and supply-side igidi ies (which, in he model, a e mani es ed ia a limi ed capaci y
o adjus he use o p oduc i e ac o s). In he case o he model es ima ed o he US, he
deg ee o wage indexa ion is compa a i ely lowe , while he lexibili y o p ices is g ea e .
Consequen ly, in la ion expec a ions in he US economy a e less sensi i e o pas in la ion,
mainly in he medium and long e m. Speci ically, he coe icien s es ima ed o βπ4and
βπ20 (i.e. 1 and 5 yea s ahead) a e app oxima ely hal hose ob ained o he Eu o A ea,
meaning ha he de ia ion by expec a ions in he ace o a shock is less bo h in e ms o
le el and du a ion.
56
Figu e 2. Sensi i i y o in la ion expec a ion o las alue obse ed: EA s US
The es ima ion esul s can be somewha sensi i e o he model used. One way o assessing
he es ima es o e ed wi h is o compa e he in la ion expec a ions a he one-yea o ecas
ho izon ob ained om he model and hose d awn om he ECB’s Su ey o P o essional
Fo ecas e s (SPF). This qua e ly su ey e lec s he expec a ions o pa icipan esponden s
– who a e expe s om inancial and non- inancial ins i u ions alike in he Eu o A ea –
abou in la ion a es, GDP g ow h and Eu o A ea unemploymen a di e en ho izons. The
compa ison be ween bo h sou ces o expec a ions shows ha he dynamics cap u ed in he
model a e consis en wi h he SPF se ies (see Cha 3), which suppo s he empi ical alidi y
o he es ima es associa ed wi h he adap i e lea ning expec a ion o ma ion.
Figu e 3. ELMo s SPF one-yea -ahead in la ion expec a ions in he EA
57
Re e ences
•Aguila , P., and J. Vázquez. 2019. “An es ima ed DSGE model wi h lea ning based on
e m s uc u e in o ma ion.” Mac oeconomic Dynamics, 1-31.
•Ál a ez e al. 2006. “S icky p ices in he Eu o A ea: A summa y o new mic o e i-
dence.” Jou nal o he Eu opean Economic Associa ion, Vol. 4, No 2/3, pp. 575-584.
•Be nanke, B. S. 2017. “Mone a y Policy in a New E a.” Pe e son Ins i u e o In e na-
ional Economics, Oc obe 12–13.
•Bobeica, E. A. Sokol. 2019. “D i e s o unde lying in la ion in he Eu o A ea o e ime:
a Phillips cu e pe spec i e.” ECB Economic Bulle in, Issue 4/2019.
•Bouakez, H., Ca dia, E. and Ruge-Mu cia, F. 2014. “Sec o al P ice Rigidi y and Ag-
g ega e Dynamics.” Eu opean Economic Re iew, Vol. 65(C), pp. 1-22.
•Coibion, O., Go odnichenko, Y. and Kamda , R. 2018. “The Fo ma ion o Expec a ions,
In la ion, and he Phillips Cu e” Jou nal o Economic Li e a u e 56, pp. 1447-91.
•Eusepi, S., and B. P es on. 2011. “Expec a ions, lea ning, and business cycle luc ua-
ions.” Ame ican Economic Re iew 101, pp. 2844-2872.
•Eusepi, S., and B. P es on. 2018. “The Science o Mone a y Policy: An Impe ec
Knowledge Pe spec i e.” Jou nal o Economic Li e a u e 56, pp. 3-59.
•E ans, G. and S. Honkapohja. 2001. “Lea ning and Expec a ions in Economics.”
P ince on Uni e si y P ess 376.
•E ans, G. and S. Honkapohja. 2005. “Policy in e ac ion, expec a ions and he liquidi y
ap.” Re iew o Economics Dynamics 8, pp. 303-323.
64
•G ishchenko, O. S. Mouabbi, and J.P. Renne. 2019. “Measu ing In la ion Ancho ing
and Unce ain y: A U.S. and Eu o A ea Compa ison.” Jou nal o Money, C edi , and
Banking, Blackwell Publishing 51, pp. 1053-1096.
•Honkapohja, S., and Mi a, K. 2020. “P ice le el a ge ing wi h e ol ing c edibili y.”
Jou nal o Mone a y Economics 116, pp. 88-103.
•Ma ce , A., and T.J. Sa gen . 1989. “Con e gence o leas -squa es lea ning in en i-
onmen s wi h hidden s a es a iables and p i a e in o ma ion.” Jou nal o Poli ical
Economy 97, pp. 1306-1322.
•Me ens, T., M and Ra n, M. 2014. “Fiscal Policy in an Expec a ions-D i en Liquidi y
T ap.” The Re iew o Economic S udies 81, pp. 1637–1667.
•Me ens, T., M and J., C. Williams. 2019. “Mone a y policy amewo ks and he
e ec i e lowe bound on in e es a e.” Ame ican Economic Associa ion pape s and
p oceedings, pp. 109: 427-32.
•Na oli F. and L. Sigalo i. 2018. “Tail Co-mo emen in In la ion Expec a ions as an
Indica o o Ancho ing.” In e na ional Jou nal o Cen al Banking 14, pp. 35-71.
•Slobodyan, Se gey, and R. Wou e s. 2012. “Lea ning in a medium-scale DSGE model wi h ex-
pec a ions based on small o ecas ing models.” Ame ican Economic Jou nal: Mac oeconomics
4, 65-101.
•Sme s, F., and R. Wou e s. 2007. “Shocks and ic ions in US business cycles: A
Bayesian DSGE app oach.” Ame ican Economic Re iew 97, pp. 586-606.
•Vázquez J., and Aguila P. 2021. “Adap i e lea ning wi h e m s uc u e in o ma ion.”
Eu opean Economic Re iew 134
65
Pa III
The impo ance o da a e isions
1 In oduc ion
The exis ence o da a e ision mus be acknowledged when mac oeconomic se ies a e used
o business analysis. This chap e p o ides a de ailed analysis o he s a is ical p ope ies o
da a e isions o he eu o a ea and s udies he app op ia e modeling o eal- ime da a and
i s e ision in DSGE models o business cycle analysis.
The main mac oeconomic se ies a e egula ly e ised ela i e o hei eal- ime elease o
inco po a e new in o ma ion ha was no a ailable a he ime o he ini ial announcemen
o o inco po a e changes, such as in he de ini ion o he indica o o he measu emen o
he a iable. A dis inc ion be ween whe he he da a comp ises ini ial eleases and/o inal
e ised da a mus be aken in o accoun by esea che s when cons uc ing da ase s. I da a
e isions a e no well-beha ed, meaning ha hey can be o ecas ed, esea che s who igno e
his ac may su e om a bias in hei analysis. This chap e s udies he p ope ies o
eal- ime da a and hei e isions o he eu o a ea and p oposes a modeling amewo k o
inco po a e his phenomenon in o a DSGE model.
In one o he ea lies s udies o da a e ision p ope ies, Mankiw, Runkle and Shapi o
(1984) ocus on he p edic abili y o da a e isions. They analyze whe he he p elimina y
announcemen s o money s ock a e a ional o ecas s o he inal announcemen s o obse -
a ions con aining a measu emen e o o he e ised se ies. Mankiw and Shapi o (1986)
ex end his s udy o he se ies o GNP.1These wo pape s conclude ha money s ock e isions
a e p edic able bu GNP e isions a e no . This led o a p ima y classi ica ion o e isions
as adding news o educing noise. Re isions add news when he ini ial announcemen is an
op imal o ecas o he inal da a, in which case hey a e o hogonal o ini ial da a and he e-
1O he ele an pape s o he ma e du ing ha pe iods a e Mo k (1987, 1990)
66
o e unp edic able. Re isions educe noise when he ini ial announcemen is an es ima e o
he inal da a wi h a measu emen e o . In ha case he ini ial announcemen is co ela ed
wi h he e ision, hus, becoming p edic able. Diebold and Rudebusch (1991) subsequen ly
highligh he impo ance o da a e isions in mac oeconomics. They show ha he US index
o leading economic indica o s does a ine job a p edic ing ecessions ex-pos bu ails in
p edic ing u u e ecessions. This is because he indica o is cons uc ed o explain e ised
pas da a, and hus igno es he ac ha ini ial da a eleases may look e y di e en once
hey a e e ised.
The pape by C ousho e and S a k (2001) inc eased he popula i y o eal- ime da a and
hei e isions by p o iding a egula ly upda ed eal- ime da ase o he main mac oeconomic
a iables. In pa icula , C ousho e (2011) ex ensi ely e iews he li e a u e and discusses
he da a implica ions o eal- ime da a o da a e isions, o ecas s, mone a y policy analysis,
mac oeconomic esea ch, and cu en analysis o inancial and business condi ions. The use o
eal- ime mac oeconomic da ase s appea s o become mo e impo an o policy ins i u ions
wi h he de elopmen o new da ase s by s a is ical agencies, such as he Fede al Rese e
Bank o Philadelphia, he Eu opean Cen al Bank, and he OECD.
Mo e ecen ly, A uoba (2008) de ines he desi able s a is ical p ope ies o da a e isions,
namely i) he mean is expec ed o be ze o; ii) small a iance compa ed o ha o he e ised
a iable; and iii) unp edic abili y. He inds ha hese p ope ies a e no sa is ied in he
e isions o majo mac oeconomic a iables in he Uni ed S a es, as hey ha e a non ze o
mean, hei ola ili y is la ge compa ed o he inal da a, and hey can be p edic ed using
he in o ma ion se a he ime o he ini ial announcemen .2
Ano he ele an aspec is he impac o da a e isions on he es ima ion o DSGE models,
which a e now popula o mac oeconomic analysis a cen al banks. Casa es and Vázquez
(2016) in oduce an ex ension o he Sme s and Wou e s DSGE model (2007) ha includes
bo h eal- ime and e ised da a om he U.S. economy. Thei es ima es show a le el o bo h
2A simila s udy is p esen in Faus e al (2005) o he G7 coun ies
67
habi o ma ion and p ice indexa ion which is lowe han he s anda d model. They also
ind ha shocks in da a e isions explain oughly 10% o ou pu a iabili y. This means ha
omi ing e isions may cause wo p oblems: Fi s , a bias in he pa ame e es ima ion; and
second, o e es ima ion in he sou ces o business cycle a iabili y.
This chap e con ibu es o he li e a u e on da a e isions by p o iding a de ailed analysis
o he s a is ical p ope ies o da a e isions o he eu o a ea and s udying he app op ia e
modeling o eal- ime da a and i s e ision in DSGE modeling. Mo e p ecisely, ollowing
Casa es and Vazquez (2016), he Sme s and Wou e s (2007) DSGE model is augmen ed
o include eal- ime da a (by assuming ha indexa ion ules and he mone a y policy ule
a e based on eal- ime da a) and o inco po a e da a e isions. The aim is o pinpoin
he sou ce o da a e isions (whe he hey educe noise o add news) and o assess hei
mac oeconomic implica ions. One o he main indings is ha da a e isions a e no well-
beha ed, i.e. hey a e co ela ed wi h ini ial announcemen s and show high ola ili y. These
empi ical indings a e con i med in educed- o m eg ession analysis and in an es ima ed
DSGE model augmen ed wi h da a e isions. These indings a e in line wi h hose o Casa es
and Vázquez (2016) o he US. As a consequence, e isions become a majo sou ce in he
business cycle decomposi ion. In he case o he Eu o A ea hey accoun o one- hi d o he
ou pu a iabili y, which is oughly h ee imes he igu e es ima ed o he US in Casa es
and Vázquez (2016). This inding leads o he conclusion ha DSGE models o business
cycle analysis which omi eal- ime da a and da a e isions may in oduce a majo sou ce o
bias in o he es ima ed a iance decomposi ion and encou ages u he imp o emen s in he
es ima ion o eal- ime da a om he s a is ical agencies.
The es o his chap e is s uc u ed as ollows: Sec ion Two in oduces he concep o
e isions, desc ibes hei main p ope ies, and p oposes a speci ic amewo k o he inclusion
o da a e isions in DSGE models. Sec ion Th ee de i es he eal- ime equa ions ha en e
in o he ex ended DSGE model. Sec ion Fou p esen s he da a and es ima ion p ocedu e
and Sec ion Fi e discusses he main indings o he es ima ed DSGE-ex ended model. Sec ion
68
Six concludes.
2 Da a e isions
This sec ion is di ided in o wo pa s and p o ides a a ionale o he inclusion o da a
e isions in mac o models. The i s pa de ines he concep o da a e isions and he main
poin s o be conside ed when aking hem in o accoun , some o hem o en igno ed in he
li e a u e. The second pa s udies he s a is ical p ope ies o da a e isions in he eu o
a ea and p o ides an empi ical jus i ica ion o hei inclusion in DSGE models.
2.1 The concep o da a e isions
Da a e isions can be de ined as he di e ence be ween he da a ini ially announced and
he inal e ised da a . In he case o he eu o a ea, he i s announcemen s o qua e ly eal
GDP, GPD de la o , and eal consump ion a e gene ally eleased wi h a lag o one qua e ,
while he inal e ised da a a e published be ween ou and wel e qua e s la e .3This
de ini ion can be exp essed o mally as ollows:
y =y
, +1 + e y
, +S,(10)
whe e y e e s o he inal e ised obse a ion o GDP, y
, +1 ep esen s he ini ial an-
nouncemen wi h one qua e delay, and e y
, +Scap u es he o al alue o e ision a e
+Spe iods. A simila o mula can be applied o he consump ion and in la ion e ision
p ocesses.
The in age ma e s
The li e a u e abs ac s om he impo ance o he in age in de ining da a e isions.4
3
Benchma k e isions may also occu du ing he e ision p ocess. They in ol e me hodological changes,
such as he concep s included in he de ini ion o he a iable o he e e ence yea in he se ies.
4The pape by C ousho e and S a k (2001) is an excep ion. They discuss he elec ion o da a in ages,
bu in he con ex o economic o ecas ing.
69
Howe e , au ho s such as C ousho e and S a k (2001) a e an excep ion in ha hey ocus hei
esea ch on he choice o da a in ages in he con ex o economic o ecas ing. The choice
o he in age, howe e , becomes highly impo an when i comes o a iables exp essed
in g ow h a es, as e isions be ween in ages a e a po en ial sou ce o “noisy” e isions.
Table 2.A shows he di e en in age publica ions o US GDP, which help o illus a e he
impo ance o he choice o in age in compu ing ou pu g ow h a es.
Table 2.A: GDP US
Pe iod Vin age 1990:Q2 1990:Q3 1990:Q4 1991:Q1
1990:Q1 4195.8 4150.6 4150.6 4150.6
1990:Q2 4163.2 4155.1 4155.1
1990:Q3 4173.6 4170
1990:Q4 4147.6
GDP: Billions o eal Dolla s
Depending on he choice o he in age, ou pu g ow h a es can be calcula ed in wo
ways: Ac oss di e en in ages o wi hin he same in age. In he i s case, he g ow h
a e is ob ained using he i s qua e ly da a announcemen s om wo consecu i e in ages,
while in he second g ow h a es a e compu ed using he i s in age in which bo h qua e ly
a iables a e a ailable. Fo mally, hey can be exp essed as ollows:
g1= (y
+1, +2/y
, +1 −1) ×100,
g2= (y
+1, +2/y
, +2 −1) ×100.
Unde he i s op ion, g1, he g ow h a es a e always compu ed using he i s elease,
while he second me hod, g2, may al eady inco po a e a e ision in he i s obse a ion.
Howe e , using he same in age a oids he impac o benchma k e isions be ween in ages.5
5Fo ou US sample da a, 1983Q1:2008Q1, he e a e in all i e benchma k e isions (1985:Q3, 1991:Q3,
1995:Q4, 1999:Q3 and 2003:Q4), while o he eu o a ea he e was one main benchma k e ision in 2005.
Vázquez, Ma ía-Dolo es, and Londoño (2012) adjus benchma k e isions by eplacing hem wi h he a e age
70
The qua e ly g ow h a e o ou pu in 1990Q2, depending on he me hod, would be ei he :
∆y1990Q2,g1= (y
1990Q2,1990Q3/y
1990Q1,1990Q2−1)x100 = (4163.2/4195.8−1) ×100 = −0.776%.
∆y1990Q2,g2= (y
1990Q2,1990Q3/y
1990Q1,1990Q3−1)x100 = (4150.6/4163.2−1) ×100 = 0.303%.
As illus a ed in he example, di e en choices o in age p o ide opposi e-sign g ow h
a es. The size o he e isions a e he e o e di ec ly a ec ed by his choice, so his esea ch
acknowledges he p ope ies o da a e isions unde bo h al e na i es.
2.2 Reg ession analysis o da a e isions
This subsec ion s udies he main s a is ical p ope ies o da a e isions in he eu o a ea
o explain why hey a e ele an and should be included in mac o models. The analysis is
di ided in o wo pa s: The i s se s ou he main desc ip i e s a is ics o da a e isions
unde bo h app oaches (g1and g2) o he qua e ly g ow h a es o eal GDP, consump ion,
and in la ion. The second pa es ima es he ela ionship be ween ini ial announcemen s and
da a e isions o de e mine whe he e isions add news o he ini ial announcemen o educe
e o s, and p o ides an es ima ion o he p ocess o da a e isions.
Main desc ip i e s a is ics
Acco ding o A uoba (2008), i da a e isions a e well-beha ed hey should ha e he
ollowing p ope ies: Fi s , he mean is expec ed o be ze o. This would imply ha he
ini ial announcemen is an unbiased es ima e o he inal e ised alue. Second, he a iance
should be small when compa ed o ha o he e ised alue. This is measu ed by he noise o
alue o he wo obse a ions be o e and a e . In his pape , benchma k e isions a e managed by eplacing
hem wi h he alue ob ained om g2, which g ea ly simpli ies he p ocedu e.
71
signal a io, which is he a io be ween he s anda d de ia ion o he inal e isions and he
inal da a. Finally, he e ision should be unco ela ed wi h he ini ial announcemen , i.e. i
should be unp edic able. Table 2.B shows he main desc ip i e s a is ics o da a e isions
acco ding o he lis o in e es o he qua e ly g ow h a es (g1and g2) o qua e ly eal
GDP, consump ion and in la ion.
Table 2.B Eu o A ea desc ip i e s a is ics o da a e isions
Re ision in g1Re ision in g2
GDP Consump ion In la ion GDP Consump ion In la ion
Mean 0.110 -0.111 -0.126 0.276 0.357 0.079
Absolu e Mean 1.645 1.708 0.716 0.940 0.845 0.531
Median 0.172 -0.088 -0.088 0.478 0.413 0.095
Min -4.640 -7.440 -3.003 -2.978 -2.204 -1.637
Max 4.827 4.830 2.055 2.479 3.131 2.202
S d. D. Re ision 2.126 2.273 0.957 1.153 1.032 0.686
Noise/Signal 1.602 1.658 0.761 0.720 0.622 0.901
Co ela ion wi h Ini ial -0.708 -0.712 -0.683 -0.376 -0.215 -0.414
Co ela ion wi h inal 0.415 0.481 0.400 0.337 0.422 0.509
Co ela ion Ini ial-Final 0.348 0.272 0.395 0.744 0.793 0.571
The o e all esul s sugges ha e isions a e no well-beha ed. Da a e isions o ou pu ,
consump ion, and in la ion ha e s a is ically non-ze o means. The ou pu and consump ion
e isions also ha e a noise o signal a io g ea e han one unde bo h me hods o compu-
a ion. Finally, all a iables show a ela i ely high le el o (nega i e) co ela ion be ween
e isions and he ini ial elease.6
Rega ding he choice o in age in e ms o he s a is ical p ope ies o he e isions, i can
be seen ha when he second me hod o compu ing g ow h a es (i.e. using he same in age)
6In he case o he US (see Appendix 1.C.2), he esul s a e somewha simila and he p ope ies lis ed
by A uoba (2008) a e no sa is ied ei he .
72
is used in he case o he US (see Appendix 1.C.2) he esul s a e somewha simila ; no do
hey sa is y he p ope ies lis ed by A uoba (2008). g2 educes he a iabili y o he e isions
(and hus, he noise o signal a io) and educes co ela ion wi h he ini ial announcemen ,
bu he co ela ion wi h he inal da a emains low. In addi ion, he co ela ion be ween he
ini ial announcemen and he inal da a is close when g ow h a es a e compu ed o he
same in age. The ac ha he mean is lowe when g1is used han when g2is used is a
consequence o la ge e o o se ing signs, so he absolu e mean is smalle when g2is used.
These esul s may p omp he eade o use g ow h a es compu ed o he same in age, bu
i mus be ealized ha one e ision may al eady be included in one o he obse a ions used
o compu e he g ow h a e. Conce ning he use o ei he me hod in he li e a u e, C ousho e
and S a k (2001) ely on g ow h a es unde he same in age (al hough hey men ion he
possibili y o using g1 oo), Casa es and Vázquez (2016) and Vázquez, Ma ia-Dolo es and
Londoño (2012) use he g1app oach and make no speci ic men ion o he me hod used in
A uoba (2008).
Noise o news?
We o mally es he hypo hesis o whe he e isions educe noise o add news. They
educe noise when he ini ial announcemen is an ea ly es ima e o he e ised a iable
wi h a measu emen e o . This implies ha he e ision is unco ela ed wi h he inal
alue bu co ela ed wi h he ini ial da a elease. By con as , e isions add news when
he ini ial announcemen is an e icien es ima e o he e ised a iable and he e ision is
co ela ed wi h he inal da a bu unco ela ed wi h he ini ial announcemen (as he e ision
is unp edic able). Following A uoba (2008), we es bo h hypo heses unde he wo me hods
p oposed o compu ing g ow h a es wi h eal- ime da a:
-Noise: y
, +1 =α1+β1y +u1
-News: y =α2+β2y
, +1 +u2
whe e he i s join hypo hesis α1= 0, β1= 1 es s he noise hypo hesis and he second
73
ac oss agen s, he exp ession below is achie ed
c = (h/γ)c
−1, −(h/γ)E c
, +1 +E c +1 +(1−h/γ)(σc−1)L1+σl
σc(l −E l +1)−
1−h/γ
σc(R −E π +1 +εb
).(25)
The E c
, +1 e e s o he eal- ime announcemen o agg ega e consump ion in + 1
which a ec s he ex e nal habi in . The de ini ion o his exp ession can be ob ained using
c =E c
, +1+ e c
, +S(as shown in equa ion 1, bu o consump ion) and subs i u ing e c
, +S
by e c
, +S=bc(c
, +1 +δcc
−1, ) + ρS
chεc
−1, +S−1+ (δc/ρc)εc
−2, +S−2i.Consequen ly we ge
c = (1 + bc)c
, +1 +bcδcc
−1, +ρS
chεc
−1, +S−1+ (δc/ρc)εc
−2, +S−2i,
and isola ing c
, +1, an explici e m is ob ained
c
, +1 =
c −bcδcc
−1, −ρS
chεc
−1, +S−1+ (δc/ρc)εc
−2, +S−2i
1 + bc
.(26)
By subs i u ing he la e equa ion in o (16)
c +(h/γ)
1 + bc
c = (h/γ)c
−1, +(h/γ)
1 + bcbcδcc
−1, −ρS
chεc
−1, +S−1+ (δc/ρc)εc
−2, +S−2i+
E c +1 +(1−h/γ)(σc−1)L1+σl
σc(l −E l +1)−1−h/γ
σc(R −E π +1 +εb
),
and g ouping c
−1, and isola ing c we ge o inal exp ession o his new Eule equa ion:
c =c11 + δc(1 + bc)−1c
−1, + (1 −c1)E c +1 +c2(l −E l +1)−c3(R −E π +1 +εb
)+
c4εc
−1, +S−1+ (δc/ρc)εc
−2, +S−2,(27)
whe e:
c1=h/γ
1+(h/γ)(1+bcc)−1, c2=(σc−1)wL/(φwC)
σc(1+(h/γ)(1+bcc)−1), c3=1−h/γ
σc(1+(h/γ)(1+bcc)−1),
and c4=(h/γ)ρS
c
(1+bcc)(1+(h/γ)(1+bcc)−1).
80
As a esul , eal- ime da a en e s in he equa ion in he o m o lagged alues o ex e nal
consump ion. Mo eo e , shocks in he e ision p ocess o consump ion do play a ole. La e
on, a speci ic s uc u e will be p o ided o he shocks and i s impac in he es ima ion
discussed.
3.2.2 Mone a y policy ule
We use equa ion (1) o ew i e ou pu in he mone a y policy ule as we assume ha
he mone a y au ho i y akes decisions based on he in o ma ion a ailable on ou pu and
in la ion. This implies ha o lagged alues o ou pu , he obse a ion ha he au ho i y
uses co esponds o he i s announcemen o agg ega e ou pu , which is published wi h a
one-qua e delay. Simila easoning is used in Casa es and Vázquez (2016); howe e , he
p esence o lagged e isions a ec s he de ini ion o e isions in ou pu , and equi es he
de i a ion o a new mone a y policy ule. S a ing om he Sme s and Wou e s (2007)
model, we ha e he ollowing policy ule:11
R =ρR −1+(1−ρ)[ ππ −1+ yy −1−yp
−1]+ ∆yy −1−yp
−1−y −2−yp
−2+εR
.(28)
Including he equa ions o da a e isions on ou pu (7) and in la ion (9) in o he de ini ion
o eal- ime da a (1), we can exp ess de ine y and π as ollows:
y = (1 + by)y
, +1 +byδyy
−1, +ρS
yhεy
−1, +S−1+ (δy/ρy)εy
−2, +S−2i,
π = (1 + bπ)π
, +1 +ρS
πεπ
−1, +S−1.
Placing he las wo exp essions o y −1,y −2,π −1in o (19) we ha e he ollowing ex-
p ession
R =ρR −1+ (1 −ρ)( πh(1 + bπ)π
−1, +ρS−1
πεπ
−2, +S−2i+
11No e ha in his exp ession in la ion and he ou pu gap a e lagged by one mo e pe iod han in he
o iginal e sion. This makes i easie o in oduce in la ion in eal- ime.
81
yh(1 + by)y
−1, +byδyy
−2, −1+ρS−1
yεy
−2, +S−2+ (δy/ρy)εy
−3, +S−3i−yp
−1)+
4y(h(1 + by)y
−1, +byδyy
−2, −1+ρS−1
yεy
−2, +S−2+ (δy/ρy)εy
−3, +S−3−yp
−1i−
h(1 + by)y
−2, −1+byδyy
−3, −2+ρS−2
yεy
−3, +S−3+ (δy/ρy)εy
−4, +S−4−yp
−2i)+εR
.
Finally, ope a ing wi h he e ms measu ing he change in he eal- ime ou pu gap, a
new mone a y policy ule in eal- ime is ob ained
R =ρR −1+ (1 −ρ)( πh(1 + bπ)π
−1, +ρS−1
πεπ
−2, +S−2i+
yh(1 + by)y
−1, +byδyy
−2, −1+ρS−1
yεy
−2, +S−2+ (δy/ρy)εy
−3, +S−3i−yp
−1)+
4y((1 + by)hy
−1, −y
−2, −1i+byδyhy
−2, −1−y
−3, −2i+
ρS−1
yhεy
−2, +S−2−(1/ρy)εy
−3, +S−3i+ρS−2
yδyhεy
−3, +S−3−(1/ρy)εy
−4, +S−4i+
(yp
−1−yp
−2))+εR
.(29)
82
4 Da a and es ima ion p ocedu e
This sec ion seeks o s udy he impac o eal- ime da a and da a e isions on DSGE
models h ough he h ee channels men ioned abo e. The sample pe iod used o he eu o
a ea is 1995Q1-2008Q1. The se o obse able a iables comp ises qua e ly se ies o he
in la ion a e (exp essed as he i s di e ence in logs o he implici GDP de la o ), he ECB
in e es a e, he log o employmen , and he qua e ly log di e ences o eal consump ion,
eal in es men , eal wages, and GDP. In addi ion, o he ex ended model we inco po a e
eal- ime se ies o qua e ly in la ion (exp essed as he i s di e ence in logs o he eal- ime
GDP de la o ), and qua e ly log di e ences o GDP and eal consump ion om he ECB
Real-Time Da abase.12 Va iables displaying a long- un end a e exp essed in log di e ences
o emo e he non-s a iona y componen . The lis o obse able a iables is measu ed as
ollows:
X =
dlGDP
dlCONS
dlINV
dlWAGT
dlEMPL
dlP
lECB&lFEDFUNDS
dlGDP
dlCONS
dlP
=
γ
γ
γ
γ
¯
l
π
γ
γ
π
+
y −y −1
c −c −1
i −i −1
w −w −1
l
π
y
−y
−1
c
−c
−1
π
whe e land dl espec i ely deno e he log and he log di e ence. γ= 100(γ−1) , is he
common qua e ly end g ow h a e o eal GDP, consump ion (also o eal- ime a iables)
12Real ime g ow h a es a e compu ed using he g1app oach. The ex ended model is also es ima ed using
g2bu is no shown he e due o space cons ain s. The o e all esul using he la e app oach is simila , bu
he iden i ica ion o he e ision p ocesses becomes mo e sensi i e.
83
in es men and wages, which a e he a iables p esen ing a long un end. ¯
l,π, a e he
s eady s a e he le el o employmen pe capi a, and he s eady s a e alues o in la ion and
he sho - e m in e es a e.
The app oach used is a wo-s ep Bayesian es ima ion p ocedu e in Dyna e. Fi s , he log
pos e io unc ion is maximized by combining p io in o ma ion on he pa ame e s and he
likelihood o he da a. Then he Me opolis-Has ings algo i hm is implemen ed, which uns a
massi e sequence o d aws o all he possible ealiza ions o each pa ame e o ge a pic u e
o he subsequen dis ibu ion. Fo he SW model his algo i hm is execu ed using 3 blocks
o 200,000 ealiza ions each. The same is done o he ex ended model. The accep ance a es
o bo h models o he US and eu o a ea a e be ween 20-30%.
5 Es ima ion esul s
This sec ion discusses he main esul s o he DSGE es ima ion. The i s pa a gues he
main esul s in e ms o pa ame e es ima ion o he eu o a ea. The second p o ides he
main indings in e ms o second momen s and a iance decomposi ion.
5.1 Pa ame e es ima es
The baseline SW o he EA s he US
Table 3.A epo s he mean and he 5 h and 95 h pe cen iles ob ained om he Me opolis-
Has ings es ima ion o bo h he ex ended and baseline model (wi hou eal- ime da a) pa-
ame e s o he eu o a ea. This subsec ion compa es he baseline es ima es ( igh -hand side
o he able) wi h hose es ima ed o he US, as epo ed in Table 3.B. 3.B.13 The con idence
in e als o he main g oup o pa ame e s o e lap o a g ea ex en wi h hose o he US.
Howe e , he e a e some no ewo hy disc epancies. The deg ee o p ice and wage s ickiness
(ξp,ξw) is sligh ly smalle (0.45 and 0.63 o he eu o a ea agains 0.66 and 0.70 o he US).
Rega ding he indexa ion pa ame e s (iwand ip), he p ice indexa ion is oughly he same
13We compa e ou esul s wi h hose o Sme s and Wou e s (2007) since hey a e he main e e ence.
None heless hese commen s apply o a la ge ex en o he es ima es epo ed in Casa es and Vázquez (2016)
84
(ip= 0.24), while he wage indexa ion coe icien is less han one-hal o he US es ima e
(0.21 e sus 0.58). This makes he wage equa ion mo e o wa d-looking in he case o he
eu o a ea. Ano he impo an di e ence lies in in es men decisions, namely he elas ici y o
capi al u iliza ion and he le el o ixed cos s (ψand φ). The o me , ψ, is signi ican ly lowe
(0.19 e sus 0.54), while he la e is es ima ed o be highe (1.90 e sus 1.60). Wi h espec
o he pa ame e es ima es in he policy ule, he smoo hing pa ame e (ρ) and he coe icien
measu ing he change in ou pu gap ( 4y) a e bo h a he simila o he US. Howe e , he
eac ion o he in la ion gap is smalle (1.72 e sus 2.01) and he ou pu gap is nea ly ze o.
Finally, in e ms o s uc u al shocks, he esul s sugges a g ea e pe sis ence o spending
and isk p emium shocks (ρb,ρR, 0.77 and 0.48 e sus 0.22 and 0.15), while in es men
adjus men and p ice and wage ma k-up shocks (ρi,µpand µw) a e less pe sis en .
The SW model wi h EA eal- ime da a
The assump ion ha agen ’s economic decisions a e based on eal- ime da a has wo
impo an e ec s in he Eule equa ion. I educes he impo ance o he habi in consump ion
pa ame e (hd ops om 0.68 o 0.4) and educes he F isch elas ici y (σlinc eases om 1.09
o 3.07). In e ms o nominal igidi ies, i educes he Cal o p obabili y in wages (ξwd ops
om 0.65 o 0.44) bu inc eases wage indexa ion (iwinc eases om 0.21 o 0.45). Thus, wages
a e upda ed mo e equen ly bu a e mo e backwa d-looking. Conce ning he new mone a y
policy ule, he es ima es show a simila eac ion o eal- ime da a as o he model wi h inal
da a. Rega ding he es ima es o he s uc u al shocks, he model wi h eal- ime da a shows
a smalle au oco ela ion coe icien in he spending and isk p emium shocks (ρg,ρR), and
a lowe es ima e in he mo ing-a e age componen o bo h p ices and wage ma k-up shocks
(µp,µw).
The es ima ion o he da a e ision p ocess suppo s he idea ha da a e isions a e no
well-beha ed. In he case o ou pu and consump ion he ini ial announcemen an icipa es
a u u e nega i e e ision (by,bcbeing -0.15 and -0.13 espec i ely) and hey a e co ela ed
wi h pas e isions. In he case o in la ion he es ima es show ha he ini ial elease an ic-
85
ipa es an upwa d e ision (bπ=2.2). The e o componen shows a high le el o pe sis ence
o all he a iables (ρy = 0.66,ρc = 0.72, and ρπ = 0.94 ) and he es ima ed ola ili y o
he inno a ions (σy ,σc and σπ ) is on a e age wice as high as he es o he shocks in he
model. These esul s a e in line wi h he eg ession analysis o he e isions o ou pu and
consump ion. Bo h ( educed- o m and s uc u al) me hodologies cap u e a nega i e co e-
la ion wi h he ini ial elease, he pe sis ence in he e o e m, and he nega i e coe icien
associa ed wi h pas e ision. Conce ning he in la ion e ision p ocess, he es ima ions o
he DSGE and he eg ession model show opposi e signs in he coe icien ela ing e isions
o he ini ial announcemen , which migh be due o he a o emen ioned di e ences be ween
he Bayesian s uc u al econome ic app oach and he educed- o m OLS app oach. In any
case, he o e all conclusion (especially o ou pu and consump ion) emains obus , da a
e isions a e co ela ed wi h hei ini ial announcemen , and hei e o s show high a iance
and pe sis ence.
5.2 Second-momen s a is ics
Table 4 epo s he main second-momen s a is ics: S anda d de ia ion, con empo aneous
co ela ion wi h ou pu g ow h, and i s -o de au oco ela ion. These s a is ics ela e o
ac ual and syn he ic da a om bo h he o iginal and he ex ended SW models. In pa icula ,
Panel A o Table 4 ep oduces he second-momen s a is ics o eal- ime a iables (y ,c ,
and π ) as well as hei e isions ( e y, e c, and e π). The ex ended model ul ills a
mode a e ask when eplica ing hem . Fi s , se ial au oco ela ion is well app oxima ed o
all a iables. Second, he es ima ed ola ili y o e isions in ou pu and in la ion is p ac ically
he same as in he ac ual da a. Howe e , he es ima ed a iance o ou pu and consump ion
g ow h is h ee imes highe han in he ac ual da a. This highe ola ili y is due in p inciple
o he inclusion o new shocks ( he speci ic impac is seen in subsec ions 5.3 and 5.4). Finally,
wi h espec o he co ela ion wi h inal ou pu g ow h, he eal- ime es ima es o y ,c , and
π a e e y close o he ue alues, while hei e isions a e less closely co ela ed (abou
hal o he ac ual alues).
86
Table 4, Panel B shows he same s a is ics o he emaining endogenous a iables (y,
c,i, w,l,Rand π). The i s conclusion ha can be d awn is ha he o iginal model
does a be e job in e ms o ola ili y. This ein o ces he idea ha he ex ended model
wi h eal- ime da a ampli ies ola ili y. Conce ning co ela ion wi h ou pu , bo h models i
he da a easonably well. Finally, he model pe o ms mode a ely well in ega d o se ial
au oco ela ion.
5.3 Va iance decomposi ion
Table 5 shows he a iance decomposi ion analysis o he EA baseline model and he
model wi h eal- ime. The a iabili y o ou pu g ow h is d i en by demand-side shocks
in bo h models: he isk-p emium shock (ηb), exogenous spending shock (ηg), in es men
adjus men cos shock (ηi) and in e es a e shock (ηR) accoun o mo e han hal o he
o al a iabili y (61% in he o iginal model and 57.2% in he ex ended model), wi h he
isk p emium shock as he main sou ce (be ween 30-40% o bo h). Wi h espec o supply
shocks, he p ice ma k-up shocks (ηp) a e he main sou ce o a ia ion o wages, employmen ,
in e es a e and in la ion.
The in oduc ion o da a e ision shocks in he ex ended model (η y,η c and η π) accoun s
o oughly 30% o he a ia ion in in la ion and in consump ion and ou pu g ow h. In pa -
icula , shocks in he in la ion e ision p ocess become he majo sou ce o business ola ili y
in he model. This esul highligh s he impo ance o acknowledging he signi icance o da a
e isions.
6 Conclusions
This chap e p o ides a de ailed analysis o he s a is ical p ope ies o da a e isions
o he EA. I also s udies wha ype o modeling is app op ia e o eal- ime da a and i s
e ision in DSGE models.
F om a p ac ical s andpoin , he s a is ical p ope ies o da a e isions a e s udied unde
di e en app oaches, leading o his i s conclusion: Re isions depend on ini ial announce-
87
men s and show high ola ili y, which sugges s ha hey a e no well-beha ed. In addi ion,
a educed- o m eg ession analysis is ca ied ou o p opose an empi ically based s uc u e
o he da a e ision p ocesses. This cha ac e iza ion o da a e isions is in oduced in o he
Sme s and Wou e s (2007) DSGE model by assuming ha he economic decisions o house-
holds, i ms, and mone a y au ho i ies depend on eal- ime da a. As a esul , an ex ended
e sion o he model is de i ed, enabling us o es ima e he implica ions o eal- ime da a
and hei e isions in he con ex o a DSGE model.
The es ima es o he DSGE model co obo a e ha da a e isions a e co ela ed wi h
hei i s elease, highly ola ile, and highly au oco ela ed. In he eu o a ea, o ins ance,
a posi i e announcemen o ou pu and consump ion is likely o lead o a nega i e u u e
e ision. In he case o in la ion, he co ela ion be ween he ini ial elease and he i s e-
ision is ela i ely close and posi i e. Fu he mo e, in e ms o modeling, he inco po a ion
o eal- ime da a and da a e isions a ec s he DSGE model in h ee ele an aspec s. Fi s ,
he es ima ed alues o some o he main pa ame e s a y, e.g. lowe habi o ma ion alues
a e ound. Second, e ision shocks become a signi ican sou ce in he business cycle decom-
posi ion. Fo ins ance, in he case o he eu o a ea hey accoun o up o one- hi d o ou pu
a iabili y. Finally, he in oduc ion o new shocks inc eases he ola ili y o he a iables
obse ed. In sum, hese indings sugges ha da a e isions a e no well-beha ed, so DSGE
models omi ing eal- ime da a and da a e isions migh be igno ing impo an sou ces o
agg ega e luc ua ions. This wo k p esen s a way o accommoda e his ac s in business cycle
analysis while i encou ages u he imp o emen s in he es ima ion o eal- ime da a om
he s a is ical agencies.
88
Re e ences
A uoba, B. S. 2008. “Da a Re isions A e No Well-Beha ed”, Jou nal o Money, C edi and
Banking 40, 319-340.
Casa es, M., and Jesús Vázquez. 2016. "Da a e isions in es ima ed DSGE models."
Mac oeconomics Dynamics 20, 1683-1716.
Ch is iano, L. J., Ma in Eichenbaum, and Cha les L. E ans. 2005. “Nominal Rigidi ies
and he Dynamic E ec s o a Shock o Mone a y Policy”, Jou nal o Poli ical Economy 113,
1-45.
C ousho e, D., and Tom S a k. 2001. “A Real-Time Da a Se o Mac oeconomis s”,
Jou nal o Econome ics 105,111-130.
C ousho e, D., and Cha les L. E ans. 2006. “Da a Re isions and he Iden i ica ion o
Mone a y Policy Shocks”, Jou nal o Mone a y Economics 53, 1135-1160.
C ousho e, D.. 2011. “F on ie s o Real-Time Da a Analysis”, Jou nal o Economic
Li e a u e 49, 72-100.
Diebold, F. X., and Glenn D. Rudebusch. 1991. “Fo ecas ing Ou pu Wi h he Composi e
Leading Index: A Real-Time Analysis,” Jou nal o he Ame ican S a is ical Associa ion 86,
603-610.
Fagan,G., Hen y Jê ome, and Rica do Mes e. 2005. “An A ea-Wide Model o he Eu o
A ea”, Eu opean Cen al Bank, Resea ch Depa men , Kaise s asse 29, D-60311 5, 40.
Faus , J., R., John H. and W igh , Jona han H. 2005. "News and Noise in G-7 GDP
Announcemen s.." Jou nal o Money, C edi , and Banking 37: 403–419.
Mankiw, N. G., Da id E. Runkle, and Ma hew D. Shapi o. 1984. “A e P elimina y
Announcemen s o he Money S ock Ra ional Fo ecas s?”, Jou nal o Mone a y Economics
14, 15-27.
Mankiw, N. G. and Shapi o, Ma hew D. 1986. "News o Noise: An Analysis o GNP
Re isions." Su ey o Cu en Business: 20-5.
Mo k, K. A. 1990. "Fo ecas able Money-G ow h Re isions: A Close Look a he Da a."
89
Table 3.A.1 P io s and es ima ed pos e io s o he s uc u al pa ame e s: Eu o A ea
P io s Pos e io s
Ex ended model SW model
Dis Mean S d D. Mean 5% 95% Mean 5% 95%
ϕNo mal 4.00 1.50 7.22 5.24 9.11 6.00 4.22 7.80
hBe a 0.70 0.10 0.40 0.28 0.53 0.68 0.60 0.77
σcNo mal 1.50 0.37 1.40 - - 1.40 - -
σlNo mal 2.00 0.75 3.07 1.95 4.20 1.09 -0.01 2.2
ξpBe a 0.50 0.10 0.42 0.33 0.52 0.45 0.34 0.55
ξwBe a 0.50 0.10 0.44 0.32 0.56 0.63 0.53 0.75
ιwBe a 0.50 0.15 0.45 0.21 0.65 0.21 0.06 0.36
ιpBe a 0.50 0.15 0.17 0.04 0.29 0.24 0.17 0.43
ψBe a 0.50 0.15 0.40 0.22 0.59 0.19 0.07 0.30
ΦNo mal 1.25 0.12 1.84 1.69 2.01 1.90 1.79 2.01
πNo mal 1.50 0.25 1.72 1.56 1.89 1.72 1.55 1.89
ρBe a 0.75 0.10 0.81 0.75 0.87 0.79 0.74 0.85
yNo mal 0.12 0.05 0.06 -0.01 0.12 -0.01 -0.05 0.05
∆yNo mal 0.12 0.05 0.07 0.01 0.12 0.20 0.12 0.27
πGamma 0.62 0.10 0.41 0.27 0.54 0.57 0.42 0.72
100(β−1−1) Gamma 0.25 0.10 0.33 0.16 0.50 0.30 0.17 0.43
lNo mal 0.00 2.00 -1.60 -3.28 0.81 0.86 -2.15 3.20
100(γ−1) No mal 0.40 0.10 0.4 - - 0.4 - -
αNo mal 0.30 0.05 0.25 0.18 0.32 0.23 0.16 0.29
96
Table 3.A.2 P io s and es ima ed pos e io s o he shock p ocesses: Eu o A ea
P io s Pos e io s
Ex ended model SW model
Dis Mean S d D. Mean 5% 95% Mean 5% 95%
σaIn gamma 0.10 2.00 0.08 0.064 0.11 0.07 0.05 0.08
σbIn gamma 0.10 2.00 0.07 0.04 0.10 0.03 0.02 0.04
σgIn gamma 0.10 2.00 0.10 0.08 0.13 0.10 0.08 0.12
σiIn gamma 0.10 2.00 0.22 0.15 0.29 0.21 0.15 0.27
σRIn gamma 0.10 2.00 0.07 0.05 0.08 0.09 0.07 0.11
σpIn gamma 0.10 2.00 0.05 0.03 0.07 0.06 0.04 0.08
σwIn gamma 0.10 2.00 0.06 0.04 0.08 0.05 0.03 0.06
ρaBe a 0.50 0.20 0.97 0.94 0.99 0.96 088 0.99
ρbBe a 0.50 0.20 0.92 0.81 0.99 0.77 0.66 0.89
ρgBe a 0.50 0.20 0.82 0.74 0.90 0.92 0.86 0.98
ρiBe a 0.50 0.20 0.43 0.17 0.67 0.32 0.08 0.55
ρRBe a 0.50 0.20 0.39 0.23 0.54 0.48 0.33 0.62
ρpBe a 0.50 0.20 0.99 0.98 0.99 0.99 0.98 0.99
ρwBe a 0.50 0.20 0.96 0.93 0.99 0.91 0.86 0.96
µpBe a 0.50 0.20 0.30 0.07 0.51 0.54 0.24 0.73
µwBe a 0.50 0.20 0.39 0.16 0.61 0.51 0.25 0.76
ρga Be a 0.50 0.20 0.37 0.12 0.61 0.46 0.18 0.73
97
Table 3.A.3 P io s and es ima ed pos e io s o e ision p ocesses pa ame e s: Eu o A ea
P io s Pos e io s
Ex ended model SW model
Dis Mean S d D. Mean 5% 95% Mean 5% 95%
δyNo mal 0.00 2.00 0.24 -0.14 0.67 - - -
δcNo mal 0.00 2.00 -0.10 -0.36 0.14 - - -
byNo mal 0.00 2.00 -0.15 -0.22 0.11 - - -
bπNo mal 0.00 2.00 2.20 1.35 3.02 - - -
bcNo mal 0.00 2.00 -0.13 -0.14 -0.11 - - -
σy In gamma 0.10 2.00 0.21 0.17 0.25 - - -
σπ In gamma 0.10 2.00 0.20 0.16 0.23 - - -
σc In gamma 0.10 2.00 0.25 0.20 0.30 - - -
ρy Be a 0.50 0.20 0.66 0.33 0.95 - - -
ρπ Be a 0.50 0.20 0.94 0.89 0.98 - - -
ρc Be a 0.50 0.20 0.72 0.56 0.89 - - -
98
Table 3.B.1 P io s and es ima ed pos e io s o he s uc u al pa ame e s: US
P io s Pos e io s
Ex ended model SW model
Dis Mean S d D. Mean 5% 95% Mean 5% 95%
ϕNo mal 4.00 1.50 5.30 3.43 7.13 5.93 4.06 7.85
hBe a 0.70 0.10 0.13 0.10 0.16 0.57 0.45 0.67
σcNo mal 1.50 0.37 1.33 1.05 1.59 1.07 0.76 1.35
σlNo mal 2.00 0.75 1.79 0.79 2.75 1.95 0.99 2.85
ξpBe a 0.50 0.10 0.66 0.57 0.75 0.72 0.63 0.81
ξwBe a 0.50 0.10 0.51 0.37 0.65 0.59 0.45 0.72
ιwBe a 0.50 0.15 0.34 0.14 0.53 0.48 0.24 0.72
ιpBe a 0.50 0.15 0.09 0.03 0.15 0.33 0.14 0.51
ψBe a 0.50 0.15 0.76 0.57 0.75 0.72 0.57 0.88
ΦNo mal 1.25 0.12 1.43 1.30 1.57 1.48 1.34 1.61
πNo mal 1.50 0.25 1.86 1.58 2.15 2.09 1.78 2.42
ρBe a 0.75 0.10 0.84 0.81 0.87 0.83 0.80 0.87
yNo mal 0.12 0.05 -0.01 -0.03 0.01 0.04 0.01 0.08
∆yNo mal 0.12 0.05 0.09 0.07 0.11 0.18 0.13 0.22
πGamma 0.62 0.10 0.67 0.53 0.80 0.70 0.57 0.85
100(β−1−1) Gamma 0.25 0.10 0.17 0.07 0.27 0.20 0.10 0.31
lNo mal 0.00 2.00 -1.44 -3.75 0.86 0.18 −1.77 2.30
100(γ−1) No mal 0.40 0.10 0.4 - - 0.39 0.35 0.43
αNo mal 0.30 0.05 0.16 0.13 0.20 0.17 0.14 0.21
99
Table 3.B.2 P io s and es ima ed pos e io s o he shock p ocesses: US
P io s Pos e io s
Ex ended model SW model
Dis Mean S d D. Mean 5% 95% Mean 5% 95%
σaIn gamma 0.10 2.00 0.39 0.34 0.44 0.38 0.34 0.43
σbIn gamma 0.10 2.00 0.12 0.08 0.16 0.09 0.05 0.13
σgIn gamma 0.10 2.00 0.39 0.35 0.44 0.40 0.35 0.45
σiIn gamma 0.10 2.00 0.29 0.21 0.36 0.35 0.25 0.43
σRIn gamma 0.10 2.00 0.12 0.11 0.14 0.13 0.11 0.14
σpIn gamma 0.10 2.00 0.12 0.09 0.15 0.11 0.09 0.14
σwIn gamma 0.10 2.00 0.33 0.25 0.40 0.30 0.23 0.36
ρaBe a 0.50 0.20 0.91 0.87 0.95 0.92 0.87 0.97
ρbBe a 0.50 0.20 0.84 0.77 0.90 0.74 0.55 0.93
ρgBe a 0.50 0.20 0.98 0.96 0.99 0.97 0.96 0.99
ρiBe a 0.50 0.20 0.82 0.70 0.94 0.70 0.57 0.84
ρRBe a 0.50 0.20 0.09 0.01 0.16 0.27 0.13 0.40
ρpBe a 0.50 0.20 0.87 0.78 0.97 0.81 0.68 0.95
ρwBe a 0.50 0.20 0.97 0.94 0.99 0.96 0.93 0.99
µpBe a 0.50 0.20 0.56 0.35 0.78 0.60 0.38 0.82
µwBe a 0.50 0.20 0.64 0.44 0.87 0.66 0.46 0.86
ρga Be a 0.50 0.20 0.40 0.25 0.56 0.40 0.24 0.56
100
Table 3.B.3 P io s and es ima ed pos e io s o e ision p ocesses pa ame e s: US
P io s Pos e io s
Ex ended model SW model
Dis Mean S d D. Mean 5% 95% Mean 5% 95%
δyNo mal 0.00 2.00 -0.10 -0.32 0.09 - - -
δcNo mal 0.00 2.00 0 - - - - -
byy No mal 0.00 2.00 0.25 0.06 0.43 - - -
bππ No mal 0.00 2.00 -0.13 -0.25 -0.1 - - -
bcc No mal 0.00 2.00 0.19 0.10 0.28 - - -
σy In gamma 0.10 2.00 0.65 0.54 0.77 - - -
σπ In gamma 0.10 2.00 0.23 0.19 0.26 - - -
σc In gamma 0.10 2.00 0.71 0.61 0.81 - - -
ρy Be a 0.50 0.20 0.91 0.85 0.97 - - -
ρπ Be a 0.50 0.20 0.09 0.01 0.16 - - -
ρc Be a 0.50 0.20 0.80 0.73 0.87 - - -
101
Table 4. Second-momen s a is ics: Eu o A ea
Panel A ∆y π ∆c e ∆y e π e ∆c
Eu o A ea da a:
S and. de ia ion (%) 0.22 0.02 0.22 0.23 0.13 0.23
Co ela ion wi h ∆y0.26 -0.056 0.19 0.63 -0.35 0.47
Au oco ela ion 0.11 0.02 0.04 -0.05 0.25 -0.25
Ex ended model:
S and. de ia ion (%) 0.64 0.04 0.86 0.24 0.37 0.28
(0.33,0.92) (0.01,0.07) (0.56,1.17) (0.20,0.28) (0.19,0.45) (0.23,0.32)
Co ela ion wi h ∆y0.22 -0.03 0.24 0.31 -0.13 0.28
(0,0.37) (-0.10,0.01) (0,0.39) (0.05,0.55) (-0.21,-0.06) (0.14,0.4)
Au oco ela ion 0.22 0.17 0.59 0.00 0.55 -0.13
(0,0.38) (0,0.32) (0.43,0.90) (-0.07,0.07) (0.23,0.83) (-0.19,-0.07)
102
Table 4. (Con inued)
Panel B ∆y∆c∆i∆w l R π
Eu o A ea da a:
S and. de ia ion (%) 0.14 0.14 0.45 0.13 0.03 0.31 0.13
Co ela ion wi h ∆y1 0.47 0.65 0.25 -0.02 -0.06 -0.32
Au oco ela ion 0.50 0.01 -0.04 0.34 0.94 0.88 0.27
Ex ended:
S and. de ia ion (%) 0.53 0.64 1.05 0.27 2.11 0.19 0.23
(0.28,0.75) (0.36,0.92) (0.47,1.62) (0.08,0.44) (0.47,3.70) (0.04,0.35) (0.10,0.37)
Co ela ion wi h ∆y1 0.24 0.10 0.19 -0.07 -0.12 -0.11
(0,0.39) (0,0.22) (0,0.33) (-0.12,0) (-0.23,0) (-0.19,0)
Au oco ela ion 0.23 0.18 0.30 0.41 0.71 0.69 0.64
(0,0.39) (0,0.34) (0,0.49) (0,0.60) (0,0.97) (0,0.95) (0,0.90)
SW model: ∆y∆c∆i∆w l R π
S and. de ia ion (%) 0.24 0.16 0.82 0.12 10.6 0.55 0.56
(0.14,0.34) (0.09,0.24) (0.43,1.23) (0.05,0.18) (1.21,20.3) (0.07,1.17 (0.08,1.16)
Co ela ion wi h ∆y1 0.30 0.22 0.18 0 -0.08 -0.11
(0,0.66) (0,0.52) (0,0.45) (-0.02,0) (-0.23,0) (-0.32,0)
Au oco ela ion 0.28 0.31 0.26 0.30 0.48 0.47 0.40
(0,0.63) (0,0.69) (0,0.61) (0,0.66) (0,0.99) (0,0.99) (0,0.99)
The pa en hesis e e o 95% pos e io con idence in e als o second-momen s a is ics
103
Table 5. Va iance decomposi ion (pe cen )
Ex ended model
Inno a ions ∆y∆y ∆c∆c ∆i∆w l R π π
Technology, ηa1.3 1.2 1.2 0.9 0.2 0.5 0.7 1.5 0.6 0.4
Risk p emium, ηb32.8 30.5 37.3 29.5 7.8 22.4 8.3 53.5 25.2 17.2
Fiscal/Ne expo s, ηg2.9 2.6 0.0 0.1 0.1 0.2 0.6 0.2 0.1 0.1
In es men adj. cos s, ηi11.9 11.0 0.0 0.5 75.6 3.3 4.8 7.4 3.2 2.1
In e es - a e, ηR9.6 8.9 10.7 8.4 2.3 7.1 2.7 10.5 7.7 5.2
Wage-push, ηw1.3 1.2 2.8 2.2 0.1 2.5 16.7 1.5 2.2 1.3
P ice-push, ηp8.7 8.1 9.7 7.7 0.1 37.5 53.8 19.0 30.9 21.2
Ou pu e ision, η y 0.1 7.0 0.1 0.1 0.1 0.1 0.1 0.2 0.1 0.1
In la ion e ision, η π 23.2 21.6 22.4 17.4 9.8 20.7 11.1 2.6 28.3 51.2
Consump ion e ision, η c 7.9 7.4 14.5 32.8 1.4 5.4 1.5 3.4 1.5 1.0
SW model
Inno a ions ∆y∆y ∆c∆c ∆i∆w l R π π
Technology, ηa18.5 - 11.0 - 0.9 0.8 1.4 0.4 0.2 -
Risk p emium, ηb29.8 - 39.3 - 18.0 4.5 3.4 27.5 11.2 -
Fiscal/Ne expo s, ηg7.1 - 0.5 - 0.3 0.3 0.4 0.2 0.7 -
In es men adj. cos s, ηi8.4 - 2.5 - 43.1 0.2 0.6 1.0 0.4 -
In e es - a e, ηR16.1 - 18.9 - 11.9 2.8 2.4 2.8 8.2 -
Wage-push, ηw10.9 - 11.5 - 16.0 18.4 11.6 3.4 8.5 -
P ice-push, ηp25.5 - 28.7 - 9.5 73.0 80.0 64.0 71.2 -
104
Pa IV
Bo owe -based measu es in a DSGE
model
1 In oduc ion
Mac op uden ial policies a e an impo an oolki o cen al banks nowadays o ensu e i-
nancial s abili y. Bo owe -based mac op uden ial measu es such as limi s on loan- o- alue
and loan- o-income ha e been ound o be e ec i e o in luence c edi s anda ds and lows
h ough quan i a i e es ic ions (see Claessens, Ghosh and Mihe (2014); BCBS (2010);
JMCB special issue (2015)). No only do hey a ec he c edi low o house pu chases,
bu hey a e pa icula ly impo an o inancial s abili y by limi ing isk- aking o bo owe s
and lende s. Gi en hei ansmission h ough quan i ies and di ec ly a ec ing bo owe s,
hese ins umen s a e impo an o complemen capi al-based ones o coun e he build-up
sys emic isks. While c oss-coun y s udies indica e ha loan- o- alue, loan- o-income o
deb -se icing- o-income limi s a e e ec i e o es ic c edi , he indi idual measu es di e
in hei ansmission o coun e isks and he way hey in luence inancial s abili y, o his
ex en , his chap e uses a mac o- inancial DSGE model o add ess he eedback e ec s o
mac op uden ial policies in ensu ing inancial s abili y.
Limi s on LTV a ios limi le e age ela i e o he alue o he colla e al and p ima ily
limi losses o he lende in he e en o a bo owe de aul . They he eby s eng hen he
esilience o lende s, mos ly banks. In coun ies whe e mo gage deb is non- ecou se deb ,
a igh e LTV a io also educes he incen i es o s a egic de aul s and he eby educes
p obabili y o de aul s, which is especially ele an when house p ice ola ili y is s uc u ally
high and amo iza ion a es a e low. S a egic de aul s ha e played an impo an ole in he
Wi h S ephan Fah (ECB) and F ancesco Sanna (ECB)
105
he LTV a ios. The o iginal calib a ion o he model ocused on mac oeconomic and banking
a iables such as o al capi al, he de aul a e o banks and he e u ns on hei equi y. In
o de o accoun o household le e age in o m o LTV a ios, he ex ended calib a ion s a -
egy inco po a es loan- o- alue a ios o ou s anding loans as a momen o ma ch in addi ion
o he a iables in he o iginal calib a ion. An al e na i e would be o use he LTI a io as
explici a ge . We ins ead use he LTI a ios as a iables o alida e he model and compa e
he LTI a io in he da a o hose ob ained om he calib a ed model.
The HFCS p o ides da a on he inancial si ua ion o households in Eu opean coun ies.
I p o ides he loan and house alue a o igina ion and a he ime o he su ey, as well as
income a ime o he in e iew. The da a is used o cons uc he LTV a io a he momen
o su ey o he calib a ion o LTV a ios o ou s anding loans. Using he HFCS as main
sou ce o he LTV a io is consis en wi h he da a sou ce o o he wo calib a ed a iables
in he model, namely he ac ion o bo owe s and housing weal h held by bo owe s.
The LTV a io o ou s anding loans o bo owe s is compu ed by di iding mo gage loans
o he household’s main esidence (HMR ,HB170x) by he cu en housing alue (HB0900)
mul iplied by he sha e o home owne ship (HB0500). The a e age ac oss all bo owe s
is compu ed by weigh ing by mo gage size (HB170x)3. In o de o limi he in luence o
ou lie s in he HFCS da abase, LTV a ios o indi idual bo owe s a e censo ed a 200%
LTV. We p oceed simila ly o LTV a ios o a o igina ion. We use loans o he household’s
main esidence HMR a o igina ion (HB140x) and di ide i by he esponden ’s eply o he
house alue a o igina ion (HB0800) and he weigh ed coun y mean is ob ained by using
he loan amoun a o igina ion. The LTV a ios o he 1s and 2nd wa e a e p esen ed in
Table 1, whe eby wa e 1 o he HFCS da ase , conduc ed in 2010, exhibi s a smalle coun y
co e age and wa e 2 conduc ed in 2013 and 2014 p o ides a la ge coun y co e age and
allows assessing e olu ion o e ime.
3An addi ional weigh ing by su ey weigh s has also been conside ed, bu has no been applied because,
i s , i does no signi ican ly al e he a e age alue and, second, i is unclea o wha deg ee he social
weigh s help in aising ep esen a i i y o he bo owe ’s sample.
112
The alues used in he o iginal model calib a ion sligh ly di e as he o iginal calib a ion
was done based on a censo ing o 150% ins ead o he 200% used in subsequen assessmen s. In
addi ion o he LTV a ios, Table 1 also documen s loan- o-income (LTI) a ios a o igina ion
and o ou s anding mo gage loans. While he LTI a io can be di ec ly compu ed based
on he cu en ou s anding loan o he household’s main esidence HMR (HB170x) and
he cu en income (DI2000). Fo he LTI a io a o igina ion we use he loan amoun s
a o igina ion (HB140x) and de la e he cu en income using he agg ega e consump ion
de la o 4. The LTI a ios a e censo ed a 20 imes annual incomes (addi ional se ies a e
p esen ed in he appendix).
As indica ed, he model ma ches he LTV a ios ela i ely well and he model-implied
LTI a ios a e in he ange o hose in he da a, indica ing he b oad i o he model o he
HFCS da a. We do no expec ha LTI a ios om he model and in da a would i pe ec ly
gi en ha he model does no accoun o axa ion no o capi al incomes by households.
Table 1: LTV and LTI a ios a o igina ion and o ou s anding mo gage loans
AT BE CY DE ES GR IT LU MT NL PT SI SK
LTV a io a o igina ion o mo gage loans (in %)
200% WM 80.7 93 86.2 83.3 87.2 87.4 83.4 - 90.8 103.8 93.7 71.9 84.8
LTV a io o ou s anding mo gage loans (in %)
200% WM 62.2 52.6 50.5 57.3 49.5 57.2 48.6 56.6 37.1 68.9 60.6 48.2 51.2
150% Model 61.7 52.4 49.5 56.9 58.4 56.7 48.4 55.3 35.1 68.2 59.8 59.5 49.5
LTI a io o loans a o igina ion o mo gage loans (in yea s o income)
20 WM 4.0 3.3 4.9 3.0 4.1 3.9 3.8 3.6 3.2 4.0 4.5 2.8 4.0
LTI a io o ou s anding loans (in yea s o income)
20 WM 3.5 3.1 4.5 2.5 3.7 3.3 3.0 3.2 2.7 3.9 4.0 1.9 3.5
As indica ed, he model ma ches he LTV a ios ela i ely well and he model-implied
4This app oach does no accoun o he income changes o each indi idual bo owe be ween he o igina-
ion o he loan and he cu en income. S ill, an assessmen by mean loans using na ional da a o Po ugal
deli e ed compa able amoun s o mean incomes using income a o igina ion and using de la ed income.
113
LTI a ios a e in he ange o hose in he da a, indica ing he b oad i o he model o he
HFCS da a. We do no expec ha LTI a ios om he model and in da a would i pe ec ly
gi en ha he model does no accoun o axa ion no o capi al incomes by households.
2.3 E ec s o a ying household le e age in he 3D model
A 1 pe cen age poin educ ion in LTV a ios o ou s anding loans
The c edi s anda ds in he 3D model a e applied o he ou s anding loans o he ep e-
sen a i e household. This sec ion assesses he long- e m (s eady s a e) e ec s o changes o
LTV and LTI a ios o ou s anding loans. The nex sec ion sheds ligh on he implica ions
o changes in he LTV and LTI a ios on he ail o he dis ibu ion o o igina ing loans
ins umen s. The quan i ica ion conside ed ocuses on he implica ions when educing LTV
a ios by 1 p.p. and LTI a ios by one en h o annual income, i.e. by 10 p.p.. The egula o y
cons ain s a e implied by subs i u ing he endogenous loan con ac be ween households and
banks h ough an exogenous c edi amoun ha is lowe ed om he calib a ed alue up o
he poin whe e i eaches he a ge ed LTV o LTI es ic ion
114
Figu e 1. S eady s a e impac o a educ ion o LTV a ios o ou s anding loans by 1
pe cen age poin
Table 1. S eady s a e impac o a educ ion o LTV a ios o ou s anding loans by 1
pe cen age poin . Max and min e ec s
LTV LTI GDP Consump ion Mo gage To al Housing NFC In . Mo gage Mo gage
deb deb In . In . sp eads de aul s
(Ou s.) (Ou s.) le el le el le el le el le el le el bps %
p.p. p.p. % % % % % % bps p.p.
Min -1.00 -23.29 -0.29 0.06 -11.95 -6.50 -7.49 -0.34 -12.70 -0.37
Max -1.00 4.12 -0.05 0.23 -5.70 -2.27 -1.86 -0.09 -4.31 -0.13
The e ec s o a 1 pe cen age poin educ ion in LTV a ios o ou s anding loans on eigh
key model a iables is depic ed in Figu e 1. The educ ion in LTV a ios has o e all a limi ed
e ec on agg ega e long- e m GDP, anging om 0.02 o 0.30% o na ional GDP le els. The
115
size o he e ec s depends on he sha e o bo owe s in he economy and he ela i e size o he
eal es a e cons uc ion sec o as well as he ini ial LTV le el. Indeed, an impo an elemen
explaining he mu ed esponse in GDP is he shi in agg ega e expendi u e away om
housing in es men owa ds consump ion. In addi ion, sa e s inc ease hei expendi u e o
housing as housing appea s ela i ely cheape . An economy wi h sizable housing in es men
sees a ela i ely s onge all in GDP, bu also a s onge shi inc ease in consump ion.
The LTV es ic ions imply a educ ion in agg ega e deb le els by be ween 6 and 12%
ac oss coun ies, whe eas he e ec s on agg ega e c edi a e be ween 2.5 and 7%. The educed
le e age in he household sec o implies also a educ ion in he mo gage de aul s because
lowe LTV a ios imply ha u u e a ia ions in housing alue igge less o de aul s. De aul
a es dec ease by be ween 0.03 up o 0.15 pe cen age poin s. O e all, banks ace a educ ion in
losses om de aul s which allow banks o educe sp eads on mo gage loans. These educ ions
amoun o be ween 1 and 8 bps poin s.
A 10 pe cen age poin educ ion in LTI a ios o ou s anding loans
An al e na i e o a educ ion in LTV a ios consis s in a decline in LTI limi s. The decline
in LTI a ios is implemen ed by educing c edi amoun s by as much is necessa y o educe
he impu ed LTI a ios by he desi ed amoun s, in line wi h he me hodology o LTV a ios.
The e ec s o a 10 pe cen age poin educ ion in he LTI a io is depic ed in Figu e 2 and
summa ized in Table 2. A 10 pe cen age poin educ ion consis s o a decline om e.g. 3.2
o 3.1 imes he annual income.
The educ ion in LTI a io by he chosen alue has, on a e age, a sligh ly la ge e ec
compa ed o he conside ed 1 p.p. educ ion in he LTV a io. Ne e heless, he ela i e
e ec s ac oss coun ies depend on he ela i e ini ial indeb edness. The educ ion in LTI
a ios implies limi ed e ec s on GDP, accompanied by a shi owa ds consump ion and a
sizable all in housing in es men . Mo gage deb educes by be ween 4 o 11% (17% o one
coun y) educes mo gage de aul a es by be ween 0.1 o 0.8 pe cen age poin s and 2.6 p.p.
116
o 26.9 p.p. o sp eads.
Ne e heless, o some coun ies majo quan i a i e di e ences exis . The eason o
he di e ences esides especially in he lowe le el o mo gage loans and lowe housing
in es men ela i e o GDP in hese coun ies. This esul s in a highe pe cen age a ia ion
when educing LTI a ios in pe cen age poin s.
Figu e 2. S eady s a e impac o a educ ion o loan- o-income a ios o ou s anding loans
117
Table 2. S eady s a e impac o a educ ion o LTI a ios o ou s anding loans by 10
pe cen age poin s. Max and Min e ec s
LTV LTI GDP Consump ion Mo gage To al Housing NFC In . Mo gage Mo gage
deb deb In . In . sp eads de aul s
(Ou s.) (Ou s.) le el le el le el le el le el le el bps %
p.p. p.p. % % % % % % bps p.p.
Min -3.0 -10.0 -0.2 0.1 -17.2 -5.5 -6.2 -0.2 -26.9 -0.8
Max -0.4 -10.0 -0.1 0.1 -4.3 -2.5 -1.5 -0.1 -2.7 -0.1
Ca ea s o he me hodology
The simula ions p o ided abo e a e compu a ions o s eady s a e changes in LTV and LTI
limi s. The choice o ocus on s eady s a e impac s is due o he ac ha loans in he 3D
model a e modeled as one-pe iod loans wi h a oll-o e o he en i e loan mass e e y pe iod.
As a esul , a educ ion in LTV o LTI a ios would a ec he en i e s ock o loans, whe eas
in eali y, he policy ins umen s only a ec he low o loans. Fu he mo e, he model is se
up in eal e ms. I hence neglec s he possibili y ha in la ion could make nominal mo e
sus ainable in imes o high in la ion. Likewise, i neglec s he Fishe ian deb de la ion in
consume goods, while i does accoun o he e ec s o declining housing alue.
An addi ional limi a ion is he ac ha LTV o LTI a ios a e modeled as pe manen ly
binding o he ep esen a i e bo owe . This does no allow elaxing c edi condi ions beyond
hose p e ailing in he ma ke . I is likely ha his is a condi ion o any mac op uden ial
policies. The de aul o mo gage loans in he 3D model occu s when loan size is la ge han
he housing alue o he bo owe (house alues a e subjec o i.i.d shocks). In a si ua ion in
which house alue shocks a e he p edominan sou ce o de aul s, such modelling is adequa e.
Ins ead, when income shocks a e he main sou ce o unce ain y and de aul s, he 3D model
only impe ec ly cap u es he ansmission o shocks. The sho coming is concep ually mo e
ele an when conside ing limi s o LTI a ios ins ead o LTV a ios.
Finally, as men ioned, he LTV and LTI limi s a e applied o he ep esen a i e bo owe
118
on ou s anding loans. In eali y, he a ailable policy ins umen s ac only on pa s o he
c oss-sec ional dis ibu ion o bo owe s and only on he low o lending. By ac ing on he
c oss-sec ional dis ibu ion, he policy ins umen s cu ail loans om he mos isky ones.
Ins ead, he model – by ac ing on he ep esen a i e bo owe – canno o e weigh he iskie
loans. As a esul , he declines in de aul s a e likely o be an unde es ima ion o wha is
achie able when educing he high isk pa s o he dis ibu ion.
In o de o add ess he sho coming, he nex sec ion p o ides he necessa y s eps o
ela e he policy ins umen s o he model alues.
3 Rela ing LTV and LTI policies a loan o igina ion o
he dynamic model
The le e age conside ed in he 3D model ela es o ha o ou s anding loans. Ins ead,
policymake s use ins umen s ha limi c edi s anda ds in he low o loans. This sec ion
p o ides he in o ma ion o ela e c edi s anda ds a o igina ion o hose o ou s anding
loans. In o de o ela e he policy ins umen o he model- ele an c edi s anda d equi es
wo s eps:
1. Assessing he impac o he LTV o LTI policy limi s a loan o igina ion on he mean
o he LTV(LTI) dis ibu ions a o igina ion. The policy ins umen limi s he igh -hand
segmen o he dis ibu ion and he eby educes he mean LTV(LTI) a io a o igina ion.
2. Compu ing he e ec on LTV (LTI) a ios o ou s anding loans based on he mean
LTV(LTI) a io a o igina ion. The quan i a i e e ec is ob ained by using a long- un ela-
ionship be ween c edi condi ions a o igina ion and hose o ou s anding loans, assuming
ixed- a e annui y mo gage con ac .
119
3.1 LTV (LTI) limi s and i s e ec s on a e age c edi s anda ds a
loan o igina ion
The i s s ep in compu ing he e ec s o he policy ins umen o he model equi es assess-
ing he impac on he a e age c edi condi ion a o igina ion. The unca ion/censo ing o
he igh -hand ail o he LTV o LTI dis ibu ion educes he mean o he dis ibu ion. The
ollowing assessmen elies on wo assump ions, discussed in mo e de ail below. Fi s , con-
s ained bo owe s a e assumed o con inue bo owing, bu a a lowe loan amoun . Second,
in line wi h implemen ed policies, we assume ha he LTV limi s can be applied only o a
p opo ion o loans while a sha e o loans is exemp ed om he c edi s anda d limi . In his
case he loans exceeding he c edi limi a e uni o mly educed in o de o hei sha e o
equa e he imposed exemp ion sha e.
The uppe hand panel o Figu e 3 p esen s a s ylized LTV dis ibu ion a loan o igina ion.
By imposing an LTV limi a a h eshold o e.g. 90% implies ha all loans abo e ha
h eshold a e cu ailed. I is assumed ha cons ained bo owe s con inue bo owing, bu
he amoun hey bo ow is limi ed o he egula o y LTV limi , esul ing in an inc ease in
loan amoun s wi h an LTV a io o 90%. This inc ease is iden ical o he o iginally a ec ed
mass o he igh o he limi (blue a ea). As a esul o he es ic ion, bo owe s a e now
concen a ed a he limi ed LTV a io which is lowe han hei o iginally in ended a io and
he a e age LTV a io a o igina ion declines ( om 62% o 61% in he diag am).
The lowe panel o Figu e 3 illus a es he e ec s on he dis ibu ional mean ( e ical
axis) o imposing an LTV limi (ho izon al axis)5. When educing he LTV limi o e.g.
110% o 100%, he a e age mean LTV emains i ually una ec ed (62%). This is because
he ma ke -based dis ibu ion ea u es only e y ew bo owe s a LTV a ios abo e 100%,
gi en ha he mass o he dis ibu ion is concen a ed a LTV a ios a ound 75%. Reducing
he limi u he o 80% esul s in an a e age o abou 60% and an LTV limi o 70% would
imply an a e age LTV a io o abou 67%. The lowe ( igh e ) he LTV limi , he mo e
5The example is based on a log-no mal dis ibu ion.
120
bo owe s a e a ec ed and he e ec s would e en ually become p opo ional (a educ ion o
he LTV limi by 1 p.p. would educe he mean by 1 p.p.).
Figu e 3. S ylized dis ibu ion o LTV a ios a o igina ion and implica ion o LTV limi s
on mean LTV a o igina ion
Sou ce: OMR Task Fo ce calcula ion. No e: The s ylized dis ibu ion is based on a log-no mal dis ibu-
ion. Cons ained bo owe s a e assumed o con inue bo owing a he imposed egula o y LTV limi .
When se ing limi s on c edi s anda d, policymake s ha e in p ac ice also speci ied a
p opo ion o which he limi applies, indica ing ha only a sha e o mo gage loans a e
equi ed o comply wi h he limi whe eas he emaining sha e o loans can exceed he limi .
Fo example, he 2016 e iew o he LTV limi s in I eland imposes a 90% LTV limi om
which 5% o loans o i s ime buye s and 20% o subsequen buye s a e exemp ed. This
p o ides he policymake s wo ma gins o adjus men : he limi on he c edi s anda d and
he p opo ion o which he limi applies. I also implici ly o e s a ade-o when adjus ing
he mac op uden ial be ween he limi o he c edi s anda ds and he exemp ion sha e.
In o de o assess he implica ion o he exemp ion sha es equi es assuming how c edi
condi ions beha e o loans exceeding he limi . Fo modelling pu poses, we assume ha
121
cases a educ ion in he LTV limi s implici ly a ge s he iskies bo owe s and would make
hem mo e esilien . In coun ies whe e de aul a es a e s ongly co ela ed wi h LTV a ios
a smalle adjus men in he LTV limi s would su ice o educe agg ega e de aul s and bols e
inancial s abili y.
Especially as ega ds he subs i u ion o housing expendi u e wi h NFC in es men and
consump ion, he mac oeconomic e ec s may be o e s a ed. The model assumes a ealloca-
ion be ween sec o s which is only a ec ed in he sho - un by capi al adjus men cos s, bu
is no a ec ed by skill misma ch o wo ke s.
Table 4a. Impac o a 5 p.p. educ ion in LTV a ios ( om 95 o 90%) a loan o igina ion
LTV Policy Min Max
LTV limi p.p. -5 -5
A e age LTVO p.p. -3.2 -1.2
A e age LTV a io (ou s anding) p.p. -1.9 -0.7
A e age LTI (ou s anding) p.p. -39.9 -2.9
GDP le el % -0.55 -0.04
Consump ion le el % 0.05 0.42
Mo gage deb le el % -19.5 -5.1
To al deb le el % -12.2 -1.6
Housing in . le el % -14.1 -1.9
NFC in . le el % -0.6 -0.1
Mo gage sp ead bps -15.1 -7.6
Mo gage de aul a e p.p. -0.4 -0.2
Sou ce: OMR Task Fo ce calcula ions based on HFCS da a (1s wa e) and on 3D model. No e: The
epo ed changes a e in pe cen o he long- e m s eady s a e alue o he a iable. Eu o a ea coun ies
no pa icipa ing in he i s wa e o he HFCS a e no conside ed. Fo some ew small and open eu o a ea
coun ies, he model is assessed no o pe o m adequa ely and esul s a e he e o e excluded om his ange.
128
Table 4b Impac o a 5 p.p. educ ion in LTV a o igina ion on mac o- inancial a iables
AT BE CY DE ES GR IT NL PT SI
4mean LTV a o igin p.p. -1.8 -2.5 -1.8 -1.7 -2.3 -2.4 -2.1 -3.2 -2.9 -1.2
4mean ILTV ou s . p.p. -1.0 -1.5 -1.1 -1.0 -1.3 -1.4 -1.2 -1.9 -1.7 -0.7
GDP le el % -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.1 -0.5 -0.2 0.0
Housing in es . % -4.9 -2.9 -4.5 -5.1 -3.5 -4.2 -2.2 -14.1 -7.0 -1.9
Mo gage deb % -12.3 -8.5 -8.0 -9.9 -8.8 -11.4 -9.5 -19.5 -17.1 -5.1
Mo gage sp eads bps -10.7 -7.6 -9.6 -12.5 -10.9 -15.1 -14.2 -8.1 -10.9 -7.9
Mo gage de aul a e p.p. -0.3 -0.2 -0.3 -0.4 -0.3 -0.4 -0.4 -0.2 -0.3 -0.2
Sou ce: OMR Task Fo ce calcula ions based on HFCS da a (1s wa e) and on 3D model.
Figu e 4. Impac o a 5 p.p. educ ion in LTV a o igina ion on mac o- inancial a iables
129
3.3.2 Reduc ions o LTI limi s a o igina ion
Simila ly o he policy simula ions on LTV limi s, we conside igh e limi s on LTI a ios
a loan o igina ion o inc ease household esilience. The main policy exe cise is a decline in
LTI limi s a loan o igina ion by 50 p.p. om 5 o 4.5 imes annual income, while exemp ing
10% o loans om his limi . The me hodology i s assesses he impac o he LTI cons ain
on he mean LTI condi ions a loan o igina ion. In a second s ep i con e s he LTI a io a
loan o igina ion in o a a io o ou s anding loans. The esul s o such policy a e p esen ed
in Table 5a and 5b and Figu e 5.
Table 5a. Impac on mac o- inancial a iables o a 50 p.p. educ ion in LTI a o igina ion
om 5 o 4.5 imes annual income
LTI Policy Min Max
LTV limi p.p. -0.5 -0.5
A e age LTIO p.p. 23.8 -4.39
A e age LTV a io (ou s anding) p.p. -0.9 -0.4
A e age LTI (ou s anding) p.p. -13.9 -2.6
GDP le el % -0.26 -0.03
Consump ion le el % 0.04 0.2
Mo gage deb le el % -9.1 -2.3
To al deb le el % -5.7 -1.4
Housing in . le el % -6.6 -0.8
NFC in . le el % -0.3 -0.1
Mo gage sp ead bps -10.4 -2.1
Mo gage de aul a e p.p. -0.3 -0.1
Sou ce: OMR Task Fo ce calcula ions based on HFCS da a (1s wa e) and on 3D model. No e: The
epo ed changes a e in pe cen o he calib a ed s eady s a e alue o he a iable. The alue epo ed o
mo gage de aul a ios and mo gage sp eads a e he calib a ed alue and he alue a e implemen a ion,
o ease o in e p e a ion. A educ ion in he LTI a io om 5 o 4.5 has no impac in Ge many and Slo enia,
because he mass o he dis ibu ion is concen a ed a lowe LTI a ios.
130
Table 5b. Impac o a 50 p.p. educ ion in LTI a o igina ion on mac o- inancial a iables
AT BE CY DE ES GR IT NL PT SI
4mean LTV a o igin p.p. -12.9 -4.4 -20.9 - -18.4 -15.8 -18.5 -23.9 -20.9 -
4mean ILTV ou s . p.p. -7.5 -2.6 -12.2 - -10.7 -9.3 -10.8 -14.0 -12.2 -
GDP le el % -0.1 0.0 -0.2 - -0.2 -0.1 -0.1 -0.3 -0.1 -
Housing in es . % -2.1 -0.8 -3.5 - -2.5 -2.5 -1.7 -6.6 -2.2 -
Mo gage deb % -5.3 -2.3 -6.2 - -6.4 -6.9 -7.0 -9.1 -5.3 -
Mo gage sp eads bps -4.4 -2.1 -7.3 - -8.0 -9.1 -10.4 -3.7 -3.2 -
Mo gage de aul a e p.p. -0.1 -0.1 -0.2 - -0.2 -0.3 -0.3 -0.1 -0.1 -
No e: The epo ed changes a e in pe cen o he calib a ed s eady s a e alue o he a iable. The
alue epo ed o mo gage de aul a ios and mo gage sp eads a e he calib a ed alue and he alue a e
implemen a ion, o ease o in e p e a ion. A educ ion in he LTI a io om 5 o 4.5 has no impac in
Ge many and Slo enia, because he mass o he dis ibu ion is concen a ed a lowe LTI a ios.
Figu e 5. Impac o a 50 p.p. educ ion in LTI a o igina ion on mac o- inancial a iables
131
4 Conclusions
This chap e uses a mac o- inancial DSGE model whe e excessi e isk beha io ha ms he
economy in oducing an incen i e o mac op uden ial egula ion, in which he bene i o
igh ening policies in e ms o educing isks may be o se by a educ ion in bank ac i i y
and leading o a dep ession in he economy, p o iding a good se -up o analyzing he mac oe-
conomic bene i s o mac op uden ial egula ion. By combining he model wi h in o ma ion
on he dis ibu ion o loans in da a, his pape acks he impac o bo owe -based measu es
om hei impac on c edi condi ions a loan o igina ion, he policy a iable, o he a iable
a ec ing he economy, ou s anding loans, as well as o he long- e m mac oeconomic e ec s
on GDP, c edi , eal es a e in es men as well as mo gage de aul s and mo gage sp eads.
The assessmen e eals ha bo owe -based measu es ha e sizable e ec s on c edi amoun s
and can educe long- un de aul s. Fo ins ance, a educ ion o he loan o alue limi om
90 o 85% leads o educ ions o agg ega e c edi a e be ween 2.5 and 7%, he esul ing
lowe le e age in he household sec o educes mo gage de aul s by be ween 0.2 and 0.4 p.p.
compa ed wi h he his o ical a e ages used in he calib a ion. The lowe de aul a es, in
u n, allow banks o educe sp eads on mo gage loans by be ween 7.6 o 15.1 bps. O e all,
he mac op uden ial ins umen is e ec i e in educing c edi lows and p omo ing household
esilience h ough less mo gage de aul s. The igh e loan o alue limi induces a shi in
household expendi u e away om housing expendi u e, esul ing in a s ong all in housing
in es men , owa ds consump ion, wi h an o e all limi e ec on GDP.
The assessmen e eals ha bo owe -based measu es ha e sizeable e ec s on c edi
amoun s and can educe long- un de aul s. I s assessmen is ne e heless limi ed o long-
e m e ec s, gi en limi a ion in he ela i ely simple way he eal es a e ma ke is modeled.
I opens up ex ension possibili ies o de elop addi ional models o shed ligh on he de ailed
wo king o he eal es a e ma ke by ocusing on addi ional sou ces o shocks and he ole
played by expec a ions o house p ices.
132
Re e ences
•A ezki R., Beck T., Deyoung R., V. Duca J.V, Loungani P., and Mu phy, A. 2015.
"Con e ence on Housing, S abili y, and he Mac oeconomy: In e na ional Pe spec-
i es," Jou nal o Money, C edi and Banking, special issue 47.
•Basel Commi ee on Banking Supe ision. 2010. “An assessmen o he long- e m
economic impac o s onge capi al and liquidi y equi emen s”, Augus .
•Be nanke, B. S., M. Ge le and S. Gilch is . 1999. “The inancial accele a o in a
quan i a i e business cycle amewo k”, Handbook o Mac oeconomics 1, p.p. 1341-1393.
•Bianchi, J., and Mendoza, E. G. 2018. “Op imal ime-consis en mac op uden ial pol-
icy" Jou nal o Poli ical Economy 126, pp. 588-634.
•B uneau, G., Ch is ensen, I., and Meh C., 2016. "Housing Ma ke Dynamics and
Mac op uden ial Policy," Bank o Canada. Wo king Pape s 16-31,
•Chen, J. and F. Columba. 2016. “Mac op uden ial and Mone a y Policy In e ac ions
in a DSGE Model o Sweden”, IMF Wo king Pape WP/16/74.
•Claessens, S., S. R. Ghosh and R. Mihe . 2014. “Mac o-P uden ial Policies o Mi iga e
Financial Sys em Vulne abili ies”, IMF Wo king Pape 14/155.
•Cle c, L., A. De iz, C. Mendicino, S. Moyen, K. Nikolo , L. S acca, J. Sua ez and
A. P. Va doulakis. 2015. "Capi al Regula ion in a Mac oeconomic Model wi h Th ee
Laye s o De aul ", In e na ional Jou nal o Cen al Banking , June.
•De Nicol, M. G., Fa a a, G., and Ra no ski, L. 2012. “Mac op uden ial policy" In e -
na ional Mone a y Fund
•Fa hi, E., and We ning, I. 2016. “A heo y o mac op uden ial policies in he p esence
o nominal igidi ies" Econome ica 84, pp. 1645-1704.
133
•Fe e o, A., R., Ha ison, R. and B. Nelson. 2017. "Conce ed e o s? Mone a y and
mac o-p uden ial policies", Mimeo, May.
•Mendicino, C., Nikolo , K., Sua ez, J., and Supe a, D. 2018. “Op imal dynamic capi al
equi emen s". Jou nal o Money, C edi and Banking, 50(6), 1271-1297.
•Walen in, K. 2014. “Housing colla e al and he mone a y ansmission mechanism”,
The Scandina ian Jou nal o Economics 116, p.p. 635-668.
134
Figu es
135
Appendix Chap e 1
Supplemen a y appendix (No in ended o publica ion)
Log-linea ized dynamic equa ions
In addi ion o equa ion (3) wi h n= 4 cha ac e izing he 1-yea bond yield, espec i ely, he se o
he emaining log-linea ized dynamic equa ions cha ac e izing he es ima ed DSGE model a e he
ollowing:
•Agg ega e esou ce cons ain :
y =cyc +iyi +zyz +εg
,(30)
whe e cy=C
Y= 1−gy−iy,iy=I
Y= (γ−1 + δ)K
Y, and zy= kK
Ya e s eady-s a e a ios. As
in Sme s and Wou e s (2007), he dep ecia ion a e and he exogenous spending-GDP a io
a e ixed in he es ima ion p ocedu e a δ= 0.025 and gy= 0.18.
•Consump ion equa ion:
x =E x +1 −1−x1
σch −E π +1 +εb
i,(31)
whe e : x =c −x1c −1,x1=h
γ,hdeno es he habi o ma ion pa ame e and γdeno es he
balanced-g ow h a e.
•In es men equa ion:
i =i1i −1+ (1 −i1)E i +1 +i2q +εi
,(32)
whe e i1=1
1+β, and i2=1
(1+β)γ2ϕwi h β=βγ(1−σc).
•A bi age condi ion ( alue o capi al, q ):
q =q1E q +1 + (1 −q1)E k
+1 −(R −E π +1) + c−1
3εb
,(33)
whe e q1=βγ−1(1 −δ) = (1−δ)
( k+1−δ).
136
•Log-linea ized agg ega e p oduc ion unc ion:
y = Φ (αks
+ (1 −α)l +εa
),(34)
whe e Φ = 1 + φ
Y= 1 + S eady-s a e ixed cos
Yand αis he capi al-sha e in he p oduc ion
unc ion.7
•E ec i e capi al (wi h one pe iod ime- o-build):
ks
=k −1+z .(35)
•Capi al u iliza ion:
z =z1 k
,(36)
whe e z1=1−ψ
ψ.
•Capi al accumula ion equa ion:
k =k1k −1+ (1 −k1)i +k2εi
,(37)
whe e k1=1−δ
γand k2=1−1−δ
γ1 + βγ2ϕ.
•Ma ginal cos :
mc = (1 −α)w +α k
−εa
.(38)
•New-Keynesian Phillips cu e (p ice in la ion dynamics):
π =π1π −1+π2E π +1 −π3mc +π4εp
,(39)
whe e π1=ιp
1+βιp,π2=β
1+βιp,π3=A
1+βιp(1−βξp)(1−ξp)
ξp, and π4=1+βιp
1+βιp. The coe icien
o he cu a u e o he Kimball goods ma ke agg ega o , included in he de ini ion o A, is
ixed in he es ima ion p ocedu e a εp= 10 as in Sme s and Wou e s (2007).
7F om he ze o p o i condi ion in s eady-s a e, i should be no iced ha φpalso ep esen s he
alue o he s eady-s a e p ice ma k-up.
137
Appendix Chap e 3
Supplemen a y appendix (No in ended o publica ion)
Lis o new equa ions in he ex ended model:
1) Equa ions de i ed wi h a new s uc u e in he e o e m
-Eule equa ion
c =c11 + δc(1 + bc)−1c
−1, + (1 −c1)E c +1 +c2(l −E l +1)−c3(R −E π +1 +εb
)+
c4εc
−1, +S−1+ (δc/ρc)εc
−2, +S−2,
whe e:
c1=h/γ
1+(h/γ)(1+bcc)−1, c2=(σc−1)wL/(φwC)
σc(1+(h/γ)(1+bcc)−1), c3=1−h/γ
σc(1+(h/γ)(1+bcc)−1),
and c4=(h/γ)ρS
c
(1+bcc)(1+(h/γ)(1+bcc)−1).
-Mone a y policy ule
R =ρR −1+ (1 −ρ)( πh(1 + bπ)π
−1, +ρS−1
πεπ
−2, +S−2i+
yh(1 + by)y
−1, +byδyy
−2, −1+ρS−1
yεy
−2, +S−2+ (δy/ρy)εy
−3, +S−3i−yp
−1)+
4y((1 + by)hy
−1, −y
−2, −1i+byδyhy
−2, −1−y
−3, −2i+
ρS−1
yhεy
−2, +S−2−(1/ρy)εy
−3, +S−3i+ρS−2
yδyhεy
−3, +S−3−(1/ρy)εy
−4, +S−4i+
(yp
−1−yp
−2) + εR
).
144
2) Remaining equa ions, as in Casa es and Vazquez (2012)
-NKPC
π =ιp
1+βιpBπ
−1, +β
1+βιpBE π +1 −A(1−βξp)(1−ξp)
(1+βιpB)ξpµp
+1+βιp
1+βιpBεp
+βιpB
1+βιpBρS
πεπ
−S, .
wi h β =βγ(1−σc)
-Wage dynamics
w =w1w −1+ (1 −w1) (E w +1 +E π +1)−w11 + βιwBπ +w2π
−1, −w3µw
+w1βιwBρS
πεπ
−S, +εw
.
whe e:
w1=1
1 + β, w2=ιw
1 + β, and w3=1
1 + β"1−βξw(1 −ξw)
ξw((φw−1) εw+ 1)#.
-Wage ma k-up equa ion
µw
=w −m s =w −σll +1
1−h/γ c −(h/γ)c
−1, .
.
145
Lis o pa ame e s A.1. Model pa ame e desc ip ion
γgamma1 S eady-S a e g ow h a e
δdel a Capi al dep ecia ion a e
gygy S eady-s a e exogenous spending-ou pu a io
σwphiw S eady-s a e labo ma k-up
pepsilonp Cu a u e o he Kimball labo good agg ega o
wepsilonw Cu a u e o he Kimball labo ma ke agg ega e
ϕ a phi S eady-s a e elas ici y o he capi al adjusmen unc ion
hlambda1 Habi o ma ion pa ama e
σcsigmac In . Elas ici y o he in e empo al subs i u ion be ween leisu e and wo k
σlsigmal In . Elas ici y o labo supply wi h espec o eal wages
ξpxip Cal o p obabili y in p ices
ξwxiw Cal o p obabili y in wages
ιwio aw wage indexa ion coe icien
ιpio ap p ice indexa ion coe icien
ψpsi Elas ici y o capi al u iliza ion
Φphip Le el o ixed cos (1+le el)
π hopi In la ion coe icien in he MPR
ρ ho Smoo hing pa ama e in he MPR
Y hoy Ou pu gap coe icien in he MPR
πcons pi Cons an in la ion coe icien
100(β−1−1) be a1 Pe sonal discoun ac o
lcons l Cons an labo coe icien
100(γ−1) gamma S eady-s a e g ow h a e
αalpha Capi al sha e
146
Lis o pa ame e s A.2 Shock pa ame e s
εa
epsa Technology shock
εb
epsb Risk p emium shock
εg
epsg Expendi u e shock
εi
epsi In es men adjus men shock
εR
eps Mone a y policy shock
εw
epsw Wage ma k-up shock
εp
epsp P ice ma k-up shock
εy
, +Sey Ou pu e ision shock
επ
, +Sepi In la ion e ision shock
εc
, +Sec Consump ion e ision shock
σas de e_a S anda d de ia ion o p oduc i i y inno a ion
σbs de e_b S anda d de ia ion o isk p emium inno a ion
σgs de e_g S anda d de ia ion o exogenous spending inno a ion
σis de e_i S anda d de ia ion o in es men -speci ic inno a ion
σRs de e_ S anda d de ia ion o mone a y policy ule inno a ion
σps de e_p S anda d de ia ion o p ice ma k-up inno a ion
σws de e_w S anda d de ia ion o wage ma k-up inno a ion
σ
ys de e_y S anda d de ia ion o ou pu e ision inno a ion
σ
πs de e_pi S anda d de ia ion o in la ion e ision inno a ion
σ
cs de e_c S anda d de ia ion o consump ion e ision inno a ion
ρa hoa AR coe icien o p oduc i i y shock
ρb hob AR coe icien o isk p emium shock
ρg hog AR coe icien o exogenous spending shock
ρi hoi AR coe icien o in es men -speci ic shock
ρR ho AR coe icien o policy ule shock
ρp hop AR coe icien o p ice ma k-up shock
ρw how AR coe icien o wage ma k-up shock
µpcmap MA coe icien o p ice ma k-up shock
µwcmaw MA coe icien o wage ma k-up shock
ρga hoga Co ela ion coe icien be ween p oduc i i y and exogenous spending shocks
ρy hoy AR coe icien o ou pu e ision shock
ρπ hopi AR coe icien o in la ion e ision shock
ρc hoc AR coe icien o consump ion e ision shock
bybyy Coe icien measu ing he co ela ion be ween he ini ial announcemen and e ision
bπbpipi Coe icien measu ing he co ela ion be ween he ini ial announcemen and e ision
bcbcc Coe icien measu ing he co ela ion be ween he ini ial announcemen and e ision
δydel ay Coe icien o he lagged e ision in he ou pu e ision
δcdel ac Coe icien o he lagged e ision in he consump ion e ision
147
148
Lis o a iables B.1. Endogenous a iables
y y Ou pu
c c Consump ion
i i In es men
z z Capi al u iliza ion a e
l l Employmen le el
R In e es a e
π pi In la ion
q q Capi al alue
k
k Ren al a e o capi al
ks
ks Capi al supply
k k Capi al
µw
muw Wage ma k-up
µp
mup P ices ma k-up
w w Wages
y
y Real- ime ou pu
π
pi Real- ime in la ion
c
c Real- ime consump ion
y
y Ou pu e ision
c
c Consump ion e ision
π
pi In la ion e ision
yp
yp Po en ial Ou pu
ip
ip Po en ial in e es a e
zp
zp Po en ial capi al u iliza ion a e
lp
lp Po en ial employmen
Rp
p Po en ial in e es a e
πp
pip Po en ial in la ion
qp
qp Po en ial capi al alue
k,p
kp Po en ial capi al in e es a e
ks,p
ksp Po en ial capi al supply
kp
kp Po en ial capi al
wp
wp Po en ial wages
Lis o a iables B.2 Exogenous a iables: Shocks
εa
epsa Tecnhology shock
εb
epsb Risk p emium shock
εg
epsg Expendi u e shock
εi
epsi In es men adjus men shock
εR
eps Mone a y policy shock
εw
epsw Wage ma k-up shock
εp
epsp P ice ma k-up shock
εy
, +Sey Ou pu e ision shock
επ
, +Sepi In la ion e ision shock
εc
, +Sec Consump ion e ision shock
149
Lis o a iables B.3 P ede e mina ed a iables
c −1,i −1,k −1,π −1,w −1,R −1,y −1,y
−1,π
−1,
c
−1, y
−1, π
−1, c
−1,cp
−1,ip
−1,kp
−1, p
−1
150
