Decline of interest rates under inflation targeting and previous regimes: Evidence from Latin America and developed countries

Chión-Chacón, Se gio Julio; Ál a ez Ga cía, Ke in An onio
A icle
Decline o in e es a es unde in la ion a ge ing and
p e ious egimes: E idence om La in Ame ica and
de eloped coun ies
Ekonomika
P o ided in Coope a ion wi h:
Vilnius Uni e si y P ess
Sugges ed Ci a ion: Chión-Chacón, Se gio Julio; Ál a ez Ga cía, Ke in An onio (2025) : Decline o
in e es a es unde in la ion a ge ing and p e ious egimes: E idence om La in Ame ica and
de eloped coun ies, Ekonomika, ISSN 2424-6166, Vilnius Uni e si y P ess, Vilnius, Vol. 104, Iss. 1,
pp. 6-29,
h ps://doi.o g/10.15388/Ekon.2025.104.1.1
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Ekonomika ISSN 1392-1258 eISSN 2424-6166
2025, ol. 104(1), pp. 6–29 DOI: h ps://doi.o g/10.15388/Ekon.2025.104.1.1
Decline o In e es Ra es unde In la ion
Ta ge ing and P e ious Regimes: E idence
om La in Ame ica and De eloped Coun ies
Se gio Julio Chión-Chacón
CENTRUM Ca ólica G adua e Business School, Lima, Pe ú
Pon i icia Uni e sidad Ca ólica del Pe ú, Lima, Pe ú
Email: [email p o ec ed]
ORCID: h ps://o cid.o g/0000-0002-7955-3163
Ke in An onio Ál a ez Ga cía
CENTRUM Ca ólica G adua e Business School, Lima, Pe ú
Pon i icia Uni e sidad Ca ólica del Pe ú, Lima, Pe ú
Email: [email p o ec ed]
ORCID: h ps://o cid.o g/0000-0003-0037-4865
Abs ac . This s udy empi ically in es iga es he impac o In la ion Ta ge ing (IT) on nominal in e es a es
o e he pas 40 yea s, ocusing on 10 ad anced and eme ging economies. By using a Bina y Regime Model
embedded wi hin a Backwa d-Looking Taylo , ou indings con i m ha IT adop ion has signi ican ly con ibu ed
o educing in e es a es, wi h he s onges e ec s obse ed in La in Ame ican coun ies. To ein o ce hese
esul s, we inco po a e Smoo h T ansi ion Reg ession (STR) models, wi h and wi hou ins umen al a iables,
allowing o a mo e sui able ep esen a ion o g adual policy ansi ions. The STR es ima es consis en ly suppo
ou main indings, alida ing he obus ness o he obse ed impac s. Fu he mo e, we show ha , bo h be o e
and a e IT implemen a ion, cen al banks display a s onge emphasis on esponding o in la ion han o he
ou pu gap, wi h his ocus in ensi ying unde IT egimes.
Keywo ds: Mone a y policy, in la ion a ge ing, in e es a es, Taylo Rule, Smoo h T ansi ion Reg ession.
1. In oduc ion
In he las 40 yea s, in e es a es ha e exhibi ed a clea dec easing end in bo h de eloped
and eme ging economies1 (Li, 2012; Be nanke, 2022). Despi e he global economy going
h ough a ious expansiona y and con ac iona y phases, e en wi h signi ican luc ua ions
in sho - e m in e es a es, he long- e m end emains in ac . Many a gumen s ha e been
pu o h ega ding he ac o s behind his educ ion.
Be nanke (2022) emphasizes ha he decline in in la ion could ha e been a decisi e
ac o , as lende s end o demand lowe p emiums (in e es a es) when in la ion is e-
1 See Figu e 1.
Recei ed: 15/09/2024. Re ised: 20/12/2024. Accep ed: 05/01/2025
Copy igh © 2025 Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Published by Vilnius Uni e si y P ess
This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion License, which pe mi s un es ic ed use,
dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal au ho and sou ce a e c edi ed.
Con en s lis s a ailable a Vilnius Uni e si y P ess
Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Decline o In e es Ra es unde In la ion Ta ge ing and P e ious Regimes:...
7
duced. This obse a ion unde sco es he impo ance o unde s anding he mechanisms
ha ha e led o a dec ease in in la ion as a ele an con ibu ing ac o . Mo eo e , he
li e a u e shows ha he de e minan s o in e es a es ha e an impo an ela ionship wi h
he mone a y policy amewo k (Bambe, 2023).
Empi ical s udies ha e shown ha in la ion a ge ing egimes ha e been success ul in
main aining low, s able, and less ola ile in la ion le els (Mishkin and Schmid -Hebbel,
2007; Vega and Winkel ied, 2005; Visoka iciene, 2010; S ojano ikj and Pe e ski, 2020;
A sić e al., 2022; Bhalla e al., 2023). The e o e, while he e is subs an ial li e a u e on
he e ec i eness o in la ion a ge ing in s abilizing in la ion, he e a e no s udies ha
di ec ly explo e i s impac on nominal in e es a es. Ou s udy seeks o ill his gap by
examining he ole o in la ion a ge ing in educing in e es a es, ocusing on he p e- and
pos -IT pe iods in bo h eme ging and ad anced economies. This compa a i e analysis o
he pe iods be o e and a e he adop ion o IT is a key inno a ion o ou esea ch, o e ing
new insigh s in o he mechanisms behind in e es a e dynamics.
The ansmission mechanism is qui e in ui i e. I in la ion a ge ing (IT) gene a es a
clima e o us and c edibili y, i will ancho in la ion expec a ions and esul in lowe
long- e m in la ion, he eby leading o a educ ion in in e es a es. Addi ionally, he adop-
ion o IT may encou age a g ea e iscal discipline (Ape i e al., 2024), which could, in
u n, con ibu e o lowe ing bo h in la ion and in e es a es.
Unde s anding whe he IT has been an impo an ac o in he alling a es becomes
undamen ally impo an because i would demons a e he e ec i eness o in la ion a -
ge ing as a mone a y policy ool o p omo e no only p ice s abili y bu also mo e a o able
inancial condi ions. P ac ically, his could suppo he c edibili y and con idence in he
mone a y policies implemen ed by he cen al banks ha adop hese a ge s.
0
5
10
15
20
25
30
In e bank In e es Ra e
(A e age %)
P e ious IT IT egime
-2
0
2
4
6
8
10
12
14
16
18
1980 1986 1992 1998 2004 2010 2016
2022
Pe cen
10-yea T easu y Yields o De eloped
Coun ies
US
UK
Canada
Eu o A ea
Japan
Figu e 1. In e bank in e es a e and T easu y Yields
No e: Figu e 1 (a) shows he a e age o he in e bank in e es a e in IT he egime and be o e. The o al sample
co e s om 1962Q2 o 2022Q4 ( he s a da e a ies among coun ies), whe eas he pe iods in IT s a om
1992 o 2022 (see Table 1). Fo B azil, pe iods wi h a ypical in e es a es a e omi ed, and he sample om
1995Q3–1999Q2 is conside ed as p e-IT. The a e o Japan is 0.36 be o e IT and 0.07 in IT; o g aphical
pu poses, we mul iply hese alues by 10. Sou ce: Fede al Rese e Economic Da a (FRED).
(b)(a)
ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 104(1)
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The objec i e o his s udy is o explo e whe he In la ion Ta ge ing (IT) has played a
ole in he his o ical decline o in e es a es obse ed ac oss a sample o ep esen a i e
economies om bo h eme ging and ad anced coun ies. Also, we s udy i in la ion and he
ou pu gap play any ole in he p ocess o pu suing he in la ion a ge by cen al banks.
To add ess his issue, we es ima e a bina y swi ching eg ession embedded wi hin a back-
wa d-looking Taylo Rule while using he o dina y leas squa es (OLS) eg ession model.
Table 1. In la ion Ta ge ing Adop ion
Coun y Da e I.T. adop ed Cu en Ta ge
Canada Feb ua y 1991 1% – 3%
Chile Sep embe 1999 1% – 3%
Colombia Oc obe 1999 2% – 4%
Mexico 2001 1% – 3%
Pe u Janua y 2002 1% – 3%
Uni ed Kingdom Oc obe 1992 2%
Uni ed S a es Janua y 2012 2%
Japan Janua y 2013 2%
B azil June 1999 1.5% – 4.5%
Eu o A ea 1999 2%
No e: The leng h o he in la ion a ge a ies among na ions. In he cases o Pe u and he Uni ed Kingdom,
he a ge is es ablished inde ini ely, encompassing all pe iods. Chile’s in la ion a ge spans app oxima ely
wo yea s. Meanwhile, Colombia and Mexico employ a medium- e m a ge , while B azil op s o a yea ly
a ge . Las ly, Canada’s in la ion a ge ex ends o e a pe iod o six o eigh qua e s. The in la ion a ge s o
2022 a e conside ed as cu en a ge s. Sou ces: Bank o England and Reu e s.
The use o a backwa d-looking Taylo Rule is jus i ied by se e al conside a ions. Fi s ,
o wa d-looking ules ely on expec a ions o in la ion and ou pu gaps, which a e o en
subjec o measu emen e o s and un eliable eal- ime da a (Mankiew e al., 2004; Reid and
Siklos, 2021). Backwa d-looking ules, by ocusing on obse ed his o ical da a, minimize
hese issues and educe he po en ial endogenei y conce ns. Addi ionally, such ules help
ensu e de e minacy in s uc u al models, as highligh ed in he li e a u e (Ca ls om and
Fue s , 2000), whe e backwa d-looking ules con ibu e o s able and unique equilib ia.
While an ex ension o his analysis could in ol e he conside a ion o a o wa d-looking
ule, he backwa d-looking app oach emains obus o he pu poses o his s udy and
aligns wi h empi ical e idence in his o ical con ex s.
We u ilize a simple eg ession model es ima ed unde OLS since he e is ecen e idence
ha his es ima ion me hod pe o ms be e in es ima ing Taylo - ype ules (Ca alho e
al., 2021). The analysis is conduc ed o a se composed o Ad anced economies and o
La in Ame ican economies (US, UK, Canada, Japan, Eu o A ea, Pe u, Chile, Colombia,
Mexico, and B azil) ha ha e adop ed In la ion Ta ge ing (see Table 1). Addi ionally, o
analyze and compa e he a ia ions o he a es in bo h pe iods, elas ici ies a e calcula ed
in bo h egimes.
Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Decline o In e es Ra es unde In la ion Ta ge ing and P e ious Regimes:...
9
Ou a icle con ibu es o he li e a u e by expanding empi ical e idence on he e ec
o In la ion Ta ge ing (IT) in educing he in e es a es, pa icula ly in eme ging La in
Ame ican economies. I u he con as s hese expe iences wi h hose obse ed in he
de eloped coun ies, hus p o iding a compa a i e analysis which is bound o highligh
di e ences and simila i ies in he impac o IT ac oss a ying economic con ex s.
The empi ical esul s show ha he adop ion o IT has played a subs an ial ole in low-
e ing he in e es a es in ecen yea s, pa icula ly wi h a s onge impac being obse ed
in La in Ame ican economies. Also, ou analysis e eals ha cen al banks ha e exhibi ed
a mo e p onounced esponse o in la ion compa ed o he ou pu gap, bo h p io o and
ollowing he implemen a ion o in la ion a ge ing (IT), and he esponse o cen al banks
o in la ion has shown an upwa d end a e he adop ion o IT.
The ollowing sec ions p oceed as ollows. Sec ion 2 p o ides a b ie li e a u e e iew.
Sec ion 3 demons a es he me hodology applied in his s udy. Sec ion 4 p esen s he
ob ained esul s and discusses he ele an conside a ions and ac s. Finally, in Sec ion
5, conclusions a e p esen ed.
2. Li e a u e Re iew
The ela ionship be ween in la ion a ge ing (IT) and in e es a es has been he subjec
o ex ensi e esea ch, ye he e idence emains mixed. Fo ins ance, Fouejieu and Roge
(2013) explo e how IT in luences c oss-coun y in e es a e sp eads in bo h eme ging
and ad anced economies. By using a dynamic panel da a app oach and sys em GMM o
add ess endogenei y, hey ind ha IT leads o a decline in coun y isk p emium sp eads,
pa icula ly unde condi ions o a educed poli ical unce ain y.
Simila ly, De Mendoça and Souza (2009) examine he ela ionship be ween he mon-
e a y policy c edibili y and in e es a es. By cons uc ing a no el c edibili y index based
on expe su eys, hey demons a e h ough OLS eg ession ha , du ing he IT pe iod,
in e es a es exhibi ed less a iabili y due o an enhanced mone a y policy c edibili y.
Al e na i ely, Geh inge and Maye (2019) in es iga e he ac o s d i ing nominal
long- e m in e es a es. By using a VAR model wi h a DOLS p ocedu e, hey conclude
ha , in majo indus ialized economies, cen al banks’ mone a y policies ha e signi ican ly
con ibu ed o main aining low in e es a es. They a gue ha he close connec ion be ween
sho - e m a es (con olled by cen al banks) and long- e m a es is mo e e lec i e o
cen al bank pe cep ions han hose o he ma ke pa icipan s.
The s udies suppo ing a posi i e e ec o IT on in e es a es gene ally a gue ha
IT os e s a clima e o con idence and expec a ion managemen , leading o consis en
educ ions in in e es a es. Addi ionally, o he esea ch highligh s a s ong link be ween
he in la ion con ol and lowe in e es a es. Fo example, Fazlollahi and Eb ahimijan
(2022) p o ide econome ic e idence o a bidi ec ional causali y be ween in e es a es
and in la ion a es in Canada, he eby suppo ing Be nanke’s (2022) p emise ha in la ion
a es signi ican ly in luence his o ical in e es a es.

ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 104(1)
10
Howe e , no all esea ch suppo s he hypo hesis ha IT has a subs an ial impac on
in e es a es. Lin and Ye (2007), by using P opensi y Sco e Ma ching, ind ha IT does no
signi ican ly a ec in la ion o in la ion a iabili y in indus ialized coun ies. Simila ly, Ball
and She idan (2005), by employing a di e ence-in-di e ences model, ind ha IT does no
exe signi ican e ec s on long- e m in e es a es in ad anced economies. They a ibu e
he obse ed in la ion decline o a mean- e e sion phenomenon a he han o IT i sel .
Beyond IT, o he ac o s ha e been iden i ied as in luencing he decline in eal in e es
a es. Fo ins ance, esea ch by Dell’E ba and Sola (2016), Ba nejee e al. (2022) and
K egzde and Mu auskas (2015) poin s o a s ong ela ionship be ween iscal policy man-
agemen and in e es a es. The abo e-lis ed au ho s a gue ha educing sp eads can lowe
o he in e es a es in he economy. Howe e , Dau o ic (2017) claims ha he ela ionship
be ween iscal policy a iables – such as go e nmen spending o budge de ici s – and
long- e m in e es a es ends o weaken o e en disappea once he pe sis en na u e o
in e es a es has been accoun ed o in econome ic models. Ano he c ucial ac o is
he ‘global sa ing glu ’, a concep in oduced by Be nanke (2005a), which e e s o a
wo ldwide inc ease in sa ings, leading o educed in e es a es. Be nanke iden i ies de-
mog aphic changes and income g ow h as he key d i e s o his global sa ings inc ease.
While suppo ing his iew, Ba sky and Eas on (2021) a gue ha he global sa ing glu
hypo hesis explains he decline in long- e m eal in e es a es om 2002 o 2006 bu may
no ully accoun o he u he dec ease obse ed a e he G ea Recession.
Upon e iewing he li e a u e, se e al conside a ions eme ge. Fi s , s udies elying
on expec a ion da a may be lawed. In his con ex , Reid and Siklos (2021) highligh ha
measu ing in la ion expec a ions is challenging due o hei unobse able na u e and he
esponden s’ misunde s anding o economic concep s, leading o biased and inconsis en
da a. Second, much o he empi ical li e a u e ocuses on ad anced indus ialized coun ies,
he eby limi ing he gene alizabili y o he indings. These coun ies had a low in la ion
and mo e e icien ins i u ions e en be o e adop ing IT. Finally, s udies using ea men
e ec s may be biased. Fo example, di e ence-in-di e ences models ha do no accoun
o ime- a ying ea men e ec s can in oduce bias (Goodman-Bacon, 2021). Mo eo-
e , i coun ies in he sample a e no genuine in la ion a ge e s bu beha e as such, he
es ima ed ea men e ec s may be misleading.
This esea ch seeks o ill hese gaps by p o iding e idence o eme ging La in Ame -
ican coun ies. Ins ead o elying on expec a ion da a, we adop a mo e s aigh o wa d
and me hodologically obus app oach o add ess hese issues.
3. Me hod
3.1. Resea ch Model
3.1.1. Bina y Regime Model
We es ima e eg essions o he Backwa d-Looking ype Taylo Rule o en di e en
coun ies as ollows:
Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Decline o In e es Ra es unde In la ion Ta ge ing and P e ious Regimes:...
11
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
(1)
whe e is he nominal in e bank in e es a e, π is he in la ion a e gap, while
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
is he
ou pu gap (de ined as he pe cen age di e ence be ween he ou pu and i s long- e m
end le el). Cen al o ou analysis is he in oduc ion o a dummy a iable, D , which
akes he alue o ‘1’ du ing he in la ion a ge ing pe iod and ‘0’ o he wise. This allows
us o cap u e he e ec s o bo h he in la ion a ge ing pe iod and he p eceding mone a y
policy egimes.
We use he O dina y Leas Squa ed (OLS) me hod o es ima e he coe icien o he
eg essions o bo h La in Ame ican and de eloped coun ies. We cap u e he es ima o
o he wo mone a y policy egimes as ollows:
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
; I.T. egime
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
; p e ious egimes
Endogenei y in s uc u al models like he Taylo Rule can lead o biased es ima o s.
The common app oach in he li e a u e is o use Ins umen al Va iables (IV) o GMM
(Mahe e al., 2022; Ho a h e al., 2022). Howe e , ensu ing he exogenei y and alid-
i y o ins umen s, especially in ime se ies, is challenging. Empi ical e idence sugges s
ha O dina y Leas Squa es (OLS) p o ides a be e pe o mance as well as a smalle
endogenei y bias in easonably sized samples (Ca alho e al., 2021). Following Miles
and Sch eye (2012) and Ca alho e al. (2021), we op o OLS ins ead o 2SLS2. To
add ess se ial co ela ion, he e oskedas ici y, and au oco ela ion, we use HAC s anda d
e o s and boo s ap echniques.
3.1.2. Smoo h T ansi ion Reg ession (STR)
The smoo h ansi ion model cap u es g adual changes in he s uc u al pa ame e s o
an equa ion, as opposed o ab up shi s, hus making i pa icula ly use ul o analyzing
policies wi h po en ial egime changes. In his con ex , he model inco po a es a ansi ion
dynamic which depends on a h eshold a iable (such as he empo al dis ance om he
implemen a ion da e o a egime). We es ima e he model bo h wi hou and wi h ins u-
men al a iable (IV) es ima ion o add ess po en ial endogenei y issues. The gene al o m
o he model is:
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
(2)
In his model, ep esen s he in e bank in e es a e,
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
is he in la ion a e ela i e o
i s a ge , and
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
is he ou pu gap. G(τ ; κ) is he ansi ion unc ion, which depends on he
h eshold a iable τ (in his case, ep esen ing he empo al dis ance om he da e o IT
adop ion), and κ is he smoo hness pa ame e . In his amewo k, wo ypes o ansi ion
unc ions a e easible, as ollows:
2 To enhance he obus ness o ou esul s, we also es ima e Equa ion (1) by using Ins umen al Va iables (IV).
ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 104(1)
12
Logis ic unc ion
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
Exponen ial unc ion:
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
The selec ion be ween he wo unc ions is made by minimizing he sum o squa ed
esiduals (SSR) o di e en alues o he smoo hness pa ame e 𝜅3. To add ess po en ial
in e ence issues caused by se e e au oco ela ion, Boo s ap was used o es ima e he
s anda d e o s o he model4. The e o e, unde his speci ica ion, he aim is o add ess
(i) he g adual na u e o he e ec s o IT adop ion, (ii) po en ial endogenei y issues, and
(iii) possible au oco ela ion p oblems by p o iding a mo e obus es ima ion o he
s anda d e o s, he eby enhancing he eliabili y o he esul s.
3.2. Da a and Va iables
We collec ed qua e ly da a on he in e bank in e es a e, in la ion and ou pu o he
en coun ies included in ou sample. The speci ic a iables employed we e dic a ed by
he bes da a a ailable. We ollow Miles and Sch eye (2012), who used a measu e o
sho e m in e es a es5. Fo he de eloped economies and B azil, we use he 3-mon h
in e bank a e6. Fo Mexico, we use he ‘28 days in e bank a e’, while o Pe u, Chile
and Colombia, we e e o he 1-day in e bank a e. The in e bank a e, he in la ion, and
he eal ou pu we e aken om he Fede al Rese e Economic Da a (FRED), Economic
Commission o La in Ame ica (CEPAL) he In e na ional Mone a y Fund (IMF) and he
cen al banks websi es o each coun y o be analyzed. We conside he in la ion a e as
he yea - o-yea a ia ion o he Consume P ice Index (CPI). This measu e includes he
in e annual a ia ion o he qua e ly a e age7 o CPI
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
. The
ou pu gap was ob ained by he Hod ick-P esco il e 8.
Acco ding o he sample, Canada has he la ges da a se ies, unning om 1962Q1 o
2022Q4. I is ollowed by he Uni ed S a es, wi h he da a spanning he pe iod om 1964Q3
o 2022Q2. The Uni ed Kingdom’s da a un om 1986Q1 o 2022Q2. The Eu o A ea
p o ides da a om 1995Q1 o 2022Q4, while Japan’s da a un om 2002Q2 o 2022Q4.
3 Values om 0.1 o 10 we e used wi h an inc ease a e o 0.20.
4 2000 simula ions we e conside ed.
5 In ou analysis, we employ he same dependen a iable, namely, he in e bank a e, ac oss all coun ies. How-
e e , we a y he e ms associa ed wi h he in e bank a e, speci ically conside ing in e als o 1, 28 and 30 days.
6 Qua e ly da a a e ob ained om he 3-mon h a e age o mon hly da a.
7 The CPI is he mon hly a e age index, while he QACPI is he qua e ly a e age o CPI.
8 The alue o λ conside ed in his analysis was 1600. Howe e , he Hod ick-P esco il e (1997) is known o
ha e weaknesses, including sensi i i y o he choice o λ, end-poin bias ha a ec s es ima es nea he sample edges
(Cogley and Nason, 1995; Ra n and Uhlig, 2002), and i s inabili y o accoun o s uc u al b eaks o economic
shocks, which may lead o misleading esul s in ola ile con ex s (Hamil on, 2018).
Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Decline o In e es Ra es unde In la ion Ta ge ing and P e ious Regimes:...
13
Table 2. Summa y s a is ics on in la ion and in e bank in e es a e (% annual a es)
Pe ú Chile Colombia Mexico B azil U.S. U.K. E.A. Canada Japan
In la ion
Be o e
Mean 8.3 5.9 18.3 21.2 587.9 4.3 5.4 1.5 5.5 -0.2
Median 8.2 5.7 19.5 17.6 14.0 3.4 5.0 1.5 4.6 -0.2
S.D. 2.7 1.4 3.6 12.1 1273.8 2.9 1.8 0.3 3.4 0.8
In la ion
Ta ge ing
Mean 2.9 3.6 5.1 4.4 6.4 2.4 2.3 2.0 2.0 0.6
Median 2.8 3.0 4.8 4.1 6.1 1.8 2.0 1.9 1.7 0.5
S.D. 1.7 2.6 2.4 1.2 2.7 2.1 1.3 1.7 1.6 1.0
Full
pe iod
Mean 3.7 3.9 7.2 8.2 111.7 3.9 2.8 1.9 3.7 0.2
Median 3.1 3.4 5.3 4.7 6.2 3.2 2.3 1.8 2.5 0.0
S.D. 2.7 2.6 5.5 9.1 576.9 1.4 1.9 1.6 3.2 0.9
In e bank
Ra e
Be o e
Mean 13.4 14.3 26.7 27.2 131.3 6.0 11.7 5.0 8.7 0.4
Median 12.8 14.5 25.6 22.4 23.8 5.6 11.2 4.5 8.5 0.3
S.D. 4.6 3.7 5.7 12.0 242.6 3.4 2.0 1.2 3.5 0.3
In la ion
Ta ge ing
Mean 3.5 4.1 6.0 6.4 10.5 0.9 3.3 1.5 3.1 0.1
Median 3.7 3.5 5.5 6.6 10.8 0.3 3.9 1.0 2.7 0.0
S.D. 1.4 2.5 2.6 2.0 4.5 0.9 2.6 1.8 2.3 0.1
Full
pe iod
Mean 5.7 5.4 9.4 11.0 32.3 5.0 4.8 2.0 5.8 0.2
Median 4.2 4.3 6.3 7.6 11.8 5.5 4.9 2.0 5.1 0.1
S.D. 4.9 4.4 8.3 10.5 111.5 3.7 4.1 2.1 4.0 0.2
No e: The da a in his able a e p esen ed in qua e ly equency. The sample p io o in la ion a ge ing was chosen based on he a ailabili y o da a. The da a sample
o each coun y co esponds exac ly o he one speci ied in he da a sec ion. Sou ces: Fede al Rese e Da abase (FRED) and Cen al Banks o each coun y.
ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 104(1)
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Table 5. Smoo h ansi ion eg ession model es ima ed using ins umen al a iables (IV)
Pe u Chile Colombia Mexico B azil U.S. U.K. Canada E.A. Japan
In e cep 12.62***
(2.42)
23.00***
(6.30)
11.02
(8.89)
6.66
(12.9)
44.99**
(20.59)
6.47***
(0.54)
17.76***
(4.03)
12.21***
(2.42)
20.27***
(5.17)
0.89***
(0.17)
Ou pu gap 0.17
(0.33)
0.56**
(0.26)
0.24
(0.98)
1.00*
(0.58)
0.61
(0.74)
0.40
(0.27)
0.52**
(0.24)
0.74***
(0.27)
0.31
(0.24)
-0.02
(0.04)
In la ion
gap
0.61**
(0.24)
0.52***
(0.19)
1.03
(0.64)
0.96
(0.65)
0.43
(0.58)
0.54***
(0.16)
-0.14
(0.35)
-0.12
(0.37)
0.21
(0.17)
0.15
(0.09)
T ansi ion -10.93***
(5.13)
-22.38***
(8.64)
-6.73
(11.21)
1.34
(14.09)
-39.99
(25.93)
-18.58
(11.66)
-14.38***
(5.33)
-14.25**
(6.17)
-21.8***
(6.33)
-0.89***
(0.16)
In e cep –
p e-IT
12.624***
(2.42)
23.00***
(6.30)
11.02
(8.89)
6.66
(12.87)
44.985**
(20.59)
6.47***
(0.54)
17.76***
(4.04)
12.21***
(2.42)
20.27***
(5.17)
0.89***
(0.17)
In e cep –
pos -IT
1.72
(2.89)
0.63
(2.43)
4.29**
(2.38)
7.99***
(1.49)
4.99
(5.48)
-12.12
(11.45)
3.39**
(1.36)
-2.03
(3.80)
-1.54
(1.27)
-0.00
(0.24)
No es: The smoo h ansi ion eg ession model used a con inuous logis ic unc ion in all cases, a e e alua ion o he nonlinea es based on Te äs i a (1994). The
model uses es ima es unde ins umen al a iables (IV), whe e he ins umen s we e he lags (2) o he independen a iables. I is wo h no ing ha he esul s a e
subjec o he possible weakness o he ins umen s. The s anda d e o in pa en heses was es ima ed by using he boo s ap me hod wi h 2000 i e a ions.
Table 6. Smoo h ansi ion eg ession model es ima ed by OLS
Pe u Chile Colombia Mexico B azil U.S. U.K. Canada E.A. Japan
In e cep 10.10***
(0.94)
16.45***
(1.20)
8.04***
(1.06)
17.85***
(2.11)
29.20***
(0.95)
4.61***
(0.17)
13.99***
(0.80)
7.43***
(0.26)
7.61***
(0.45)
0.53***
(0.07)
Ou pu gap 0.10
(0.09)
0.28***
(0.09)
0.06
(0.13)
0.11
(0.18)
-0.16
(0.26)
0.20*
(0.12)
0.15*
(0.08)
0.36***
(0.10)
0.17
(0.10)
0.00
(0.02)
In la ion
gap
0.62***
(0.13)
0.52***
(0.08)
1.19***
(0.11)
0.72***
(0.12)
-0.05
(0.11)
0.73***
(0.06)
0.22
(0.13)
0.54***
(0.08)
0.16
(0.15)
0.07***
(0.02)
T ansi ion -7.54***
(0.94)
-13.67***
(1.26)
-4.60***
(1.20)
-13.18***
(2.11)
-20.20***
(1.24)
-5.08***
(0.39)
-11.17***
(0.88)
-4.60***
(0.33)
-6.66***
(0.54)
-0.38***
(0.05)
In e cep –
p e-IT
10.10***
(0.94)
16.45***
(1.20)
8.04***
(1.06)
17.85***
(2.11)
29.20***
(0.95)
4.61***
(0.17)
13.99***
(0.80)
7.43***
(0.26)
7.61***
(0.45)
0.53***
(0.08)
In e cep –
pos -IT
2.57*
(1.33)
2.79
(1.73)
3.43**
(1.60)
4.67
(3.00)
8.98***
(1.56)
-0.46
(0.43)
2.83**
(1.20)
2.83***
(0.41)
0.95
(0.71)
0.15
(0.09)
No es: The smoo h ansi ion eg ession model used a con inuous logis ic unc ion in all cases, a e e alua ion o he nonlinea es based on Te äs i a (1994). The
s anda d e o in pa en heses was es ima ed by using he boo s ap me hod wi h 2000 i e a ions.

Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Decline o In e es Ra es unde In la ion Ta ge ing and P e ious Regimes:...
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indica ing a s uc u al shi consis en wi h a egime change. Addi ionally, compa ing he
baseline model o he one wi hou he dummy e eals whe he he inclusion o he dummy
imp o es he explana o y powe . A highe R2 and signi ican coe icien s in he baseline
model sugges ha he dummy e ec i ely cap u es egime-speci ic dynamics.
Table 10 shows subs an ial changes in pa ame e s ac oss subsamples o he 10 coun-
ies, hus indica ing a po en ial egime shi . All eg essions, excep o he Eu o A ea,
display a highe R2 alue in he baseline model, hus sugges ing ha he model wi h he
dummy is obus and cap u es egime-speci ic dynamics be e in mos cases.
6. Conclusions
This s udy aims o answe he ques ion whe he he in la ion a ge ing (IT) egime and
i s a ia ion ha e con ibu ed o he his o ic educ ion in in e es a es expe ienced by
bo h de eloped and eme ging economies. Fu he mo e, i examines whe he he ou pu
gap and he in la ion le el ha e played a signi ican ole in his p ocess o a e educ ion.
A Bina y Regime Model embedded wi hin a Backwa d-Looking Taylo and STR was
es ima ed o cap u e he mone a y policy egime, and i has been ound ha he in la ion
a ge ing egime has played a c ucial ole in he his o ic educ ion o in e es a es in
he eme ging economies o La in Ame ica and he de eloped economies o ou sample.
The empi ical esul s show ha his e ec has had a s onge impac in La in Ame ican
economies. These esul s a e consis en wi h he asse ions made by Be nanke (2022) and
Fazlollahi and Eb ahimijan (2022).
Howe e , while he e idence indica es ha he adop ion o IT has been an impo an
ac o in explaining he decline in in e es a es, in B azil, he Uni ed Kingdom, and he
Eu ozone, in la ion and he ou pu gap would no ha e played a signi ican ole, and o he
mechanisms would be behind his educ ion (e.g., he eal exchange a e, e ms o ade,
e c.). Rega ding he ou pu gap, he e idence shows ha i has only been a signi ican
ac o in Pe u, Chile, Canada, and Colombia.
Addi ionally, wo key conclusions eme ge om ou indings. Fi s , he elas ici y o
in la ion has no ably inc eased o e ime. Second, in bo h p e- and pos -IT pe iods, he
magni ude o in la ion elas ici ies exceeds ha o he ou pu gap. These esul s sugges ha
cen al banks, adhe ing o a backwa d-looking Taylo Rule, ha e consis en ly esponded
mo e s ongly o in la ion han o he ou pu gap, wi h his esponse in ensi ying a e he
adop ion o IT.
The educ ion in nominal in e es a es unde he IT egime sugges s be e in la ion
expec a ion ancho ing, leading o lowe in la ion and bo owing cos s. Howe e , as a es
app oach hei lowe bound, he adi ional mone a y policy becomes less e ec i e, he eby
o cing cen al banks o ely on uncon en ional measu es wi h unce ain long- e m impac s.
Gi en he use o pos -pandemic da a, he esul s may be subjec o s uc u al b eaks
due o signi ican changes in he global economy. An ex ension o his s udy could in ol e
add essing hese b eaks, possibly h ough echniques like Ma ko -swi ching models, so
ha o be e cap u e he impac o he pandemic on mone a y policy.
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Appendices
Appendix A. Econome ic Me hods and Es ima ions
1. G ow h a e o Na u al Ou pu Es ima ion
Table 7. Po en ial GDP g ow h a e
Coun y Sample A e age po en ial GDP g ow h a e (%)
Pe u 1997Q1 – 2022Q4 4.0
Chile 1997Q1 – 2022Q4 3.5
Colombia 1996Q2 – 2022Q4 3.0
Mexico 1996Q2 – 2022Q4 2.1
B azil 1997Q1 – 2022Q4 2.1
US 1965Q3 – 2022Q4 2.8
UK 1987Q1 – 2022Q4 1.8
Canada 1963Q1 – 2022Q4 2.9
Eu o A ea 1996Q1 – 2022Q4 1.4
Japan 1995Q1 – 2022Q4 0.6
No e. The end o ou pu gap ob ained by he HP il e is conside ed as he po en ial GDP. Sou ce: Own
elabo a ion.
2. Weigh A e age o In la ion Ta ge
In o de o compu e he in la ion elas ici ies p esen ed in Table 5, we employ a weigh ed
a e age o he in la ion a ge , whe e he weigh ing is de e mined by he du a ion o which
he a ge was main ained. The Fo mula used o his calcula ion is as ollows:
A e age o π*
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
(7)
whe e πi* is he in la ion a ge , and i = 1, 2, 3, … N indica es he numbe o objec i es
ha each coun y has had. wj indica es he pe iod o ime ha said objec i e has been
main ained, hus j = 1, 2, 3, … K indica es he qua e s. De ails a e gi en in Table 6.
Table 8. A e age a ge in la ion
Pe u Chile Colombia Mexico B azil U.K. Canada
Ta ge (%)
( ime ame
in qua e s)
2.5
(13Q)
3.5
(4Q)
5.5
(4Q)
4
(7QQ)
8
(3Q)
2.5
(47Q)
3
(5Q)
2
(64Q)
3
(56Q)
4.5
(3)
3
(69Q)
6
(4Q)
2
(77Q)
2.5
(7Q)
-2.5
(24Q)
4
(16)
3.75
(3Q)
4.5
(53Q) -2
(108Q)
-2.4
(10)
3.5
(8)
3.5
(5Q)
4
(12Q) - -
- - 3
(41) -3.75
(5Q) - -
----3.5
(8Q) - -
----3.25
(4Q) - -
----3
(6Q) - -
A e age 2.1 2.8 1.8 3.1 4.3 2.2 2.1
No es: US, Japan and EA ha e had an in la ion a ge o 2% since he adop ion o IT. ‘Q’ ep esen s qua e s.
Sou ce: Own elabo a ion.
Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Decline o In e es Ra es unde In la ion Ta ge ing and P e ious Regimes:...
25
3. In e bank In e es Ra e Es ima ion
We es ima e he eg ession by assuming ha in la ion is a i s a ge ed le el and he ou pu
gap is ze o. The a ionale behind his es ima ion app oach s ems om ou objec i e o
compa ing pe iods du ing which he economy ope a ed a i s na u al le el.
A e IT:
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
(8)
Be o e IT:
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
(9)
whe e he pa ame e s a e hose ha we ob ain om he model, whe eas he a e age a ge
in la ion le el pa ame e s (π*) a e he ones we es ima e in Figu e 2.
4. Elas ici ies o In la ion and Ou pu
Fo e e ence pu poses, we es ima e he elas ici ies o in la ion and he ou pu gap in bo h
pe iods (p e- and pos -IT). The es ima e is as ollows (Table 4):
Elas ici y o in la ion =
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
(10)
Elas ici y o ou pu gap =
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
(11)
whe e he only hing ha changes is
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
o bo h pe iods (es ima e is ob ained om Equa-
ions (11) and (12),
𝑟𝑟𝑡𝑡= 𝜃𝜃0+𝜃𝜃1𝜋𝜋𝑡𝑡−1 +𝜃𝜃2𝑦𝑦𝑡𝑡−1 +𝜃𝜃3𝐷𝐷𝑡𝑡+𝜀𝜀𝑡𝑡
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 1)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 +𝜃𝜃
3; I.T. egime
𝐸𝐸(𝑟𝑟𝑡𝑡|𝜋𝜋𝑡𝑡−1,𝑦𝑦𝑡𝑡−1,𝐷𝐷𝑡𝑡= 0)= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋𝑡𝑡−1 +𝜃𝜃
2𝑦𝑦𝑡𝑡−1 ; p e ious egimes
𝑟𝑟𝑡𝑡= 𝛽𝛽0+𝛽𝛽1𝜋𝜋𝑡𝑡+ 𝛽𝛽2𝑦𝑦𝑡𝑡+𝛾𝛾𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)+𝜖𝜖𝑡𝑡 (2)
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)=1
1+𝑒𝑒−𝑘𝑘𝜏𝜏𝑡𝑡
Exponen ial unc ion:
𝛾𝛾(𝜏𝜏𝑡𝑡;𝜅𝜅)= 𝑒𝑒^(−𝑘𝑘|𝜏𝜏𝑡𝑡|)
𝜋𝜋 = (𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4
𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝐼𝐼𝑡𝑡−4 )∗100 .
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1) (3)
𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗+𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0) (4)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗ (5)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
 (6)
𝐴𝐴𝐴𝐴𝑒𝑒𝑟𝑟𝐴𝐴𝐴𝐴𝑒𝑒 𝑜𝑜𝑜𝑜 𝜋𝜋∗=∑ ∑ 𝜋𝜋𝑖𝑖
∗𝑤𝑤𝑗𝑗
𝑁𝑁
𝑖𝑖=1
𝐾𝐾
𝑗𝑗=1 (7)
A e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(1)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3 (8)
Be o e IT: 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗−𝜃𝜃
3𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑦𝑦(0)= 𝑟𝑟𝑡𝑡= 𝜃𝜃
0+𝜃𝜃
1𝜋𝜋∗ (9)
Elas ici y o in la ion = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗= 𝜃𝜃
1×𝜕𝜕∗
𝜕𝜕𝑡𝑡 (10)
Elas ici y o ou pu gap = 𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕 ×𝜕𝜕
𝜕𝜕|𝜕𝜕=𝜕𝜕∗; 𝜕𝜕=𝜕𝜕
=𝜃𝜃
2
𝜕𝜕×𝜕𝜕
𝜕𝜕𝑡𝑡=𝜃𝜃
2
𝜕𝜕𝑡𝑡 (11)
is he g ow h a e o na u al ou pu o each coun y (Table 5).

ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 104(1)
26
Appendix B. Tables and Figu es
Table 9. Resul s wi h IV es ima ion (Equa ion (1))
In e cep In la ion Ou pu Gap Dummy R2 (pseudo)
Pe u
(1996Q1-2022Q4)
13.43***
(0.97)
1.18***
(0.20)
-0.03
(0.22)
-10.67***
(1.02) 0.47
Chile
(1996Q2-2022Q4)
20.17***
(2.12)
0.58***
(0.11)
0.34**
(0.16)
-16.9***
(2.12) 0.42
Colombia
(1995Q3-2021Q4)
2.75*
(1.66)
2.09***
(0.19)
-0.74**
(0.25)
-1.01
(1.58) 0.70
Mexico
(1995Q3-2022Q4)
12.15***
(1.71)
1.00***
(0.21)
0.71***
(0.24)
-8.57***
(1.58) 0.68
B azil
(1996Q2-2022Q4)
22.15***
(4.20)
0.09
(0.17)
-0.16
(0.38)
-12.13**
(4.44) 0.41
Uni ed S a es
(1964Q4-2022Q4)
4.05
(7.84)
0.69***
(0.15)
0.02
(0.19)
1.42
(7.59) 0.25
Uni ed Kingdom
(1986Q2-2022Q4)
22.90***
(3.53)
-1.07**
(0.44)
0.13
(0.22)
-19.00***
(3.50) 0.14
Eu o A ea
(1997Q2-2022Q4)
-92.80
(87.83)
-0.42
(1.15)
0.42
(1.39)
94.21
(87.82) 0.03
Canada
(1962Q2-2022Q4)
12.49***
(1.25)
-0.16
(0.19)
0.80***
(0.20)
-9.73***
(1.33) 0.26
Japan
(2002Q2-2022Q4)
0.35***
(0.10)
0.00
(0.04)
0.04*
(0.02)
-0.29***
(0.06) 0.37
No es: S anda d e o s a e epo ed in pa en heses. As e isks deno e s a is ical signi icance a he 1% (*), 5%
(**), and 10% (***) le els. S anda d e o s we e calcula ed by using he HAC obus es ima o . The ins umen s
used we e he own lags o each a iable. The Akaike In o ma ion C i e ion (AIC) was used o de e mine he
op imal numbe o lags, wi h a maximum o 12 lags (6 o he Eu o A ea o a oid ank issues). Fo indi idual
coun ies: o Pe u, we used 10 lags o in la ion and 1 lag o he ou pu gap; o Chile, we used 4 lags o he
ou pu gap and 10 lags o in la ion; o Colombia, we used 10 lags o in la ion and 5 lags o he ou pu gap;
o Mexico, we used 12 lags o in la ion and 1 lag o he ou pu gap; o B azil, we used 2 lags o in la ion
and 3 lags o he ou pu gap; o Canada, we used 9 lags o in la ion and 1 lag o he ou pu gap; o he
U.K., we used 9 lags o in la ion and 4 lags o he ou pu gap; o he U.S., we used 10 lags o in la ion and
4 lags o he ou pu gap; o Japan, we used 5 lags o in la ion and 1 lag o he ou pu gap; and, o he Eu o
A ea, we used 6 lags o in la ion and 1 lag o he ou pu gap.
Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Decline o In e es Ra es unde In la ion Ta ge ing and P e ious Regimes:...
27
28
Figu e 3. T ansi ion unc ions
No es: Dynamic o logis ic ansi ion unc ions o each coun y a e p esen ed. These esul s a e de i ed om he
es ima ion o Equa ion (2).
28
Figu e 3. T ansi ion unc ions
No es: Dynamic o logis ic ansi ion unc ions o each coun y a e p esen ed. These esul s a e de i ed om he
es ima ion o Equa ion (2).
28
Figu e 3. T ansi ion unc ions
No es: Dynamic o logis ic ansi ion unc ions o each coun y a e p esen ed. These esul s a e de i ed om he
es ima ion o Equa ion (2).
28
Figu e 3. T ansi ion unc ions
No es: Dynamic o logis ic ansi ion unc ions o each coun y a e p esen ed. These esul s a e de i ed om he
es ima ion o Equa ion (2).
Figu e 3. T ansi ion unc ions
No es: Dynamic o logis ic ansi ion unc ions o each coun y a e p esen ed. These esul s a e de i ed
om he es ima ion o Equa ion (2).
ISSN 1392-1258 eISSN 2424-6166 Ekonomika. 2024, ol. 104(1)
28
Table 10. Robus ness check
Coun y Model In e cep In la ion gap Ou pu gap Dummy R2
Pe u
Comple e 10.88***
(1.45)
0.41***
(0.15)
0.11***
(0.04)
-8.57***
(1.26) 0.78
No dummy 4.23***
(0.46)
1.00***
(0.15)
0.05
(0.12) - 0.30
Be o e IT 9.07***
(1.10)
0.81***
(0.24)
0.31
(0.49) - 0.30
A e IT 3.04***
(0.16)
0.42***
(0.08)
0.09**
(0.04) - 0.34
Chile
Comple e 11.34***
(0.85)
0.50***
(0.08)
0.35***
(0.09)
-8.92***
(0.85) 0.75
No dummy 4.60***
(0.39)
0.80***
(0.15)
0.21
(0.15) - 0.27
Be o e IT 12.38***
(2.37)
0.59
(0.75)
0.60
(0.41) - 0.19
A e IT 3.76***
(0.23)
0.48***
(0.09)
0.19**
(0.09) - 0.32
Colombia
Comple e 9.95***
(2.09)
0.89***
(0.10)
0.30*
(0.18)
-8.41***
(1.86) 0.92
No dummy 4.19***
(0.38)
1.44***
(0.06)
-0.04
(0.12) - 0.85
Be o e IT 4.76***
(1.27)
1.45***
(0.12)
0.53
(0.42) - 0.84
A e IT 4.73***
(0.23)
0.55***
(0.11)
0.10
(0.08) - 0.36
Mexico
Comple e 12.05***
(2.62)
0.62***
(0.10)
0.15
(0.09)
-8.36***
(2.30) 0.89
No dummy 5.89
(0.49)
1.08
(0.05)
0.24
(0.17) - 0.83
Be o e IT 23.65
(4.70)
0.35
(0.21)
-3.67
(1.42) - 0.70
A e IT 5.33
(0.38)
1.05
(0.24)
0.16
(0.09) - 0.22
B azil
Comple e 20.13***
(2.02)
0.22
(0.22)
-0.08
(0.35)
-11.10***
(1.43) 0.45
No dummy 12.12***
(0.62)
-0.15
(0.16)
-0.13
(0.30) - 0.59
Be o e IT 21.80***
(0.48)
-0.05
(0.08)
0.64
(0.39) - 0.28
A e IT 10.24***
(0.56)
0.10
(0.16)
-0.27
(0.24) - 0.45
Se gio Julio Chión-Chacón, Ke in An onio Ál a ez Ga cía. Decline o In e es Ra es unde In la ion Ta ge ing and P e ious Regimes:...
29
Coun y Model In e cep In la ion gap Ou pu gap Dummy R2
U.S.
Comple e 2.81***
(0.54)
0.75***
(0.12)
0.33
(0.20)
-3.71***
(0.58) 0.67
No dummy 3.34***
(0.20)
0.90***
(0.06)
0.16
(0.11) - 0.50
Be o e IT 4.13***
(0.21)
0.84***
(0.06)
0.26**
(0.11) - 0.55
A e IT 0.83***
(0.14)
0.14**
(0.07)
0.15*
(0.09) - 0.18
U.K.
Comple e 10.40***
(1.51)
0.23
(0.25)
0.17
(0.10)
-7.56***
(1.16) 0.64
No dummy 4.22***
(0.31)
1.08***
(0.16)
0.04
(0.12) - 0.24
Be o e IT 9.67***
(0.59)
0.69***
(0.17)
0.34*
(0.18) - 0.54
A e IT 3.52***
(0.25)
-0.00
(0.17)
0.08
(0.09) -0.00
(0.73)
Canada
Comple e 5.24***
(0.74)
0.62***
(0.13)
0.41**
(0.17)
-3.29***
(0.67) 0.68
No dummy 4.77***
(0.20)
0.89***
(0.07)
0.32***
(0.12) - 0.45
Be o e IT 6.97***
(0.26)
0.68***
(0.06)
0.52***
(0.14) - 0.53
A e IT 2.73***
(0.17)
-0.30**
(0.12)
0.42***
(0.11) - 0.13
Japan
Comple e 0.38***
(0.07)
0.07**
(0.03)
0.02
(0.03)
-0.34***
(0.09) 0.44
No dummy 0.20***
(0.06)
-0.01
(0.03)
0.02
(0.02) - 0.01
Be o e IT 0.66***
(0.14)
0.14**
(0.06)
-0.00
(0.02) - 0.14
A e IT 0.12***
(0.02)
0.04***
(0.01)
0.01
(0.00) - 0.19
Eu o A ea
Comple e 3.81***
(0.49)
0.25
(0.29)
0.18
(0.16)
-2.78***
(0.36) 0.23
No dummy 1.71***
(0.18)
0.11
(0.12)
0.17*
(0.10) - 0.05
Be o e IT 4.68***
(0.11)
0.80***
(0.15)
0.21*
(0.12) - 0.85
A e IT 1.50***
(0.18)
0.14
(0.11)
0.19**
(0.09) - 0.08
No es: The da es be o e and a e IT co espond o a speci ic da e o each coun y. S anda d e o s a e epo ed
in pa en heses. As e isks deno e s a is ical signi icance a he 1% (*), 5% (**), and 10% (***) le els. S anda d
e o s we e calcula ed by using he HAC obus es ima o .