Vechsu uck, Tanadej
A icle
A global ace o he bo om: The neo-Goodwinian
agg ega i e-sys ems es ima ion o income dis ibu ion
and capaci y u iliza ion in e ac ions
PSL Qua e ly Re iew
P o ided in Coope a ion wi h:
Associazione Economia ci ile, Rome
Sugges ed Ci a ion: Vechsu uck, Tanadej (2024) : A global ace o he bo om: The neo-Goodwinian
agg ega i e-sys ems es ima ion o income dis ibu ion and capaci y u iliza ion in e ac ions, PSL
Qua e ly Re iew, ISSN 2037-3643, Associazione Economia ci ile, Rome, Vol. 77, Iss. 308, pp. 59-87,
h ps://doi.o g/10.13133/2037-3643/18186
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ol. 77 n. 308 (Ma ch 2024)
A global ace o he bo om: The neo-Goodwinian
agg ega i e-sys ems es ima ion o income dis ibu ion
and capaci y u iliza ion in e ac ions
TANADEJ VECHSURUCK*
Abs ac :
The neolibe al e o ms since he 1980s ha e esul ed in apid
globaliza ion pa alleled by wo sening income dis ibu ion. In
his pape , I i s show ha mos coun ies wo ldwide (58 o
81) ha e expe ienced a decline in he labo sha e o income, o
he wage sha e, du ing 1950-2019. Second, I es ima e he
demand and dis ibu i e egimes om 81-coun y panel da a
based on he neo-Goodwinian model. A he global le el, he
sho - un es ima ion shows ha he dis ibu i e egime
appea s o be Ma xian/p o i -squeeze and he demand egime
exhibi s p o i -led. I u he sepa a e he es ima ion in o wo
g oups: ad anced and de eloping coun ies. The es ima ion
s ill con i ms he p o i -led/p o i -squeeze egimes in bo h
g oups, e en hough he demand and dis ibu i e egimes a e
s onge in ad anced economies. In he long un, he esul s
e eal a global ace o he bo om: a decline in he long- un
wage sha e. Nei he posi i e no nega i e gain is ounded on
capaci y u iliza ion in ad anced and de eloping coun ies.
Uni e si y o Rhode Island, Kings on, USA,
email: echsu uck@u i.edu
How o ci e his a icle:
Vechsu uck T. (2024), “A global ace o he bo om: The neo-
Goodwinian agg ega i e-sys ems es ima ion o income
dis ibu ion and capaci y u iliza ion in e ac ions”, PSL
Qua e ly Re iew, 77 (308), pp. 59-87.
DOI: h ps://doi.o g/10.13133/2037-3643/18186
JEL codes:
C23, E12, E25, O47, O57
Keywo ds:
Panel analysis, pos -Keynesian, neo-Goodwinian model,
dis ibu i e-demand dynamics, globaliza ion
Jou nal homepage:
h p: //www.pslqua e ly e iew.in o
Income dis ibu ion has become one o he ho es economic opics in he pas ew decades
(A kinson, 2015; Galb ai h, 2012; Milano ic, 2005, and 2016). Pike y (2014) e i ed he in e es
in unc ional income dis ibu ion ( he sha es o income be ween labo and capi al)
1
among
mains eam economis s. Se e al schola s on bo h he mains eam and he he e odox sides,
including Pike y himsel , ound ha he labo sha e o income o he wage sha e has allen ac oss
he wo ld (UNCTAD, 2012; Ka aba bounis and Neiman, 2014; IMF, 2017; Dao e al., 2019; Suzuki
e al., 2019; Au o e al., 2020; Paul, 2020; S ansbu y and Summe s, 2020). This phenomenon
con as s wi h one o Kaldo ’s s ylized ac s (Kaldo , 1957), ha he sha e be ween labo and
capi al should be cons an ac oss ime. Al hough he main culp i o his labo sha e decline is s ill
* This pape is de eloped om he i s chap e o Vechsu uck (2018), he au ho ’s PhD disse a ion. The au ho wan s
o hank he managing edi o and wo anonymous e e ees o hei aluable commen s and sugges ions. The usual
disclaime applies.
1
Func ional income dis ibu ion is sepa a ed in o he income sha e o labo (labo sha e o wage sha e) and he income
sha e o capi al (capi al sha e o p o i sha e). The sum o bo h sha es is always 1 (o 100%). Fo ins ance, i he wage
sha e equals 60% (o 0.6), he p o i sha e is 40% (o 0.4). No e ha he wage sha e, he labo sha e, he labo income
sha e, and he labo sha e o income a e he same. All e ms will be used in e changeably in his pape .
A icles
60 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
inconclusi e, he possible d i e s include apid globaliza ion in ade and inance, au oma ion,
inancializa ion, and wel a e s a e e enchmen (Amsden and Hoe en, 1996; C o y e al., 1998;
Jayade , 2007; Ona an, 2009; Ona an and Galanis, 2012; S ockhamme , 2013).
The cha ac e is ics o dynamics be ween agg ega e demand and income dis ibu ion ha e
become one o he main esea ch ques ions in pos -Keynesian economics. In con as o
neoclassical economis s, pos -Keynesian economis s belie e ha a change in income dis ibu ion
impac s agg ega e demand. The neo-Goodwinian model (Ba bosa-Filho and Taylo , 2006), one o
he pos -Keynesian mac oeconomic business cycle models, conside s he economy o be
composed o wo egimes: he demand egime and he dis ibu i e egime. The demand egime
cap u es he causal e ec om income dis ibu ion o e ec i e demand. In a closed economy
wi hou a go e nmen , he demand egime is conside ed p o i -led
2
when a posi i e e ec o a
highe p o i sha e on in es men domina es he nega i e e ec o a highe p o i sha e on
consump ion. The opposi e case is called wage-led, when he posi i e e ec o a highe wage sha e
on consump ion is signi ican enough o o se he nega i e e ec o a highe wage sha e on
in es men . The dis ibu i e egime, on he o he hand, cap u es he causal e ec om e ec i e
demand o income dis ibu ion. The dis ibu i e egime could ac in wo main ways. I inc easing
economic ac i i y hu s he wage sha e, we say he dis ibu i e egime is wage-squeeze, o ced-
sa ing, o Kaldo ian.
3
Howe e , i highe demand, which usually causes lowe unemploymen , li s
he ba gaining powe o labo and leads o a ising wage sha e, he dis ibu i e egime is labeled
as p o i -squeeze o Ma xian.
In his pape , based on he neo-Goodwinian model, I examine he in e ac ions be ween income
dis ibu ion, in e ms o he wage sha e, and capaci y u iliza ion, in e ms o he ou pu gap, along
he lines o he agg ega i e-sys ems app oach (see below). To he au ho ’s knowledge, his is he
i s panel da a analysis o a neo-Goodwinian model ha examines bo h ad anced and de eloping
coun ies. The p ima y da ase is he la es Penn Wo ld Table (PWT) 10.0. I c ea ed an unbalanced
panel da ase o he wage sha e and ou pu gap o 81 coun ies (47 de eloping and 34 ad anced)
co e ing 1950-2019, o in es iga e he global dynamics o ou pu and dis ibu ion in he sho and
he long un. Fi s , compa ing he i s i e yea s and he las i e yea s o da a a ailable o each
coun y, I ind ha 58 o 81 coun ies expe ienced a decline in hei wage sha es. Second, I apply
he neo-Goodwinian amewo k o es he unbalanced panel da a.
Se e al ecen s udies elied on he con en ional Hod ick-P essco il e o ob ain he
po en ial ou pu and he ou pu gap. Howe e , he il e has been exposed o c i icism, as i may
c ea e spu ious cycles (Cogley and Nason, 1995) o o ce he long- e m ou pu gap o be ze o
(Blecke , 2016), uling ou he a ia ions in he ou pu gaps (see appendix B o mo e de ails on
he il e s). I he e o e use i e il e s o es ima e he po en ial ou pu and ob ain he ou pu gap:
he Hod ick-P essco (HP), he Bax e -King equency (band-pass), he mo ing a e age, he
Be e idge-Nelson (BN), and he Hamil on. Di e en il e s a e used o a oid selec ion bias and
ensu e he obus ness o he esul s. Using he panel da a econome ic eg ession based on he
s anda d seemingly un ela ed eg ession (SUR) model, I ind ha , in he sho un, he global
dis ibu i e egime is p o i -squeeze o Ma xis and he global demand egime is p o i -led. The
esul s a e obus ac oss di e en ou pu gaps. I also es ima e he panel and allow o coe icien s
2
The p o i -led/wage-led de ini ion was coined by Taylo (1991); he meaning is compa able o he e ms in Bhadu i
and Ma glin (1990), exhila a ionis /s agna ionis , espec i ely.
3
Kaldo (1956) hypo hesized ha an economy needs o shi dis ibu ion in a o o capi alis s du ing he booming
pe iod, so hey can ha e su icien unds o make in es men s in he ollowing pe iod. Ma x, on he o he hand,
emphasized he ole o he ese e a my o unemployed, which makes labo 's ba gaining powe , and hus he eal wage,
a y p ocyclically.
T. Vechsu uck 61
a ying be ween wo g oups o coun ies: ad anced and de eloping coun ies. In bo h g oups, he
demand and dis ibu i e egimes a e s ill p o i -led/p o i -squeeze. Howe e , bo h egimes a e
s onge in ad anced economies han in eme ging economies. Las ly, he long- un es ima ion
e eals no long- e m gain o loss on he ou pu gap, bu he wage sha e has a long- e m decline.
The decline in he wage sha e is mo e pe e se in de eloping coun ies. These esul s sugges
ha , al hough coun ies implemen wage ep ession o sho - e m bene i s, he e a e unclea
gains in he long un. The global ace o he bo om esul s in a long- e m decline in only he labo
sha e.
The s uc u e o his s udy is as ollows: A e he in oduc ion, he heo e ical model sec ion
explains he cons uc ion o he neo-Goodwinian model. The subsequen sec ion, empi ical
analysis, is sepa a ed in o ou subsec ions. The i s and second subsec ions explo e he wage
sha e and he ou pu gap da a. The hi d subsec ion explains he econome ic models on which
his s udy is based and analyzes he indings. The ou h subsec ion conside s he implica ions o
he esul s. Finally, he las pa summa izes he essence o his wo k.
1. The Neo-Goodwinian model
Following Ma x’s idea on social con lic and he Lo ka-Vol e a ma hema ical model on he
compe i ion be ween species, Goodwin (1967) cons uc ed a mac oeconomic model o show ha
a business cycle can be explained by wo endogenous a iables: income dis ibu ion, o he
p eda o , and employmen , o he p ey. Based on he li e a u e om Keynes, Kalecki, and S eindl,
pos -Keynesian wo ks, including Bhadu i and Ma glin (1990), Du (1984), Taylo (1991),
Row ho n (1981), Foley and Michl (1999), and Blecke (1989), among o he s, ha e de eloped a
Keynesian economic g ow h heo y in which e ec i e demand is emphasized as c ucial o
economic g ow h. The impo ance o income dis ibu ion is e i ed along he lines o classical
economics da ing back o Smi h, Rica do, and Ma x. The neo-Goodwinian model p esen ed below
closely ollows he business cycle model de eloped in Ba bosa-Filho (2001), Ba bosa-Filho and
Taylo (2006), and Taylo (2004), in which income dis ibu ion and capaci y u iliza ion a e
endogenized.
4
In pa icula , his he e odox business cycle model inco po a es e ec i e demand
in o social con lic o examine how income dis ibu ion in e ac s wi h business luc ua ions. The
concep o dis ibu ion-demand in e ac ions has been u he sc u inized in a nonlinea ashion
(Ta ani e al., 2011; Niki o os and Foley, 2012).
Suppose a closed economy p oduces only one good and a go e nmen has no ole. A socie y is
di ided in o wo classes: capi alis s, whose income is mainly de i ed om p o i , and wo ke s,
whose income is mainly de i ed om wage. Capaci y u iliza ion (𝑢) is de ined as eal ou pu (𝑋)
o e exis ing capi al o po en ial ou pu (𝐾). Wage sha e (𝜓) is de ined as eal wage (ω) o e labo
p oduc i i y (𝜉). By di e en ia ing 𝑢 and 𝜓 wi h espec o ime (gi en ha 𝑥=𝑥
𝑥 when 𝑥 is
con inually di e en iable), we ha e:
𝑢=𝑋
−𝐾
(1)
ψ
=ω−ξ (2)
4
This model was o iginally called he s uc u alis Goodwin model (Ba bosa-Filho and Taylo , 2006). S ockhamme
(2017) and Blecke and Se e ield (2019) la e popula ized he i les he neo-Goodwin cycles and he neo-Goodwinian
model. No e ha , in his pape , hey a e all he same.
62 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
The g ow h a e o u iliza ion elies on he di e ence be ween he g ow h a es o ou pu and
capi al (suppose he e is no capi al dep ecia ion), whe eas he g ow h a e o he wage sha e is
he di e ence be ween eal wage g ow h and labo p oduc i i y g ow h. The ela ionship
be ween u iliza ion and wage sha e can be u he sc u inized using he Two-Species Model
(Shone, 2002, chap e 14) since hey can be conside ed wo species demons a ing ei he i al y
o p eda ion. Ou pu , capi al, eal wage, and labo p oduc i i y a e cons uc ed as a linea unc ion
consis ing o ou wo species, u iliza ion and wage sha e, as ollows:
𝑋
=𝛼0+𝛼𝑢𝑢+𝛼𝜓𝜓 (3)
𝐾
=𝛽0+𝛽𝑢𝑢+𝛽𝜓𝜓 (4)
𝜔=𝛾0+𝛾𝑢𝑢+𝛾𝜓𝜓 (5)
𝜉=𝛿0+𝛿𝑢𝑢+𝛿𝜓𝜓 (6)
Theo e ical ounda ions jus i y he signs o all coe icien s αj,βj,γj,δj (see appendix A o mo e
de ails). Then equa ion (3) and equa ion (4) a e subs i u ed in o equa ion (1). Equa ion (5) and
equa ion (6) a e subs i u ed in o equa ion (2). Also, le ϕj=αj−βj and θj=γj−δj o j = 0,u
o ψ. We can ob ain:
𝑢 =𝑢(𝜙0+𝜙𝑢𝑢+𝜙𝜓𝜓) (7)
𝜓=𝜓(𝜃0+𝜃𝑢𝑢+𝜃𝜓𝜓) (8)
Equa ion (7) and equa ion (8) can be cons uc ed as he u iliza ion nullcline and dis ibu i e
nullcline, espec i ely, a e hey a e equa ed o ze o. The slopes o bo h nullclines, he s a iona y
solu ion, he long- un solu ion, and he s abili y analysis a e elabo a ed in appendix A. The slope
o he u iliza ion nullcline depends on he sign o 𝜙𝜓 o he di e ence be ween he e ec s o wage
sha e changes on ou pu and capi al. When he sign o 𝜙𝜓 is posi i e, he u iliza ion nullcline is
posi i ely sloped o he demand egime is wage-led. The nega i e 𝜙𝜓 causes he u iliza ion
nullcline o be nega i ely sloped, o he demand egime is p o i -led. The slope o he dis ibu i e
nullcline, on he o he hand, la gely es s on he sign o 𝜃𝑢 o he di e ence be ween he e ec s o
u iliza ion changes on eal wage and labo p oduc i i y. The posi i e 𝜃𝑢 esul s in a posi i ely
sloped dis ibu i e nullcline, o he dis ibu i e egime is p o i -squeeze. The dis ibu i e egime
is conside ed as wage-squeeze when 𝜃𝑢 is nega i e, which causes he slope o he dis ibu i e
nullcline o be nega i e as well.
Figu e 1a illus a es he sys em wi h p o i -squeeze dis ibu i e and p o i -led u iliza ion
egimes. The sys em mani es s coun e clockwise p eda o -p ey dynamics, whe e he wage sha e
is a p eda o , and capaci y u iliza ion is he p ey. A he beginning o he business cycle, a
educ ion in he wage sha e induces a highe in es men ha o e shadows a all in consump ion.
An inc ease in capaci y u iliza ion s eng hens labo ’s ba gaining powe , e en ually leading o a
highe labo sha e, which would se he s age o an economic slowdown, ending he cycle. The
new cycle will s a when a lowe ing wage sha e s imula es agg ega e demand again. The dynamic
beha io can be cha ac e ized as spi al sink as i con e ges o he long- un s eady s a e. In his
sys em, a p olabo dis ibu i e shock, o a le wa d shi o he dis ibu i e nullcline, will imp o e
T. Vechsu uck 63
he wage sha e while wo sening u iliza ion. A posi i e demand shock, o a igh wa d shi o he
u iliza ion schedule, will imp o e wage sha e and u iliza ion in his sys em.
Wage-led and wage-squeeze dynamics egimes a e shown in igu e 1b. The sys em exhibi s
clockwise p eda o -p ey dynamics, whe e a p eda o is ins ead pe o med by capaci y u iliza ion
while he wage sha e u ns ou o be he p ey. The business cycle s a s when an inc ease in he
wage sha e boos s he economy. Highe consump ion is la ge enough o compensa e o a
educ ion in in es men . The economy expands un il he p o i sha e s a s o inc ease. The pe iod
o ecession s alls he economy un il he wage sha e ises again, and he new cycle begins.
Likewise, he dynamic beha io is s ill conside ed as spi al sink. Ne e heless, a p olabo shock in
his sys em will imp o e bo h labo sha e and u iliza ion, whe eas a posi i e demand shock will
imp o e only u iliza ion bu discou age he labo sha e.
In igu e 1c, he dis ibu i e cu e shows he o ced-sa ing/Kaldo ian cha ac e is ic o he
p o i -led demand egime. In his case, he dis ibu i e schedule mus cu he demand schedule
om abo e o make he sys em s able (Taylo , 2004). In o he wo ds, he dis ibu i e schedule
mus be s eepe han he demand schedule o ha e a posi i e de e minan o he Jacobian ma ix
(see appendix A). As a esul , he sys em also emb aces coun e clockwise p eda o -p ey, spi al
sink dynamics, as in he i s case. Howe e , whe eas a p olabo dis ibu i e shock causes he
same e ec as he case abo e, a posi i e demand shock will, in his case, cause he wage sha e o
su e . In he nex sec ion, he panel da a analysis is u ilized o see how he dis ibu i e and
demand egimes look in ad anced and de eloping coun ies.
Figu e 1 – Th ee scena ios o he neo-Goodwinian model
1a – P o i -led/p o i -squeeze
64 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
1b – Wage-led/wage-squeeze
1c – P o i -led/wage-squeeze
No e: Figu e 1a ep esen s he p o i -led/p o i -squeeze neo-Goodwinian model wi h s able wage sha e dynamics.
Figu e 1b ep esen s he wage-led/wage-squeeze neo-Goodwinian model wi h s able wage sha e dynamics. Figu e 1c
ep esen s he p o i -led/wage-squeeze neo-Goodwinian model wi h uns able wage sha e dynamics.
T. Vechsu uck 65
2. Empi ical analysis
This sec ion will ansla e he neo-Goodwinian model desc ibed ea lie in o he empi ical
model. Rega ding he heo e ical model abo e, we ecognize ha any econome ic model ha
a emp s o empi ically es he model equi es wo endogenous a iables’ ime se ies da a: labo
sha e and capaci y u iliza ion. The wo a iables a e de ined below.
2.1. Wage sha e da a
Fo he wage sha e da a in his pape , I use he labo sha es (LABSH) om he Penn Wo ld
Tables (PWT) 10.0 da ase , since i co e s mo e han 100 coun ies ac oss con inen s, and many
se ies a e da ed om 1950 up o igh be o e he COVID-19 pandemic in 2019. Acco ding o
Feens a e al. (2015, pp. 21-27), he da ase also adjus s o sel -employmen income, which is
p e alen in de eloping coun ies ollowing Gollin (2002), Timme e al. (2012), and hei
es ima ions.
5
Table 1 summa izes he lis o coun ies and he wage sha e o each coun y. O e all, he e
a e 81 coun ies om all egions a ound he wo ld. Coun ies a e ca ego ized in o ad anced and
de eloping coun ies, acco ding o he IMF (2023). The low-income de eloping coun ies a e
excluded. Selec ed coun ies mus ha e a leas 10 yea s o wage sha e da a. O e all, he e a e 81
coun ies: 34 ad anced economies and 47 de eloping economies. The a e age wage sha e is 0.52
(0.58 o ad anced and 0.47 o de eloping coun ies). Un o una ely, only a hand ul o coun ies
ha e he ull ange o da a o wage sha e, bu mos coun ies ha e di e en anges, om mo e
han 68 yea s o only 14 yea s.
Figu e 2 shows ad anced coun ies ha expe ience a long- e m decline in hei wage sha es,
including Aus alia, Canada, F ance, Ne he lands, and he Uni ed S a es. In Aus alia, o example,
he wage sha e peaked in 1974 a 0.72 be o e i bo omed ou in 2008 a 0.57. Figu e 3 shows he
ends o selec ed de eloping economies. Many coun ies, such as Boli ia, India, Sou h A ica,
China, and Mexico, exhibi ed a declining end be o e 2008, wi h he sha es picking up a e wa d.
In India, o ins ance, he wage sha e dec eased om 0.7 in he 1970s o 0.48 in 2007. In China,
he wage sha e declined om 0.6 in 2002 o 0.55 in 2010 be o e inc easing o 0.59 in 2016. This
U-shaped end in China is con i med by se e al s udies, including hose by Zhou (2015), Qi
(2020), and Vechsu uck (2023). In Mexico, he wage sha e did no ha e a clea end. Howe e ,
he absolu e le el o he wage sha e was al eady low, a less han 0.4, he lowes in hese i e
coun ies.
5
Acco ding o Feens a e al. (2015), h ee me hods we e used o cons uc a ‘bes es ima e’ labo sha e. Fi s , when
mixed income da a a e a ailable, hey calcula e he labo sha e o income as Compensa ion o Employees o e GDP –
Mixed Income. This me hod applies o almos hal he coun ies in he sample (Feens a e al., 2015, sec. Appendix C).
Second, o a ew coun ies whose unadjus ed labo sha e exceeds 0.7, he unadjus ed labo sha e is used since i al eady
includes he sel -employed labo income. This me hod applies only o a ew coun ies in he da ase . Thi d, when he
mixed income da a a e no a ailable and he unadjus ed labo sha e is below 0.7, he es ima ion o labo sha e o his
g oup o coun ies compa es wo me hods. The i s me hod es ima es he labo sha e o income as compensa ion o
employee mul iplied by he o al numbe o wage employees o e o al employees o e GDP. The second me hod uses
he alue added o ag icul u e as a p oxy o mixed income. I ollows he calcula ion ha he labo sha e equals
compensa ion o employees + mixed income o e GDP. The inal s ep is o pick he lowe numbe om he wo me hods
as he labo sha e o income o he coun y. O e all, 127 coun ies a e co e ed (ou o 167). In 2005, he a e age labo
sha e was 0.52, which is lowe han he 0.7 ha Gollin (2002) p e e ed o he wo- hi ds (0.67) ule o humb.
66 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
Table 1 – Wage sha e summa y o all coun ies
Coun y
Pe iod
Ad anced o
de eloping
Mean
Median
Min
Max
Fi s 5-
yea
a e age
Las 5-
yea
a e age
Change
Angola
2002-2018
De eloping
0.29
0.29
0.23
0.36
0.26
0.33
0.07
A gen ina
1993-2013
De eloping
0.40
0.39
0.31
0.54
0.4
0.48
0.08
A menia
1991-2017
De eloping
0.65
0.64
0.55
0.75
0.74
0.57
–0.17
Aus alia
1959-2018
Ad anced
0.63
0.62
0.57
0.72
0.68
0.59
–0.09
Aus ia
1995-2018
Ad anced
0.58
0.58
0.55
0.63
0.62
0.58
–0.04
Aze baijan
1994-2017
De eloping
0.33
0.32
0.21
0.57
0.48
0.26
–0.22
Bah ain
1992-2010
De eloping
0.33
0.34
0.30
0.38
0.35
0.3
–0.05
Bela us
1990-2015
De eloping
0.55
0.55
0.43
0.63
0.49
0.57
0.08
Belgium
1985-2018
Ad anced
0.62
0.62
0.59
0.64
0.63
0.6
–0.03
Boli ia
1970-2015
De eloping
0.53
0.53
0.45
0.72
0.53
0.47
–0.06
B azil
1992-2017
De eloping
0.55
0.55
0.49
0.58
0.53
0.52
–0.01
Bulga ia
1995-2018
De eloping
0.48
0.48
0.39
0.54
0.46
0.52
0.06
Canada
1970-2018
Ad anced
0.68
0.67
0.63
0.77
0.76
0.66
–0.1
Chile
1996-2009
De eloping
0.46
0.48
0.38
0.52
0.5
0.41
–0.09
China
1992-2016
De eloping
0.58
0.57
0.55
0.61
0.58
0.58
0
Colombia
1992-2018
De eloping
0.48
0.48
0.45
0.51
0.49
0.49
0
C oa ia
1995-2018
De eloping
0.64
0.64
0.59
0.71
0.67
0.59
–0.08
Czech Republic
1992-2018
Ad anced
0.52
0.52
0.51
0.55
0.52
0.53
0.01
Denma k
1995-2018
Ad anced
0.64
0.64
0.62
0.67
0.65
0.62
–0.03
Dominican Rep.
1991-2016
De eloping
0.54
0.52
0.43
0.67
0.64
0.44
–0.2
Ecuado
1970-2013
De eloping
0.48
0.47
0.35
0.68
0.57
0.66
0.09
Egyp
1996-2015
De eloping
0.37
0.38
0.31
0.42
0.4
0.35
–0.05
Es onia
1994-2018
Ad anced
0.59
0.59
0.55
0.66
0.64
0.58
–0.06
Finland
1975-2018
Ad anced
0.62
0.61
0.56
0.71
0.68
0.58
–0.1
F ance
1950-2018
Ad anced
0.65
0.65
0.61
0.69
0.68
0.62
–0.06
Gabon
1972-2004
De eloping
0.37
0.37
0.28
0.50
0.37
0.33
–0.04
Geo gia
1999-2018
De eloping
0.35
0.37
0.23
0.45
0.36
0.43
0.07
Ge many
1991-2018
Ad anced
0.64
0.63
0.59
0.68
0.67
0.63
–0.04
G eece
1996-2018
Ad anced
0.53
0.54
0.48
0.55
0.49
0.53
0.04
Gua emala
2001-2018
De eloping
0.51
0.50
0.48
0.55
0.53
0.49
–0.04
Hong Kong
1980-2017
Ad anced
0.49
0.49
0.45
0.52
0.47
0.52
0.05
Hunga y
1995-2018
De eloping
0.59
0.59
0.55
0.65
0.62
0.56
–0.06
Iceland
1995-2018
Ad anced
0.61
0.61
0.51
0.68
0.63
0.6
–0.03
Indonesia
2000-2014
De eloping
0.45
0.45
0.44
0.47
0.45
0.46
0.01
India
1975-2017
De eloping
0.62
0.62
0.48
0.75
0.74
0.52
–0.22
I an
1994-2016
De eloping
0.32
0.31
0.25
0.41
0.38
0.32
–0.06
I aq
1997-2010
De eloping
0.20
0.21
0.09
0.32
0.14
0.27
0.13
I eland
1995-2018
Ad anced
0.46
0.48
0.32
0.56
0.53
0.35
–0.18
Is ael
2000-2018
Ad anced
0.56
0.55
0.54
0.60
0.58
0.54
–0.04
I aly
1980-2018
Ad anced
0.54
0.52
0.50
0.60
0.59
0.52
–0.07
Jamaica
1970-2018
De eloping
0.56
0.58
0.46
0.63
0.58
0.6
0.02
Japan
1980-2017
Ad anced
0.58
0.58
0.55
0.63
0.62
0.56
–0.06
Jo dan
1970-2009
De eloping
0.48
0.49
0.45
0.50
0.49
0.46
–0.03
Kazakhs an
1990-2016
De eloping
0.48
0.45
0.38
0.61
0.52
0.4
–0.12
Ko ea
1970-2017
Ad anced
0.56
0.56
0.50
0.65
0.63
0.52
–0.11
La ia
1994-2018
Ad anced
0.52
0.52
0.46
0.62
0.56
0.54
–0.02
Li huania
1995-2018
Ad anced
0.51
0.51
0.46
0.58
0.54
0.51
–0.03
Luxembou g
1995-2018
Ad anced
0.56
0.56
0.54
0.60
0.55
0.55
0
Mau i ius
1990-2010
De eloping
0.48
0.48
0.43
0.55
0.53
0.43
–0.1
Mexico
1993-2018
De eloping
0.38
0.38
0.36
0.43
0.4
0.37
–0.03
Mongolia
1995-2018
De eloping
0.40
0.40
0.33
0.46
0.42
0.41
–0.01
Mo occo
1998-2018
De eloping
0.49
0.49
0.47
0.51
0.5
0.49
–0.01
T. Vechsu uck 73
egime is p o i -led, anging om 0.01% o 0.07%. These esul s a e in he same ange as he wo
s udies abo e sugges ed o he U.S. and OECD economies.
9
Figu e 5 simula es he esul s om he i s column o able A1 (HP il e ) o c ea e ajec o ies
o he sys em when he dis ibu i e nullcline is posi i ely sloped (p o i -squeeze) and he
u iliza ion nullcline is nega i ely sloped (p o i -led). Fo simplici y, he long- un ou pu gap is
assumed o be ze o. The coun e clockwise con e gence o he long- un equilib ium (ze o GDP
gap) seemingly slows in he e y i s yea s bu speeds up in la e yea s. This implies ha any
nega i e ou pu shock migh c ea e p olonged s agna ion in he o al sys em be o e i can each
eco e y yea s.
Figu e 5 – T ajec o ies om he HP ou pu gap in able A1
The linea ends o bo h he long- un coo dina es a e in oduced o es i he long- un
equilib ium migh mo e downwa ds o upwa ds. The ψ0
∗ coe icien is ein e p e ed as he 1970
wage sha e equilib ium and u0
∗ as he 1970 u iliza ion equilib ium. The ends can be nega i e o
posi i e. The equa ions can be speci ied as:
9
No e ha his agg ega i e es ima ion can be biased o sho - un e ec s and play down he long- un e ec s. Blecke
(2016) s essed he ime ho izon di e ences. He a gued ha agg ega e demand ends o be p o i -led in he sho un
and wage-led in he long un because consump ion posi i ely esponds o a highe wage sha e mo e in he longe un.
Rolim (2021) ag eed and added ha mos s uc u al analysis s ill emphasized mo e he sho - un e ec s and sugges ed
ha he coin eg a ion es can be used o de ec he exis ence o he long- un ela ionship be ween income dis ibu ion
and consump ion. The economy can become mo e and mo e wage-led in he long un i consump ion is mo e posi i ely
esponsi e o a highe labo sha e.
74 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
𝜓𝑡−𝜓𝑡−1 =𝛼0(𝜓𝑡−1−(𝜓0
∗−𝛼1𝑢0
∗+(𝜓1
∗−𝛼1𝑢1
∗)(𝑑𝑎𝑡𝑒−1970))−𝛼1𝑢𝑡−1)+𝜖𝑡 (11)
𝑢𝑡−𝑢𝑡−1 =β0(ψ𝑡−1−(ψ0
∗−β1𝑢0
∗+(ψ1
∗−β1𝑢1
∗)(𝑑𝑎𝑡𝑒−1970))−β1𝑢𝑡−1)+υ𝑡 (12)
whe e 𝜓1
∗ is a long- un wage sha e end, and 𝑢1
∗ is a long- un u iliza ion end.
The es ima ion esul s a e p esen ed in able A2. Mos coe icien s co espond o he p e ious
esul s. Howe e , he las wo coe icien s pose wo c ucial poin s. Fi s , he sign o he long- un
u iliza ion end is inconclusi e. The coe icien s om he band-pass and he mo ing a e age gaps
a e nega i e, whe eas hose om he BN and Hamil on il e s a e posi i e. The coe icien om
he HP il e is insigni ican a any le el. This ambiguous esul implies ha he e a e nei he
posi i e no nega i e e ec s o he ou pu gap in he long un. Second, he long- un wage end is
nega i e and signi ican ac oss all il e s excep o he BN gap. In o he wo ds, he e is a long-
e m downwa d mo emen o wage sha e. These esul s sugges ha he e is a collec i e e o o
supp ess labo income e en hough he bene i is no isible in he long un.
2.3.2. Ad anced s. de eloping coun y esul s
The es ima ion when he wo ld economy is di ided in o de eloped and de eloping g oups o
coun ies is p esen ed in able A3. The magni udes ac oss di e en il e s a y. Howe e , some
pa e ns a e conclusi e. Fi s , he wage slope coe icien s a e all posi i e ac oss all il e s. The
dis ibu i e egime is s ill Ma xis /p o i -squeeze. Howe e , he esul s show ha his pa e n is
always s onge in ad anced han in de eloping coun ies. Fo example, om he HP gap, a
pe cen age inc ease in he ou pu gap esul s in a 2.64% inc ease in he wage sha e in de eloping
coun ies, bu i inc eases o 3.54% in ad anced coun ies. These esul s can e lec s onge labo
ins i u ions o unions, igh e labo ma ke s wi h less in o mal employmen , and a la ge wel a e
s a e in he ad anced coun ies ha allow wages o inc ease in andem wi h economic upswings.
The p o i -led demand egime can be obse ed ac oss he boa d (nega i e u iliza ion slopes).
This egime is also s onge in de eloped coun ies han in de eloping coun ies based on all
di e en il e s. Fo example, om he HP gap, a pe cen age inc ease in he wage sha e esul s in
a 0.08% (o 1/12.74) inc ease in he ou pu gap in ad anced coun ies, whe eas i leads o a 0.07%
(o 1/14.42) inc ease in de eloping coun ies. The esul s o he long- un u iliza ion in e cep a e
s ill ambiguous. The coe icien s a e nega i e o he band-pass and he mo ing a e age gaps, bu
hey a e posi i e o he HP, BN, and Hamil on gaps. These unclea esul s con i m he esul
abo e, ha he e is no mo emen o he ou pu gap in he long un.
In sum, bo h dis ibu i e and demand egimes in de eloping coun ies a e p o i -led/p o i
squeeze. Howe e , he egimes in de eloping coun ies a e weake han in ad anced coun ies.
To be e illus a e his poin , igu e 6 compa es he demand egimes and dis ibu i e egimes
be ween wo g oups o coun ies. This diag am is based on he coe icien s om he HP gap. The
do ed lines ep esen de eloping coun ies’ dis ibu i e/demand egimes, and he dashed lines
ep esen ad anced coun ies’ wo egimes. As analyzed abo e, he ad anced coun ies’
dis ibu i e cu e is s onge o s eepe , indica ing he highe ba gaining powe o labo unions
in ad anced coun ies ha a e mo e likely o be able o p essu e o highe wages amids he
economic up u ns. The s eepe slope o de eloping coun ies’ demand egime in his 𝑢−𝜓 plane
au oma ically ansla es in o he la e slope o he egime in he 𝜓−𝑢 plane. In o he wo ds, in
he sho un, highe u iliza ion can be achie ed mo e o de eloped coun ies o e e y
pe cen age educ ion in wage sha e, gi en o he condi ions.
T. Vechsu uck 75
Figu e 6 – Compa ison o demand-dis ibu ion egimes in ad anced s. de eloping coun ies (HP
ou pu gap)
Las ly, he es ima ion wi h linea ends is sepa a ed be ween de eloping and ad anced
coun ies o analyze i he e is any di e ence in e ms o hei coe icien s and long- e m ends.
The esul s a e in able A4. Simila o he esul s in able A3, i e eals ha he long- un u iliza ion
ends a e s ill inconclusi e o bo h g oups o coun ies. On he o he hand, he long- un wage
end is nega i e and signi ican o all il e s. The esul s also show ha he wage end is wo se
o mo e nega i e in de eloping coun ies han in ad anced coun ies. This inding implies ha ,
e en hough all he coun ies ha e a emp ed o supp ess wages, he labo sha e in de eloping
coun ies has su e ed mo e in he las ew decades.
2.4. Discussion: A global ace o he bo om
A na ion may aim o educe a uni labo cos o become mo e compe i i e in e na ionally.
Howe e , once e e y na ion commi s o he same s a egy, i can esul in un a o able ou comes
o all na ions as a whole. Robinson (1947) a gued ha an inc ease in he balance o ade is
an amoun o an inc ease in in es men , which usually leads o an inc ease in employmen . As
he global ma ke does no g ow as enough o accommoda e all sales, each na ion seeks o
inc ease he sha e in he ma ke ha will bene i i s people; bu his comes a he expense o o he
na ions, because he balance o ade o he wo ld as a whole mus be ze o. This ze o-sum game
means an inc ease in expo s o one coun y implies an inc ease in impo s in ano he . In o he
76 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
wo ds, unde in e na ional compe i ion, coun ies aim o inc ease hei employmen by expo ing
unemploymen o he es o he wo ld. The e o e, a so-called begga -my-neighbo game is played
be ween na ions, such as du ing he in e wa pe iod (Ro he mund, 2002, pp. 6-9). A e one
na ion succeeds a he expense o o he s, he o he na ions will e alia e. The p incipal de ices o
inc ease a ade balance en ail impo es ic ions, expo subsidies, exchange a e dep ecia ion,
and wage cu s. Fo ins ance, an exchange a e dep ecia ion o a all in money wages would
s imula e a p ima y inc ease in employmen in expo indus ies, assuming he Ma shal-Le ne
condi ion holds. Pu simply, he e a e ou sui s in he pack, and a coun y ies o play a highe
ca d ou o any sui o be ahead o o he s (Robinson, 1947, p. 69).
The long- un consequence o he global ace o he bo om can be illus a ed by he p o i -
led/p o i -squeeze neo-Goodwinian model ex ended om igu e 1a. The compa a i e s a ics is
shown in igu e 7. When coun ies y o gain compe i i eness by using any one o he ou ca ds
abo e, i can be in e p e ed as he an ilabo dis ibu i e shock o a igh wa d shi o he upwa d-
sloping dis ibu i e cu e (nullcline). The s eady-s a e mo es om poin A o poin B. Wi h a
lowe long- un wage sha e, he p o i -led egime should allow he economy o mo e owa d a
highe long- un capaci y u iliza ion because in es men esponds posi i ely o a ise in p o i
sha e. Howe e , his migh no be he case ega ding he weakening p o i -in es men nexus
ecen ly mani es ed in many coun ies. Ins ead, i could imply ha a nega i e demand shock may
occu , and he u iliza ion cu e is simul aneously shi ed o he le . In es men in his si ua ion
does no posi i ely espond o he lowe wage sha e, which implies ha he long- un u iliza ion
migh inc ease only a li le o no a all. The ou come can be simply a all in wage sha e wi hou
any gain in capaci y u iliza ion in he long un, shown by he s eady s a e mo ing om poin B o
poin C. The global economy has been apped in he so-called secula s agna ion (Hein, 2016).
Figu e 7 – The ace o he bo om in he neo-Goodwinian model
T. Vechsu uck 77
This global shi co esponds o he econome ic esul s shown abo e; in he sho un, he
demand is p o i -led and he dis ibu ion is p o i -squeeze. Howe e , in he long un, he ace o
he bo om, cap u ed by alling wage sha es, yields nei he posi i e no nega i e ou comes on he
long- un capaci y u iliza ion. The shi in he demand egime domina es he shi in he
dis ibu i e egime. The sho - un, cyclical beha io can be econciled wi h he medium- e m and
long- e m ends in alling labo sha es and slowed-down economic g ow h obse ed wo ldwide
in he pas ew decades (Blecke , 2020).
3. Conclusion
In his s udy, I show ha in he e a o apid globaliza ion o he pas ew decades, he e is
e idence o he ace o he bo om ac oss he wo ld. Fi s , om he PWT 10.0, I s udied he
ela ionship be ween income dis ibu ion and capaci y u iliza ion o 34 ad anced and 47
de eloping coun ies. O 81 coun ies, 58 ha e expe ienced a decline in he wage sha e. The
a e age wage sha e in de eloping coun ies is also lowe han in ad anced coun ies.
Second, I employed he neo-Goodwinian model o es ima e he in e ac ions be ween he wage
sha e and he ou pu gap ac oss he globe. The ou pu gap is ob ained h ough i e il e s o
p e en any bias and o s eng hen he esul s’ obus ness: he Hod ick-P essco (HP), he
Bax e -King equency (band-pass), he mo ing a e age, he Be e idge-Nelson (BN), and he
Hamil on. The panel da a es ima ion shows ha he wo ld sys em exhibi s a coun e clockwise
oscilla o y con e gence o he equilib ium poin whe e wage sha e is he p eda o and capaci y
u iliza ion is he p ey. The dis ibu i e cu e is upwa d-sloping, which ep esen s a
Ma xian/p o i -squeeze egime. The demand cu e is downwa d-sloping, which implies he
egime is p o i -led. The esul s ha e been con i med bo h in ad anced and de eloping coun ies.
Howe e , he demand and dis ibu i e egimes a e s onge in ad anced economies han in
de eloped coun ies. In he long un, he e is no posi i e gain in u iliza ion bu he decline in wage
sha e is in ensi ied, especially in de eloping coun ies. The ou come could be in e p e ed as a
esul o he global begga -my-neighbo game in which na ions a emp o supp ess labo income
sha es while he global demand becomes s agnan . The global ace o he bo om bene i s
coun ies in he sho un bu no in he long un.
Appendices
A. Theo e ical model
Rega ding equa ion (7) and equa ion (8), a non i ial s a iona y solu ion, whe e 𝑢 =0
and 𝜓=0, yields he u iliza ion and dis ibu i e nullclines o he sys em, espec i ely:
𝑢 =0→𝑢=−𝜙0
𝜙𝑢−𝜙𝜓
𝜙𝑢𝜓 (A.1)
𝜓=0→𝜓=−𝜃0
𝜃𝜓−𝜃𝑢
𝜃𝜓𝑢 (A.2)
78 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
On he 𝑢−𝜓 plane, he slopes o demand and dis ibu i e cu es a e impo an as hey signi y
he cha ac e is ics o each egime. The slopes can be de i ed as:
𝑑𝜓
𝑑𝑢|𝑢=0 =−𝜙𝑢
𝜙𝜓=𝛽𝑢−𝛼𝑢
𝛼𝜓−𝛽𝜓≶0 (A.3)
𝑑𝜓
𝑑𝑢|𝜓=0 =−𝜃𝑢
𝜃𝜓=𝛿𝑢−𝛾𝑢
𝛾𝜓−𝛿𝜓≶0 (A.4)
The long- un solu ion o s able node, whe e wage sha e and u iliza ion a e cons an , can be
sol ed by equa ing wo nullclines o equa ion A.1 and equa ion A.2 o ha e:
𝑢∗=𝜃0𝜙𝜓−𝜙0𝜃𝜓
𝜙𝑢𝜃𝜓−𝜃𝑢𝜙𝜓 𝜓∗=𝜙0𝜃𝑢−𝜃0𝜙𝑢
𝜙𝑢𝜃𝜓−𝜃𝑢𝜙𝜓 (A.5)
To de e mine he dynamics and he s abili y o he sys em a he s a iona y poin s whe e 𝑢 =
𝜓=0, he Jacobian ma ix, ace, and de e minan can be ob ained as:
𝐽=(𝜙𝑢𝜙𝜓
𝜃𝑢𝜃𝜓) 𝑇𝑟(𝐽)=𝜙𝑢+𝜃𝜓 𝐷𝑒𝑡(𝐽)=𝜙𝑢𝜃𝜓−𝜃𝑢𝜙𝜓 (A.6)
F om his sys em, he s abili y condi ion, as well as he cha ac e is ics o each cu e, canno
be de e mined a p io i, since he slopes o bo h cu es, he ace, and he de e minan o he
Jacobian ma ix undamen ally depend on how he wage sha e and u iliza ion a ec ou pu ,
po en ial ou pu , eal wage, and labo p oduc i i y along he economic cycle. In he nex s ep,
some economically meaning ul closu es will be analyzed o ha e phase diag ams o he sys em.
No e ha he ocus is mo e on he cases whe e he nullclines a e s able in isola ion (𝜙𝑢,𝜃𝜓<0)
and he sys em is locally s able (𝑇𝑟(𝐽)<0 and 𝐷𝑒𝑡(𝐽)>𝑜), which implies ha only he signs o
𝜙𝜓 and 𝜃𝑢 a e le o be explo ed.
Conside ing he demand egime, wi h he Keynesian s abili y condi ion, 𝛼𝑢 is assumed o be
nega i e o decele a e economic g ow h in he long un as sa ing is g owing as e han
in es men . Capi al accumula ion has esponded posi i ely o u iliza ion because, by p o i a e
accoun ing, an inc ease in u iliza ion, gi en he a es o p o i sha e and o ganic composi ion o
capi al, leads o an inc ease in he p o i a e. Simila ly, a ise in p o i sha e can boos p o i abili y
and in es men demand. Bo h a gumen s hus implici ly mean ha 𝛽𝑢>0 and 𝛽𝜓<0. F om
equa ion A.3, we can de e mine he sign o he nomina o as posi i e. The sign o he slope now
depends only upon he sign o 𝛼𝜓 o whe he he demand schedule is wage-led o p o i -led. As
he demand egime is de e mined by whe he o no he size o a posi i e e ec o an inc easing
wage sha e on consump ion can domina e he nega i e o an inc easing wage sha e on in es men ,
he economy is always wage-led (posi i e slope) when demand is wage-led (αψ>0). On he o he
hand, i demand is p o i -led (𝛼𝜓<0), he o e all demand egime is inconclusi e. Ba bosa-Filho
and Taylo (2006) ound ha , in he Uni ed S a es, he size o he nega i e e ec on demand
ou pe o ms he nega i e e ec on in es men and capi al accumula ion (|𝛼𝜓|>|𝛽𝜓|), which
T. Vechsu uck 79
o ces he slope o be nega i e, o a p o i -led egime. I he opposi e case holds, he demand
egime is wage-led.
The dis ibu i e egime is sligh ly mo e complica ed when we y o de e mine he signs o
each coe icien . Acco ding o Ma x's Rese e A my o Labo hypo hesis, an economic upswing
will inc ease labo 's ba gaining powe as he unemployed a e deple ed. The eal wage he e o e
ends o a y p ocyclically (𝛾𝑢>0). Labo p oduc i i y is also assumed o eac posi i ely o
u iliza ion as i ms in es mo e in new echnology while hey see imp o ing p o i abili y (𝛿𝑢>0).
We can see ha he sign o he nomina o o equa ion A.5 canno be de e mined a p io i. Acco ding
o Ba bosa-Filho (2001), suppose ha he eal wage g ow h a e is a nega i e unc ion o he eal
wage le el and a posi i e unc ion o labo p oduc i i y. We hus ha e a nega i e ela ion be ween
wage sha e and eal wage (𝛾𝜓<0). Fu he , since we emphasize he case in which he dis ibu i e
nullcline is s able in isola ion (𝜃𝜓<0), 𝛿𝜓 mus be posi i e. I he 𝛿𝜓 sign is nega i e, he sign o
𝜃𝜓 will depend on he di e ence be ween 𝛾𝜓 and 𝛿𝜓. In he p io case (𝜃𝜓<0), he denomina o
is o ced o be nega i e. The sign o he dis ibu i e cu e will ely only upon he nomina o sign.
In pa icula , i 𝛿𝑢>𝛾𝑢, we will ha e a o ced-sa ing/Kaldo ian dis ibu i e egime (nega i e
slope dis ibu i e nullcline). I 𝛿𝑢<𝛾𝑢, we will ins ead ha e a p o i -squeeze/Ma xian dis ibu i e
egime (posi i e slope dis ibu i e nullcline). Fo he s abili y condi ion, we dis ega d he saddle
poin case, so he de e minan o Jacobian ma ix in equa ion A.6 mus only be posi i e.
B. Fil e s used o ob aining ou pu gaps
In he neo-Kaleckian and neo-Goodwinian li e a u e, i is common o use he il e o ob ain
he long- e m end o he eal ou pu and calcula e o he capaci y u iliza ion o ou pu gaps.
Also, il e ing me hods can be used o ha e a long- un economic g ow h end, al hough some
me hods a e exposed o con o e sies (see o example Niki o os, 2016, 2020, 2021; José Gahn,
2020; Haluska, 2020).
The Hod ick P essco (HP) il e has been one o he mos popula il e s o sepa a e he long-
e m end om he sho - e m luc ua ions in he mac oeconomic ime se ies. Howe e , he e
a e se e al c i icisms ega ding he use o he HP il e o ob aining he po en ial ou pu . Cogley
and Nason (1995) claimed ha he HP il e can po en ially c ea e spu ious cycles. In addi ion,
Hamil on (2017) a gued ha he HP il e has h ee main issues. Fi s , i gene a es se ies wi h
spu ious dynamic ela ions. Second, il e ed alues a bo h ends o he sample di e g ea ly om
hose in he middle. Thi d, i p oduces alues o he smoo hing pa ame e ha a e e y di e en
om common p ac ice. Blecke (2016) compa ed U.S. u iliza ion a es ob ained om he HP il e
wi h hose om a su ey by U.S. i ms. He ound ha he u iliza ion a es om he HP il e
downplayed he ad e se e ec o he 2008 inancial c isis.
A i ze (2022) examined he ela ionship be ween he long- un capaci y u iliza ion,
economic g ow h, and he wage sha e o he US. By applying di e en il e s, including HP,
mo ing a e age, Hamil on, and band-pass, she ound ha he long- un capaci y u iliza ion is
endogenous o he long- un income dis ibu ion. E en hough she claimed ha he esul s a e no
much di e en ac oss di e en il e s, she showed ha he band-pass and he HP showed a
nega i e ela ionship be ween he long- un wage sha e and long- un capaci y u iliza ion, whe eas
he Hamil on and he mo ing-a e age il e s did no show any signi ican esul s.
I he e o e ollow A i ze (2022) by using di e en il e s o es ima e he econome ic
ela ionship. The di e en il e s should p e en bias when using any il e alone and hey
enhance he obus ness o he esul s. The il e s used a e:
80 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
1. Hod ick-P esco il e (HP il e ). This s anda d il e is o en used in mac oeconomics o
ob ain he ou pu ends and cycles sugges ed by Hod ick and P esco (1997) a e he
wo king pape was ci cula ed du ing he 1980s. Since he da a a e a an annual le el, I use he
smoo hing pa ame e (lambda) equals 100.
2. Bax e -King equency il e (band-pass il e ). The band-pass il e , sugges ed by Bax e and
King (1999), is a linea il e ha calcula es he wo-sided weigh ed mo ing a e age whe e
cycles in a “band,” o in e media e alues, a e “passed” h ough o ex ac ed, gi en speci ied
lowe and uppe bounds. Acco ding o Bena i (2001), he band-pass il e allows us o a ge
a speci ic equency band while disca ding all he o he s. Howe e , he band-pass il e may
dis o key business cycle s ylized ac s as cap u ed by he cyclical componen o GDP and may
c ea e en i ely spu ious s ylized ac s (p. 7). He e I se he uppe and lowe bounds equal o
he s anda d le els a 2 and 8, espec i ely. This ixed leng h il e equi es ha , o e e y
weigh ed mo ing a e age, I use he same numbe o lead and lag e ms a 3.
3. Mo ing a e age. I decided o calcula e a mo ing a e age o i e yea s cen e ed on ob aining
he end o GDP.
4. Be e idge-Nelson il e (BN il e ). I use he Kambe e al. (2018) modi ica ion o he
Be e idge and Nelson (1981) decomposi ion ha imposes a lowe signal- o-noise a io on an
AR model, which esul ed in a pe sis en ou pu gap wi h la ge ampli ude. Unlike he HP o
bandpass il e , his modi ied BN il e also equi es ewe es ima ion e isions o ma ch
obse able da a. Kambe e al. (2018) used AR(12) o he qua e ly da a, so I use AR(3) o
my annual da a.
5. Hamil on il e . Hamil on (2017) p oposed a much simple way o ex ac ends and cycles
om a ime se ies. He sugges ed using a linea ime se ies model shi ed ahead by ℎ pe iods
eg essed agains lags o he se ies o 𝑝 pe iods. In mos s udies, he da a a e qua e ly wi h 𝑝
= 4 and ℎ = 8, bu he e I ha e da a a an annual le el. Because Hamil on s a ed ha a 2-yea
ho izon should be a s anda d benchma k i we a e in e es ed in business cycles (p. 838), I
choose a combina ion o 𝑝 = 2 and ℎ = 2. So a modi ied au o eg essi e AR(2) model can be
exp essed as:
𝑦𝑡=β0+β1𝑦𝑡−2+β2𝑦𝑡−3+υ𝑡 (B.1)
𝜐𝑡=𝑦𝑡−(𝛽0+𝛽1𝑦𝑡−2+𝛽2𝑦𝑡−3) (B.2)
whe e υ𝑡 es ima es cyclical componen s and he i ed alues a e he ends. No e ha he
Hamil on il e may p oduce a e y noisy measu e o po en ial GDP. Quas and Wol e s (2022, p.
152) showed ha he il e does no e enly co e ypical business cycle equencies om 6 o 32
qua e s. I mu es sho and ampli ies medium leng h economic cycles. The ex ac ed GDP end
o po en ial ou pu is he e o e no smoo h.
C. Econome ic model
Gi en ha he a e o change is de ined as 𝛥𝑥
𝑥=𝑥𝑡−𝑥𝑡−1
𝑥𝑡−1 , he pu e o o iginal Goodwin model,
a he han in di e en ial equa ion o m, can be es ima ed by he ollowing di e ence-equa ion
speci ica ion:
T. Vechsu uck 81
𝜓𝑡−𝜓𝑡−1 =𝛼0𝜓𝑡−1(𝑢𝑡−1−𝑢0
∗)+𝜖𝑡 (C1)
𝑢𝑡−𝑢𝑡−1 =β0𝑢𝑡−1(ψ𝑡−1−ψ0
∗)+υ𝑡 (C2)
whe e 𝜖 and 𝜐 a e e o e ms, 𝛼0 is wage sha e scaling, 𝛽0 is gap scaling, and 𝜓0
∗ is a long- un
wage in e cep . The long- un gap in e cep is 𝑢0
∗ and es ic ed a ze o.
The o iginal e sion o he Goodwin model o en canno p o ide s ong esul s, as i shows
closed o bi s a ound a unique ixed poin (Kie e and Rada, 2015, p. 7). The e o e, he e mus be
some adjus men s o he equa ions. The gene al Goodwin model is an adap ed e sion o he
o iginal Goodwin model abo e and can be shown as:
𝜓𝑡−𝜓𝑡−1 =𝛼0(𝜓𝑡−1−(𝛿1+𝛿2𝑢𝑡−1))+𝜖𝑡 (C.3)
𝑢𝑡−𝑢𝑡−1 =β0(ψ𝑡−1−(δ3+δ4𝑢𝑡−1))+υ𝑡 (C.4)
A he s eady s a e, 𝛥𝜓 and 𝛥𝑢=0, e o s a e gone, and 𝜓𝑡−1 and 𝑢𝑡−1 u n in o 𝜓0
∗ and 𝑢0
∗,
espec i ely. We ha e:
𝜓0
∗=𝛿1+𝛿2𝑢0
∗ (C.5)
ψ0
∗=δ3+δ4𝑢0
∗ (C.6)
Then we sol e o 𝛿1 and 𝛿3 o ha e:
𝛿1=𝜓0
∗−𝛿2𝑢0
∗ (C.7)
δ3=ψ0
∗−δ4𝑢0
∗ (C.8)
Then we plug back 𝛿1and 𝛿3 in o equa ion (C.5) and equa ion (C.6) o ha e:
𝜓𝑡−𝜓𝑡−1 =𝛼0(𝜓𝑡−1−(𝜓0
∗−𝛿2𝑢0
∗)−𝛿2𝑢𝑡−1)) + 𝜖𝑡 (C.9)
𝑢𝑡−𝑢𝑡−1 =β0(ψ𝑡−1−(ψ0
∗−δ4𝑢0
∗)−δ4𝑢𝑡−1))+𝜐𝑡 (C.10)
whe e 𝛼0 is a wage sha e scaling, 𝜓0
∗ is he long- un wage end, 𝛿2 (o 𝛼1) is a wage slope, 𝑢0
∗ is
he long- un gap end, 𝛽0 is a gap scaling, and 𝛿4 (o 𝛽1) is a gap slope. These equa ions a e
es ima ed, and he esul s a e shown in able A1. Fo ad anced/de eloping coun ies di e ences,
he wage and u iliza ion slopes a e allowed o a y ac oss di e en g oups o coun ies.
82 A global ace o he bo om: The neo-Goodwinian agg ega i e-sys ems es ima ion
PSL Qua e ly Re iew
Table A1 – Econome ic esul s o he globe
HP
Band-pass
Mo ing a e age
BN
Hamil on
Wage slope (𝛼1)
2.86
(32.12)
5.83
(–60.65)
5.36
(98.55)
3.21
(18.96)
0.64
(33.63)
U iliza ion slope (𝛽1)
–14.04
(–39.53)
–39.31
(–62.74)
–45.39
(–105.98)
–95.53
(–6.26)
–32.36
(–30.65)
Wage sha e scaling (𝛼0)
–0.07
(–36.82)
–0.07
(–68.09)
–0.07
(–106.92)
–0.02
(–21.95)
–0.07
(–49.64)
U iliza ion scaling (𝛽0)
–0.03
(–41.25)
–0.02
(–58.9)
–0.02
(–101.5)
–0.002
(–6.15)
–0.02
(–30.83)
Long- un wage in e cep (𝛼0
∗)
98.95
(703.56)
98.2
(884.45)
98.52
(854.15)
88.57
(191.25)
97.92
(930.75)
Long- un u iliza ion in e cep (𝑢0
∗)
0.16
(6.69)
–0.1
(–33.82)
–0.09
(–75.46)
1.01
(37.75)
0.74
(34.62)
Schwa z Bayesian C i e ion (SBC)
–830.17
–5526.54
–5027.69
–4606.72
4238.9
Akaike In o ma ion C i e ion (AIC)
–843.58
–5539.5
–5040.83
–4620.04
4225.77
No e: All coe icien s a e signi ican a a 1% signi icance le el ( -s a is ics in he pa en heses), excep as deno ed
o he wise. As e isks * and ** indica e a signi icance le el o 10% and 5%, espec i ely.
Table A2 – Econome ic esul s wi h linea ends o he globe
HP
Band-pass
Mo ing a e age
BN
Hamil on
Wage slope (𝛼1)
2.72
(30.98)
5.57
(57.67)
5.15
(85.38)
2.89
(15.2)
0.61
(32.56)
U iliza ion slope (𝛽1)
–13.41
(–39.2)
–35.95
(–58.63)
–43.06
(–79.21)
–93.15
(–6.3)
–36.94
(–25.58)
Wage sha e scaling (𝛼0)
–0.07
(–35.67)
–0.07
(–64.9)
–0.07
(–93.39)
–0.02
(–18.52)
–0.08
(–46.2)
U iliza ion scaling (𝛽0)
–0.03
(–41.06)
–0.02
(–57.1)
–0.02
(–78.72)
–0.002
(–6.19)
–0.02
(–25.83)
Long- un wage in e cep (𝛼0
∗)
102.16
(192.87)
102.17
(223.1)
101.74
(232.26)
71.56
(30.64)
100.69
(217.16)
Long- un u iliza ion in e cep (𝑢0
∗)
0.22
(2.05)**
–0.02
(–0.63)a
–0.06
(–5.62)
–1.1
(–8.82)
0.34
(3.2)
Long- un wage end (𝜓1
∗)
–0.1
(–6.95)
–0.13
(–10.04)
–0.1
(–9.03)
0.55
(9.37)
–0.08
(–6.97)
Long- un u iliza ion end (𝑢1
∗)
–0.002
(–0.64)a
–0.003
(–4.54)
–0.001
(–3.08)
0.07
(20.52)
0.01
(4.36)
Schwa z Bayesian C i e ion (SBC)
–836.6
–5532.66
–5023.54
–4589.27
4239.7
Akaike In o ma ion C i e ion (AIC)
–854.47
–5549.93
–5041.06
–4607.02
4222.18
No e: All coe icien s a e signi ican a a 1% signi icance le el ( -s a is ics in he pa en heses), excep as deno ed
o he wise. As e isks * and ** indica e a signi icance le el o 10% and 5%, espec i ely.
a insigni ican a any le el.
