Peláez-He e os, Ósca
A icle
Unboxing Okun's ela ion be ween economic g ow h and
unemploymen a e: E idence om he Uni ed S a es,
1948-2024
Economies
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Sugges ed Ci a ion: Peláez-He e os, Ósca (2025) : Unboxing Okun's ela ion be ween economic
g ow h and unemploymen a e: E idence om he Uni ed S a es, 1948-2024, Economies, ISSN
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Academic Edi o : Adol o Maza
Recei ed: 13 Janua y 2025
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Accep ed: 12 Feb ua y 2025
Published: 20 Feb ua y 2025
Ci a ion: Peláez-He e os, Ó. (2025).
Unboxing Okun’s Rela ion Be ween
Economic G ow h and Unemploymen
Ra e: E idence om he Uni ed S a es,
1948–2024. Economies,13(3), 59.
h ps://doi.o g/10.3390/
economies13030059
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A icle
Unboxing Okun’s Rela ion Be ween Economic G ow h and
Unemploymen Ra e: E idence om he Uni ed S a es, 1948–2024
Ósca Peláez-He e os
Depa men o Economics, El Colegio de la F on e a No e, Tijuana 22560, Baja Cali o nia, Mexico;
[email p o ec ed]
Abs ac : We de elop he i s disagg ega ion o Okun’s law ha quan i ies all o he
in o ma ion ha is subsumed wi hin i s coe icien s. The p oposed me hod decomposes he
coe icien s in o he sum o he di ec e ec o he change in ou pu upon he unemploymen
a e, plus he indi ec e ec s o he a ia ions in he ou pu pe hou wo ked, he hou s
wo ked pe employed pe son, he pa icipa ion a e, and he size o he wo king-age
popula ion. Wi h qua e ly da a o he Uni ed S a es om 1948 o 2024, we ound ha
he alue o he in e cep in Okun’s ela ion is de e mined by he inc eases in wo king-age
popula ion and ou pu pe hou o wo k, along wi h he dec ease in he numbe o hou s
wo ked pe employed pe son, plus he g ow h o he pa icipa ion a e un il he 1990s
and i s subsequen decline. Fo i s pa , he slope, ha is, he alue o Okun’s coe icien ,
depends mainly upon he a ia ions in ou pu pe hou o wo k and he hou s pe employed
pe son. The o he ac o s we e sca cely ele an . Changes in hese componen s caused he
Okun’s ela ion o a y o e ime, showing a g ea e sensi i i y o he unemploymen a e
o a ia ions in p oduc ion since he 2008 c isis.
Keywo ds: Okun’s law; ac o decomposi ion; unemploymen a e; labo p oduc i i y;
hou s wo ked; pa icipa ion a e; wo king age popula ion
1. In oduc ion
Ea ly in he 1960s, A hu Okun desc ibed he ela ion be ween unemploymen and
economic g ow h as simply as possible. His pu pose was, indeed, o p o ide a “simple and
di ec ” o mula (Okun,1962, p. 2). The esul , which he ob ained by examining qua e ly
da a om he Uni ed S a es o he yea s 1947–1960, was ha “on he a e age, each ex a
pe cen age poin in he unemploymen a e abo e ou pe cen has been associa ed wi h
abou a h ee pe cen dec emen in eal GNP [g oss na ional p oduc ]” (Okun,1962, p. 2).
Thi lwall (1969) soon ga e he name “Okun’s law” o his ela ionship o in e change o
h ee pe cen o eal GNP o each addi ional pe cen age poin in he unemploymen a e.
Go don (1984, p. 539) a gues ha Okun’s law owes i s popula i y bo h o he s abili y
o ha ela ionship du ing he space o wo decades, and o he ac ha “i sho –ci cui s
he a he complex iden i y ha links ou pu and unemploymen ”. Simila ly, Ande on e al.
(2014, p. 6) no ed ha he “elegance and simplici y” o Okun’s app oach is an impo an
eason why Okun’s law is s ill a ecu en heme hal a cen u y a e i s i s o mula ion.
In ecen yea s, se e al au ho s ha e discussed he p ecision and empo al s abili y o
Okun’s ule o humb. Fo example, Ball e al. (2017, p. 1439) conclude ha Okun’s law “is
s ong and s able by he s anda ds o mac oeconomics”. Simila ly, Daly e al. (2017, p. 18)
ad ise us ha in he Uni ed S a es, “ he Okun coe icien is ela i ely s able o e ime”.
Howe e , Huang and Lin (2008) obse e ha a ixed coe icien may be inapp op ia e,
Economies 2025,13, 59 h ps://doi.o g/10.3390/economies13030059
Economies 2025,13, 59 2 o 21
and G an (2018) inds ha he coe icien changed a e he 1980s. O he au ho s who
ha e examined he empo al s abili y o Okun’s law include Aguia -Con a ia e al. (2020),
Ka lsson and Ös e holm (2020), and K üge and Neuga (2021). Also, some analyses o
Okun’s law compa e a ious coun ies (Fu ce i e al.,2020;Fon ana i e al.,2022;Po as-
A ena & Ma ín-Román,2023) o egions (Guisinge e al.,2018;Maza,2022;Po as-A ena
e al.,2024). In addi ion, he a ia ion in Okun’s coe icien has been analyzed acco ding o
he phase o he economic cycle (Nebo e al.,2019;Benos & S a akoudis,2022;Donay e,
2022) and he ype o shock ha p oduced each economic c isis (Ande on e al.,2014;
Gel e ,2020;Ziegenbein,2021).
In gene al, such in es iga ions o Okun’s law ha e modi ied i by including addi ional
o lagged a iables, o by using o he unc ional o ms and echniques o es ima ion. These
modi ica ions we e a emp s o imp o e i s o he cases ha we e s udied, bu ha e mo ed
away om he essence o Okun’s p oblem and do no ake ad an age o in o ma ion ha is
con ained in Okun’s o iginal o mula ion.
To unde s and his poin , please ecall ha Okun (1962) desc ibed he ela ion be-
ween he unemploymen a e and inc ease in p oduc ion ia “ educed o m” equa ions
(Mai esse,1984). Okun was awa e ha o he ac o s a ec his ela ion, bu assumed ha
he unemploymen a e is a sa is ac o y p oxy o hem. In he las pages o his 1962 a icle,
Okun a emp ed o sepa a e he e ec s o each ac o , bu desc ibed only hei in luence, in
hopes ha u u e ad ances in analy ical echniques and a ailabili y o da a would allow a
mo e sys ema ic s udy. Along hose lines, la e au ho s (e.g., Hamada & Ku osaka,1984;
Sögne & S iassny,2002;Ismihan,2016) a emp ed o disagg ega e Okun’s coe icien s in o
s uc u al pa ame e s ha comple e he ou pu –unemploymen ela ion. Howe e , he
esul s we e only app oxima e.
The p incipal con ibu ion o he p esen a icle is he de elopmen o a p ocedu e ha
disagg ega es he slope and in e cep o Okun’s law in o an exac sum o he di ec e ec o
a ia ions in p oduc ion upon he unemploymen a e, and he indi ec e ec s o a ia ions
in ou pu pe hou wo ked, hou s wo ked pe employed pe son, pa icipa ion a e, and
wo king-age popula ion. This p ocedu e eco e s he in o ma ion ha is implici in Okun’s
equa ion and quan i ies he con ibu ion o each ac o o he alue o Okun’s coe icien s.
The p esen a icle will limi i sel o he case o he Uni ed S a es du ing 1948–2024.
Howe e , he p oposed disagg ega ion enables in es iga o s o s udy how each ac o ’s
con ibu ion a ies wi h ime, as well as among coun ies and egions. This ma kedly
en iches he possibili ies o pe o ming sys ema ic mul i a ia e analyses based on Okun’s
law. An ini ial and much sho e e sion o his a icle, published as a le e (Peláez-
He e os,2025), only decomposes he slope o he Okun ela ionship om a di e en
concep ual basis. Tha ea lie e sion does no analyze he in e cep , no he in e se
ela ionship, no does i use qua e ly da a o olling eg essions; i only di ides he pe iod
1970–2021 in o wo subpe iods and no es ha he e a e di e ences be ween hem, bu i
does no analyze he e olu ion o he pa ame e s o e ime, which will be pe o med in he
ollowing pages.
The causes o geog aphic and empo al a ia ions in Okun’s coe icien s ha e been
analyzed p e iously by au ho s such as Blackley (1991), He wa z and Niebuh (2011), and
K aim e al. (2023). These au ho s used a wo-s ep analysis. Fi s , hey es ima ed Okun’s
coe icien s o he ime pe iods, coun ies, o egions ha we e being compa ed. Then, he
au ho s explained he di e ences ia c oss-sec ional o panel da a eg ession models. They
included eg esso a iables such as he indus ial s uc u e (Gonzalez-P ie o e al.,2018),
he pe cen age o public employmen (Bine & Facchini,2013;Fu ce i e al.,2020), o he
pe cen age o women and you hs in he employed popula ion (Maza,2022), among o he
a iables ha can a ec he Okun’s coe icien .
Economies 2025,13, 59 3 o 21
Those ea lie in es iga ions analyzed a wide ange o seconda y a iables. He e, we
analyze only hose which, by de ini ion, gene a e he alue o he coe icien s in Okun’s
law. Ou objec i e is o es ima e he Okun’s law coe icien s o he Uni ed S a es du ing
dis inc ime pe iods, so ha we can de e mine no only whe he he alues o hese
coe icien s a e s able o e ime, bu also iden i y, p ecisely, which in insic ac o s gi e ise
o hose alues and associa ed dynamics. Ou analyses include da a om qua e s ha
all wi hin he pe iod o he COVID-19 pandemic, so ha we may examine whe he he
associa ed a ia ion in p oduc ion a ec ed he employmen a e di e en ly du ing ha
ime, as has been indica ed by Ba isic and Ko ac (2022), and Po as-A ena e al. (2024). The
hypo hesis is ha he in ensi y and composi ion o he ela ion be ween economic g ow h
and unemploymen a e changed o e ime. The p oposed me hod allows us o de ec and
analyze he in insic causes o hese changes.
The s uc u e o his a icle is as ollows. Sec ion 2 e iews Okun’s app oach, including
i s bases and implica ions. Sec ion 3de elops he p ocedu e o decomposing he Okun’s
law coe icien s in o hei in insic ac o s. Sec ion 4shows he esul s o analyses o he
Uni ed S a es, a e which Sec ion 5p esen s conclusions.
2. The Essence o Okun’s P oposal
Okun (1962, p. 1) sough o answe he ques ion, “How much ou pu can he economy
p oduce unde condi ions o ull employmen ?” To ha end, he analyzed he ela ion
be ween a ia ions in p oduc ion and unemploymen . Al hough Okun ecognized ha
o he ac o s a ec his ela ion, o simplici y, he assumed he ollowing:
wha e e he in luence o slack economic ac i i y on a e age hou s, labo o ce
pa icipa ion, and manhou p oduc i i y, he magni udes o all hese e ec s a e
ela ed o he unemploymen a e. Wi h his assump ion, he unemploymen a e
can be iewed as a p oxy a iable o all he ways in which ou pu is a ec ed by
idle esou ces. (Okun,1962, p. 2)
This simpli ica ion allowed Okun o model he ela ion be ween he wo p incipal
a iables (p oduc ion and unemploymen ) as ollows:
∆U =α0+α1y +ε0(1)
whe e U
is he unemploymen a e o he yea , and Y
is he eal g oss domes ic p oduc
(GDP).
1
Thus,
∆
U
=U
−
U
−1
is he change in unemploymen a e be ween
−
1 and ,
and y
=
∆
Y
/Y
−1
is he pe cen age change in eal GDP. The symbols
α0
and
α1
a e model
pa ame e s, and ε0is he e o e m.
Okun (1962) es ima ed ha o 55 qua e ly a ia ions om 1947 o 1960,
α0
= 0.30 and
α1
=
−
0.30, wi h a co ela ion o = 0.79. Okun con i med hese esul s by analyzing he
same da a acco ding o wo o he models.
Okun’s second model explained he unemploymen a e by means o a cons an e m
(which ep esen s he na u al unemploymen a e) and he gap be ween obse ed and
po en ial ou pu . Okun (1962) ound ha he cons an e m was equal o 3.72, and he slope
o he model was 0.36. The la e alue indica ed ha an inc ease o 1% in he di e ence
be ween he eal and po en ial ou pu is associa ed wi h an inc ease o 0.36 poin s in he
unemploymen a e. Ball e al. (2017) explain ha his second model is mo e gene al han
he i s . When he na u al unemploymen a e is cons an and he po en ial ou pu g ows
a a cons an a e, his second model exp essed in di e ences yields Equa ion (1). The e o e,
Equa ion (1) assumes he cons ancy o hese elemen s.
The hi d model ela ed he loga i hm o he employmen a e o he loga i hm o
ou pu , a ime end, and a cons an . Okun (1962, p. 3) ound ha , depending upon he
Economies 2025,13, 59 4 o 21
selec ed ime pe iod, “ he es ima ed elas ici y coe icien an 0.35 o 0.40, sugges ing ha
each one pe cen age poin educ ion in unemploymen means sligh ly less han a 3 pe cen
inc emen in ou pu ”.
As Okun (1962, p. 3) no es, “The uni o mi y ha eme ged om hese a ious ech-
niques was he app oxima e 3– o–1 link be ween ou pu and he unemploymen a e”.
This h ee- o-one a io (Okun’s law) had a g ea impac upon na ional poli ics and eco-
nomics because i showed ha he link be ween he g ow h in p oduc ion and dec ease in
unemploymen was s onge han was commonly accep ed.
Okun (1962, p. 5) explains ha “ he simple addi ion o one pe cen o a gi en labo
o ce o he anks o he employed would inc ease employmen by only sligh ly mo e
han one pe cen : 100/100–Upe cen o be exac . I he wo kweek and p oduc i i y we e
unchanged, he inc emen o ou pu would be only ha one + pe cen . The h ee pe cen
esul implies ha conside able ou pu gains in a pe iod o ising u iliza ion a es s em
om some o all o he ollowing: induced inc eases in he size o he labo o ce; longe
a e age weekly hou s; and g ea e p oduc i i y”.
Okun cau ions ha he coe icien s o app oxima ely one- hi d ha de i e om his
models do no e lec a ce e is pa ibus ela ion be ween changes in ou pu and he un-
employmen a e. The ce e is pa ibus Okun coe icien o an unemploymen a e o ( o
example) 6% would be app oxima ely (1 + 0.06)
−1
= 0.94. As Okun was awa e, his coe -
icien s cap u e no only his di ec e ec , bu also he indi ec e ec s o o he a iables
ha do no appea explici ly in his model, bu do a ec
∆
U h ough hei co ela ions wi h
y. The alue o Okun’s coe icien ,
α1
, indica es he amoun by which
∆
Uwill change
o each uni change in y, when all o he implici a iables co-e ol e as hey did, on he
a e age, du ing he pe iod analyzed. In con as ,
α1
will change, and cease o be s able, i
he co ela ions be ween he implici a iables and ychange; o example, i he dec ease in
p oduc ion ha occu s du ing one ecession is due mo e o he educ ion in hou s wo ked,
han was he case du ing o he ecessions.2
The echnique ha will be de eloped in he nex sec ion allows an analysis o he
changes in he alues and con en o Okun’s coe icien s.
3. Analysis Techniques and Da a Sou ces
Okun p oposed Equa ion (1) in o de o summa ize as simply as possible he ela ion
be ween changes in ou pu and he unemploymen a e. Fo ha eason, Okun omi ed
some a iables ha a ec ha ela ion. Howe e , hese a iables a e known. Okun himsel
men ions hem, and Go don (1973)— o example—has used hem o de ine a comple e
ela ion be ween changes in ou pu and he employmen a e.
Go don’s mos ecen a emp along hose lines (Go don,2010a) decomposes he eal
GDP in o he p oduc o i e ac o s:
Y ≡Y
H
·H
E
·E
A
·A
N
·N (2)
whe e H
is he numbe o hou s wo ked du ing he pe iod ,E
is he numbe o wo ke s,
A
is he numbe o ac i e pe sons (employed and unemployed), and N
is he wo king-age
popula ion. Each a io has a speci ic in e p e a ion: Y
/H
ep esen s he ou pu pe hou
wo ked (p oduc i i y), H
/E
is he numbe o hou s wo ked pe employed pe son, E
/A
is he p opo ion o wo ke s in he ac i e popula ion ( he employmen a e), and A /N is
he p opo ion o ac i e pe sons in ha popula ion ( he pa icipa ion a e).
Go don (2010a) akes loga i hms in Equa ion (2), p oposes ha he endencies o he
a iables ha e he same s uc u al decomposi ion as he obse ed alues, and analyzes he
esponses o he componen s o a ia ions in he ou pu gap. Howe e , Go don (2010a)
Economies 2025,13, 59 5 o 21
does no di ec ly link changes in ou pu and he unemploymen a e, as Okun (1962)
had. Pe haps ha is why ew subsequen analyses ha e inco po a ed Go don’s (2010a)
me hodological app oach.
He e, we will show how Equa ion (2) can indeed be ans o med o ela e
∆
U o y, and
o exp ess Go don’s iden i y in e ms o Okun’s (1962) equa ions, hus allowing analys s o
decompose he coe icien s α0and α1. The ans o ma ion consis s o se e al s eps.
Fi s , he no a ion in Equa ion (2) is simpli ied by le ing Y
/H
=X
2
,H
/E
=X
3
,
E
/A
=L
,A
/N
=X
4
, and N
=X
5
. Then, we di ide Equa ion (2) by i sel , e alua ed a
−
1. (Fo example, he le -hand side becomes Y
/Y
−1
). A e his, we ake loga i hms
and eplace he loga i hm o each quo ien by he pe cen age change in he co esponding
a iable. Rea anging e ms, he esul is w i en as ollows:
y ∼
=l +
5
∑
j=2
xj (3)
whe e lowe -case le e s deno e pe cen age changes. Equa ion (3) indica es ha he pe -
cen age change in he eal GDP (y) is app oxima ely equal o he sum o he pe cen age
changes in he employmen a e (l), he ou pu pe hou wo ked (x
2
), he hou s wo ked
pe employed pe son (x
3
), he pa icipa ion a e (x
4
), and he wo king-age popula ion
(x
5
). This iden i y is no exac because he pe cen age changes ha e been app oxima ed by
loga i hms.
Because Equa ion (3) does no include he unemploymen a e explici ly, he nex s ep
in he ans o ma ion is o ecognize ha he unemploymen a e is he complemen o he
employmen a e: U
= 1
−
L
. The e o e, he ela ion be ween he a ia ions o hese wo
a es is
∆
U
=
−∆
L
. Using his esul , and ecognizing ha he pe cen age change in he
employmen a e is l
=
∆
L
/L
−1
, we see ha l
=
−∆
U
/L
−1
. Now, a e subs i u ing ha
exp ession in Equa ion (3) and sol ing o ∆U , we ob ain he ollowing:
∆U ∼
=L −1 −y +
5
∑
j=2
xj !(4)
Like Equa ion (1) (Okun’s i s di e ences model), Equa ion (4) ela es
∆
U o ydi ec ly,
bu also ela es
∆
U o all o he o he ac o s ha a ec ha ela ion. I we include hese
o he ac o s in Equa ion (1), we ob ain a ela ion ha is almos de e minis ic because
Equa ion (4) is an app oxima e iden i y. Conc e ely, i we es ima e he eg ession
∆U =β0+β1y +
5
∑
j=2
βjxj +ε1(5)
we would expec ha
β0≈
0,
β1≈ −
L
−1
, and
βj≈
L
−1
, wi h R
2≈
1. Thus, hese
pa ame e s a e p ac ically p ede e mined. Fo ha eason, Equa ion (5) p o ides li le
in o ma ion. Howe e , ha in o ma ion is impo an because i allows he analys o
es ima e he pa ame e s by o dina y leas squa es (OLS), hus a oiding he imp ecision
ha a ises in Ismihan’s (2016) decomposi ion o Okun’s coe icien .3
As he nex s ep, we ollow Johns on (1984, p. 260) o ex ac he in o ma ion ha is
a ailable ia Equa ion (5). Acco ding o he p ope ies o OLS es ima o s, he coe icien s
α0
and
α1
in Equa ion (1) (a educed- o m ela ion be ween
∆
Uand y) a e linked o he
pa ame e s in Equa ion (5) (an ex ended e sion) as ollows:
α0=β0+
5
∑
j=2
βjλj(6)
Economies 2025,13, 59 6 o 21
α1=β1+
5
∑
j=2
βjγj(7)
whe e
β0
h ough
β5
a e he pa ame e s in Equa ion (5), and
λj
and
γj
a e he pa ame e s
o he auxilia y eg essions:
xj =λj+γjy +εj(8)
The εj e ms a e e o e ms, and j= 2, . . ., 5.4
Kmen a (1997, p. 443) explains ha hese auxilia y eg essions a e no eg ession
equa ions in he usual sense; ins ead, hey a e used as an a i ice o acili a e in e p e a ion.
Ismihan (2016, p. 182) in e p e s hese auxilia y pa ame e s wi hin he amewo k o Okun’s
law, poin ing ou ha
γj
“ ep esen he e ec o a one–pe cen age–poin change in ou pu
g ow h on [x
j
]”, while
λj
“ ep esen he g ow h a e o [X
j
] independen o he g ow h a e
o ou pu demand”. These e ec s a e implici in Okun’s educed- o m equa ion, as Go don
(1984) and P achowny (1993) ecognized.
I should be poin ed ou ha Go don (1984) used simila auxilia y equa ions o explain
he employmen a e ( a he han he unemploymen a e) as a unc ion o ou pu . Daly
e al. (2017), o hei pa , disagg ega ed Okun’s coe icien o he in e se ela ion by
decomposing he co a iance h ough he use o accoun ing iden i ies. Kau man (1988)
decomposed he elas ici y o he employmen a e wi h espec o eal p oduc ion (i.e., he
coe icien in Okun’s hi d model). And, om he pe spec i e o p oduc ion unc ions,
P achowny (1993) as well as Huang and Lin (2006,2008) disagg ega ed Okun’s coe icien ,
bu did no speci y comple ely he ela ionship be ween g ow h and unemploymen .
5
O he pa ial disagg ega ions o Okun’s coe icien we e de i ed by Fa e eau and Mouilla
(1981), Hamada and Ku osaka (1984), and Sögne and S iassny (2002). The mos comple e
disagg ega ion was ha o Ismihan (2016).
Equa ions (6) and (7) comple ely disagg ega e he in e cep and slope o Equa ion (1).
Speci ically, Equa ion (7) decomposes he o iginal Okun coe icien , α1, in o he ollowing:
•
The di ec e ec o yupon
∆
U. This e ec is cap u ed by he coe icien
β1
, which is
in e p e ed in ce e is pa ibus e ms because i no longe includes o he in luences.
•
The indi ec e ec o o he ac o s (no made explici in Equa ion (1)) whose a ia ions
a ec ∆U ia y. These ac o s a e as ollows:
# he ou pu pe hou o wo k, β2γ2;
# he hou s wo ked pe employed pe son, β3γ3;
# he pa icipa ion a e, β4γ4;
#and he wo king-age popula ion, β5γ5.
The decomposi ion o he in e cep ,
α0
, is analogous o ha o Okun’s coe icien :
Equa ion (6) disagg ega es he cons an con ibu ion o each ac o o ∆U.
Al e na i ely, he pa ame e s in Equa ion (1) end o be es ima ed ia he in e sion
o causali y. Okun (1962) es ima ed his equa ions wi h unemploymen as he dependen
a iable, al hough he in e p e ed he ecip ocals o he coe icien s o explain he e olu ion
o GDP as a unc ion o unemploymen . The de ail is ha Equa ion (1) is “a educed– o m
ela ionship be ween wo endogenous a iables” (Ball e al.,2017, p. 1416), and he cause–
e ec ela ionship o be speci ied depends on he ques ion o be answe ed. The e o e, i is
also possible o w i e
y =α′
0+α′
1∆U +ε′
0(9)
In his case, he equa ion ha includes all o he ac o s is
y =β′
0+β′
1∆U +
5
∑
j=2
β′
jxj +ε′
1(10)
Economies 2025,13, 59 7 o 21
F om Equa ion (4), i would be expec ed ha he pa ame e s in Equa ion (10) ake he
alues β′0≈0, β′1≈ −1/L −1,β′j≈1, and R2≈1.
The pa ame e
β′1
indica es he pe cen age inc ease in p oduc ion ha occu s when
he unemploymen a e alls by one pe cen age poin , ce e is pa ibus. This is because he
alue o L
−1
ends o be abou 0.94,
β′1≈ −
1.06, which is he igu e posi ed by Okun (1962,
p. 5): “sligh ly mo e han one pe cen : 100/100–Upe cen o be exac [
. . .
] he inc emen
o ou pu would be only ha 1 + pe cen ”. Mo eo e , his case is no suscep ible o he
c i icism ha a ious au ho s (Plosse & Schwe ,1979;Ba e o & Howland,1993) di ec ed
a he way in which Okun (1962) in e p e ed he ecip ocals o his es ima ions. Speci ically,
because
β1β′1≈
1 in he ex ended equa ions, he ecip ocal o
β1
e ec i ely app oaches
β′1
.
In con as , 1/
α1=α′1
in Okun’s equa ions, because
2=
1, as Okun himsel no ed in he
“gene al discussion” o Pe y (1971, p. 578).
The ela ion be ween he coe icien s in Equa ions (9) and (10) can be unde s ood by
ollowing he same logic as was desc ibed ea lie o Equa ions (1) and (5). The in e cep
and slope a e disagg ega ed in o he coe icien o he pu e di ec ela ion, plus he indi ec
e ec s o he a iables ha a e no speci ied:
α′
0=β′
0+
5
∑
j=2
β′
jλ′
j(11)
α′
1=β′
1+
5
∑
j=2
β′
jγ′
j(12)
The auxilia y eg essions a e as ollows:
xj =λ′
j+γ′
j∆U +ε′
j(13)
In his case, because
β′0≈
0 and
β′j≈
1, he
α′0
and
α′1
in Equa ions (11) and (12) can
be app oxima ed as
α′
0≈
5
∑
j=2
λ′
j(14)
α′
1≈β′
1+
5
∑
j=2
γ′
j(15)
Nex , we apply he esul ing equa ions o a da a se ha is basically he same as used
by Go don (2010b), bu upda ed o include he la es a ailable igu es. Da a o eal GDP
o he Uni ed S a es a e om he Bu eau o Economic Analysis (BEA,2024), and span he
pe iod om he i s qua e o 1947 o he i s qua e o 2024 (1947Q1–2024Q1). Values
o H
,E
,A
and N
a e om he Bu eau o Labo S a is ics (BLS,2024) o he pe iod
1948Q1 o 2024Q1.
6
This da a se limi s he analysis o 1948Q1–2024Q1, o which a o al o
305 qua e ly obse a ions a e a ailable o each a iable.
These da a allow us o calcula e he a ios ha appea in Equa ion (2), as well as he
unemploymen a es and hei changes, plus he pe cen age changes o he a ios, Y
, and
N
, as can be seen in he Supplemen a y Ma e ials. We did no use qua e ly a ia ions;
ins ead, we ollowed Zanin and Ma a (2012, p. 97) and used in e annual a ia ions “in
o de o educe he a iabili y and au oco ela ion in he da a”. F om he 301 in e annual
a ia ions ha we e a ailable o each se ies, we calcula ed Reg essions (1), (5), and (8),
which p o ide coe icien s o pe o ming he disagg ega ions in Equa ions (6) and (7).
Simila ly, we calcula ed Reg essions (9), (10), and (13) (which a e o he in e se ela ion) in
o de o pe o m he disagg ega ions ha a e p oposed in Equa ions (11) and (12).
Economies 2025,13, 59 8 o 21
We calcula ed he es ima es o he en i e 1948Q1–2024Q1 pe iod and a ious sub-
pe iods, as well as ia olling eg essions. Fo he la e , we ollowed Kno ek (2007) in
using a window size o 13 yea s. This size ensu ed ha each eg ession con ained a leas
one ecession, as was also he case o he analyses published by Owyang and Sekhposyan
(2012) and Mussida and Zanin (2023). The i s o he olling eg essions was o he
window o 52 in e annual a ia ions om 1949Q1 o 1961Q4—p ac ically he same pe iod
ha Okun ea ed in his seminal 1962 a icle. The second eg ession omi ed he 1949Q1
a ia ions and added hose o 1962Q1. This pa e n o ad ancing he window one qua e
a a ime con inued un il he las eg ession, which ea ed he a ia ions om 2011Q2 o
2024Q1. In he sec ion ha ollows, he es ima es o each window a e associa ed wi h he
las da e o each window. In o al, we es ima ed 250 olling eg essions o he p incipal and
auxilia y equa ions. F om hese esul s, i was possible o disce n how he alues o Okun’s
coe icien s and hei componen s e ol ed h ough ime, and hus o no e he changes ha
ha e occu ed o e he las 76 yea s.
4. Resul s and Discussion
4.1. Co ela ions and E olu ions
The s onges co ela ion was he one be ween yand
∆
U(=
−
0.789; Table 1). These
a e he only wo a iables ha Okun (1962) speci ied in his models. The second s onges
(=
−
0.501) was be ween
∆
Uand he hou s wo ked pe employed pe son (x
3
). These
esul s indica e ha al hough he a iables sha e a common e olu ion, hey also p o ide
di e en ia ed in o ma ion.
Table 1. Coe icien s o he co ela ion among a iables in Equa ion (5) du ing 1948Q1–2024Q1.
Change in he
Unemploymen Ra e
∆U
Pe cen age Change
Real
GDP
y
Ou pu pe
Hou Wo ked
x2
Hou s Wo ked pe
Employed Pe son
x3
Pa icipa ion
Ra e
x4
Wo king-Age
Popula ion
x5
y−0.789 1
x20.171 0.291 1
x3−0.501 0.455 −0.471 1
x4−0.371 0.279 −0.452 0.192 1
x50.083 0.030 −0.163 −0.099 0.236 1
Sou ce: p epa ed by au ho s wi h da a om BEA (2024) and BLS (2024).
Figu e 1shows he e olu ion o he six a iables ha a e in ol ed in he ela ion
be ween ou pu and unemploymen a e. All six o hese a y, bu a ound dis inc le els
and wi h dis inc ampli udes. The a ia ions in unemploymen a e and pa icipa ion
a e oscilla e a ound 0, as would be expec ed because nei he can inc ease o dec ease
inde ini ely: bo h a es a e bounded by 0 and 1. Fo bo h a iables, he posi i e changes
end o be compensa ed by he nega i e ones.
The same is no ue o he o he a iables. Fo he GDP, p oduc i i y, and wo king-age
popula ion, he posi i e a ia ions ou weigh he nega i e ones. The e o e, all h ee ac o s
inc eased o e he long un. This beha io is e lec ed in he ac ha he alues o hese
a iables luc ua ed a ound posi i e numbe s (3.1%, 1.8%, and 1.3%, espec i ely). Fo ha
eason, hese a iables con ibu ed o making he Okun equa ion’s in e cep posi i e, as we
will see in he nex sec ion. Howe e , he ou pu pe hou wo ked also has an impo an
impac on he slope due o i s wide a ia ion a ound i s a e age.
Economies 2025,13, 59 15 o 21
0.583 in 1974Q4. Since hen,
β2γ2
has dec eased, becoming nega i e as a esul o he 2008
c isis, and eaching i s his o ic minimum o
−
0.542 in 2022Q2 a e alling ab up ly du ing
he COVID-19 pandemic. In he mos ecen decades, educ ions in p oduc ion co espond
o inc eases in p oduc i i y, which has now become coun e -cyclical. Fo ha eason, a
la ge pa o he adjus men is achie ed ia he unemploymen a e, and he absolu e
alue o Okun’s coe icien is g ea e . In ac , he
α1
coe icien s o pe iods ha include
qua e s du ing which COVID-19 was mos widesp ead a e almos equal o he di ec e ec
β1
. Fo such pe iods, he indi ec e ec s
βjγj
compensa ed each o he . Conc e ely, he e ec
o he a ia ion in ou pu pe hou o wo k (
β2γ2
) compensa ed o he a ia ions in he
pa icipa ion a e (β4γ4) and he hou s wo ked pe employed pe son (β3γ3).
Economies 2025, 13, x FOR PEER REVIEW 17 o 23
he p oduc i e dynamic and he labo ma ke was dis inc ; compa ed o ea lie c isis pe-
iods, he a es o unemploymen and pa icipa ion o e eac ed. Howe e , ha a ypical
pe iod should no cause us o o e look he changes ha ook place du ing p e ious dec-
ades. In 2001Q2, he absolu e alue o he Okun coe icien o he olling eg essions
eached a minimum o 0.289. The coe icien hen emained s able o a ew yea s be o e
beginning o ise sha ply a e he 2008 c isis. In 2020Q1, jus be o e he eme gence o
COVID-19, he coe icien had al eady eached −0.637.
The in e cep (which ep esen s he long- e m e ec o all o he o he ac o s) ook
posi i e alues be ween i s minimum o 0.827 (2001Q2; Figu e 4) and i s maximum o
1.687 (1962Q1). The elemen s ha con ibu ed o inc easing he in e cep we e he a ia-
ions in wo king-age popula ion, he ou pu pe hou o wo k, and (un il 1995Q2) he pa -
icipa ion a e. The alue o he in e cep was dec eased by a ia ions in he pa icipa ion
a e (a e 1995Q3) and he hou s wo ked pe employed pe son.
Figu e 4. Values o he in e cep and i s componen ac o s: olling eg ession es ima es. No es: α
0
is
he in e cep om Equa ion (1), β
0
is he di ec e ec , and he β
j
λ
j
a e he indi ec e ec s h ough he
a ia ions in ou pu pe hou o wo k (β
2
λ
2
), hou s wo ked pe employed pe son (β
3
λ
3
), he pa ici-
pa ion a e (β
4
λ
4
), and he wo king-age popula ion (β
5
λ
5
). The sum o hese i e ac o s is exac ly
equal o α
0
.
Figu e 4 e eals ha hese ac o s did no emain s able. Ins ead, he e ec s o hei
in ensi ies changed, hus causing a endency o he in e cep o dec ease om 1.5 du ing
he i s decades o alues nea e o 1 in he ecen ones. Es ima es om he olling eg es-
sions show ha du ing he c ises o 2008 and 2020, he in e cep ose again o 1.5. How-
e e , hese inc eases could be due o he ac ha we a e con ounding pa o he cycle
wi h he end, because each eg ession co e s only 52 qua e s. In ha ega d, i should
be no ed ha Huang and Lin (2008), as well as o he eg essions ha used longe pe iods,
such as hose in Table 2, also show an e olu ion owa ds a dec easing in e cep .
The key ac o in his dynamic was he slowe g ow h o he wo king-age popula ion.
The impac o ha ac o was s eng hened by he decline in he pa icipa ion a e, bu
compensa ed by he posi i e (and ising) con ibu ion o he ou pu pe hou o wo k. The
Figu e 4. Values o he in e cep and i s componen ac o s: olling eg ession es ima es. No es:
α0
is
he in e cep om Equa ion (1),
β0
is he di ec e ec , and he
βjλj
a e he indi ec e ec s h ough
he a ia ions in ou pu pe hou o wo k (
β2λ2
), hou s wo ked pe employed pe son (
β3λ3
), he
pa icipa ion a e (
β4λ4
), and he wo king-age popula ion (
β5λ5
). The sum o hese i e ac o s is
exac ly equal o α0.
The alue o
β3γ3
was qui e s able (be ween 0.119 and 0.288) un il 2007, when i began
a p og essi e ise, eaching a maximum o 0.454 in 2019Q2. Tha inc ease compensa ed
in pa o he e olu ion in he p oduc ion pe hou o wo k. The qua e s o he COVID-
19 pandemic, du ing which he decline in ou pu mainly a ec ed unemploymen and
pa icipa ion a es, educed he con ibu ion o his ac o o 0.270 in 2024Q1.
The a ia ion in he pa icipa ion a e had li le e ec un il he end o he 1970s,
a e which i became ano he p o-cyclical p oduc ion–adjus men mechanism. The p e-
dominance o he discou aged wo ke e ec o e he added wo ke e ec mean ha he
a ia ions in he pa icipa ion a e le less oom o adjus men ia he unemploymen
a e (Lee & Pa asnis,2014). In imes o economic c isis, some po en ial wo ke s d opped
ou o he labo ma ke a he han emain unemployed. The COVID-19 pandemic was an
ex eme case, in which he impossibili y o seeking wo k made many people inac i e. The
e ec o his ac o (
β4γ4
) upon he Okun coe icien ose om 0.042 in 2020Q1 o 0.138 in
2020Q2, hen ose u he o 0.250 in 2024Q1.
Economies 2025,13, 59 16 o 21
As poin ed ou p e iously by Ba isic and Ko ac (2022) and Po as-A ena e al. (2024),
es ima es o Okun’s coe icien s change subs an ially when he analyses include qua e s in
which p oduc ion ell because o COVID-19. Du ing he pandemic, he ela ion be ween he
p oduc i e dynamic and he labo ma ke was dis inc ; compa ed o ea lie c isis pe iods,
he a es o unemploymen and pa icipa ion o e eac ed. Howe e , ha a ypical pe iod
should no cause us o o e look he changes ha ook place du ing p e ious decades. In
2001Q2, he absolu e alue o he Okun coe icien o he olling eg essions eached a
minimum o 0.289. The coe icien hen emained s able o a ew yea s be o e beginning o
ise sha ply a e he 2008 c isis. In 2020Q1, jus be o e he eme gence o COVID-19, he
coe icien had al eady eached −0.637.
The in e cep (which ep esen s he long- e m e ec o all o he o he ac o s) ook
posi i e alues be ween i s minimum o 0.827 (2001Q2; Figu e 4) and i s maximum o 1.687
(1962Q1). The elemen s ha con ibu ed o inc easing he in e cep we e he a ia ions in
wo king-age popula ion, he ou pu pe hou o wo k, and (un il 1995Q2) he pa icipa ion
a e. The alue o he in e cep was dec eased by a ia ions in he pa icipa ion a e (a e
1995Q3) and he hou s wo ked pe employed pe son.
Figu e 4 e eals ha hese ac o s did no emain s able. Ins ead, he e ec s o hei
in ensi ies changed, hus causing a endency o he in e cep o dec ease om 1.5 du ing he
i s decades o alues nea e o 1 in he ecen ones. Es ima es om he olling eg essions
show ha du ing he c ises o 2008 and 2020, he in e cep ose again o 1.5. Howe e , hese
inc eases could be due o he ac ha we a e con ounding pa o he cycle wi h he end,
because each eg ession co e s only 52 qua e s. In ha ega d, i should be no ed ha
Huang and Lin (2008), as well as o he eg essions ha used longe pe iods, such as hose
in Table 2, also show an e olu ion owa ds a dec easing in e cep .
The key ac o in his dynamic was he slowe g ow h o he wo king-age popula ion.
The impac o ha ac o was s eng hened by he decline in he pa icipa ion a e, bu
compensa ed by he posi i e (and ising) con ibu ion o he ou pu pe hou o wo k.
The con ibu ion o he change in wo king-age popula ion o he alue o he in e cep
inc eased ( eaching a maximum o 1.939 in 1974Q3) as he baby-boom gene a ion en e ed
he wo k o ce, bu hen dec eased slowly un il he beginning o he 1980s, a e which i
ell mo e apidly o abou 1 du ing 1995–2010. I has con inued o all du ing ecen yea s,
eaching 0.784 in 2024Q1.
Simila dynamics, bu weake ones, can be seen in he e ec o he pa icipa ion a e
(
β4λ4
). I s alue inc eased du ing he i s yea s, eaching a maximum o 0.616 in 1974Q3.
I hen en e ed a decline ha has las ed o he p esen . I has been nega i e since 1995Q3,
and ell o i s minimum o −0.930 in 2022Q3.
The numbe o hou s wo ked pe employed pe son declined h oughou 1948Q1–
2024Q1. The e o e, he con ibu ion o his ac o o he in e cep ’s alue is nega i e. Un il
1982, and om 2006 o 2020,
β3λ3
was close o
−
1, while he es o he ime i was nea e
o −0.5.
In con as , he ou pu pe hou o wo k ended o inc ease. The e o e,
β2λ2
made a
posi i e con ibu ion o he alue o he in e cep . Un il 1967Q2, and a e 2002Q1,
β2λ2
was g ea e han 1. Howe e , i was nea ze o du ing he pe iod 1971Q3–1991Q1, which
coincides wi h he yea s when he con ibu ions o pa icipa ion a e and wo king-age
popula ion we e g ea es .
5. Conclusions
Okun (1962) summa ized he ela ion be ween economic g ow h and he labo ma ke
in a single numbe : he a io o exchange be ween eal GNP and he unemploymen a e. In
doing so, Okun no ed ha his coe icien subsumes he e ec s o o he a iables ha a e no
Economies 2025,13, 59 17 o 21
explici in his model, bu do a ec he ou pu –unemploymen ela ion. Se e al subsequen
in es iga ions a emp ed o eco e in o ma ion abou e ec s o hose o he a iables in
o de o o e a mo e comple e in e p e a ion o he ela ion, bu did so only app oxima ely.
The disagg ega ion p oposed in he p esen a icle allows economis s o iden i y all
o he ac o s ha a ec Okun’s ela ion, and o quan i y hei e ec s wi h p ecision. This
is achie ed by unpacking he con en s o Okun’s ela ion, speci ically he s uc u e o
long- e m g ow h and i s cyclical a ia ions. By applying his me hod o he case o he
Uni ed S a es du ing he pe iod 1948Q1–2024Q1, we ound ha he alue o he in e cep
in Okun’s ela ion is de e mined by he inc eases in wo king-age popula ion and ou pu
pe hou o wo k, along wi h he dec ease in he numbe o hou s wo ked pe employed
pe son, plus he g ow h o he pa icipa ion a e un il he 1990s and i s subsequen decline.
Fo i s pa , he alue o Okun’s coe icien depends mainly upon he a ia ions in ou pu
pe hou o wo k and he hou s pe employed pe son, which oge he educe by hal he
di ec e ec o he a ia ion in p oduc ion upon he unemploymen a e. The ou pu pe
hou o wo k had he g ea es impac du ing he i s decades o he analyzed pe iod, while
hou s pe employed pe son we e mo e impo an in ecen decades. The o he ac o s we e
sca cely ele an .
Changes in he abo e-men ioned componen s caused Okun’s ela ion o a y o e
ime: he in e cep ended o dec ease, and he slope inc eased. These ends indica e a
g ea e sensi i i y o he unemploymen a e o a ia ions in p oduc ion, e en be o e he
COVID-19 pandemic. Compa ed o hei beha io du ing p e ious economic c ises, he
pos -2020Q2 a es o unemploymen and pa icipa ion eac ed mo e s ongly o adjus men s
in p oduc ion.
In essence, he e olu ion o Okun’s coe icien ha we epo he e is simila o ha
desc ibed by Huang and Lin (2008), G an (2018), and Aguia -Con a ia e al. (2020), e en
hough hose esea che s used o he es ima ion echniques. In his a icle, we ha e p o ided
he in e - ela ions and dynamics o all o he ac o s ha con ibu e o ha e olu ion, he eby
ma kedly en iching he possibili ies o pe o ming sys ema ic mul i a ia e analyses o he
bases o Okun’s law.
Among he limi a ions o he analysis de eloped, i can be men ioned ha he mos
ecen da a a e s ill p elimina y and could change. In addi ion, we ha e only used a window
size o 13 yea s in he olling eg essions. O he window sizes would yield somewha
di e en esul s. Mo eo e , he disagg ega ion o he coe icien s has only been o mula ed
o Okun’s i s di e ences model. Ismihan (2016) ex ends his app oach o he gap e sion,
so a simila adap a ion could be a emp ed.
O he u u e wo k could include in eg a ing his a icle’s decomposi ions in o o he
de elopmen s ha ha e been aking place, such as he di e en ia ed analysis o expansi e
and ecessi e phases o p oduc ion, plus compa isons among coun ies and egions.
Supplemen a y Ma e ials: The ollowing supplemen a y ma e ial con ains he da ase used o
analysis in his manusc ip : h ps://www.mdpi.com/a icle/10.3390/economies13030059/s1.
Funding: This esea ch ecei ed no ex e nal unding.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : The a icle uses publicly a ailable da a. The sou ces and da a a e
de ined in Sec ion 3.
Con lic s o In e es : The au ho decla es no con lic s o in e es .
Economies 2025,13, 59 18 o 21
Abb e ia ions
The ollowing abb e ia ions a e used in his manusc ip :
BEA Bu eau o Economic Analysis
BLS Bu eau o Labo S a is ics
GDP G oss domes ic p oduc
GNP G oss na ional p oduc
OLS O dina y leas squa es
Appendix A
Table A1. Es ima ions o Equa ion (5) o a ious ime pe iods.
Pe iod β0β1β2β3β4β5R2
1948Q1–2024Q1 −0.013
(0.012)
−0.898
(0.003) ***
0.907
(0.004) ***
0.912
(0.006) ***
0.920
(0.009) ***
0.913
(0.009) *** 0.998
1948Q1–2001Q2 −0.005
(0.017)
−0.902
(0.005) ***
0.911
(0.007) ***
0.916
(0.009) ***
0.914
(0.012) ***
0.914
(0.011) *** 0.997
2001Q3–2020Q1 0.009
(0.015)
−0.920
(0.005) ***
0.911
(0.006) ***
0.927
(0.010) ***
0.936
(0.010) ***
0.932
(0.014) *** 0.999
2001Q3–2024Q1 −0.002
(0.029)
−0.896
(0.007) ***
0.906
(0.009) ***
0.910
(0.017) ***
0.925
(0.020) ***
0.893
(0.026) *** 0.999
No es: s anda d e o s a e in pa en hesis. *** deno es s a is ical signi icance a he 0.1% le el. Sou ce: p epa ed by
au ho s wi h da a om BEA (2024) and BLS (2024).
Table A2. Es ima ions o Equa ion (8) o a ious ime pe iods.
Equa ion x2 =λ2+γ2∆U +ε2Equa ion x3 =λ3+γ3∆U +ε3
Pe iod λ2γ2 2λ3γ3 2
1948Q1–2024Q1 1.1365
(0.1752) ***
0.2246
(0.0427) *** 0.085 −0.7870
(0.1025) ***
0.2205
(0.0250) *** 0.207
1948Q1–2001Q2 0.6535
(0.2068) **
0.3757
(0.0459) 0.244 −0.8275
(0.1470) ***
0.2056
(0.0326) *** 0.160
2001Q3–2020Q1 1.6034
(0.2466) ***
−0.1121
(0.0957) *** 0.018 −0.9277
(0.1200) ***
0.4156
(0.0466) *** 0.522
2001Q3–2024Q1 2.2554
(0.2592) ***
−0.3813
(0.0869) *** 0.178 −0.8324
(0.0949) ***
0.3470
(0.0318) *** 0.572
Equa ion x4 =λ4+γ4∆U +ε4Equa ion x5 =λ5+γ5∆U +ε5
Pe iod λ4γ4 2λ5γ5 2
1948Q1–2024Q1 −0.1470
(0.0607) *
0.0744
(0.0148) *** 0.078 1.2583
(0.0445) ***
0.0056
(0.0108) 0.001
1948Q1–2001Q2 0.1838
(0.0690) **
0.0180
(0.0153) 0.007 1.4807
(0.0583) ***
−0.0222
(0.0129) 0.014
2001Q3–2020Q1 −0.4157
(0.0906) ***
0.0496
(0.0352) 0.027 0.9611
(0.0544) ***
0.0374
(0.0211) 0.041
2001Q3–2024Q1 −0.6757
(0.0993) ***
0.1865
(0.0333) *** 0.261 0.9536
(0.0454) ***
0.0162
(0.0152) 0.012
No es: s anda d e o s a e in pa en hesis. The symbols *, **, and *** deno e s a is ical signi icance a he 5%, 1%,
and 0.1% le els, espec i ely. Sou ce: p epa ed by au ho s wi h da a om BEA (2024) and BLS (2024).
No es
1Okun (1962) used he GNP, bu he GDP has been used in hese analyses since he 1990s (Palley,1993;Guisinge e al.,2018).
2
Simila easoning applies o compa isons among coun ies. Fo example, in Japan, he changes in ou pu a e ela ed mo e closely
o changes in ou pu pe hou and o hou s wo ked pe employed pe son, han o he e olu ion in he unemploymen a e
Economies 2025,13, 59 19 o 21
(Hamada & Ku osaka,1984;Ismihan,2016). The e e se is ue in he Uni ed S a es. Fo ha eason, Japan’s Okun coe icien is
di e en om ha o he US. Speci ically, he absolu e alue o Japan’s coe icien is smalle (Ball e al.,2019;Fu ce i e al.,2020;
Fon ana i e al.,2022).
3
Ismihan (2016) does no es ima e he pa ame e s
β1
h ough
β5
ia eg ession, as in Equa ion (5). Ins ead, Ismihan assigns hese
pa ame e s “ he a e age alue o he employmen a e o e he ime pe iod unde conside a ion” (p. 179). In his way, Ismihan
ob ains a decomposi ion o Okun’s coe icien ha is e y app oxima e, a he han exac .
4
Equa ions (6) and (7) can be de i ed by subs i u ing Equa ion (8) in Equa ion (5), eo de ing he e ms, and compa ing he
in e cep and slope o hose in Equa ion (1).
5
P achowny (1993, p. 332) explains ha “Okun’s coe icien o h ee is de i ed om a complica ed weigh ed sum o all o he
changes”. Simila ly, ou Equa ion (12) disagg ega es Okun’s coe icien (in he ela ion y= (
∆
U)) in o a “weigh ed sum o all
o he changes”.
6
Speci ically, he BEA (2024) da a co espond o he GDP se ies in chained millions o dolla s (2017), seasonally adjus ed a annual
a es. The se ies ob ained om BLS (2024) we e as ollows: LNU02033120Q o H
/E
, LNS12000000Q o E
, LNS11000000Q o
A , and LNU00000000Q o N .
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