The Solow residual, a distributional approach: The case of Chile, 1985-2019

Villanue a Melo, Fe nando
A icle
The Solow esidual, a dis ibu ional app oach: The case o
Chile, 1985-2019
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: Villanue a Melo, Fe nando (2024) : The Solow esidual, a dis ibu ional app oach:
The case o Chile, 1985-2019, PSL Qua e ly Re iew, ISSN 2037-3643, Associazione Economia ci ile,
Rome, Vol. 77, Iss. 310, pp. 409-436,
h ps://doi.o g/10.13133/2037-3643/18663
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/324119
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ol. 77 n. 310 (Sep embe 2024)
The Solow esidual, a dis ibu ional app oach:
The case o Chile, 1985-2019
FERNANDO VILLANUEVA MELO
Abs ac :
The p ima y goal o his pape is o p esen a dis ibu i e
p oposal o ein e p e ing Solow’s esidual and apply i
wi hin he Chilean con ex . We a gue ha Solow’s esidual
can only indi ec ly cap u e echnological phenomena.
This c i ique d aws upon he con ibu ion o Felipe and
McCombie (2020), who con end ha p oduc ion unc ions
me ely e lec an iden i y accoun . Hence, he so-called
To al Fac o P oduc i i y (TFP) mi o s he dynamic o
eal wages and he a e o p o i .
We adop a desc ip i e app oach o es ima e and
decompose he Solow esidual g ow h o he Chilean
economy, o disce n he o igins o dis ibu ional changes
be ween 1985 and 2019. A key pa e ns is ha h oughou
almos he en i e pe iod, he dynamic o he Solow
esidual is closely in e wined wi h luc ua ions in he
p o i a e. Addi ionally, we decompose he p o i a e o
highligh ha he decline in he Chilean economy’s p o i
a e s ems om bo h dis ibu ional and echnological
ac o s.
Na ional S a is ics Ins i u e o Chile (INE),
email: illanue @ en.uchile.cl
How o ci e his a icle:
Villanue a Melo F. (2024), “The Solow esidual, a
dis ibu ional app oach: The case o Chile, 1985-2019” PSL
Qua e ly Re iew, 77 (310), pp. 409-436.
DOI: h ps://doi.o g/10.13133/2037-3643/18663
JEL codes:
D33, E01, E24, O47, O54
Keywo ds:
Solow esidual, o al ac o p oduc i i y, unc ional income
dis ibu ion, wages, p oduc i i y, a e o p o i , Chile, g ow h
accoun ing
Jou nal homepage:
h p: //www.pslqua e ly e iew.in o
Mains eam app oaches o economic g ow h pos ula e a bina y iewpoin , whe ein ou pu
g ow h can o canno be a ibu ed o he accumula ion o ac o s o p oduc ion. Acco ding o his
adi ion, and in line wi h Solow’s (1957) seminal con ibu ion, he long- un g ow h o capi alis
economies elies on “unobse able” ac o s a he han on he accumula ion o labo o capi al (p.
316). These unobse able ac o s, empi ically labeled as he “Solow esidual”, would e lec he
e olu ion o To al Fac o P oduc i i y (TFP) o he con ibu ion o echnological p og ess o
economic g ow h. None heless, his a gumen hinges on a pa icula economic heo y ha claims
ha agg ega e p oduc ion can be ep esen ed by a unc ion wi h speci ic p ope ies.
We con end ha bo h his app oach and he mains eam p esc ip ions aimed a obse ing and
enhancing p oduc i i y a e misleading. TFP is me ely a heo e ical cons uc , and he so-called
Solow esidual p ima ily e lec s dis ibu ional dynamics wi hin he economy a he han
echnological change. Hence o h, we pu o h an al e na i e p oposal based on he wo k o Felipe
and McCombie (2020). They a gued ha ou pu , employmen , and capi al s ock a e al eady
Special issue on s uc u al change, social inclusion, and en i onmen al sus ainabili y
410 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
ela ed h ough an accoun iden i y. Hence o h, empi ical esea ch based on p oduc ion
unc ions me ely e lec s his iden i y a he han ac ual p oduc ion pa e ns. As Anwa Shaikh
s essed: “ his is a law o algeb a, no a law o p oduc ion” (Shaikh, 1974, p. 118). The implica ions
o his a gumen a e p o ound. Economic analysis and policy o mula ion ely on economy heo y.
I he unde lying economic heo y is lawed, i can lead o misleading analyses and, wo se s ill,
could esul in ad e se e ec s when applied o economic policy. This a gumen holds pa icula
ele ance in he cu en deba e in Chile, as he coun y has expe ienced a lacklus e
mac oeconomic pe o mance since 1998. Mo eo e , he e is a widesp ead ag eemen ha
p oduc i i y lies a he oo o his issue, and con en ional measu es o i o en ely on TFP.
In sec ion 1, we will p esen he a gumen o Felipe and McCombie (2020), demons a ing ha
he p oduc ion unc ions e lec an accoun iden i y and ha he Solow esidual is jus an indica o
o dis ibu ional dynamics. Addi ionally, we s ess ha his a gumen is no a no el, as i has been
a icula ed by a ious hinke s since 1950. In sec ion 2, we conduc a compa a i e analysis o
a ious g ow h accoun ing exe cises applied in he Chilean economy and discuss he implica ions
o obse ing p oduc i i y h ough TFP and i s ole in in o ming economic analysis and policies. In
sec ion 3, we es ima e he Solow esidual o Chile du ing 1985-2019, aiming o unco e i s
unde lying componen s. No ably, in he case o Chile, he e olu ion o he Solow esidual mi o s
he dynamics o he p o i a e, pa icula ly e iden pos -2000. In sec ion 4 we del e in o he
analysis o he unde lying o ces d i ing he dynamics o he p o i a e in Chile. In sec ion 5, we
unde ake a b ie p oduc i i y analysis o he Chilean economy, seeking o comp ehend i s
ela ionship wi h he all in he p o i a e o e he las decade, and in sec ion 6 we d aw
conclusions based on ou indings.
1. G ow h accoun ing and income accoun iden i ies
The neoclassical app oach o economic g ow h is g ounded on he assump ion ha he economy’s
o al p oduc ion can be e ec i ely ep esen ed by a p oduc ion unc ion wi h speci ic p ope ies.
Typically, he p oduc ion unc ion is s uc u ed as ollows:
𝑌=𝑓(𝐴,𝐾,𝐿)
whe e 𝑌 ep esen s he eal le el o ou pu (GDP), 𝐴 deno es he TFP le el, 𝐾 is he mone a y alue
o he capi al s ock o he economy, and 𝐿 s ands o labo , which can be measu ed by he numbe
o wo ke s employed o he o al hou s wo ked. This app oach a gues ha economic g ow h can
only occu i , and only i , one o mo e o he componen s o he p oduc ion unc ion g ows. G ow h
accoun ing exe cises a e essen ially aimed a decomposing GDP g ow h in o he con ibu ions o
hese a iables.
I we assume ha : (1) he p oduc ion unc ion is di e en iable wi h espec o e e y inpu (𝐾
and 𝐿), (2) he e exis posi i e and diminishing ma ginal p oduc i i ies o capi al and labo , (3)
he e a e cons an e u ns o scale, and (4) he o e all economy ope a es unde pe ec
compe i ion, we can decompose GDP g ow h using he ollowing equa ion:
𝑔𝑦=𝑔𝐴+𝑠𝑘⋅𝑔𝐾+(1−𝑠𝑘)𝑔𝐿 (1)
whe e 𝑔𝑦 ep esen s he g ow h in eal GDP, 𝑔𝐴 deno es TFP g ow h, 𝑠𝑘 ep esen s he sha e o
capi al income in o al income, 𝑔𝐾 indica es he g ow h in capi al s ock, and 𝑔𝐿 s ands o he
g ow h in labo inpu s’. Howe e , as 𝑔𝐴 is empi ically no obse able, i is es ima ed as he
F. Villanue a Melo 411
PSL Qua e ly Re iew
di e ence be ween GDP g ow h and he weigh ed g ow h o capi al and labo . Consequen ly, in
g ow h accoun ing exe cises, he e is a componen explained by he accumula ion o capi al and
labo and a non-obse able componen 𝑔𝐴. Thus, 𝑔𝐴 is p ac ically es ima ed as a esidual:
𝑔𝐴
=𝑔𝑦−𝑠𝑘⋅𝑔𝐾−(1−𝑠𝑘)𝑔𝐿 (2)
Acco ding o his heo y, he g ow h o he esidual cap u es he expansion o TFP o he
con ibu ion o echnological change o economic g ow h. Fu he mo e, empi ical s udies oo ed
in his economic amewo k a gue ha GDP g ow h is p edominan ly a ibu able o unexplained
ac o s and conclude ha i is due o imp o emen s in he echnology implemen ed in he
p oduc ion p ocess ha enhances long- e m economic g ow h (Solow, 1957; Ba o and Sala-i-
Ma in, 2004; Acemoglu, 2008). Economis s ha e in oduced e inemen s o his app oach,
co ec ing labo inpu s by educa ion, highligh ing he ole o human capi al in economic g ow h,
and co ec ing capi al by in ensi y use. None heless, he heo e ical ounda ion emains
unchanged.
Howe e , using he app oach o Felipe and McCombie (2020), we can de i e he exac
exp ession o equa ion (1) wi hou elying on any heo y o p oduc ion o compe i ion bu based
solely on accoun ing iden i ies. Thus, his app oach is heo y- ee in he sense ha we ely jus on
he bounda ies o p oduc ion and income de ined by he Sys em o Na ional Accoun s (SNA).
1
None heless, he p ima y dis inc ion is ha his exp ession e lec s an income iden i y and no he
con ibu ion o each ac o o p oduc ion o achie e a speci ic ou pu le el.
In he cu en SNA, p ima y income is de ined as he “income ha acc ues o ins i u ional uni s
as a consequence o hei in ol emen in p ocesses o p oduc ion o owne ship o asse s ha may
be needed o pu poses o p oduc ion.” (UNSC, 2008, p. 131) Consequen ly, he g oss alue
gene a ed in he p oduc ion p ocess is dis ibu ed o a ious economic agen s. This is known as
he unc ional dis ibu ion o income. As pe he SNA, p ima y income encompasses wage-
wo ke s’ labo income o hei pa icipa ion in he p oduc ion p ocess, p ope y income, and ne
axes on p oduc ion and impo s.
𝑃𝑟𝑖𝑚𝑎𝑟𝑦
𝐼𝑛𝑐𝑜𝑚𝑒 ≡𝐶𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛
𝑜𝑓 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒𝑠 +𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦
𝐼𝑛𝑐𝑜𝑚𝑒 +𝑁𝑒𝑡 𝑡𝑎𝑥𝑒𝑠 𝑜𝑛
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑖𝑚𝑝𝑜𝑟𝑡𝑠 (3)
This accoun ing p inciple is applicable o speci ic i ms, indus ies, o he whole economy.
Thus, his app oach’s conclusion can be used a e e y economic le el. Sub ac ing ne axes on
p ima y income yields he ma ke alue o GDP a ac o cos (GDPFC). Acco ding o he SNA, GDP
a ac o cos is “essen ially a measu e o income and no ou pu . I ep esen s he amoun
emaining o dis ibu ion ou o g oss alue added.” (UNSC, 2008, p. 104) Thus, GDP a ac o cos
is di ided be ween wages and p ope y income, labeled as g oss ope a ing su plus (GOS) since i
is he low o all income o he han compensa ion o employees.
2
Consequen ly, GDP a ac o cos
can be decomposed in o o e all labo income (∑𝑤𝑖
𝑛
𝑖=1 ) and GOS. The eal alue o hese a iables
can be ob ained by de la ing hem using he same p ice index, and, i we di ide he o e all wage
bill and GOS by he o al numbe o wo ke s (𝐿) and asse s used in he p oduc ion p ocess (𝐾),
1
These bounda ies a e based on a se ies o assump ions and de ini ions aimed a delinea ing accoun able ela ionships
o obse e and desc ibe hem. Howe e , hese assump ions do no explain economic ela ionships o beha io a he
mic o o mac o le el. In his ega d, he SNA is conside ed “ heo y ee”.
2
I is ele an o s ess ha we o e es ima e p ope y income unde his app oach, since g oss alue added includes
capi al consump ion (dep ecia ion), mixed income, en s, di ec axes, in e es , and di idend paymen s.
412 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
espec i ely, we will de i e he a e age eal wage (𝑤) and he a e age a e o p o i (𝑟). Thus, he
ollowing exp ession is de i ed:
𝐺𝐷𝑃𝐹𝐶 ≡∑𝑤𝑖
𝑛
𝑖=1 +𝐺𝑂𝑆=𝑤𝐿+𝑟𝐾 (3.1)
Neoclassical heo y e e s o his iden i y as Eule ’s heo em, p emised on he assump ion ha
he agg ega e p oduc ion unc ion exhibi s cons an e u ns o scale. Howe e , he
a o emen ioned accoun does no depend on any heo y o p oduc ion o compe i ion; a he , i
elies solely on he bounda ies o income and p oduc ion de ined by he SNA.
By di e en ia ing he p e ious exp ession wi h espec o ime ( he a iables wi h he do a
he op s and o he i s di e ence) and di iding i by he ini ial le el o GDP, we de i e he
g ow h in eal GDP a ac o cos and i s componen s:
𝑔𝑦≡w
𝑤󰇗[𝐿𝑤
𝑌]+L
𝐿󰇗[𝐿𝑤
𝑌]+
𝑟󰇗[𝐾𝑟
𝑌]+K
𝐾󰇗[𝐾𝑟
𝑌] (4)
I we de ine he GOS sha e in GDP a ac o cos as 𝑠𝑘, we ob ain he ollowing exp ession:
𝑔𝑦≡𝑔𝑤(1−𝑠𝑘)+𝑔𝑟𝑠𝑘+𝑔𝐿(1−𝑠𝑘)+𝑔𝐾𝑠𝑘 (4.1)
whe e 𝑔𝑤 ep esen s he g ow h a e o eal wages and 𝑔𝑟 deno es he g ow h o he p o i a e.
The e o e, ollowing he SNA, we can decompose he g ow h o GDP a ac o cos in he
weigh ed g ow h o labo , p oduc i e asse s, and a dis ibu ional componen ha cap u es he
weigh ed g ow h o eal wages and he a e o p o i . This la e componen is iden i ied by
mains eam economis s as he inc ease in p oduc ion ha is no a ibu ed o he accumula ion o
ac o s o p oduc ion. We can obse e ha iden i y (4.1) is he same exp ession as equa ion (1).
Hence, wha economis s ypically label as TFP g ow h is essen ially he weigh ed g ow h o wages
and he a e o p o i . Speci ically:
𝑔𝐴=𝑔𝑤(1−𝑠𝑘)+𝑔𝑟𝑠𝑘=𝑔𝑤+𝑠𝑘(𝑔𝑟−𝑔𝑤) (5)
Economis s o en e e o TFP as he “measu e o ou igno ance” (Ab amo i z, 1956), since
hey label wha e e is no cap u ed in he accumula ion o capi al and labo as echnological
change (Solow, 1957, p. 312). Ne e heless, wi h a clea e unde s anding o he SNA, we ecognize
ha his unobse able elemen o neoclassical heo y can indeed o e insigh s in o dis ibu ion
and p o i abili y dynamics (Shaikh, 2016, p. 658). Fu he mo e, empi ical es ima ions o TFP
consis en ly e eal i s p ocyclical na u e (Fuen es e al., 2006; Field, 2010; Schmölle and Spi ze ,
2020). This o ms he base o eal business cycles heo y, which seeks o explain economic
luc ua ions based on exogenous shocks in TFP. Howe e , he p ocyclical na u e o TFP can be
a ibu ed o he s onge (weake ) g ow h o bo h eal wages and he p o i a e du ing he
upswing (downswing) phase o he business cycle. This is because eal wage g ow h is pa ly
de e mined by labo demand, which is linked o i ms’ expec a ions o sales/p oduc ion, and he
in ensi y o sales de e mines i ms’ p o i abili y, in luencing decisions o expand ou pu and
capi al.
I is pe inen o emphasize ha his c i ique is no a no el y. In 1957, he same yea Solow
published his seminal con ibu ion, B own c i iqued Cobb and Douglas’s wo k, a guing ha
p oduc ion unc ion es ima ions a e p ede e mined by an accoun ing iden i y (B own, 1957).

F. Villanue a Melo 413
PSL Qua e ly Re iew
Decades la e , he same a gumen was ei e a ed by Simon and Le y (1963) and Shaikh (1974).
Howe e , despi e hese c i iques, neoclassical g ow h heo y emained la gely una ec ed.
2. G ow h accoun ing exe cise in he Chilean economy
The asse ion ha p oduc ion unc ions e lec an accoun ing iden i y implies ha analysis
u ilizing his app oach can ne e be ejec ed on an empi ical o econome ical g ound.
Consequen ly, p oduc ion unc ions seem o unc ion well empi ically, i ing da a e ec i ely.
Howe e , hey do no p o ide any suppo o neoclassical heo y since i s esul s a e
p ede e mined (B own, 1957; Shaikh, 2016, p. 659). The e o e, we will summa ize g ow h
accoun ing exe cises conduc ed o he Chilean economy, bea ing in mind ha he TFP
es ima ions e lec he dis ibu ional dynamics exp essed in equa ion (5).
Figu e 1 – GDP g ow h a e in Chile, 1985-2019 (3-yea mo ing a e age)
Sou ce: Own elabo a ion based on SNA da a p o ided by he Cen al Bank o Chile
(h ps://si3.bcen al.cl/Sie e/ES/Sie e/Cuad o/CAP_CCNN/MN_CCNN76/CCNN_HIST18_ENC/).
Since he end o he 1980s, he Chilean economy expe ienced a pe iod o his o ically high GDP
g ow h un il 1998. This e a, o en e e ed o as he ‘golden age’ o he Chilean economy,
3
p o ided
he backd op o nume ous g ow h accoun ing exe cises aimed a unde s anding he economic
boom om 1986 o 1998 and he subsequen decline in g ow h a es a e he Asian c isis. Figu e
1 illus a es he ela i ely high GDP g ow h a es achie ed du ing he 1990s, jux aposed wi h he
inabili y o he Chilean economy o sus ain hese le els pos -1998. Indeed, he g aph also e eals
a downwa d ajec o y in GDP g ow h o e he las ew decades. The a e age GDP g ow h a e
3
Du ing hose yea s, GDP g ow h in Chile was among he ou h highes in he wo ld (Gallegos and Loayza, 2002).
-2%
0%
2%
4%
6%
8%
10%
12%
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
2017
2019
GDP g ow h 3-yea mo ing a e age
414 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
s ood a 7% du ing 1990-1998; i declined o 4.4% du ing 1999-2007 and u he dec eased o
3% du ing 2008-2019.
The g ow h accoun ing exe cises conduc ed o analyze he ‘golden age’ p ima ily
concen a ed on o e ing insigh s in o he dynamics o TFP g ow h and i s ole in achie ing high
GDP g ow h a es. Be o e he wo ld inancial c isis, he e was a complacen iewpoin in which
se e al economis s a gued ha his pe iod was he p oduc o he ins i u ional amewo k se by
he economic e o ms o he dic a o ship a he han o he cu en economic policies
implemen ed by democ a ic go e nmen s. Howe e , hese explana ions became mo e complex
a e wa d, as he same ins i u ional amewo k exhibi ed a end owa d economic s agna ion.
We a gue ha insigh s aimed a desc ibing and explaining p oduc i i y g ow h and echnological
change based solely on TFP a e misleading, as he Solow esidual p ima ily e lec s he dynamics
o he a e o p o i and wages a he han p o iding a comple e pic u e o echnological p og ess.
Be o e he wo ld inancial c isis, g ow h accoun ing exe cises aimed a explaining he sou ces
o he excep ional GDP g ow h du ing he 1990s. These exe cises p ima ily o igina ed om he
academic sphe e, wi h es ima ions made i egula ly o e ime and o speci ic pe iods (CNP, 2016,
p. 20). Mos o he me hodologies did no co ec o human capi al and capi al u iliza ion. We
ha e selec ed in Table 1 some g ow h accoun ing exe cises conduc ed by p ominen Chilean
mac oeconomis s who hold signi icance in bo h he academic and he economic policy ealms. The
pu pose o selec ing hese exe cises is o highligh hei a gumen s and o gain insigh in o he
na a i e cons uc ion o he Chilean economy’s pe o mance.
Table 1 – Fi s gene a ion o g ow h accoun ing exe cises
Au ho
S udy
pe iod
Adjus men
in K and/o
L
𝜶 o 𝒔𝑲
Sub-pe iods
TFP
g ow h
GDP
g ow h
De G ego io
(1997)
1975-1997
No
40%
1985-1989
2.0%
6.6%
1990-1997
2.6%
6.7%
Beye and Ve ga a
(2002)
1976-2001
No
40%
1986-1990
2.3%
6.8%
1991-1995
3.7%
8.7%
1996-2000
0.1%
4.1%
1998-2001
–0.6%
2.4%
De G ego io
(2004)
1970-2004
No
40%
1985-1989
1.8%
6.4%
1990-1999
2.0%
6.3%
2000-2004
0.8%
3.7%
Ve ga a
(2005)
1960-2004
No
55%
1986-1990
2.1%
6.7%
1991-1995
4.9%
8.7%
1996-2000
0.9%
4.2%
2001-2004
1.0%
3.8%
Fuen es, La aín and
Schmid -Hebbel
(2006)
1960-2005
No
40%
1990-1997
3.9%
7.1%
1998-2005
1.0%
3.1%
F. Villanue a Melo 415
PSL Qua e ly Re iew
Acco ding o De G ego io (1997), he high g ow h a he end o he 1980s was p ima ily
a ibu ed o he employmen eco e y ha ollowed he deb c isis o 1982, du ing which he
unemploymen a e exceeded 20% o he labo o ce. In con as , in he 1990s, he g ow h was led
by a capi al accumula ion and TFP g ow h. In his pape , De G ego io explo es he unde lying
de e minan s o g ow h. He highligh s he p imo dial ole o inc eased co e age in seconda y
educa ion, he educ ion in in la ion, and he con ac ion in go e nmen expendi u e as ac o s
ha os e ed economic g ow h (De G ego io, 1997, p. 32).
In a mo e ecen analysis, De G ego io (2004) highligh s he decline in GDP and TFP g ow h
ollowing he 1998 Asian c isis and del es in o he a eas he conside s c ucial o explaining
economic g ow h in Chile du ing he ‘golden age’. Among hese ac o s a e low in la ion, sound
iscal policy (including low iscal de ici s and public deb ), a s ong inancial sec o , and openness
o ade. In a b oade explo a ion o he undamen al causes o economic g ow h, he concludes
ha ce ain p ope y igh s and an app op ia e s uc u e o ewa ds a e he main de e minan s
o encou aging economic g ow h (De G ego io, 2004, p. 47). This pe spec i e aligns wi h he
p e ailing iew in mains eam mac oeconomics and in e na ional inancial ins i u ions du ing he
1990s, which emphasized ha mac oeconomic undamen als, such as low in la ion and iscal
balances, we e he mos ele an a iables o enhancing economic de elopmen . Despi e se e al
La in Ame ican economies achie ing hese a ge s du ing he 1990s, hei mac oeconomic
pe o mance has been disappoin ing (F ench-Da is, 2005).
Beye and Ve ga a (2002) a gue ha he g ow h o he golden age esul ed om he e o ms
ha “ ans o med Chile om a e y closed and o e egula ed economy o an open and
compe i i e one” (p. 328). The a gumen goes u he : “I he Coun y is able o main ain and
imp o e hese policies and ins i u ions, i will ensu e an addi ional pe iod o high g ow h” (p.
337). Pa adoxically, hey also highligh he slowdown in economic g ow h and he nega i e
con ibu ion o TFP o g ow h a e 1998. The au ho s a gue ha he coun y needed a “new
shock” o ini ia e a new pe iod o high economic g ow h. These shocks in ol ed ex ending
p e ious e o ms, such as he ex ensi e p i a iza ion o he heal h sys em, inc easing he labo
ma ke ’s lexibili y, and educing social p og am co e age (pp. 317-319). A simila a gumen can
be ound in Ve ga a (2005), which claims ha he golden age is explained by he delayed ui s o
he e o m o he dic a o ship. Fu he mo e, his au ho also s esses ha TFP in Chile is ola ile
and highly p ocyclical, wi h a co ela ion index o 0.91 be ween GDP and TFP g ow h (Ve ga a,
2005).
Fuen es e al. (2006) also highligh he signi ican d op in he con ibu ion o TFP g ow h a e
1999. These au ho s emphasize he p o-cyclical na u e o TFP in he Chilean economy and a emp
o explain i s e olu ions h ough a eg ession analysis. They use as independen a iables he
e ms o ade, he eal exchange a e unde alua ion index, he ci il libe y and mac oeconomic
ins abili y index, and a iables ha y o cap u e s uc u al e o ms. The au ho s conclude ha
cyclical ac o s, pa icula ly he e ms o ade, domina e o e s uc u al ac o s o explain he
g ow h o TFP in ecen yea s in Chile. Using he SNA app oach, i becomes e iden ha he e ms
o ade would accoun o he a ia ion o he Solow esidual. This linkage a ises om he
e olu ion o he p ice o coppe , which cons i u es he p ima y componen o Chilean expo s.
Consequen ly, luc ua ions in coppe p ices impac he p o i a e o he mining sec o , he eby
a ec ing agg ega e p o i abili y and he Solow esidual. Fu he mo e, he e ms o ade play a
c ucial ole in elaxing he ex e nal cons ain , allowing a mino ecessiona y gap ( he a io
be ween e ec i e and po en ial GDP), which also enhances p o i abili y.
The e is a second g oup o g ow h accoun ing exe cises elabo a ed a e he wo ld inancial
c isis by public ins i u ions such as DIPRES (budge o ice o he go e nmen ), CORFO (Chilean
416 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
economic de elopmen agency), and he CNP (na ional commission o p oduc i i y). These
ep esen a s age in which economic g ow h ne e eco e ed i s 1990s le els and exhibi ed a
con inued end o economic s agna ion, especially a e 2014. These second-gene a ion g ow h
accoun ing exe cises a e conduc ed egula ly o e ime. Fu he mo e, he in ol emen o public
ins i u ions in hese exe cises indica es a ecogni ion ha add essing he p oduc i i y slowdown
pos -1998 has become a p io i y in economic policy. TFP se es as a c ucial me ic o assessing
p oduc i i y in his ega d. Fo ins ance, DIPRES annually ga he s a eam o mac oeconomis s o
es ima e po en ial GDP, es ima ing se e al TFPs, o in o m he go e nmen ’s iscal policy
decisions. DIPRES’s long- e m g ow h accoun ing exe cise spanning 1960 o 2019 unde sco es
he ola ile and p ocyclical na u e o TFP.
Addi ionally, acco ding o hese ins i u ions ha pe o med sys ema ically g ow h accoun ing
ece sies, Chile’s a e age TFP g ow h has been nega i e (-0.8%) since he wo ld inancial c isis
(2009-2019).
Table 2 – Second gene a ion o g ow h accoun ing exe cises
Au ho
S udy
pe iod
Adjus men in
K and/o L
𝜶 o 𝒔𝑲
Sub-pe iods
TFP
g ow h
GDP
g ow h
UAI and CORFO
(2014)
1993-2014
K and L
53%
1993-1998
2.4%
6.5%
2000-2008
0.8%
4.7%
2010-2014
0.4%
4.6%
CNP
(2018)
1990-2018
No
48%
1991-1998
3.2%
7.2%
1999-2008
0.8%
4.0%
2009-2018
–0.02%
3.0%
DIPRES
(2020)
1960-2019
K and L
48%
1990-1998
2.2%
6.8%
1999-2008
0.7%
4.3%
2009-2019
–0.8%
2.9%
CLAPES UC
(2020)
1970-2018
No
48.5%
1990-1998
2.8%
n.a.
1999-2008
0.8%
n.a.
2009-2018
–0.6%
n.a.
Since 2012, CORFO, in collabo a ion wi h Uni e sidad Adol o Ibañez (UAI), has conduc ed
g ow h accoun ing exe cises based on a Cobb-Douglas p oduc ion unc ion. These exe cises
include co ec ions o human capi al and capi al u iliza ion. They ha e iden i ied he onse o
s agna ion in he Chilean economy in 2014 and a decline in TFP g ow h ollowing he golden age.
A key dis inc ion om p e ious app oaches is hei es ima ion o TFP g ow h o di e en
economic sec o s. They emphasize he he e ogenei y among economic sec o s and pinpoin he
sys ema ic all in he wage o he manu ac u ing and e ail sec o s, e en hough hey a ibu ed
his o a all in he labo o ce quali y (UAI and CORFO, 2014). Fu he mo e, hey poin ou ha
TFP g ow h o he Chilean economy appea s highe when excluding he mining and elec ici y,
wa e , and gas supply sec o s.
In 2015, he Na ional P oduc i i y Commission (CNP) was es ablished as a esea ch cen e
asked wi h p o iding ecommenda ions o enhance na ional p oduc i i y. Since 2016, he CNP
has conduc ed an annual es ima ion o TFP o he o e all economy and by economic sec o . I s
F. Villanue a Melo 423
PSL Qua e ly Re iew
wages using equa ion (5.1), and he weigh ed g ow h by he unc ional income dis ibu ion. To
delinea e he o e all 1985-2019, pe iod, we will ollow he ull economic cycles o he Chilean
economy, as ou lined by F ench-Da is (2018). I is impo an o s ess ha he p edic ed eal
wage ep esen s he eal p oduc wage, which is he nominal wage de la ed by he GDP de la o ,
no by he consume p ice index (CPI).
Table 4 – Dis ibu ional decomposi ion o he Solow esidual in Chile ( he mean o each a iable
unde speci ic pe iods)
Pe iod
𝒈𝒓
𝒈𝒘
(p edic ed)
𝒔𝒌⋅𝒈𝒓
(𝟏−𝒔𝒌)⋅𝒈𝒘
(p edic ed)
𝒈𝑨
1986-1989
8.43%
–1.17%
5.28%
–0.49%
4.79%
1990-1998
0.05%
6.12%
0.05%
2.58%
2.63%
1999-2007
1.49%
–0.25%
0.93%
–0.05%
0.88%
2008-2013
–3.28%
2.88%
–1.85%
1.27%
–0.57%
2014-2019
–3.01%
0.67%
–1.63%
0.31%
–1.32%
Sou ce: Own elabo a ion based on SNA da a p o ided by he Cen al Bank o Chile
(h ps://si3.bcen al.cl/es adis icas/P incipal1/enlaces/In o mes/Anua iosCCNN/CCNN-anua ios.h ml).
Table 4 e eals ha ei he eal wages o he p o i a e’s dynamic leads he g ow h o he
Solow esidual in Chile o e he analyzed pe iod. Addi ionally, he e exis s a nega i e ela ionship
be ween he g ow h a e o he p o i a e and o eal wages in he economy. Du ing pe iods o
apid p o i a e g ow h, wages end o decline, and ice e sa. The co ela ion index be ween
bo h a iables is –0.53.
One o he mos no able pa e ns is he s ong co ela ion be ween he g ow h o he Solow
esidual in Chile and he g ow h o he p o i a e. Indeed, he co ela ion index be ween hese
wo a iables is 0.78, whe eas he co ela ion index o he g ow h o he Solow esidual and o
eal wages is jus 0.11. Consequen ly, in Chile he dynamic o he Solow esidual mi o s he
dynamic o he a e o p o i . Fu he mo e, he g ow h a e o he p o i a e, in absolu e e ms,
exceeded ha o wages in e e y pe iod excep du ing he golden age, as a gued p e iously.
The analysis unde sco es he excep ional na u e o he golden age in Chilean economic
g ow h, whe e eal wage g ow h played a leading ole in shaping he dynamic o he Solow
esidual. Unlike o he pe iods, whe e he p o i a e p edominan ly in luenced i s ajec o y,
du ing he golden age, wage g ow h ou paced a e age labo p oduc i i y g ow h, leading o a
decline in he sha e o GOS and an inc ease in he labo income sha e.
5
This change in unc ional
income dis ibu ion and a s able p o i a e elies on con inuous inc eases in capi al p oduc i i y.
Following he wo ld inancial c isis, he s agna ion and subsequen decline o he Solow
esidual can be a ibu ed o he dec ease in he a e o p o i . This end was u he exace ba ed
by a s agna ion in eal wages pos -2014. O e all, his analysis sheds ligh on he in ica e in e play
5
Based on equa ion (3.1), we know ha 𝐺𝐷𝑃𝐹𝐶 ≡∑𝑤𝑖
𝑛
𝑖=1 +𝐺𝑂𝑆=𝑤𝐿+𝑟𝐾. The e o e, he labo income sha e is:
1−𝑠𝐾=𝑤𝐿/𝐺𝐷𝑃𝐹𝐶 =𝑤/𝐴𝑃𝐿, he a io o eal wages and eal a e age labo p oduc i i y (𝐴𝑃𝐿). Hence, he dynamic o
he labo income sha e depends on he g ow h disc epancy o hese wo a iables.

424 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
be ween wage dynamics, p o i a es, and p oduc i i y g ow h in shaping he ajec o y o he
Solow esidual in Chilean economic g ow h.
Fu he mo e, we can alida e he accoun iden i y by compa ing he p edic ed alue o wage
g ow h wi h he ac ual e olu ion o eal wages. To compu e he e ec i e g ow h a e in eal wages,
we sub ac in la ion, measu ed as he annual change in he GDP de la o (2013 p ices), om he
g ow h in he gene al index o nominal emune a ions om he Na ional S a is ics Ins i u e o
Chile. Figu e 5 illus a es ha , while he p edic ed and he e ec i e g ow h in wages a e no
iden ical, hey exhibi ema kably simila le els and dynamic. Speci ically, he p edic ed g ow h
a e o eal wages o he 1985-2019 pe iod s ands a 2% pe yea , whe eas he e ec i e g ow h
a e o wages is sligh ly highe , a 2.1%. This inding bols e s he a gumen ha he Solow esidual
unc ions no only as a p oduc i i y measu e bu also as an indica o o how income is dis ibu ed
among ac o s o p oduc ion.
Figu e 5 – P edic ed and ac ual g ow h o eal wages in Chile, 1985-2019
Sou ce: Own elabo a ion based on da a p o ided by he Cen al Bank o Chile
(h ps://si3.bcen al.cl/es adis icas/P incipal1/enlaces/In o mes/Anua iosCCNN/CCNN-anua ios.h ml
h ps://si3.bcen al.cl/Sie e/ES/Sie e/Cuad o/CAP_EMP_REM_DEM/MN_EMP_REM_DEM13/REM_HIST/REM_HIST).
4. Analysis o he Chilean a e o p o i
Ha ing es ablished ha he Solow esidual’s ajec o y is la gely dic a ed by he p o i a e’s
g ow h o e he analyzed pe iod, we can p oceed o in es iga e he ac o s unde lying he decline
o he p o i a e in Chile. This en ails examining he pi o al d i e s o p o i abili y, which a e
income dis ibu ion and echnology, encapsula ed wi hin he a e age p oduc i i y o capi al. To
acili a e a ho ough analysis, we p opose decomposing he p o i a e as ollows:
-12%
-8%
-4%
0%
4%
8%
12%
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
2017
2019
P edic ed g owh eal wages Real g owh eal wages
F. Villanue a Melo 425
PSL Qua e ly Re iew
𝑟𝑎𝑡𝑒 𝑜𝑓
𝑝𝑟𝑜𝑓𝑖𝑡 =[𝐺𝑟𝑜𝑠𝑠 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑆𝑢𝑟𝑝𝑙𝑢𝑠
𝐺𝐷𝑃 𝑎𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝑐𝑜𝑠𝑡 ]⋅[𝐺𝐷𝑃 𝑎𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝑐𝑜𝑠𝑡
𝐺𝑟𝑜𝑠𝑠 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑆𝑡𝑜𝑐𝑘]=𝑠𝑘⋅𝐴𝑃𝐾 (6)
Equa ion 6 e eals wo undamen al ac o s d i ing he p o i a e’s dynamics. Fi s ly, he e is
a dis ibu ional aspec , e lec ed in he sha e o GOS in GDP a ac o cos . Secondly, he e is a
echnological componen , ep esen ed by he in e se o he capi al-ou pu a io o he a e age
p oduc i i y o capi al. Consequen ly, all else being equal, an up ick in he capi al income sha e
will bols e he p o i a e, hus ampli ying he g ow h o he Solow esidual. Simila ly, an
enhancemen in a e age capi al p oduc i i y could ele a e he p o i a e, consequen ly ueling
he g ow h o he esidual. We posi ha he ex ao dina y pe o mance du ing he golden age
was unde pinned by a su ge in capi al p oduc i i y. This su ge sus ained he p o i a e despi e a
subs an ial inc ease in eal wages, which would ypically dep ess p o i abili y.
While i ’s possible o u he decompose he a e o p o i o accoun o he in luence o
capaci y u iliza ion on p o i abili y (Weisskop , 1979; Bhadu i and Ma glin, 1990), we op no o
pu sue his a enue in ou analysis. This decisions s ems om he necessi y o es ima ing ull o
no mal capaci y GDP, which is inhe en ly challenging due o i s non-obse abili y. I is essen ial
o ecognize ha luc ua ions in agg ega e demand can indeed impac bo h he capi al income
sha e and capi al p oduc i i y (Basu and Vasude an, 2013).
The dynamic na u e o he a e o p o i e lec s no only dis ibu ional elemen s bu also he
in e play be ween agg ega e supply and demand dynamics. Howe e , i ’s impo an o no e ha
ou s udy does no di ec ly ocus on he ela ionship be ween unc ional income dis ibu ion and
capaci y u iliza ion, no does i aim o de e mine whe he he la e is wage- o p o i -led
6
(Bhadu i and Ma glin, 1990; La oie and S ockhamme , 2013). Gi en he ime ame o ou
esea ch, we assume ha capaci y u iliza ion ho e s a ound no mal le els, and we can a o d o
o e look ealiza ion condi ions (Shaikh, 2016).
Figu e 6 illus a es a no able inc ease in GOS sha e and capi al p oduc i i y om 1985 o
1989. Consequen ly, he upsu ge in he p o i a e du ing ha pe iod can be a ibu ed o
enhancemen s in bo h dis ibu ional and echnological ac o s. Du ing he golden age, we obse e
a decline in he su plus’s sha e in GDP, which is coun e ac ed by he posi i e ajec o y o capi al
p oduc i i y. Thus, he sus ained p o i a e du ing he golden age is a esul o he o se ing
e ec s o he dis ibu ional componen and echnological ac o s. Howe e , i ’s c ucial o
acknowledge ha his end is no solely d i en by supply-side o echnological ac o s bu is also
in luenced by demand-side componen s. The subs an ial educ ion in he ecessiona y gap
be ween e ec i e and po en ial GDP du ing his pe iod unde sco es he impo ance o demand
dynamics in shaping he obse ed ends, since i is cap u ed in capi al p oduc i i y
7
(F ench-
Da is, 2018).
6
To consul an empi ical s udy o he na u e o agg ega e demand in Chile, see
h ps:// eposi o io.uchile.cl/handle/2250/175669?show= ull
7
We can exp ess a e age capi al p oduc i i y as:
𝐴𝑃𝐾=[𝐺𝐷𝑃 𝑎𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝑐𝑜𝑠𝑡
𝐺𝑟𝑜𝑠𝑠 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑆𝑡𝑜𝑐𝑘]=[ 𝐺𝐷𝑃𝑓𝑐
𝑁𝑜𝑟𝑚𝑎𝑙 𝑜𝑟 𝑓𝑢𝑙𝑙 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝐺𝐷𝑃𝑓𝑐][𝐺𝑁𝑜𝑟𝑚𝑎𝑙 𝑜𝑟 𝑓𝑢𝑙𝑙 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝐺𝐷𝑃𝑓𝑐
𝐺𝑟𝑜𝑠𝑠 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑆𝑡𝑜𝑐𝑘 ]
The e o e, an inc ease in capaci y u iliza ion, measu ed as he a io o e ec i e o no mal/ ull capaci y GDP, would
os e capi al p oduc i i y.
426 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
Figu e 6 – GOS sha e and a e age capi al p oduc i i y in Chile, 1985-2019
Sou ce: Own elabo a ion based on SNA da a p o ided by he Cen al Bank o Chile
(h ps://si3.bcen al.cl/es adis icas/P incipal1/enlaces/In o mes/Anua iosCCNN/CCNN-anua ios.h ml).
In 1998, he Chilean economy eached i s pinnacle in e ms o capi al p oduc i i y.
Subsequen ly, bo h a iables s agna ed and, ollowing he global inancial c isis, he e was a
decline in capi al p oduc i i y le els, e e ing o p e-1990 le els. This end se es as a c i ical
indica o , sugges ing ha mac oeconomic policies aimed a mi iga ing ecessiona y gaps h ough
agg ega e demand managemen and indus ial policies aimed a enhancing capi al p oduc i i y
ha e ailed o sus ain a s able p o i a e.
F om 1999 o 2007, he e was a no able con e gence o posi i e g ow h in bo h he
dis ibu ional and he supply componen s o he p o i a e. Speci ically, he sha e o capi al
income (GOS) in GDP a ac o cos eached 63%, ma king i s second-highes peak a e 1988. This
end can be a ibu ed o a signi ican su ge in he p ice o coppe , esul ing in subs an ial g ow h
in he su plus gene a ed by he mining sec o . Fu he mo e, his pe iod wi nessed a con ac ion
in he ecessiona y gap due o he ex e nal posi i e shock.
Following he global inancial c isis, he decline in he p o i a e in he Chilean economy was
d i en by educ ions in bo h dis ibu i e and echnological a iables un il 2019. This
mac oeconomic phenomenon is no ewo hy, as a simul aneous decline in bo h a iables is
ypically obse ed only du ing speci ic yea s o economic c isis, such as 1998-1999 and 2008-
2009.
The ecen end poses a signi ican challenge o bo h he Chilean economy and economic
analysis. While he economy may expe ience shi s ha exace ba e income inequali y agains
wo ke s, he p o i a e could simul aneously expe ience an upsu ge. Mains eam economis s
50%
53%
56%
59%
62%
65%
0,15
0,17
0,19
0,21
0,23
0,25
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
2017
2019
GOS sha e
Capi al p oduc i i y
Cu en eal GDP / cu en eal g oss s ock o capi al
Nominal GOS / Nominal GDP a ac o cos
F. Villanue a Melo 427
PSL Qua e ly Re iew
migh in e p e his as an inc ease in he Solow esidual a ibu ed o echnological ad ancemen s.
This was e iden in he a e ma h o he COVID-19 c isis, whe e he CNP epo ed posi i e g ow h
in he Solow esidual du ing 2020 and 2021 (CNP, 2022, p. 17), linking i o he widesp ead
adop ion o in o ma ion echnology o emo e wo king.
8
Howe e , his appa en boos in he p o i a e, which could bols e he Solow esidual, may
be sus ainable only i capaci y u iliza ion e u ns o no mal le els and income dis ibu ion
con inues o a o su plus owne s. Fu he mo e, his sus ainabili y hinges on e e sing he
downwa d ajec o y in capi al p oduc i i y, which is cu en ly being o e shadowed by
inc easing inequali y in unc ional income dis ibu ion. Indeed, acco ding o he Cen al Bank o
Chile, he GOS pa icipa ion o GDP a ac o cos e ol ed om 54% in 2019 o 56% in 2020, o
each 58% o GDP a ac o cos in 2021. Hence, we a e obse ing a s iden de e io a ion o
unc ional income dis ibu ion a he han echnological imp o emen s when we obse e he
e olu ion o he Solow esidual a e 2020.
The cu en social and poli ical ans o ma ions in Chile make i inc easingly imp obable o
sus ain long- e m economic g ow h based on an ou da ed p oduc i e sys em and escala ing
inequali y. The sluggish g ow h in labo p oduc i i y since 2014 cons ains he po en ial o eal
wage g ow h ha does no al e unc ional income dis ibu ion.
9
This pain s a bleak pic u e o
wo ke s in Chile, especially conside ing he in la iona y p essu es pos -2020, leading o a decline
in eal wages. Fu he mo e, igh e mone a y policies aimed a comba ing in la ion could
exace ba e he ecessiona y gap and unemploymen .
In such a scena io, capi al owne s and hei poli ical allies a e likely o esis any social o
economic policies aimed a al e ing unc ional income dis ibu ion o a oid a u he decline in
he p o i a e. Howe e , he e exis s a socio-poli ical h eshold beyond which he economy’s
income dis ibu ion canno become mo e eg essi e (Minsky, 2013, p. 28). This poses a cons ain
on he po en ial boos in he p o i a e and p esen s a signi ican challenge o medium- e m
economic g ow h in Chile.
Fo ins ance, o achie e a p o i a e o 12% wi hin i e yea s, gi en he cu en ends in labo
and capi al p oduc i i y, i would be necessa y an inc ease he su plus sha e o almos 70% o
GDP a ac o cos . Achie ing such a su plus sha e would en ail an a e age annual educ ion in
eal wages o app oxima ely 5%, o a cumula i e loss o 30% in pu chasing powe o e he en i e
pe iod, all else being equal. This unde sco es he magni ude o he challenge and he
socioeconomic implica ions o pu suing such a pa h.
5. P oduc i i y ends in Chile
Gi en ou con en ion ha TFP may no accu a ely e lec echnological change in he economy, we
p o ide h ee widely ecognized indica o s o p oduc i i y o he en i e pe iod. These include
ou pu pe wo ke and ou pu pe hou wo ked, bo h o which a e ela ed o labo p oduc i i y,
along wi h he e olu ion o capi al p oduc i i y, which was p e iously examined. Fu he mo e,
we aim o dissec he e olu ion o capi al p oduc i i y o gain insigh s in o he unde lying d i e s
behind i s declining end o e he pas decade. This comp ehensi e analysis will o e a nuanced
8
None heless, hey s ess ha cyclical componen s in luence hese g ow h a es, and, indeed, he massi e economic
policies o add ess he socio-economic e ec s o he pandemic led o mo emen s in he ecessiona y gap, which also
os e ed he a e o p o i .
9
The dynamic o he labo income sha e depends on he e olu ion o eal wages ela i e o labo p oduc i i y, as we
ha e s essed p e iously.
428 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
unde s anding o he p oduc i i y dynamics in he Chilean economy and shed ligh on he ac o s
shaping i s ajec o y.
Figu e 7 – E olu ion o p oduc i i y indica o s in Chile, 1985-2019 (100=1985)
Sou ce: Own elabo a ion based on da a p o ided by he Cen al Bank o Chile and DIPRES
(h ps://si3.bcen al.cl/Sie e/ES/Sie e/Cuad o/CAP_IND_SEC/MN_IND_SEC20/CCNN2013_S1_P1_DUPLICADO/CC
NN2013_S1_P1_DUPLICADO
h ps://www.dip es.gob.cl/598/a icles-202678_doc_pd .pd )
To comp ehend he decline in he p o i a e, i ’s c ucial o examine how he ajec o y o
echnological change in Chile has in luenced he adop ion o di e en ac o -sa ing echnologies.
Figu e 7 illus a es he e olu ion o he index o ou pu pe wo ke , ou pu pe hou wo ked, and
a e age capi al p oduc i i y.
We obse e ha echnological ad ancemen s ha e p edominan ly been labo -sa ing un il he
onse o he wo ld inancial c isis, as e idenced by he s eady inc ease in labo p oduc i i y using
bo h ou pu pe wo ke and ou pu pe hou wo ked indica o s h oughou he en i e pe iod.
Howe e , a close inspec ion e eals a s agna ion in labo p oduc i i y, pa icula ly when
measu ed by ou pu pe wo ke , since 2007. While he s agna ion end is sub le when
p oduc i i y is measu ed by ou pu pe hou wo ked, i s ill indica es a slowdown in p oduc i i y
g ow h. As o capi al p oduc i i y, i s e olu ion has been de ailed in he p eceding sec ion.
No ably, he e was an inc ease in capi al p oduc i i y un il 1998, ollowed by a pe iod o
s agna ion un il he wo ld inancial c isis, and a subsequen downwa d end om 2010-2011.
80
100
120
140
160
180
200
220
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
2009
2011
2013
2015
2017
2019
A e age labo p oduc i i y
A e age labo p oduc i i y pe hou
A e age capi al p oduc i i y

F. Villanue a Melo 429
PSL Qua e ly Re iew
This analysis p o ides aluable insigh s in o he shi ing landscape o echnological change in
Chile and i s implica ions o ac o p oduc i i y, he eby con ibu ing o a be e unde s anding
o he ac o s d i ing he decline in he p o i a e.
Decomposing capi al p oduc i i y in o he a io o ou pu pe wo ke and capi al pe wo ke
allows us o un a el i s dynamics. The g ow h in capi al p oduc i i y can be a ibu ed o he
di e ence be ween he g ow h a e in ou pu pe wo ke and he g ow h a e in capi al pe
wo ke . Inc eases (o dec eases) in labo p oduc i i y co espond o highe (o lowe ) capi al
p oduc i i y, all else being equal. Howe e , a highe (o lowe ) capi al in ensi y, as measu ed by
capi al pe wo ke , will dep ess (o boos ) capi al p oduc i i y, all else being equal, as illus a ed
in equa ion (6.1). Indeed, a high g ow h a e o labo p oduc i i y can posi i ely in luence he a e
o p o i h ough his channel, assuming i is no coun e ac ed by al e a ions in he a io o capi al
pe wo ke .
𝑟𝑎𝑡𝑒 𝑜𝑓
𝑝𝑟𝑜𝑓𝑖𝑡 =[𝐺𝑟𝑜𝑠𝑠 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑆𝑢𝑟𝑝𝑙𝑢𝑠
𝐺𝐷𝑃 𝑎𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝑐𝑜𝑠𝑡 ]⋅[𝐺𝐷𝑃 𝑎𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝑐𝑜𝑠𝑡
𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 ]⋅[𝐸𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡
𝐺𝑟𝑜𝑠𝑠 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑆𝑡𝑜𝑐𝑘]=𝑠𝑘⋅𝐴𝑃𝐿
𝑘 (6.1)
Figu e 8 illus a es he a e age g ow h a es o ou pu pe wo ke , capi al pe wo ke , and
capi al p oduc i i y in Chile since 1986. This isualiza ion helps elucida e he ac o s d i ing he
e olu ion o capi al p oduc i i y o e he speci ied pe iod.
Figu e 8 – G ow h decomposi ion o capi al p oduc i i y in Chile, 1985-2019* (a e age annual
g ow h
a e)
* Fo he 1999-2010 pe iod; he yea 2009 was omi ed.
Sou ce: Own elabo a ion based on da a p o ided by he Cen al Bank o Chile and DIPRES
(h ps://si3.bcen al.cl/Sie e/ES/Sie e/Cuad o/CAP_IND_SEC/MN_IND_SEC20/CCNN2013_S1_P1_DUPLICADO/CC
NN2013_S1_P1_DUPLICADO
h ps://www.dip es.gob.cl/598/a icles-202678_doc_pd .pd ).
3,4%
1,5%
0,7%
0,5%
1,6%
2,6%
3,0%
0,0%
-1,9%
-3%
-2%
-1%
0%
1%
2%
3%
4%
1986-1998 1999-2010 2011-2019
A e age labo p oduc i i y Capi al pe wo ke Capi al p oduc i i y
430 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
Fo he pe iod spanning 1985 o 1998, bo h capi al and labo p oduc i i y expe ienced
posi i e g ow h. Speci ically, capi al p oduc i i y inc eased a an a e age a e o 3% pe yea ,
while labo p oduc i i y g ew a a sligh ly highe a e o 3.4% annually. This g ow h was
acili a ed by a modes inc ease in capi al in ensi y, a e aging jus 0.5% pe yea . Consequen ly,
he echnological ad ancemen s du ing his pe iod we e cha ac e ized by bo h labo - and capi al-
sa ing inno a ions, wi hou signi ican inc eases in capi al pe wo ke . This dynamic was highly
conduci e o p o i abili y and suppo ed a mo e equi able unc ional income dis ibu ion.
In con as , he pe iod om 1999 o 2010 wi nessed a s agna ion in capi al p oduc i i y. This
s agna ion can be a ibu ed o he o se ing e ec s o inc eased labo p oduc i i y and capi al
in ensi y. The e was a no able decline in labo p oduc i i y, by almos 2 pe cen age poin s
compa ed o he p e ious pe iod, coupled wi h a subs an ial inc ease in capi al in ensi y by nea ly
1.5 pe cen age poin s. Consequen ly, he echnological ad ancemen s du ing his pe iod leaned
owa ds labo -sa ing echnologies and signi ican inc eases in he capi al- o-labo a io in he
economy.
Finally, in he mos ecen pe iod, spanning 2011 o 2019, capi al p oduc i i y expe ienced a
decline o 2% pe yea . This decline can be a ibu ed o a hal ing o he g ow h a e in ou pu pe
wo ke and an inc ease in he economy’s capi al in ensi y. Thus, he echnological changes
implemen ed du ing his pe iod we e cha ac e ized by a deepening o capi al in ensi y in he
p oduc ion p ocess and a weakening o labo -sa ing echnologies, esul ing in a educed inc ease
in labo p oduc i i y.
Acco ding o Palma (2019), he slowdown in labo p oduc i i y in Chile can be a ibu ed o
he lack o dynamism in bo h he expo sec o , p ima ily elian on ex ac i e ac i i ies, and he
non- adable sec o , which is domina ed by labo -in ensi e and low-p oduc i i y ac i i ies. This
in e p e a ion aligns wi h he analysis pu o h by he CNP, which sugges s ha Chile’s na u al-
esou ce expo s a egy has eached i s limi s.
Howe e , i ’s no ewo hy ha he ex ac i e na u e o he Chilean economy played a ole in
boos ing labo p oduc i i y du ing he golden age. Fo ins ance, he ag icul u al sec o
expe ienced a signi ican inc ease in labo p oduc i i y om he mid-1980s onwa ds (Palma,
2019). This was he coun e pa o he obus g ow h a es in expo goods and non-coppe
expo s, a e aging 8.8% and 13%, espec i ely, du ing 1986-1989, and 9.6% and 9.8%,
espec i ely, du ing 1990-1998 (F ench-Da is, 2018). Following he global inancial c isis,
howe e , expo g ow h in Chile s agna ed. Consequen ly, he lack o economic di e si ica ion,
coupled wi h he eluc ance o he capi alis class and go e nmen o e i alize exis ing economic
sec o s o o ansi ion o sec o s wi h g ea e po en ial o p oduc i i y g ow h, a e key ac o s
con ibu ing o he s agna ion o labo p oduc i i y in Chile.
Indeed, he dynamics o labo p oduc i i y also ha e dis ibu ional implica ions, as hey
es ablish he uppe limi on which eal wages can inc ease wi hou al e ing unc ional income
dis ibu ion. By conside ing ha he sha e o capi al income (GOS) in ou pu is complemen a y o
he sha e o labo income, and ha his a iable ep esen s he di e ence be ween he a e age
eal wage and he a e age labo p oduc i i y o he economy, we can exp ess he p o i a e as
ollows:
𝑟𝑎𝑡𝑒 𝑜𝑓
𝑝𝑟𝑜𝑓𝑖𝑡 =𝑠𝑘⋅𝐴𝑃𝐿
𝑘=[1−𝑠𝐿]⋅𝐴𝑃𝐿
𝑘=[1− 𝑤
𝐴𝑃𝐿]⋅𝐴𝑃𝐿
𝑘=1
𝑘[𝐴𝑃𝐿−𝑤] (6.1)
Indeed, he p o i a e can expe ience a boos as long as labo p oduc i i y inc eases, as his
would aise he sha e o capi al income (GOS) in o al income, assuming capi al p oduc i i y
F. Villanue a Melo 431
PSL Qua e ly Re iew
emains cons an . Consequen ly, he dynamics o labo p oduc i i y ha e bo h dis ibu ional and
supply-side impac s.
Con e sely, wo ac o s dep ess he a e o p o i : he e olu ion o eal wages and he a io o
capi al pe wo ke . The inc easing capi al in ensi y o he p oduc ion p ocess, and he s agna ion
in he g ow h o eal wages ela i e o labo p oduc i i y, a e key elemen s o ack he dynamic
o he decline in he p o i a e in he Chilean economy o e he las decade.
6. Conclusion
This pape adop s he a gumen pu o h by Felipe and McCombie (2020), asse ing ha he
neoclassical p oduc ion unc ion e lec s an agg ega e iden i y accoun . Building upon his
amewo k, we analyze he e olu ion o he Chilean economy o e he pas 35 yea s. We con end
ha wha is con en ionally labeled as To al Fac o P oduc i i y (TFP) in neoclassical heo y, o
he Solow esidual, ac ually e lec s he weigh ed g ow h o he p o i a e and eal wages.
We ag ee wi h he mains eam consensus in asse ing ha he s agna ion o p oduc i i y is a
pi o al ac o in explaining Chile’s lacklus e economic pe o mance, no ably since 2014.
Howe e , we con es he eliabili y o TFP as an indica o o p oduc i i y. Relying on TFP o gauge
echnological change ac oss he en i e economy may yield misleading analyses and unsui able
policy ecommenda ions.
The Solow esidual is no me ely a “measu emen o ou igno ance”; i holds aluable insigh s
in o ele an mac oeconomic a iables. Ou es ima ion o he g ow h o he Solow esidual o he
Chilean economy spanning 1985-2019 e ealed i s s ong p o-cyclical na u e, mi o ing he p o-
cyclicali y o wages and p o i abili y g ow h. Addi ionally, we obse ed a downwa d end in he
g ow h o he Solow esidual o e his pe iod. Howe e , we a gue ha his end is no di ec ly
a ibu able o p oduc i i y shocks bu a he o a decline in he agg ega e a e o p o i .
Ou analysis emphasizes ha he dynamic o he p o i a e is he p ima y d i e o he Solow
esidual’s e olu ion h oughou he en i e pe iod, wi h he excep ion o he golden age o
economic g ow h in Chile. Du ing his las pe iod, eal wage g ow h eme ged as he leading
a iable, ma king he golden age as a his o ical excep ion in mode n Chilean economic g ow h.
We conduc ed a comp ehensi e desc ip ion and decomposi ion o he a e o p o i in o i s
dis ibu ional and echnological componen s, e ealing ha he s able a e o p o i du ing he
golden age was achie ed h ough a combina ion o highe labo income pa icipa ion in GDP and
inc eased capi al p oduc i i y. Howe e , since 1999, he Chilean economy has g appled wi h
s agnan capi al p oduc i i y, which u he declined o p e-1990 le els ollowing he wo ld
inancial c isis.
Fu he mo e, we unde sco ed ha he con luence o dis ibu ional dynamics, s agnan labo
p oduc i i y, and an escala ing a io o capi al pe wo ke elucida es he downwa d ajec o y o
he Chilean a e o p o i . This con igu a ion p esen s a pessimis ic ou look o wo ke s and
medium- e m economic g ow h p ospec s in Chile, as es o ing p o i abili y based solely on
dis ibu ional componen s would necessi a e con inual cu s in eal wages.
Consequen ly, he mos iable pa h o e i alizing p o i abili y hinges on enhancing i s
echnological componen s, equi ing sus ained and a ge ed e o s in indus ial policy o e he
medium e m. Las ly, we a gue a he economic policy le el ha he adi ional use o TFP as an
indica o o p oduc i i y is lawed and can lead o misguided economic analyses and policy
ecommenda ions. Ins ead, we ad oca e o mac oeconomic heo ies g ounded in and espec ul
o agg ega e accoun ing iden i ies.
432 The Solow esidual, a dis ibu ional app oach: The case o Chile, 1985-2019
PSL Qua e ly Re iew
Appendix
A1. GDP income componen s
Gi en he una ailabili y o a his o ical se ies o GDP income componen s beyond 1998 and he
incompa abili y o subsequen da abases, we will de i e he GDP income componen s o he
pe iod 1998-2019 using g ow h a es om se en da abases co e ing di e en ime ames: 1996-
2004, 2003-2008, 2008-2011, 2011-2014, 2014-2016, 2016-2018, and 2018-2020.
We p io i ize u ilizing g ow h a es o depic he mo emen o he Solow esidual a he han
i s absolu e le el. To ensu e he p ese a ion o he accoun ing iden i y, whe e he sum o income
componen s equals o e all GDP, we will es ima e G oss Ope a ing Su plus (GOS) as he di e ence
be ween es ima ed GDP and he es ima ed sum o ne axes and he wage bill. Ou analysis
con i ms minimal disc epancies be ween his de i ed GOS se ies and he GOS es ima ed di ec ly
h ough he g ow h a es o pos e io da abases. Fu he mo e, he impac o his app oach on
unc ional income dis ibu ion is negligible.
No ably, as capi al consump ion da a is no longe published in he Sys em o Na ional Accoun s
(SNA) o he Cen al Bank o Chile and is no essen ial o ou esea ch pu poses, i will no be
epo ed o impu ed.
Table A1 – Es ima ion o GDP income componen s
(le els in nominal millions o Chilean pesos)
Yea
Le els
G ow h a es
Es ima ed
Da abase
GDP
Ne axes
Wage bill
GDP
Ne axes
Wage bill
GOS
Da abase
1985
2,651,937
423,959
945,224
1,282,754
1985-1998
1986
3,419,209
538,369
1,162,533
1,718,307
1985-1998
1987
4,540,556
712,408
1,449,286
2,378,862
1985-1998
1988
5,917,879
765,187
1,827,207
3,325,485
1985-1998
1989
7,353,729
879,525
2,367,731
4,106,473
1985-1998
1990
9,245,504
1,179,611
3,123,435
4,942,458
1985-1998
1991
12,100,475
1,540,221
4,135,233
6,425,021
1985-1998
1992
15,185,438
2,053,179
5,356,002
7,776,257
1985-1998
1993
17,974,917
2,631,131
6,582,086
8,761,700
1985-1998
1994
21,395,185
2,955,061
7,791,601
10,648,523
1985-1998
1995
25,875,727
3,488,234
9,159,037
13,228,456
1985-1998
1996
28,268,364
4,025,258
10,666,243
13,576,863
1985-1998
1997
31,567,287
4,398,918
12,072,662
15,095,707
1985-1998
1998
33,630,367
4,469,612
13,239,136
15,921,619
1985-1998
F om his pe iod, he le els o GDP, ne axes, and he wage bill a e es ima ed om he g ow h a es.