Ellingsen, Nicolai; Fosso, Luca; Galaasen, Sigu d Møls e
Resea ch Repo
Employmen ends in No way
S a Memo, No. 1/2024
P o ided in Coope a ion wi h:
No ges Bank, Oslo
Sugges ed Ci a ion: Ellingsen, Nicolai; Fosso, Luca; Galaasen, Sigu d Møls e (2024) : Employmen
ends in No way, S a Memo, No. 1/2024, ISBN 978-82-8379-307-9, No ges Bank, Oslo,
h ps://hdl.handle.ne /11250/3170067
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S a Memo
Employmen ends in No way
Au ho s:
Nicolai Ellingsen
Luca Fosso
Sigu d Møls e Galaasen
1 | 2024
No ges Bank S a Memo 1
S a Memos p esen epo s and documen a ion w i en by s a membe s and
a ilia es o No ges Bank, he cen al bank o No way. Views and conclusions
exp essed in S a Memos should no be aken o ep esen he iews o
No ges Bank.
© 2024 No ges Bank
The ex may be quo ed o e e ed o, p o ided ha due acknowledgemen is
gi en o sou ce.
S a Memo inneholde u edninge og dokumen asjon sk e e a No ges Banks
ansa e og and e o a e e ilkny e No ges Bank. Synspunk e og konklusjone
i a beidene e ikke nød endig is ep esen a i e o No ges Banks.
© 2024 No ges Bank
De kan si e es a elle hen ises il de e a beid, gi a o a e og No ges Bank
oppgis som kilde.
ISSN 1504-2596 (online)
ISBN 978-82-8379-307-9 (online)
Employmen ends in No way*
Nicolai Ellingsen †
No ges Bank
Luca Fosso ‡
Eu opean Cen al Bank
Sigu d Møls e Galaasen §
No ges Bank
Janua y 17, 2024
Abs ac
This pape ou lines he ecen ly de eloped me hod o assessing he end le el
in employmen a es adop ed by No ges Bank. The app oach employs a Bayesian
VAR o decompose disagg ega ed employmen da a in o end and cyclical compo-
nen s, using qua e ly labo ma ke da a on 30 demog aphic sub-g oups. Applied o
he ime pe iod 1984-2019, we show ha he es ima ed end picks up known his-
o ical ac o s con ibu ing o slow-mo ing employmen dynamics. Addi ionally, he
cyclical employmen componen shows s ong co ela ion wi h he ou pu gap es i-
ma e o No way.
1 In oduc ion
Ensu ing ha a la ge pa o he popula ion is employed is a undamen al objec i e
o economic policy. To ansla e his goal in o policy ac ions, i is necessa y o bo h de-
ine wha i means o ha e a high a e o employmen and o measu e how his objec i e
changes o e ime. This is a challenging ask, as he obse ed le el o employmen is he
ou come o a wide ange o ac o s ha a y in e ms o hei obse abili y, p edic abili y,
and du a ion. Ne e heless, o decide when and how policy should in e ene i is essen-
ial o unde s and he na u e o employmen dynamics. In his pape we add ess his
ques ion by un angling he d i e s o employmen in No way.
*We a e g a e ul o aluable commen s om Knu A e Aas ei , Ka s en Ge d up, Ø jan Robs ad,
Nicolò Ma ei-Faccioli and Lo enzo Mo i. The iews exp essed in he a icle a e solely hose o he au ho s
and canno be a ibu ed o No ges Bank and o he Eu opean Cen al Bank.
†No ges Bank.: [email p o ec ed].
‡Eu opean Cen al Bank.: [email p o ec ed].
§No ges Bank.: [email p o ec ed].
1
Concep ually, i is use ul o policy pu poses o dis inguish be ween end and cycli-
cal a ia ion in employmen . The end componen is in e p e ed as ep esen ing slow-
mo ing s uc u al ac o s, whe eas he cycle componen is associa ed wi h sho - e m
economic luc ua ions. Bo h componen s de e mine he cu en le el o employmen ,
bu di e s in e ms o policy p esc ip ions. While he cycle componen is p ima ily he
conce n o cen al banks and s abiliza ion policies, he o e all end is po en ially a ma -
e o long- e m labo ma ke policies. Due o his di ision o policy, i necessa y o as-
sess in eal ime he ela i e impo ance o hese ac o s.
The e a e se e al ways o pe o ming such an assessmen . One app oach is by de-
ending he agg ega e ime se ies using s a is ical il e s such as o example he Ho-
d ick and P esco (1997)1me hod. P io o he COVID-19 pandemic, howe e , No ges
Bankadop eda mo es uc u alapp oachbased on he assump ion ha heemploymen
end was d i en en i ely by demog aphic changes. In pa icula , he me hod in ol ed
ixing age-speci ic employmen a es o hei le els in a gi en e e ence yea . Those le -
els we e in e p e ed as e lec ing hei co esponding end le els. In his se ing, ag-
g ega e end employmen hus mo es o e ime only because o changes in he age-
composi ion o he popula ion. De ia ions om his end a e hen a ibu ed o cyclical
a ia ions. Impo an ly, he e e ence yea was deemed o be neu al wi h espec o he
cycle, meaning ha he cycle componen was assumed o be ze o in ha yea .
In his pape we implemen a me hodology combining he wo app oaches. We i s
de ine demog aphic g oups ac oss a combina ion o age, sex and educa ion le els. On
he disagg ega ed da a we hen p e o m a end-cycle decomposi ion using a Bayesian
VAR in he spi i o Be e idge and Nelson (1981), allowing he end o s ochas ically
change o e ime.2Finally, we cons uc an agg ega e end as a size-weigh ed a e age o
he g oup-speci ic ends. Thus, in con as o he ea lie No ges Bank app oach, mo e-
men s in he es ima ed agg ega e end a ise om bo h demog aphic shi s and s uc-
u al changes in g oup-speci ic ends.3Compa ed wi h simply de- ending agg ega e
employmen di ec ly, ou bo om-up app oach is be e sui ed in se ings cha ac e ized
by la ge demog aphic changes and he e ogeneous employmen dynamics ac oss popu-
1. See e.g. Ve acie o (2008) o an applica ion o he labo o ce pa icipa ion and K usell e al. (2017)
on he employmen a e. Fo al e na i e il e ing me hods, see e.g. C ump e al. (2019) and D’Amu i e
al. (2021).
2. Ou me hod is ela ed o se e al ecen con ibu ions ha allow o s ochas ic ends when decom-
posing mac oeconomic da a such as labo ma ke and in la ion dynamics (see e.g., Del Neg o e al., 2017;
C ump e al., 2019; Kambe and Wong, 2020; Asca i and Fosso, 2021; Hasenzagl e al., 2022 ).
3. An al e na i e which also allows o ime a ying end mo emen s is he app oach adop ed by he
US Cong essional Budge O ice (Mon es, 2018) based on Aa onson e al. (2006). In his app oach he he
employmen a es o popula ion sub-g oups a e es ima ed on age and coho ixed e ec s, and a ious
ime- a ying s uc u al and cyclical co- a ia es.
2
la ion sub-g oups.4This cha ac e iza ion is pa icula ly i ing o No way, as shown in
Bhulle and Eika (2020).5
We employ ou me hod on No wegian adminis a i e da a o e he pe iod 1984-2019,
om which we iden i y he job s a us o indi iduals a he mon hly le el. Indi iduals a e
hen alloca ed o one o 30 demog aphic g oups, de ined based on a combina ion o i e
age g oups, h ee educa ion le els and sex. Wi hin each g oup, we agg ega e he indi id-
ual le el da a o c ea e 30 qua e ly g oup-speci ic ime se ies o employmen a es on
which we pe o m a end-cycle decomposi ion using he Bayesian VAR. Ou es ima ed
ends pick up known d i e s o mo emen s in he his o ical employmen a e, such as
changes in emale labo pa icipa ion and inc eased old-age pa icipa ion. We also iden-
i y alling pa icipa ion a e o low-educa ed wo ke s. Mo eo e , he cyclical componen
esul ing om he es ima ion seems o cap u e key business cycle mo emen s and is
highly co ela ed wi h No ges Banks’ es ima e o he ou pu gap. We con as ou me hod
wi h he p e ious app oach adop ed by No ges Bank, and show ha he wo me hods
p o ide di e en assessmen s o bo h he his o ical e olu ion and cu en assessmen o
he cyclical employmen gap. In ecen yea s, he di e ence a ises p ima ily as a esul
o ou me hod cap u ing an inc eased end employmen among olde wo ke s.6
The emainde o he a icle is o ganized as ollows. In Sec ion 2we desc ibe ou da a
and how we measu e employmen a he indi idual and g oup le el. In Sec ion 3we ou -
line ou s a is ical model, whileSec ion4p esen s hedecomposi iones ima es. We con-
clude by discussing he policy applica ions in Sec ion 5.
2 Da a
Da a sou ces To c ea e ime se ies on employmen a es disagg ega ed by age, educa-
ion and sex we ely on No wegian adminis a i e da a om S a is ics No way. The main
da a sou ce is he employe -employee (EE) egis e p o iding us wi h s a and end da e
o he nea uni e se o wage con ac s in No way be ween 1984 and 2019. Indi idual’s
wage con ac s a e combined wi h backg ound in o ma ion on educa ion and age using
unique and anonymized pe sonal iden i ie s.
4. Since Pe y (1971) he bo om-up app oach has been commonly adop ed when s udying labo ma -
ke dynamics.
5. Bhulle and Eika (2020) decompose he decline in agg ega e employmen in No way o e he pe iod
2000-2017, and show ha accoun ing o bo h demog aphic changes and changes wi hin demog aphic
g oups a e impo an o explaining he agg ega e decline.
6. This old-age employmen g ow h has in o he wo k been linked o he wo k-incen i izing ea u es o
he 2011 No wegian pension e o m, see e.g. He næs e al. (2016) and Galaasen and K use (2023).
3
De ini ion o employed A pe son is de ined as employed in a gi en mon h i he o she
has a leas one ac i e employmen con ac . I no employmen con ac is obse ed in
any mon h o a gi en yea , we c oss check using he annual ax eco ds o assess a pe -
son’s employmen s a us. An indi idual is hen conside ed employed i (i) he annual
sala y income exceeds oughly USD 10,000 in 2023 nominal e ms ( he Na ional Insu -
ance basic amoun ) o (ii) ne income abo e 1 basic amoun om sel -employmen is
epo ed ha yea .7
Demog aphic g oups We spli ou sample in o smalle uni s based on combina ions
o demog aphic cha ac e is ics. In pa icula we conside bins based on age, sex and ed-
uca ion le el. We conside i e age g oups, 16-24, 25-39, 40-54, 55-64 and 65-74 yea s o
age, and h ee educa ion g oups, based on indi iduals’ highes a ained educa ion le el.
The high-educa ion g oup co esponds o a uni e si y deg ee, he medium-educa ion
g oup o a high school diploma, and he low-educa ion g oup a e hose wi h less han
high-school. A pe son’s educa ion cha ac e is ic is a ixed a ibu e, equal o he high-
es le el o educa ion obse ed o ha pe son o e he en i e sample pe iod.8. This will
cause some igh -censo ing issues o he younge coho s, as we ypically do no know
he inal educa ion s a us by he ime ou sample ends. Typically many in he younges
coho a e 2015 will be classi ied in he lowes educa ion g oup. When es ima ing he
model we he e o e lea e ou he younges coho s du ing he la e yea s in he sample
o mi iga e his p oblem.
B eaks in he da a Benchma king agains he o icial agg ega e employmen se ies e-
eals ha he co e ageo employmen ela ions in he EE egis e changeso e ime, p o-
g essi ely becoming mo e comp ehensi e owa d he end o ou sample pe iod. How-
e e , ou use o he ax da a as an addi ional sou ce o iden i ying employed pe sons al-
mos en i ely elimina es he disc epancy be ween ou agg ega e se ies and o icial s a is-
ics. S ill, p io o 1993 we a e unable o d aw on he ax da a o iden i y employmen
s a us among hose missing om he EE egis e . This gene a es some disc epancy be-
ween ou agg ega e se ies and o icial s a is ics p io o 1993, as well as a jump in he
disagg ega e se ies om Decembe 1992 o Janua y 1993.
As ou goal is o s udy ends in agg ega e employmen , we b eak-adjus ou employ-
men se ies such ha ou agg ega e employmen ime se ies ma ches o icial s a is ics
7. As he de ailed ax eco ds s a in 1993, p io o his yea we canno pe o m he las wo s eps.
8. Fo example, indi iduals who ob ained a uni e si y deg ee in 2019 will be de ined as highly educa ed
o e he en i e sample pe iod
4
each yea . The b eak adjus men is pe o med by inc easing employmen in each de-
mog aphic g oup by he same ac o , hus keeping he ela i e sha es ac oss he g oups
cons an . To illus a e, we ha e N demog aphic g oups indexed by i wi h size and em-
ploymen a es deno ed as (popi ,Ei )in yea . We hus adjus he employmen sha e
wi h a ac o (1 + )such ha :
N
X
i=1
popi Ei (1 + ) = Eo
(1)
whe e Eo
is agg ega e numbe o employed om o icial s a is ics. Thus, he b eak-
adjus ed employmen in yea is gi en by: B =Pipopi Ei .
Table 1shows he numbe o employees iden i ied by each sou ce in selec ed yea s.
As we see, he b eak adjus men (B ) is qui e la ge o 1990.9This is mos ly due o he
ac ha we do no obse e de ailed ax s a emen s be o e 1993 which is used o c oss-
check he con ac ual employmen de ini ion. Ou adjus men implici ly assumes ha
he missing employed B is dis ibu ed ac oss he demog aphic g oups acco ding o hei
ela i e obse ed employmen sha es. I his assump ion does no hold, ou disagg e-
ga ed employmen se ies be o e 1993 migh be biased as a esul . Howe e , he b eak in
he se ies om Decembe 1992 o Janua y 1993 is qui e simila ac oss ou demog aphic
g oups, which alle ia es some o his conce n.
Table 1: Employees by iden i ica ion me hod (selec ed yea s)
Iden i ied by 1990 2005 2015
Obse ed employmen con ac 1697 1975 2422
Sel -employmen income ( ax s a emen ) > 1 Basic amoun 0 134 116
Wage income ( ax s a emen ) > 1 Basic amoun 0 104 25
B eak adjus men 338 29 1
Employmen 2035 2242 2564
Table 1displays he iden i ica ion me hod o employmen in ou da ase o selec ed yea s using
he me hod ou lined in Sec ion 2. Numbe s in housands o pe sons.
Employmen a es Employmen sha es by age, sex and educa ion le els a e displayed
in igu e 1. Some well-known ends and ac s s and ou , illus a ing subs an ial g oup-
he e ogenei y in he e olu ion o employmen a es du ing he ime pe iod we look a .
Fi s , he la ge inc ease in emale labo o ce pa icipa ion is e iden in he le panel,
9. Simila magni udes a e obse ed o all yea s p io o 1993
5
which shows a gene al inc ease in emale employmen a e om he 1980s un il he ea ly
2000s. S ill, males a e mo e likely o be employed h oughou he sample pe iod. Sec-
ond, he middle panel shows ha he co e age g oups, aged 25-54, ha e he highes em-
ploymen a es. Howe e , du ing he la e pa o he sample pe iod, he wo oldes
age g oups expe ience g ow h in hei employmen a es ha pa ially educes he age
gap. Looking a educa ion in he igh panel, we see a s iking inc ease in he educa ion-
employmen gapo e ime, d i enby asubs an ial declinein heemploymen a e among
indi iduals wi h low educa ion.
Figu e 1: Employmen a es by demog aphic g oups
3 Empi ical s a egy
The ul ima e goal o his empi ical exe cise is o ob ain an es ima e o he agg ega e
employmen end by exploi ing he weal h o in o ma ion embedded in ou da ase . As
men ioned abo e, he da ase can be desc ibed on he basis o h ee laye s o disagg e-
ga ion, om he less o he mos disagg ega ed laye : (i) sex, (ii) age, and (iii) educa ion.
In o de o ge an es ima e o he agg ega e employmen end, we use a bo om-up ap-
p oach and p oceed as ollows. Fi s , we es ima e he emale (male) employmen ends
o each educa ion le el wi hin all age g oups using he empi ical model p esen ed be-
6
Figu e 5: Employmen gap
Figu e 5plo s he ou pu gap se ies o No way and ou employmen gap se ies. The ou pu gap is
No ges Banks’ o icial es ima e, while he employmen gap is measu ed as he di e ence be ween
he ac ual employmen a e and he end employmen a e es ima ed using he me hodology in
Sec ion 3.
4.1 Compa ison wi h he demog aphic-adjus ed app oach
The me hodology de eloped in his pape p o ides a mo e lexible and obus end
assessmen compa ed wi h he p e ious No ges Bank app oach. The ea lie me hodol-
ogy is essen ially a demog aphic-adjus ed app oach, consis ing o wo s eps. In he i s
s ep, he obse ed g oup speci ic employmen a es a e assumed o be on end in a gi en
base yea . In he second s ep employmen is assumed o e ol e o e ime acco ding o
ac ual and p ojec ed popula ion sha es. This app oach is es ic i e as he es ima e is
sensi i e o bo h he base yea and he assump ion o cons an g oup ends.
As an example o his, we now con as he end es ima e o he pe iod 2007-2019
p e iously adop ed by No ges Bank wi h ou es ima ed end. The compa ison is shown
in Figu e 6. In he p e ious app oach, indica ed by he ed line, he employmen end is
de i ed by ixing employmen wi hin age g oups o hei obse ed 2013 le els, and hen
p ojec ing he e olu ion using he obse ed aging o he popula ion. In summa y, ou
es ima ed end, ep esen ed by he o ange line, sugges a lowe end le el in 2013 bu
a mo e posi i e ajec o y, leading o a sligh ly highe employmen end in he las wo
yea s be o e he pandemic. The sou ce o his di e ence is explained in Figu e 4whe e
we decompose he change in he es ima ed agg ega e end es ima es since 2013. The
di e ence is p ima ily d i en by inc eased end employmen among olde wo ke s, p e-
13
sumably caused by he 2011 No wegian pension e o m which s imula ed labo supply
among olde wo ke s (He næs e al., 2016).12 The downwa d p essu e on agg ega e em-
ploymen s emming om an aging popula ion is pa ially o se by a ise in he es ima ed
end employmen o olde wo ke s.
Figu e 6: Old and New T end Es ima e
Figu e 6plo s he old end whe e employmen wi hin age g oups a e held ixed agains ou new
es ima ed end.
5 Policy applica ion
This sec ion explains how he me hod ou lined in his pape is ope a ionalized by
No ges Bank’s mone a y policy depa men , bo h in analysing he cu en economic si -
ua ion and in making o ecas s. The es ima ed employmen gap shown in Figu e 5is
used when assessing he cu en empe a u e o he economy. The applica ion o o e-
cas ing is less s aigh o wa d as addi ional elemen s a e needed o o ecas a end le el
o ac ual employmen . The basis o he o ecas is indi idual ends o each 30 sub-
g oups. We apply he andom walk assump ion om he model in Sec ion 3and assume
ha all ends emain cons an om he la es obse a ion in he da a. Then we o e-
cas he size o each g oup by he popula ion o ecas made by S a is ics No way. These
popula ion o ecas s a e no epo ed sepa a ely by educa ion g oups, so we add he as-
sump ion ha educa ion le els wi hin age g oups ollow he end om he las i e yea s
o eliable da a (ea lie han he end o he sample o younge coho s). The o ecas ed
12. To accoun o he e ec o he old age pension e o m, he p e ious No ges Bank app oach imposed
a judgemen -based inc ease in he end employmen o olde wo ke s o e ime.
14
g oup size and he es ima ed end le els gi es us a o ecas on he le el o domes ic em-
ploymen . Fo compa ison wi h ac ual employmen we add o ecas ed non- esiden em-
ploymen o he end. Finally, he o ecas ed end could be subjec o judgemen -based
changes based on he assessmen o o he s uc u al ac o s. Fo example, i ou iew on
he NAIRU (non-accele a ing in la ion a e o unemploymen ) changes his could be e-
lec ed in ou p ojec ed end o employmen .
6 Summa y
The pu pose o his pape has been o documen he cu en me hod adop ed by
No ges Bank o es ima ing he end le el o agg ega e employmen . The me hod con-
sis s o a bo om-up app oach, whe eby we i s es ima e disagg ega ed end le els o
30 demog aphic sub-g oups using a Bayesian VAR, and he eco e he agg ega e end
as he popula ion weigh ed a e age o he disagg ega ed ends.
Compa ed wi h simply de- ending agg ega e employmen di ec ly, ou bo om-up
app oach is be e sui ed in se ings cha ac e ized by la ge demog aphic changes and
he e ogeneous employmen dynamics ac oss popula ion sub-g oups. The eason is ha
i allows o bo h demog aphic changes and changes in end employmen wi hin demo-
g aphic g oups o a ec he agg ega e end le el.
The me hod ou lined in his pape eplaces he p e ious No ges Bank app oach o
decomposing agg ega e employmen dynamics in o cycle and end componen s. We
ha e illus a ed how his he upda ed me hod imp o es and changes he assessmen o
he his o ical employmen dynamics, and he con empo aneous end le el, by allowing
g oup-speci ic ends o be ime- a ying.
Finally, weha ee alua ed howou es ima edcyclicalcomponen co-mo eswi h o he
measu es o cyclical a ia ion in ac i i y. In pa icula , ou employmen gap (de ia ion
om end employmen ) shows s ikingly simila dynamics since he 1990s o he mo e
adi ional ou pu gap measu e.
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A Algo i hm
The es ima ion is conduc ed ollowing a Bayesian app oach. The Gibbs sample is
s uc u ed acco ding o he ollowing s eps:
1. Re ie e he dis ibu ion o la en s a es condi ional on all he o he pa ame e o
he model
¯
E0:T,ˆ
E–p+1:T| ec(Φ),Σu,Σε,E1:T
D aws o he la en s a es can be ob ained by using Du bin and Koopman (2002)’s
simula ion smoo he . In addi ion, we also need o d aws he ini ial condi ion ¯
E0
and ˆ
E–p+1:0 in o de o es ima e he pa ame e s in 3and 4in he nex s eps.
2. D aw he pa ame e s o ec(Φ),Σu,Σεcondi ional on he la en s a es
ec(Φ),Σu,Σε|¯
E0:T,ˆ
E–p+1:T,E1:T.
Fo gi en ¯
E0:Tand ˆ
E–p+1:T,3and 4a e s anda d. In addi ion, we also al eady know
he au o eg essi e ma ices o he end block in 3.
Thepos e io dis ibu iono heco a iance ma ixo pe manen shocksΣuis gi en
by
p(Σu|¯
E0:T) = IW(Σu+Su, κu+T),
17
whe e Su=PT
=1(¯
E –¯
E –1)(¯
y –¯
E –1)0is he empi ical co a iance ma ix o pe ma-
nen shocks o he ends. The pos e io dis ibu ion o he s a iona y pa ame e s
in ec(Φ) and Σεis gi en by
p(Σε|ˆ
E0:T) = IW(Σε+Sε, κε+T),
p( ec(Φ)|Σε,ˆ
E0:T) = N
ec(ˆ
Φ),Σε⊗
T
X
=1
ˆ
x ˆ
x0
+ Ω–1
–1
,
whe e ˆ
x = (ˆ
E0
–1,...,ˆ
E0
–p)0collec s he VAR eg esso s,
ˆ
Φ =
T
X
=1
ˆ
x ˆ
x0
+ Ω–1
T
X
=1
ˆ
x ˆ
E0
+ Ω–1Φ
,Sε=
T
X
=1
ε ε0
+ (ˆ
Φ–Φ)0Ω–1(ˆ
Φ–Φ),
and ε =ˆ
E –ˆ
Φ0ˆ
x a e he esiduals o he s a iona y block o he model.
18
