A benchmark ecological stock-flow-consistent input-output model for Denmark

Thomsen, Simon Fløj; Raza, Hamid; By ialsen, Mikael Rand up
Wo king Pape
A benchma k ecological s ock- low-consis en inpu -ou pu
model o Denma k
FMM Wo king Pape , No. 114
P o ided in Coope a ion wi h:
Mac oeconomic Policy Ins i u e (IMK) a he Hans Boeckle Founda ion
Sugges ed Ci a ion: Thomsen, Simon Fløj; Raza, Hamid; By ialsen, Mikael Rand up (2025) : A
benchma k ecological s ock- low-consis en inpu -ou pu model o Denma k, FMM Wo king Pape ,
No. 114, Hans-Böckle -S i ung, Mac oeconomic Policy Ins i u e (IMK), Fo um o Mac oeconomics
and Mac oeconomic Policies (FMM), Düsseldo
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FMM WORKING PAPER
No. 114 • Feb ua y 2025 • Hans-Böckle -S i ung
A BENCHMARK
ECOLOGICAL
STOCK
-FLOW-CONSISTENT
INPUT
-OUTPUT MODEL FOR
DENMARK
Simon Fløj Thomsen, Hamid Raza, Mikael Rand up By ialsen
1
ABSTRACT
This pape aims o de elop an ecological mac oeconomic model o he Danish economy
ha can link he economic and inancial sys em wi h some key aspec s o he clima e. To do
so, we combine S ock- low-Consis en app oach (SFC) wi h Inpu -Ou pu ables (IO) o build
a hyb id model, which we call Ecological S ock-Flow-Consis en Inpu -Ou pu model (E-SFC-
IO). Mos pa ame e s o he model a e es ima ed using ime se ies da a om 1995 o 2019,
a e which, we ca y ou simula ions. We ind ha he model (wi h some mino adjus men s)
can eplica e he dynamics o ou key a iables pe aining o he economy, inancial sys em,
and clima e. To u he alida e he model, we analyse he esponse o he economy o
a ious shocks, inding ha i can cap u e he s ylised ac s. The model o e s a ounda ion
o p o iding a easonable assessmen o he clima e policies o he ele an s akeholde s.
—————————
1 Aalbo g Uni e si y Business School, Aalbo g Uni e si y, Denma k.
Co esponding au ho is Simon Fløj Thomsen email: s @business.aau.dk.
1
A benchma k Ecological S ock-Flow-Consis en Inpu -Ou pu model o
Denma k
Simon Fløj Thomsen∗
Hamid Raza∗
Mikael Rand up By ialsen∗
Abs ac
This pape aims o de elop an ecological mac oeconomic model o he Danish economy ha can
link he economic and inancial sys em wi h some key aspec s o he clima e. To do so, we combine
S ock- low-Consis en app oach (SFC) wi h Inpu -Ou pu ables (IO) o build a hyb id model, which
we call Ecological S ock-Flow-Consis en Inpu -Ou pu model (E-SFC-IO). Mos pa ame e s o he
model a e es ima ed using ime se ies da a om 1995 o 2019, a e which, we ca y ou simula ions.
We ind ha he model (wi h some mino adjus men s) can eplica e he dynamics o ou key a iables
pe aining o he economy, inancial sys em, and clima e. To u he alida e he model, we analyse
he esponse o he economy o a ious shocks, inding ha i can cap u e he s ylised ac s. The model
o e s a ounda ion o p o iding a easonable assessmen o he clima e policies o he ele an
s akeholde s.
Key wo ds: Empi ical S ock Flow consis en models, Inpu -Ou pu modelling, Ecological mac oeconomics,
Denma k.
JEL-codes: E12, E17, F41, L16.
∗ Aalbo g Uni e si y Business School, Aalbo g Uni e si y, Denma k. Co esponding au ho is Simon Fløj Thomsen
email: s @business.aau.dk.
∗ Aalbo g Uni e si y Business School, Aalbo g Uni e si y, Denma k, s @business.aau.dk
∗ Aalbo g Uni e si y Business School, Aalbo g Uni e si y, Denma k, s @business.aau.dk
2
1. In oduc ion
In ecen yea s, he issue o g een ansi ion and sus ainable de elopmen has played a cen al pa
in shaping na ional policies. The challenges inhe en in he pa h owa ds g een ansi ion ha e
ga ne ed conside able a en ion om a ious esea ch disciplines, anging om scien i ic esea ch -
es ing new echnologies - o social sciences, examining he complex and mul i ace ed in e ac ions
be ween socie y and en i onmen al sus ainabili y. Wi hin his discou se, signi ican emphasis is
placed on he in e play be ween economic ac o s and clima e a ge s – he unde s anding o which
emains incomple e due o he complex na u e o his ela ionship. As such, policymake s a e
s i ing o imp o e hei unde s anding o he economic cos s associa ed wi h clima e policies.
Denma k, like se e al o he coun ies, is aced wi h simila challenges. The coun y has se
ambi ious a ge s o educing g eenhouse gas emissions, aiming o a 70% educ ion by 2030
compa ed o 1990 le els, su passing he Eu opean clima e law's a ge o 55%. Howe e , cu en
measu es a e p ojec ed o achie e only a 63.1% educ ion by 2030, esul ing in a sho all o 6.9%,
equi alen o 5.5 million ons o CO2E (DEA 2023). The e is a clea lack o consensus amongs
a ious s akeholde s on how o achie e hese a ge s and whe he cu ing emissions a a as e a e is
economically easible.
To guide policy decisions on his ma e , he Danish go e nmen elies, a leas pa ly, on he
insigh s o he G een Re o m Model (Ki k e al. 2024), which is he wo kho se o s udying he
in e ac ion be ween clima e and he Danish economy. This model is buil on he p inciples o
compu able gene al equilib ium (CGE), ea u ing p o i maximisa ion by p oduce s ( i ms) and
u ili y maximisa ion by consume s (households). The model is supply-d i en, consis ing o 52
p oduc ion indus ies and 26 ene gy ypes (Ki k e al. 2024).1 While he model p o ides a e y
de ailed desc ip ion o he eal economic ac i i y, he ques ion o whe he his desc ip ion is a
ealis ic ep esen a ion o he economy is subjec o discussion. Howe e , a no able sho coming o
his model is i s ailu e o p o iding a ealis ic ep esen a ion o he inancial aspec s o he
economy, some hing ha is conside ed o be qui e c ucial in his discussion (Polli and Me cu e
2019). The inancial sys em, h ough ad hoc assump ions, is simpli ied o he ex en ha i is almos
i ele an . This in i es he same c i icism ha pos -Keynesians ha e di ec ed a supply-side models
in gene al (La oie and Godley 2001; Godley and La oie 2006).
1 Fi ms, while adhe ing o a gene ic CES (Cons an Elas ici y o Subs i u ion) p oduc ion unc ion, op imize be ween
wo complemen a y inpu s namely, capi al and ene gy.
3
In his pape , we aim o de elop an ecological mac oeconomic model ha can link he economic
and inancial sys em wi h some key aspec s o he clima e. Ou main goal is o p o ide a holis ic
o e iew o he issue using a model ha , apa om cap u ing he s ylized ac s, is capable o
e alua ing he economic and inancial isks associa ed wi h clima e policies o socio-economic
na u e. To link he economy, en i onmen and he inancial sys em, we combine S ock- low-
Consis en app oach (SFC) wi h Inpu -Ou pu ables (IO) o build a hyb id model, which we call
Ecological S ock-Flow-Consis en Inpu -Ou pu model (E-SFCIO). The in eg a ion o hese wo
app oaches allows us o connec inal demand wi h supply and inpu s o he i ms. A key elemen o
ou model is he inclusion o a inancial ma ke ; sec o al weal h and deb a e modelled in mo e
de ail, p o iding a mo e nuanced unde s anding o who is paying o he g een ansi ion. When
sol ing he model, mos pa ame e s a e es ima ed using ime se ies da a om 1995 o 2019, a e
which, we ca y ou simula ions, inding ha he model is capable o eplica ing he dynamics o
ou key a iables pe aining o he economy, inancial sys em, and clima e. To u he alida e he
model, we analyse he esponse o he economy o a ious shocks, inding ha i can cap u e he
s ylised ac s o he Danish economy.
We belie e ou p oposed model will se e as a ounda ion o p o iding a easonable assessmen o
he clima e policies o he ele an s akeholde s. Ou model s uc u e is based on a social accoun ing
ma ix whe e he mos ele an ansac ions a e egis e ed (in e media e and inal consump ion,
income and ax paymen s, ans e s, e c.) on a whom- o-whom basis wi h a cohe en ep esen a ion
o hei co esponding inancial ansac ions and en i onmen al impac s. The de ailed ep esen a ion
o he social and economic s uc u e enables he analysis o he impac o clima e policies on
income and weal h dis ibu ion - an aspec ha , s iking as i may seem, is beyond he scope o
many mac oeconomic models. Mo eo e , i allows o design and es ine- uned sec o -speci ic (o
indus y-speci ic) policies. Fu he mo e, he explici modeling o he main inancial asse s and
liabili ies o he key sec o s o he economy allow o a cohe en desc ip ion o he mul iple ways o
inancing clima e policies, as well as he isks inhe en in hei implemen a ion. Ou model, s ongly
in luenced by pos -Keynesian heo y, is buil on he no ion o demand-led g ow h and excludes
discoun a es and damage unc ions. I s main ocus will be he es ing o he easibili y and join
cohe ence o mul iple clima e policies, bu no he es ima ion o he eedback e ec s om he
en i onmen o he economy.2
2 The neglec o eedback e ec s does no imply ha hey a e conside ed unimpo an . Ra he , he scope o his p ojec
is o build a i s e sion o an E-SFCIO o Denma k. Once his model is unning and p oducing eliable esul s i will

4
The emainde o he pape is o ganized as ollows. In sec ion 2, we p o ide a b ie o e iew o he
Danish clima e a ge s. In sec ion 3, we o e a backg ound discussion o he ype o model
de eloped in his pape . In sec ion 4, will p o ide a de ailed desc ip ion o he da abank cons uc ed
o he model. In sec ion 5, we p esen he model equa ions and he o e all s uc u e o he model.
In sec ion 6, we ca y ou model e alua ion, compa ing he model simula ions wi h obse ed da a.
In he same sec ion, we show how he model esponse as we pe o m 3 simple shocks o he model.
Sec ion 7 concludes his pape .
2. The Danish Clima e goals
O e he las decade, sus ainable de elopmen and g een ansi ion ha e been a he hea o policy
discussions. In 2015, 196 coun ies a ound he wo ld joined he Pa is Ag eemen s wi h he aim o
educing he emission o g eenhouse gases (GHG) signi ican ly in such a way ha he 2°C a ge (o
a mosphe ic empe a u e inc ease abo e p e-indus ial le els) is me by 2050 (UNFCCC 2015). In
2020, he Danish Pa liamen signed he Clima e Law, acco ding o which he emission o GHG
mus be lowe ed by 50% in 2025 and by 70% in 2030 (compa ed o he le el in 1990 which was
app ox. 78 million ons3). This a ge is mo e ambi ious han he a ge se by he Eu opean clima e
law, which aims o a 55% educ ion in GHG emissions by 2030 compa ed o 1990 le els.
Fu he mo e, he Danish clima e law, in line wi h he Eu opean clima e law, has se a long- e m goal
o making he coun y clima e-neu al (i.e., ne GHG emissions equal o ze o) by 2050 (EPRS
2021).
Apa om i s own na ional a ge s, Denma k has an obliga ion o educing emissions in speci ic
sec o s no included in he ETS (Emission T ading Sys em) as pa o he EU a ge s o 2030. Mo e
speci ically, he 2023 e ised e sion o EU’s E o Sha ing Regula ion (ESR) in 2023 obliges
Denma k o educe GHG emissions in non-ETS sec o s – comp ising ag icul u e, anspo (excl.
a ia ion), building hea ing, small indus ies, and was e – by 50% collec i ely in 2030 (compa ed o
2005 le els).
be possible o mo e o a second s age, whe e he eedback e ec s a e inco po a ed in o he model. I is wo h
men ioning ha he e is no scien i ic consensus abou how hese eedback e ec s should be modeled, which d i es us o
conclude ha he in es iga ion o hese phenomena cons i u es a esea ch p ojec on i s own.
3 He e, he es ima e is based on ne emissions wi hin he Danish e i o y (excl. G eenland and Fa oe Islands) and
includes LULUCF.
5
While assessing Denma k’s pa h owa ds g een ansi ion, he Danish Ene gy Agency (DEA) and
Danish Council on Clima e Change (DCCC 2023, 2024)4 in hei assessmen s ha e epea edly
unde sco ed he signi ican challenges ha Denma k aces in achie ing bo h i s na ional as well as
EU a ge s. Acco ding o 2022 s a is ics, he ne domes ic emission was 43.3 million ons,
sugges ing a 41.7% educ ion compa ed o he 1990s. The coun y s ill needs a signi ican educ ion
o app oxima ely 20 million ons in he emaining pe iod o mee he 2030 na ional a ge . A ecen
assessmen by DEA (2023) indica es ha Denma k will mos likely miss i s a ge s unless
signi ican educ ions in ag icul u e and anspo sec o s a e achie ed, as bo h o hese sec o s
collec i ely con ibu e o mo e han hal o he o al ne emissions.5 Mo e speci ically, wi h he
cu en measu es in place, i is p ojec ed ha Denma k will achie e 63.1 pe cen educ ion by 2030
(lea ing a gap o 6.9 pe cen , which co esponds o 5.5 million ons o CO2). To close he
emaining gap, he go e nmen has ecen ly eached an ag eemen including axa ion on CO2-
equi elan (CO2E) emissions emi ed by he ag icul u al sec o s a ing om 2030. How such
policies will a ec he economy, a e he ype o ques ions, we would like o add ess using ou
model.
3. Combining S ock- low models wi h Inpu -Ou pu ables
S ock-Flow Consis en models gained a lo o a en ion a e he publica ion o Godley and La oie
(2006), and mo e so a e he 2008 c isis. The app oach o e s a consis en me hodology ha ela es
s ocks and lows by way o social accoun ing and low-o - und ma ices. Since he adi ional
na ional accoun s a e now complemen ed by he new Sys em o En i onmen al-Economic
Accoun ing (SEEA) da a, his makes SFC app oach a na u al candida e o he in eg a ion o
en i onmen al issues in o he economic models. The SFC and IO amewo ks ha e independen ly
co-exis ed o a long ime, bu he app oach o in eg a ing he wo is a ecen de elopmen . While
he s andalone SFC amewo k o e s a comp ehensi e pe spec i e on economic and inancial
dynamics, he in eg a ion o IO is pa icula ly use ul o add essing p essing clima e- ela ed issues.
This combined SFC-IO me hodology p esen s a p omising esea ch a enue and is inc easingly
a ac ing a en ion wi hin he ield o ecological economics. The numbe o exis ing s udies using
SFC-IO app oach is e y limi ed. Mos s udies in his ega d ha e used SFC-IO se up o build ei he
ully o pa ly heo e ical models (see, e.g., Be g e al 2015; Naq i 2015; Jackson & Jackson 2021;
4 The Danish Council on Clima e Change (DCCC) is assigned wi h he ask o ad ising he go e nmen on achie ing i s
in ended a ge s.
5 Acco ding o 2022 s a is ics, ag icul u e con ibu e 27% and anspo con ibu e 29% o he o al ne GHG emissions
in CO2 equi alen s.
6
Dunz e al. 2021).6 Full- ledged empi ical models based on SFC-IO app oach o indi idual
coun ies a e s ill in he making. A he ime o his w i ing, se e al p ojec s a e unde de elopmen
while only a e y small numbe o s udies a e cu en ly a ailable in he li e a u e (Valdecan os
2021).7 Thus, ou wo k is also a con ibu ion o he eme ging li e a u e in ecological
mac oeconomics.
We ex end he exis ing SFC amewo k in h ee ways: i) by in eg a ing a ull Inpu -Ou pu (IO)
able in o he modeling amewo k, ii) by in eg a ing en i onmen al aspec s (such as ene gy usage
and supply by each indus y) in o he analysis, and iii) by in oducing a ela ionship be ween ene gy
usage (in physical uni s) and economic ac i i y while cap u ing he esul ing GHG emissions.
We now p occed o p o iding a o mal desc ip ion o he s eps in ol ed in cons uc ing his model
as well as he o e all s uc u e o he model. In ou p esen a ion, we ese e he e m “sec o ” o
desc ibe ins i u ional sec o s o he economy namely, households, non- inancial co po a ions,
inancial co po a ion, go e nmen , and es o he wo ld. We use he e m “indus y” o desc ibe
di e en indus ies in ol ed in p oduc ion.
4. Da a equi emen s o he model
In his sec ion, we will desc ibe he cons uc ion o he da abank used in E-SFCIO model o
Denma k. Fo he indus y le el, we use he annual inpu -ou pu da a, and o he sec o al le el, we
use he annual na ional accoun s (including bo h ansac ions and balance shee s). To implemen
ecological aspec s in o he model, we also include ene gy and emission accoun s o he Danish
economy.
4.1. Inpu -Ou pu da a
We use IO da a om S a is ics Denma k o he pe iod 1995-2019 and di ide he p oduc ion sec o
in o nine indus ies (see appendix 8.1 o mo e in o ma ion abou he indus ies). In Table 1, we
p o ide a gene al ep esen a ion o IO lows used in ou model. The in e -indus y lows a e
cap u ed ia a 9 by 9 ma ix. The inal demand block consis s o consump ion, public consump ion,
in es men , change in in en o ies8, and expo s. Households’ consump ion baske consis s o a wide
ange o p oduc s, whe e a de ailed classi ica ion is ca ied ou o he ood p oduc s. The inal
6 In he Li e cycle assessmen li e a u e (LCA) he e has also been heo e ical con ibu ions combining he Inpu -ou pu
analysis wi h S ock-Flow Consis en modelling (Almeida e al. 2022).
7 Ongoing p ojec s include empi ical SFC-IO models o coun ies like G eece, I aly, A gen ina, and o he s.
8 To simpli y he model, we ha e added he acquisi ions less disposals o aluables o he change in in en o ies. Bo h
a iables a e held exogenous wi hin he model and will en e he same equa ions whe eas i will no impac any esul s.
7
demand lows a e cap u ed ia a 11 by 9 ma ix. We ha e classi ied he IO able in o di e en
blocks, each ep esen ing a ma ix. Unde s anding he dimensions o hese di e en blocks will play
a c ucial ole in unde s anding he equa ions in his pape . We encou age he eade o ake a
momen o ully unde s and he blocks (highligh ed in di e en colou s) and hei dimensions.
Table 1: Inpu -Ou pu Ma ix (gene al ep esen a ion)
We now mo e om a gene al ep esen a ion o he IO ma ix o he speci ic case o Denma k. Table
2 is a ep esen a ion o an IO- able using Danish da a (in nominal alues) o 2019. When mo ing
ac oss he able ho izon ally, he lows ep esen he p oduc ion o each indus y. Fo example, he
i s ow shows he p oduc ion o ag icul u al sec o . No e ha each indus y engages in wo ypes o
p oduc ion, i) p oduc ion o p oduc s sold as in e media e goods o o he indus ies (which a e used
as inpu s in p oduc ion), and ii) p oduc ion o inal p oduc s sold o a ious ins i u ional sec o s (incl.
es o he wo ld), de e mining inal demand. I we mo e e ically down he able (o ead he able
om op o bo om), he en ies (wi h he excep ion o g oss ope a ing su plus and mixed income)
ep esen he cos s o domes ic indus y associa ed wi h p oduc ion. Fo example, he i s column o
he able shows he cos o p oduc ion in he ag icul u al indus y. The cos o he indus y consis s o
h ee ca ego ies, i) domes ic and impo ed inpu s, ii) p oduc ion and alue added axes, and iii)
compensa ion o employees. The di e ence be ween he o al alue o p oduc ion and cos s, gi es us
he g oss ope a ing su plus. This will be explained in mo e de ail, when p esen ing he model
equa ions in sec ion 5.
14
In a s a ic se up, he ela ionship be ween inal demand 𝑭𝑭𝒅𝒅𝒅𝒅𝒅𝒅,𝒕𝒕
𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 and p oduc ion 𝒑𝒑𝒑𝒑𝒅𝒅𝒅𝒅𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐 would
equi e he calcula ion o he Leon ie in e se,14 bu since we use a dynamic se up, we can simply
use equa ion 4 in combina ion wi h equa ion 5d o calcula e o al p oduc ion o each indus y,
which o indus y n will esul in equa ion 6 p esen ed in sec ion 5.1.1.
4.2. T ansac ion-Flow-Ma ix om a sec o al pe spec i e
Be o e we mo e u he in o he da a equi emen s o he model, we ind i impo an o i s
p o ide an o e iew o he ansac ion lows om he pe spec i e o ins i u ional sec o s in he
economy (aka T ansac ion-Flow-Ma ix - TFM). Ou model consis s o 5 ins i u ional sec o s
namely, households, non- inancial co po a ions (NFC), inancial co po a ions (FC), go e nmen ,
and he es o he wo ld (ROW).
Table 4: T ansac ion-Flow-Ma ix
I is impo an o highligh ha he na ional accoun s, which p o ide he basis o a ull empi ical
model, can be p esen ed a bo h indus y and sec o al le el. When desc ibing p oduc ion in he
model s uc u e, we use he indus y-le el accoun s (discussed in sec ion 4.1), bu when explaining
he TFM in Table 4, we choose o use he p esen a ion om he sec o al pe spec i e. The eason is
ha da a o a iables below g oss ope a ing su plus and mixed income, such as inancial income o
changes in inancial ansac ions, is una ailable a indus ial le el. Consequen ly, he cu en model
14 In a s a ic inpu -ou pu model one should ob ain he Leon ie in e se o ela e domes ic inal demand (𝑭𝑭𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐) o
domes ic p oduc ion (𝒑𝒑𝒑𝒑𝒅𝒅𝒅𝒅𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐). This can be done using he ollowing equa ion: �𝑰𝑰𝟗𝟗−𝑨𝑨𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐�−𝟐𝟐∗𝑭𝑭𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝒊𝒊𝟐𝟐𝟐𝟐=
𝒑𝒑𝒑𝒑𝒅𝒅𝒅𝒅𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐. Whe e �𝑰𝑰𝟕𝟕−𝑨𝑨𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐�−𝟐𝟐 is e e ed o as he Leon ie in e se (𝑳𝑳𝒕𝒕𝟐𝟐𝟐𝟐𝟐𝟐𝟐𝟐−𝟐𝟐).

15
can explain he ows below g oss ope a ing su plus only a a sec o al le el. Fo example, he model
will only explain ne lending (su plus/de ici ) a a sec o al le el bu no a an indus ial le el.
We now p o ide an explana ion o how indus ies and sec o s a e connec ed. No e ha en ies abo e
he g oss ope a ing su plus a e ob ained om he IO able whe eas lows below he g oss ope a ing
su plus a e ob ained om he na ional accoun s a a sec o al le el. To es ablish a connec ion
be ween indus ies (IO da a) and ins i u ional sec o s (sec o al na ional accoun s), we use g oss
ope a ing su plus as a binding low. This equi es iden i ying, wha sha e o indus ial p o i s ( om
p oduc ion) alls unde which sec o s; in his ega d, we use he 2016 ma ix o indus y by sec o
p o ided by S a is ics Denma k (DST 2021), which con ains he sha e o g oss alue added (GVA)
om each indus y alloca ed o he co esponding ins i u ional sec o s. Fo example, he ma ix
sugges s ha wo- hi ds (app ox. 66.7 pe cen ) o he GVA om he ag icul u al indus y belongs o
he households, one- hi d (app ox. 33.3 pe cen ) belongs o he NFC, whe eas none belongs o he
o he sec o s. The e o e, i is assumed ha wo- hi ds o he g oss ope a ing su plus om he
ag icul u al indus y is owned by he household sec o , whe eas he emaining belongs o he NFC.
This implici ly sugges s ha wo- hi ds o bo h he o al p oduc ion (which includes he sale o inal
consump ion goods) and he o al cos s (pa o which include paying wages) ela ed o he
ag icul u al indus y belong o he household sec o . Howe e , o keep he p esen a ion o TFM
simple, en ies in ela ion o consump ion (as an income) and wages (as an expense) a e no
explici ly included o he household block.
To ge he weigh s o each o he 9 indus ies, we calcula e a weigh ed a e age o he sha es
ob ained om he ma ix o indus y by sec o , using he le el o g oss ope a ing su plus o each
indus y (mo e in o ma ion abou he es ima ion o hese sha es a e p o ided in appendix 8.2).15 I
is impo an o highligh ha he alloca ion o g oss ope a ing su plus (which we a he indus y
le el call p o i s) o o he ins i u ional sec o s should no be con used wi h di idend payou s agains
equi y holdings; ha mechanism is sepa a ely cap u ed in ou amewo k as will be discussed.
A e ans o ming g oss ope a ing su plus and mixed income (p o i s) om an indus y o sec o al
le el, we now ocus on sec o -speci ic income and expenses. He e, we ely on he sec o al na ional
accoun s da a p esen ed by S a is ics Denma k. This includes sec o al sa ing, which is used o
15 An al e na i e app oach is o calcula e exogenous sha es o o al p o i s ecei ed by he household, he go e nmen
sec o , inancial co po a ions, and non- inancial co po a ions based on he sec o al da a and hen di ide ou o al g oss
ope a ing su plus using hese sha es. A p oblem ha migh a ise ollowing his app oach is i ag icul u al inc ease
p o i s his will lead o an inc ease in o al p o i s and based on he exogenous sha es p o i s ob ained by he sec o s will
inc ease. In eali y, an inc ease in ag icul u e indus y p o i s should only inc ease he p o i s ob ained by he household
sec o and non- inancial co po a ions ollowing he sha es ob ained om he Ma ix o indus y by sec o s.
16
capi al o ma ion (in es men s) and o he capi al ans e s;16 i a sec o ’s sa ings a e no enough o
mee i s in es men expendi u es and o he capi al ans e s, he sec o will un in o a (sec o al)
de ici , which is epo ed by he ow called ne lending in he TFM. This de ici is co e ed by
adjus men s in he balance shee as shown by he ows below ne lending, ep esen ing he changes
in eigh ne inancial s ocks namely gold, deposi s, secu i ies, loans, equi ies, insu ances,
de i a i es, and ade c edi s.
The s uc u e o he balance shee , al hough no explici ly p esen ed, is ob ious om he lowe pa
o TFM. The ne alue o each inancial s ock is calcula ed as he di e ence be ween he asse and
liabili y o he same inancial s ock. When calcula ing he change in ne inancial weal h (as shown
by he las ow o he TFM), we also accoun o e-e alua ions o he s ock o ne inancial s ocks,
ep esen ed by he 8 ows jus abo e he ne inancial weal h.
4.2.1. Ne inancial income
One c ucial aspec o he sec o al da a is he calcula ion o a es o e u n o he 4 ypes o income
on inancial asse s ( epo ed in he ows unde he g oss ope a ing su plus) being: ne in e es
paymen s deno ed by NINT, ne income on o he in es men s ( ela ed o pension and insu ances)
deno ed by NOIR, ne income on ne equi ies deno ed by NDIV, and inally income on ne FDI
deno ed by NFDI. A c ucial s ep in calcula ing hese a es o e u ns is o ensu e ha incomes on
inancial asse s in he TFM (4 income s eams in ou case) a e linked o he holdings o inancial
s ocks (8 inancial s ocks in ou case). To clea ly es ablish a link in his ega d and o simpli y he
s uc u e o he model, we ely on ce ain assump ions.17 Fi s , we assume ha he a e o e u n on
a gi en inancial s ock is he same ac oss ins i u ional sec o s, e.g., he in e es a e on loans is he
same o all sec o s. This aises he ques ion o which sec o ’s s ocks and lows should be used o
calcula e he a es, which mo i a es ou second assump ion; i can be a gued ha , since inancial
co po a ions se e as inancial in e media o s, his sec o should be used o calcula e he a es o
e u ns on inancial s ocks. In appendix 8.3, we p esen a de ailed desc ip ion o how hese di e en
a es o e u ns a e calcula ed, which de e mine he 4 ypes o ne inancial income p esen ed in he
TFM.
We now p oceed o p esen ing he da a used in he en i onmen al block o he model.
16 He e, we use exogenous sha es o di ide he o al nominal in es men s ac oss he sec o s.
17 Ou assump ions a e mos ly dic a ed by he lack o anspa ency in he da a.
17
4.3. En i onmen al da a
We use a mix o da a sou ces o he en i onmen al a iables. Fo he ene gy supply and use, we
collec all da a om S a is ics Denma k. Fo emissions, we ha e chosen o use a combina ion o he
da a om G eenREFORM model and S a is ics Denma k. The appealing ea u e o he emission
da a used in G eenREFORM is ha we can ela e a speci ic ype o emissions o a speci ic ype o
ene gy usage. In he ollowing sec ions, we p esen his in u he de ail, s a ing wi h he ene gy
accoun s om S a is ics Denma k.
4.3.1. Ene gy Accoun s
Fo he ene gy accoun s used in ou analysis, we conside 21 di e en ypes o end-use ene gy
p oduc s supplied and used in he economy. This da a is c ucial o unde s anding he di ec ene gy
usage pa e ns ac oss di e en economic uni s, p o iding clea insigh s in o which ene gy sou ces
a e mos u ilized by each indus y. Table 5 p o ides an o e iew o he Danish ene gy accoun s in
2019, exp essed in physical uni s.
Table 5: Ene gy supply and usage in 2019 by each indus y (in million Gigajoules)
No e: Coil (c ude oil), Oilp: Oil p oduc s), Re G (Re ine y gas), GasT (Gasoline o anspo a ion), FGas (je uel),
FGasBunk (Je uel bunke ed), DieT (Diesel o anspo a ion), Die TBunk (Diesel o anspo a ion - bunke ed),
NGasEx (Na u al gas ex ac ion), NGasCons (Na u al gas consump ion – incl. ci y gas), CC (coal and smoke), Was e
(Was e), RE (Renewable ene gy), S aw (S aw), FW (Fi ewood and wood chips), WP (wood pelle s), BioG (Biogas),
BBB (Biodiesel, bioe hanol and bio-oil), El (elec ici y), DHea (Dis ic hea ).
Fo each o he 21 ene gy ypes, we ha e bo h supply and usage da a o each indus y, ep esen ed
by he i s nine ows in each block. Speci ically o ene gy supply, ene gy can be impo ed o
18
p oduced using accessible inpu s in he o m o was e o enewable ene gy (e.g., wind o sola
powe ). In he usage block, ene gy can be expo ed o use ou side Denma k, consumed by
households, o los due o dis ibu ion losses. I he e is an excess supply (usage) o a speci ic
ene gy ype, his will inc ease (lowe ) he in en o ies o ha ene gy ype (see he ow “Change in
in en o ies”). As a esul , o al ene gy usage equals o al ene gy supply o each indus y.
Al hough we ha e bo h he supply and usage da a a an indus ial le el, in mos cases, we canno
see wha ac ion o he o al ene gy used by an economic uni is supplied by a speci ic supplie . We
can only es ablish pa ial links based on ou abduc i e easoning o he ene gy accoun s, which
could be use ul in in e p e ing he esul s. Fo ins ance, om a consump ion poin o iew, he
‘ene gy p oducing and e ine ies’ indus y shows a high consump ion o c ude oil (328.7 million
gigajoules), indica ing i s subs an ial eliance on he mining indus y. Whe eas, om a p oduc ion
poin o iew, his indus y se es as he sole p o ide o na u al gas o consump ion and he
bigges p o ide o dis ic hea ing, he la e being he la ges sou ce o ene gy o he household
sec o used in hea ing esiden ial uni s. Thus, he household sec o , o i s ene gy consump ion,
appea o ha e a s ong di ec dependence on ene gy p oducing and e ine ies indus y.
Un o una ely, we do no ha e he ull in o ma ion o anspa en ly link each and e e y uni o
ene gy be ween supplie s and use s. This limi a ion, along wi h he absence o ene gy p ices
equi ed o con e physical uni s o mone a y uni s, p e en s us om in eg a ing ene gy accoun s
in he IO se up p esen ed ea lie . None heless, i is impo an o emphasise ha he cos s ( e enue)
associa ed wi h using (selling) ene gy as an in e media e good a e implici in he IO able. In his
e sion o he model, we simply aim o es ablish a ela ionship be ween ene gy usage (in physical
uni s) and economic ac i i y while cap u ing he esul ing GHG emissions. A mo e ealis ic
ex ension o he model will equi e accoun ing o he p ice o each ene gy ype, con e ing
physical uni s o mone a y uni s, and hen in eg a ing ene gy accoun s in he IO se up.
4.3.2. Emission Accoun s
We collec da a on six ypes o emissions: ca bon dioxide (CO2), ni ous oxide (N2O), me hane
(CH4), sul u hexa luo ide (SF6), pe luo oca bons (PFC), and hyd o luo oca bons (HFC). These
emissions a e la e used o calcula e he CO2-equi alen measu e (CO2E). As men ioned, we use a
mix o da a sou ces o he emissions da a. Fo CO2, N2O, and CH4, we use da a om he
G eenREFORM model da abank (S a e e al., 2024). In con as , we use da a om S a is ics
Denma k o SF6, PFC, and HFC. The choice o da a sou ce depends on how he emission ype is
p oduced. Since CO2, N2O, and CH4 a e emi ed bo h in ela ion o ene gy usage and
19
independen ly o i , he de ailed se up o he G eenREFORM model da abank allows us o
disagg ega e ene gy- ela ed emissions down o speci ic ene gy ypes. In he able below, we p esen
his disagg ega ion o CO2 emissions ela ed o ene gy: 18
Table 6: CO2 emissions ela ed o ene gy usage
As de ailed emissions da a om he G eenREFORM da abase a e only a ailable up un il 2017, we
cons uc new emissions da a o 2018 and 2019, assuming he same ela ionship be ween ene gy
usage and emissions as in 2017 (since ene gy da a is a ailable o 2018 and 2019). This will
become clea e in sec ion 5.4.2, whe e ene gy-speci ic emissions coe icien s a e calcula ed.
Fo SF6, PFC, and HFC emissions, which a e un ela ed o ene gy usage, i is nei he necessa y no
possible o disagg ega e hese emissions in o he o ma o Table 6. This da a is a ailable o he
en i e ime pe iod, and no u he ope a ions a e equi ed.
This concludes he da a equi emen s o he model, which elies on na ional accoun ing da a a bo h
he indus y and sec o al le els, along wi h emissions and ene gy da a. In he nex sec ion, we
in oduce he s uc u e o he model.
5. The model s uc u e
The model has ou majo blocks, i) he domes ic p oduc ion block, desc ibing o al p oduc ion,
p oduc ion cos s, and p o i s o he domes ic indus ies, ii) he agg ega e (o inal) demand block,
p o iding a de ailed desc ip ion o he d i e s o agg ega e demand. Since he model is demand-
d i en, his block o a la ge deg ee de e mines indus ial p oduc ion (o he supply side), which is
p esen ed in he p oduc ion block. iii) he s ock- low consis ency block, in which we model he
18 This da a was published oge he wi h he p esen a ion o he g een e o m model used o e alua e en i onmen al
egula ions o he ag icul u al indus y in Denma k (S a e e al. 2024). Duo o inconsis ency wi h ene gy used and
emissions o wood pills o he ag icul u al indus y, we ha e modi ied he da abank by se ing emission o he
ag icul u al sec o associa ed wi h wood pelle s o 0. This only occu s in 1995, 2000, and 2003 and he highes absolu e
alue being 4.37E-13.

20
inancial aspec s o each ins i u ional sec o o cap u e he in e dependence be ween eal and
inancial sphe es o he economy, while ensu ing he e a e no leakages in he sys em, and i ) he
en i onmen al block, whe e we model he ypes o ene gies used in he p oduc ion p ocess and also
cap u e he esul ing GHG emissions o each indus y and he economy as a whole.
5.1. P oduc ion componen s
5.1.1. P oduc ion
We can o mally show he accoun ing iden i y used o calcula e o al p oduc ion. As men ioned in
sec ion 4.1.2, we use a dynamic se up whe e we ely on a single equa ion (see equa ion 4),
acco ding o which, o al domes ic p oduc ion in ixed p ices is de ined as ollows:
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=�𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑖𝑖
9
𝑖𝑖=1 +�𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1 +𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢+𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢+Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑝𝑝𝑝𝑝𝑚𝑚,𝑡𝑡
𝑖𝑖+𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢(equa ion 6a)
In he abo e equa ion, ∑𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑖𝑖
9𝑖𝑖=1 ep esen s he sum o inpu s (o o al in e media e goods) sold by
he domes ic indus y n o he domes ic indus y i (whe e i=1,2,3,…,9). Tha is, i ep esen s he
sum ac oss columns ( ep esen ing sales) while holding he ow ixed o an indus y n. Fo example,
i we ake he ow ha ep esen s he ag icul u al sec o , he sum o column 1 (le ) o column 9
( igh ) will ep esen he o al in e media e goods sold by he ag icul u al sec o . The e m
∑𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1 in he equa ion ep esen s consump ion o di e en ypes o goods (p) o e ed by
indus y n. In o he wo ds, his ep esen s he sum ac oss he columns ( ep esen ing sales o
di e en good ypes) in he household consump ion block while holding he ow ixed o an
indus y n. The emaining elemen s o equa ion 6a, gi en by 𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢,𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢,Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑝𝑝𝑝𝑝𝑚𝑚,𝑡𝑡
𝑖𝑖, and
𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 ep esen he p oduc ion o indus y n (e e y hing in de la ed alues wi h base yea 2010) o
he pu pose o public spending, in es men , changes in in en o ies, and expo s, espec i ely.19 By
including equa ion 5d (𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢= 𝑎𝑎𝑡𝑡𝑖𝑖 𝑢𝑢∗𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢) in he model we ake in o accoun he indi ec
e ec o changes in eal p oduc ion on equi ed inpu s. I is impo an o highligh ha his
ela ionship is modelled using he de la ed a iables. I his ela ionship was cap u ed using nominal
alues, an inc ease in p ices o inal consump ion goods in indus y n would esul in an inc ease in
19 F om o al p oduc ion, we can de i e he sales wi hin each indus y by deduc ing he change in in en o ies om he
p oduc ion 𝑠𝑠𝑎𝑎𝑠𝑠𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢−Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢. I indus y n p oduces mo e han wha is sold, he change in
in en o ies will be posi i e, whe eas a nega i e alue indica es ha goods p oduced in p e ious yea s we e sold in he
cu en pe iod, lowe ing he alue i he in en o ies. Since changes in in en o ies a e ela i ely small and ea ed as
exogenous, we do no dis inguish be ween sales and p oduc ion.
21
inpu s om o he indus ies (∑𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑖𝑖
9𝑖𝑖=1 ). We can now compu e o al p oduc ion (𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢) in
nominal e ms, using he p ice indices in Table 3 as ollows.
𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=�𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑖𝑖
9
𝑖𝑖=1 +�𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1 +𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢+𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢+Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢+𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 (equa ion 7a)
whe e 𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑖𝑖= 𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑖𝑖∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is nominal in e media e goods sold by indus y n o o he indus ies,
∑𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1 =∑𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1 ∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is nominal p i a e consump ion o goods, 𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗
𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is nominal go e nmen consump ion o goods p oduced by a domes ic indus y n, 𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=
𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is nominal in es men using goods o a domes ic indus y n, Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=
Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is he nominal change in in en o ies, and 𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is he
nominal expo s o goods by a domes ic indus y n.
5.1.2. Cos o p oduc ion
To es ima e he cos s o a speci ic domes ic indus y, we can mo e e ically down he IO able (see
Table 2), whe e all he en ies, excep g oss ope a ing su plus and mixed income, ep esen he cos s
associa ed wi h p oduc ion. The o al cos o p oduc ion (𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑
𝑢𝑢) o a domes ic indus y n in
nominal e ms is de e mined as ollows:
𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=�𝑍𝑍 𝑡𝑡𝑖𝑖 𝑢𝑢
9
𝑖𝑖=1 +𝑍𝑍𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢+𝑍𝑍𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 +𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢+𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢+𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑢𝑢
+𝑊𝑊𝑡𝑡𝑢𝑢 (equa ion 8)
whe e ∑𝑍𝑍 𝑡𝑡𝑖𝑖 𝑢𝑢
9𝑖𝑖=1 ep esen s o al inpu s pu chased by indus y n (incl. bo h domes ic and impo ed
inpu s). Tha is, each ype o inpu (e.g., ag icul u al inpu ) can be di ided in o domes ic and
impo ed inpu as ollows: 𝑍𝑍 𝑡𝑡𝑖𝑖 𝑢𝑢=𝑍𝑍 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢 + 𝑍𝑍 𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢 (equa ion 9a)
�𝑍𝑍 𝑡𝑡𝑖𝑖 𝑢𝑢
9
𝑖𝑖=1 = �𝑍𝑍 𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢+ �𝑍𝑍 𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢
9
𝑖𝑖=1
9
𝑖𝑖=1 (equa ion 9b)
He e, ∑𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢
9𝑖𝑖=1 is he cos o domes ic inpu s pu chased by indus y n om domes ic indus y i a
ime . The e m ∑𝑍𝑍𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢9𝑖𝑖=1 deno es he sum o inpu s pu chased by indus y n om o eign indus ies
a ime . No e ha he no a ion 𝑍𝑍𝑡𝑡𝑖𝑖 𝑢𝑢 is he sum ac oss ows i (whe e i = 1,2,3,…,9) while holding a
22
column n ixed, which gi es us inpu s as cos s o an indus y n. Fo example, o calcula e o al
domes ic inpu s pu chased by he ag icul u al sec o , we choose he column, ep esen ing he
ag icul u al sec o , and hen ake sum o ow 1 ( op) o ow 9 (bo om). No e ha he no a ion 𝑍𝑍𝑡𝑡𝑖𝑖 𝑢𝑢 in
equa ion 8 is di e en om he no a ion 𝑍𝑍𝑡𝑡𝑢𝑢 𝑖𝑖 deno ing inpu s as sales in equa ion 7 (which was he
sum ac oss columns i while holding a ow n ixed). In he es o he p esen a ion, 𝑍𝑍𝑡𝑡𝑖𝑖 𝑢𝑢 will ep esen
cos s o inpu s o an indus y n whe eas 𝑍𝑍𝑡𝑡𝑢𝑢 𝑖𝑖 will ep esen sales o an indus y n, in bo h cases wi h
indus y i as he coun e pa .
Fo he emaining no a ions in equa ion 8, 𝑍𝑍𝑢𝑢𝑖𝑖𝑑𝑑𝑝𝑝,𝑡𝑡
𝑢𝑢 deno es he unspeci ied impo s used, 𝑍𝑍𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
ep esen s he impo du ies paid, 𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢 deno es he commodi y axes, 𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢 deno es he alue added
axes, 𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑢𝑢deno es o he p oduc ion axes, and 𝑊𝑊𝑡𝑡𝑢𝑢 deno es he wage bill paid by indus y n.
The cos s ela ed o 𝑍𝑍𝑢𝑢𝑖𝑖𝑑𝑑𝑝𝑝,𝑡𝑡
𝑢𝑢 and 𝑍𝑍𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 will be add essed in sec ion 5.2.6, whe e we discuss impo s,
while he emaining cos s will be co e ed now as we begin modeling he a ious axes associa ed
wi h p oduc ion. In his con ex , commodi y axes, alue-added axes, and o he p oduc ion axes
a e calcula ed using an exogenous ime- a ying a e o each indus y. Fo commodi y axes in each
indus y (𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢), we mul iply domes ically pu chased inpu s by he co esponding ax a e as
ollows:
𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢=� �𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢
9
𝑖𝑖=1 �∗𝐶𝐶𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑢𝑢 (equa ion 10)
Using he same s a egy, we calcula e alue added axes (𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢) by mul iplying he domes ically
pu chased inpu s wi h he co esponding ax a e as ollows:
𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢=� �𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢
9
𝑖𝑖=1 �∗𝑉𝑉𝑉𝑉𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑢𝑢 (equa ion 11)
Rega ding o he p oduc ion axes paid by he 9 indus ies (𝑃𝑃𝑉𝑉𝑃𝑃𝑡𝑡𝑢𝑢), we dis inguish be ween
en i onmen al axes (𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢) and non-en i onmen al axes (𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢). The iden i y ep esen ing
o al o he p oduc ion axes can be ep esen ed as ollows:
𝑃𝑃𝑉𝑉𝑃𝑃𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢= 𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢+𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢 (equa ion 12)
To compu e non-en i onmen al (ne ) o he p oduc ion axes, we use an exogenous a e based on
o al inpu s used om domes ic p oduc ion. This can be exp essed as ollows:
23
𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢=� �𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢
9
𝑖𝑖=1 �∗𝐼𝐼𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑢𝑢 (equa ion 13)
The en i onmen al axes (𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢) a e de e mined endogenously in he model and will be u he
discussed in sec ion 5.4.3 (equa ion 144a).
The inal componen o indus y speci ic cos s is he wage bill 𝑊𝑊𝑡𝑡𝑢𝑢 paid o wo ke s by he nine
indus ies. He e we mul iply he wage a e 𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡𝑢𝑢 wi h he numbe o employees in each indus y:
𝑊𝑊𝑡𝑡𝑢𝑢=𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡𝑢𝑢∗𝑉𝑉𝑀𝑀𝑃𝑃𝑡𝑡𝑢𝑢 (equa ion 14)
I he o al nominal alue o p oduc ion (in equa ion 7) o an indus y a e highe han i s nominal
cos s (in equa ion 8), he indus y will ha e a posi i e mixed income and g oss ope a ing su plus (o
p o i s), which is ep esen ed in he las ow o he alue-added block. This iden i y can be
ep esen ed as ollows: 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢=𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢− 𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 (equa ion 15)
whe e 𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢 in equa ion 15 ep esen s he p o i (g oss ope a ing su plus and mixed income) o
indus y n. Fo example, he g oss ope a ing su plus and mixed income o he ag icul u al indus y
is 21.5 billion DKK in 2019 (see Table 2), which is equi alen o he di e ence be ween o al
p oduc ion measu ed as he sum o he i s ow and he o al cos s measu ed by he sum o he i s
column (excluding he g oss ope a ing su plus and mixed income i sel ).
The calcula ions o p o i s as a esidual ensu es ha we ha e a ull accoun o p oduc ion in he IO
amewo k whe e o al ou pu o a gi en indus y n equal i s o al ou lays (e.g., o al ou pu and
ou lays o ag icul u e sec o a e 77.232).
5.1.3. The labou ma ke : P ices, wages, and employmen
Fo p ice se ing a an indus y le el, we ollow a s anda d p icing mechanism o en used wi hin he
Pos -Keynsian li e a u e (Ha is 1974, Asimakopulos 1975, Godley and La oie 2006). We assume
ha p oduce s ha e some deg ee o ma ke powe (o monopoly) and can he e o e se p ices abo e
he uni cos o p oduc ion. This app oach o p ice se ing is ealis ic when applied a an indus ial
le el, since p oduc s ac oss he indus ies a e no close subs i u es. To es ima e he p ice wi hin each
indus y, we assume he p ice o a p oduc o e ed by indus y n is a unc ion o a ma k-up o e
uni cos o p oduc ion as ollows:
30
𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1 (equa ion 26b)
𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1 (equa ion 26c)
𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1 (equa ion 26d)
Whe e 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 ep esen s o al household consump ion o goods p oduced by he domes ic indus y
whe eas 𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 ep esen s he o al household consump ion o impo ed goods. The sha e o impo ed
goods in he Danish consume baske is qui e s able a ound 10 pe cen o e he las decade.
To include axes paid on inal consump ion we calcula e exogenous ax a es based on he obse ed
da a. All inal demand componen s a e axed h ough bo h commodi y and alue added axes
associa ed wi h each good ype p:
𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑝𝑝=𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑐𝑐𝑑𝑑𝑢𝑢𝑐𝑐,𝑝𝑝∗𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝 (equa ion 27a)
𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑝𝑝=𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑐𝑐𝑑𝑑𝑢𝑢𝑐𝑐,𝑝𝑝∗𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝 (equa ion 27b)
The e m 𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝 in equa ion 27a and 27b ep esen s consump ion o he households o each good
ype p. Thus, 𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑝𝑝 is he commodi y axes and 𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑝𝑝 he alue added axes paid on he
consump ion o each good ype p. To calcula e o al commodi y axes and alue added axes on
consump ion, we can ake he sum ac oss he good ypes in he consump ion block as ollows:
𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑝𝑝
7
𝑝𝑝=1 (equa ion 28a)
𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑝𝑝
7
𝑝𝑝=1 (equa ion 28b)
5.2.2. In es men s
To es ima e in es men , we ollow he app oach o wha is also known as he pos -Kaleckian
Bhadu i and Ma glin (1990) model. Acco ding o his app oach, in es men is de ined as a unc ion
o capaci y u iliza ion and p o i sha e. The a e o capaci y u iliza ion is cons uc ed as he a io o

31
eal GDP (𝑦𝑦𝑡𝑡) o he eal s ock o capi al (𝑘𝑘𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). P o i sha e (𝑝𝑝𝑠𝑠𝑡𝑡) is de ined as he a io o g oss
ope a ing su plus o GDP. The es ima ed equa ion gi es us he ollowing:
Δln(𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡)= 1.8∗∗∗Δln �𝑑𝑑𝑡𝑡−1
𝑘𝑘𝑡𝑡−1
𝑁𝑁𝑁𝑁𝑁𝑁�−0.09∗∗∗ln(𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡−1
𝑡𝑡𝑑𝑑𝑡𝑡)+ 1.42∗∗∗ 𝑝𝑝𝑠𝑠𝑡𝑡−1 (equa ion 29)
Acco ding o he es ima es, agg ega e in es men , in he sho un, is d i en by he a e o capaci y
u iliza ion whe eas in he long un, i is d i en by he p o i sha e. No e ha ou measu e o o al
in es men s includes bo h domes ic and impo ed goods used in capi al o ma ion (bu excludes
alue-added axes and commodi y axes o now).
We hen use in es men sha es (𝜆𝜆𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢) o di ide in es men spending on he basis o indus ies,
supplying goods used in in es men s.
𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑢𝑢=𝜆𝜆𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢∗𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 30a)
We can hen di ide in es men in each indus y in o in es men spending using domes ic p oduc s
and impo ed p oduc s. We use an impo sha e (𝜙𝜙𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢) calcula ed o each indus y:
𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=�1−𝜙𝜙𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢�∗𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑢𝑢 (equa ion 30b)
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢=�𝜙𝜙𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢�∗𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑢𝑢 (equa ion 30c)
To con e eal in es men s in o nominal, we use he co esponding p ice de la o s o domes ic and
o eign indus ies as ollows: 𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equa ion 31a)
𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (equa ion 31b)
Las ly, we agg ega e in es men ac oss indus ies o bo h nominal and eal e ms:
𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 32a)
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 32b)
𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 32c)
32
𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 32d)
We can inally use exogenously calcula ed ax a es, o calcula e he commodi y axes and alue
added axes associa ed wi h domes ically p oduced in es men p oduc s.
𝐼𝐼𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣 ∗𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 33a)
𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣 ∗𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 33b)
5.2.3. Change in in en o ies
Changes in in en o ies a e de e mined exogenously wi hin he model. We choose o keep i
exogenous in eal alues. The ollowing equa ions desc ibe eal in en o ies, including domes ic and
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 and impo ela ed 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =� Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9𝑢𝑢=1 (equa ion 34a)
Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =� Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9𝑢𝑢=1 (equa ion 34b)
Nominal in en o ies a e pa ly endogenous in a sense ha hey a e a ec ed by (endogenous)
domes ic p oduce p ices (𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢). In en o ies in nominal e ms can be ep esen ed as ollows:
Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=Δ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equa ion 35)
As a esul , he o al change in in en o ies in nominal alues a e also calcula ed wi hin he model:
Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 36)
Finally, axes pe aining o in en o ies a e exogenous and a e calcula ed wi hin he model as
ollows: Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣𝑟𝑟𝑢𝑢𝑡𝑡∗Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 37a)
Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣𝑟𝑟𝑢𝑢𝑡𝑡∗Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 37b)
33
5.2.4. Go e nmen spending
Go e nmen spending, like changes in in en o ies, is also ea ed as exogenous in eal alues. Final
go e nmen consump ion o impo ed (𝑔𝑔𝑝𝑝𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡) and domes ic goods (𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 ) in eal e ms a e
compu ed as ollows:
𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =�𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9𝑢𝑢=1 (equa ion 38a)
𝑔𝑔𝑝𝑝𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =�𝑔𝑔𝑝𝑝𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9𝑢𝑢=1 (equa ion 38b)
Again, as domes ic p ices can change in he model, so can he nominal alue o go e nmen
spending: 𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑔𝑔𝑝𝑝𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equa ion 39)
We can hen calcula e he o al go e nmen spending in nominal alues as ollows:
𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =�𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9𝑢𝑢=1 (equa ion 40)
Finally, he commodi y and alue added axes pe aining o go e nmen consump ion a e compu ed
as ollows: 𝐺𝐺𝑃𝑃𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑎𝑎𝑑𝑑𝑣𝑣 ∗𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 41a)
𝐺𝐺𝑃𝑃𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑎𝑎𝑑𝑑𝑣𝑣 ∗𝐺𝐺𝑃𝑃𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 41b)
Fo comple eness, we ha e chosen o p esen equa ions ela ed o he changes in in en o ies and
go e nmen spending, e en hough hey a e no necessa y o unning he model. I is impo an o
he eade o no e ha hese wo a iables will only change in nominal e ms and only o domes ic
indus ies.
5.2.5. Expo s
We de e mine he o al expo s o each o he nine indus ies using a a ian o he A ming on
model. Ou expo s in each indus y a e de e mined by p ice compe i i eness and global demand.
We can exp ess he expo s equa ion in log-linea o m as ollows:
ln �𝑥𝑥𝑡𝑡𝑢𝑢
𝑚𝑚𝑡𝑡𝑢𝑢∗�=
α
0
𝑢𝑢+
α
1𝑢𝑢∗ln(𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡−1
𝑢𝑢)+𝑎𝑎𝑝𝑝𝑗𝑗𝑐𝑐,𝑡𝑡
𝑢𝑢 (equa ion 42)
34
whe e 𝑚𝑚𝑡𝑡𝑢𝑢∗is he global demand (o impo s) o he ype o goods p oduced by n ype o indus ies
ac oss he globe. Fo example, when es ima ing he expo s o he ag icul u al sec o , 𝑥𝑥𝑡𝑡𝑢𝑢 ep esen s
expo s o Danish ag icul u al indus y whe eas 𝑚𝑚𝑡𝑡𝑢𝑢∗ ep esen s he global demand o ag icul u al
p oduc s. Thus, he le -hand side o equa ion 42 ep esen s he sha e o Danish expo s o o al
wo ld impo s wi hin each speci ic indus y. To calcula e he sha e o Danish expo s in he global
ma ke , we use he BACI-da ase p o iding impo and expo alues amongs coun ies in he
wo ld a a p oduc -le el.28
α
1𝑢𝑢 cap u es he expo elas ici ies o mo emen s in eal exchange a e
𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑢𝑢. Real exchange a e o each indus y is a p oxy o in e na ional compe i i eness, de ined as
ollows:
𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑢𝑢=𝑥𝑥𝑝𝑝𝑡𝑡𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢
𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (equa ion 43)
whe e 𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 is he domes ic p ice o indus y n, 𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 is he p ice o impo s o indus y n, bo h p ice
indices a e calcula ed in Danish cu ency whe eas we do no need o conside he nominal exchange
a e. To ind he expo elas ici ies ( ep esen ed by
α
1𝑢𝑢), we use es ima es ound by K onbo g,
Poulsen, and Kas up (2020) who de i e expo elas ici ies using he BACI-da ase o he Danish
economy. As he BACI-da ase does no include expo s o all indus ies, we use an a e age expo
elas ici y o he Danish economy in he mining and inancial co po a ion indus ies. The ec o o
he expo elas ici ies pe aining o each indus y is p esen ed in he able below:29
28 As he BACI-da ase does no include p oduc s o all indus ies included by Denma k s a is ics, we use an a e age
expo sha e o he whole Danish economy based on all p oduc s in he BACI-da ase .
29 As we pe o m he agg ega ion o ma ch he 9 indus ies in his pape , we use expo wi hin each indus y o calcula e
a weigh ed a e age.
35
Table 7: Expo elas ici ies
The nega i e alues o he pa ame e (s)
α
1𝑢𝑢 imply ha an inc ease (dec ease) in he domes ic p ice
in indus y 𝑖𝑖 will app ecia e (dep ecia e) he eal exchange a e, which in u n will lowe ( aise)
expo s o indus y n.30 We se he cons an (
α
0
𝑢𝑢) o ma ch he loga i hmic alue o he i s
obse a ion in he ma ke sha e o each indus y. Finally, we include an adjus men e m (𝑎𝑎𝑝𝑝𝑗𝑗𝑐𝑐,𝑡𝑡
𝑢𝑢),
which cap u es he e ec s o a iables o he han he eal exchange a e. As he p ice elas ici ies
p esen ed by K onbo g, Poulsen, and Kas up (2020) a e based on mic o da a (wi h he goal o
inding a causal ela ionship be ween ela i e p ices and expo s), hese es ima es a e ound o be
heo e ically in ui i e, bu poo ly i ing he agg ega e da a. Lea ing ou he adjus men e ms would
he e o e c ea e la ge disc epancies compa ed o he obse ed da a which could be p oblema ic in
he model simula ions. An al e na i e app oach is o ob ain hese elas ici ies using agg ega e da a.
This app oach, howe e , did no wo k in ou case, as he es ima es (using agg ega e da a) we e
ound o be non-sensical due o small sample size. We belie e i is c ucial ha he expo elas ici ies
ha e ealis ic signs and magni udes, he e o e, we make a s a egic decision o using heo e ically
in ui i e elas ici ies based on Danish mic o da a. A e es ima ing he expo sha e o each indus y,
we mul iply he ma ke sha e ( 𝑐𝑐𝑡𝑡𝑖𝑖
𝑑𝑑𝑡𝑡𝑖𝑖∗) wi h he co esponding denomina o (𝑚𝑚𝑡𝑡𝑢𝑢∗) o ob ain expo s o
each indus y in le els (𝑥𝑥𝑡𝑡𝑢𝑢).
30 We use elas ici ies whe eas an expo elas ici y o -5.13 o he ag icul u e indus y implies ha a 1% inc ease in he
eal exchange a e o his indus y lowe s i s expo by 5.13%.

36
Once we ha e he o al alue o expo s o each indus y, we spli his alue in o wo ca ego ies, i)
goods ha a e domes ically p oduced and expo ed, and ii) goods ha a e i s impo ed and hen
expo ed by he domes ic indus y. We use exogenous sha es (𝜙𝜙𝑐𝑐,𝑡𝑡
𝑢𝑢 and 1−𝜙𝜙𝑐𝑐,𝑡𝑡
𝑢𝑢) based on he
obse ed da a in he Inpu -Ou pu able (Table 2) o spli expo s:
𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=�1−𝜙𝜙𝑐𝑐,𝑡𝑡
𝑢𝑢�∗𝑥𝑥𝑡𝑡𝑢𝑢 (equa ion 44a)
𝑥𝑥𝑑𝑑,𝑡𝑡
𝑢𝑢=�𝜙𝜙𝑐𝑐,𝑡𝑡
𝑢𝑢�∗𝑥𝑥𝑡𝑡𝑢𝑢 (equa ion 44b)
whe e 𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 ep esen s goods ha a e domes ically p oduced and expo ed, and 𝑥𝑥𝑑𝑑,𝑡𝑡
𝑢𝑢 ep esen s
goods ha a e i s impo ed by indus y n and hen simply expo ed.
We can use he co esponding p ice de la o s o con e expo s om eal in o nominal alues:
𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equa ion 45a)
𝑋𝑋𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑥𝑥𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (equa ion 45b)
To compu e o al expo s o he Danish economy, we simply sum each ype o expo s ac oss he
indus ies as ollows:
𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 46a)
𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 46b)
𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 46c)
𝑋𝑋𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑋𝑋𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 46d)
whe e 𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 deno e o al ( eal) expo s o goods ha a e domes ically p oduced and 𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 deno e
expo s o goods, which i s en e he economy as impo s.31 In he abo e se o equa ions, he
no a ions in capi al le e s ep esen nominal alues.
31 No e ha an inc ease in expo s as a esul o eal exchange a e dep ecia ion will p opo iona ely inc ease hose
impo s which a e linked o expo s.
37
Finally, we can calcula e commodi y and alue added axes associa ed wi h domes ically p oduced
nominal expo s: 𝑋𝑋𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑐𝑐∗𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 47a)
𝑋𝑋𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑐𝑐∗𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 47b)
5.2.6. Impo s
To model impo s, we i s es ima e impo s a an indus ial le el, ollowed by he es ima ion o
impo s in he inal demand block. We s a by de e mining he ac ion o impo s used as inpu s in
he indus ies. Recall ha in equa ion 5d, we calcula ed o al inpu s using echnical coe icien s,
hese inpu s consis ed o bo h domes ic and impo ed inpu s used in p oduc ion (also see equa ion
5c). To isola e he alue o impo ed inpu s, we use he sha e o impo s (𝜙𝜙𝑧𝑧,𝑡𝑡
𝑖𝑖 𝑢𝑢) in he o al inpu s
and mul iply i wi h o al inpu s (𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢) as ollows: 32
𝑧𝑧𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢=𝜙𝜙𝑧𝑧,𝑡𝑡
𝑖𝑖 𝑢𝑢∗𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢 (equa ion 48a)
𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢=�1−𝜙𝜙𝑧𝑧,𝑡𝑡
𝑖𝑖 𝑢𝑢�∗𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢 (equa ion 48b)
whe e 𝑧𝑧𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢 is he alue o impo ed inpu s and 𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢 is he alue o inpu s p oduced domes ically.
We can calcula e hese inpu s in nominal e ms by using he co esponding p ice de la o s.
𝑍𝑍𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢=𝑧𝑧𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢∗𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢 (equa ion 48c)
𝑍𝑍𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢=𝑧𝑧𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑖𝑖 𝑢𝑢∗𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 (equa ion 48d)
F om he IO da a, we know ha a ac ion o impo ed inpu s canno be ca ego ized using he
Danish indus y de ini ions - his is classi ied as unspeci ied impo s. To de e mine unspeci ied
impo s, we assume a linea ela ionship be ween unspeci ied impo s and o al p oduc ion o he
domes ic indus y. 𝑧𝑧𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢=𝛾𝛾𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 (equa ion 49a)
whe e 𝛾𝛾𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 is he (exogenous) sha e o unspeci ied impo s in o al p oduc ion. We can also
calcula e he unspeci ied impo s in nominal alues as ollows:
32 No e ha 𝑧𝑧𝑡𝑡𝑖𝑖 𝑢𝑢 is he eal alue o equa ion 2a.
38
𝑍𝑍𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑧𝑧𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑚𝑚𝑢𝑢𝑖𝑖𝑑𝑑 (equa ion 49b)
We now ocus on endogenizing he sha e o impo s 𝜙𝜙𝑧𝑧,𝑡𝑡
𝑖𝑖 𝑢𝑢 in oduced in equa ion 48a-b. We assume
ha he sha e o impo ed inpu s o each indus y is pa ly d i en by he eal exchange a e. To
de e mine impo elas ici ies, we ollow a simple s a egy, known as he “ ule o wo” whe e he
impo elas ici y o an indus y is assumed o be hal he expo elas ici y.33 This app oach is also
adop ed by he G eenREFORM model (Ki k and Hansen 2023). The main a gumen is ha
domes ic esiden s, o a a ie y o easons, ha e a p e e ence o domes ically p oduced goods
e en i hey end o be mo e expensi e. The unc ional o m o his ela ionship can be ep esen ed
as ollows:
ln(𝜙𝜙𝑧𝑧,𝑡𝑡
𝑖𝑖 𝑢𝑢) = 𝛽𝛽0𝑧𝑧𝑖𝑖 𝑖𝑖+𝛽𝛽1𝑧𝑧𝑖𝑖∗𝑠𝑠𝑖𝑖(𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑢𝑢)+𝑎𝑎𝑝𝑝𝑗𝑗𝜙𝜙,𝑡𝑡
𝑢𝑢 (equa ion 50)
In he abo e equa ion, 𝛽𝛽0𝑧𝑧𝑖𝑖 𝑖𝑖 is a cons an aking he log o he s a ing alue o he impo sha e
(𝜙𝜙𝑧𝑧,𝑡𝑡
𝑖𝑖 𝑢𝑢), and 𝛽𝛽1𝑧𝑧𝑖𝑖 ep esen s he impo elas ici y (shown in able 8). We ind ha ou compu ed
elas ici ies a e heo e ically in ui i e and wi hin a jus i iable ange, when compa ed wi h a ecen
empi ical s udy; Kas up e al. (2023) use Danish indus ial da a o es ima e impo elas ici ies,
inding he mac o elas ici y o be 1.84, whe eas he implied mac o elas ici y in ou case (using
weigh ed a e age o elas ici ies ac oss he indus ies) is a ound 2.34
Finally, we ha e an exogenous de e mined adjus men e m cap u ing o he ele an e ec s han he
eal exchange a e �𝑎𝑎𝑝𝑝𝑗𝑗𝜙𝜙,𝑡𝑡
𝑢𝑢�.35
33 In gene al, he ule o wo is ound o ha e s ong empi ical suppo , e.g., Feens a e al. (2018) show ha he “ ule o
wo” canno be ejec ed o almos 80% o all p oduc ypes.
34 In gene al, hese elas ici ies end o a y a lo in he empi ical li e a u e. Fo example, Teme e (2017) ind ha he
es ima ed elas ici ies using mic o da a o Denma k anges be ween -1.14 and -32.65 wi h an o e all mean o -6.15 and
a median o -4.45. Imbs and Mejean (2009) o he US da a ind elas ici ies ac oss indus ies ange om 3.1 o 28 wi h a
s anda d de ia ion o 4.9.
35 Like in he case o expo s, he impo elas ici y is based on mic o da a es ima ions whe eas he simula ed impo o
inpu s o each indus y will i he obse ed da a poo ly i he adjus men e m is no included. We do his o no
unde es ima e he impo elas ici ies which is usually he case when using agg ega e da a (K onbo g, Poulsen, and
Kas up (2020)).
39
Table 8: Impo elas ici ies (Indus y)
We now ocus on impo s associa ed wi h he inal demand block. Focusing on household
consump ion, we i s classi y he consume baske in o domes ic and impo ed goods. Since
households’ consump ion baske consis s o 7 ypes o goods, we ca y ou he classi ica ion o all
7 ypes. Recall he se o equa ions 20a-20b, whe e he p opo ion o good ype (p) in he consume
baske impo ed om ab oad was gi en by: 𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝=�𝜙𝜙𝑐𝑐,𝑡𝑡
𝑝𝑝�∗𝑐𝑐𝑡𝑡𝑝𝑝. Whe eas he p opo ion o good
ype (p) in he consume baske domes ically p oduced was gi en by: 𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝=�1−𝜙𝜙𝑐𝑐,𝑡𝑡
𝑝𝑝�∗𝑐𝑐𝑡𝑡𝑝𝑝.
Thus by endogenizing 𝜙𝜙𝑐𝑐,𝑡𝑡
𝑝𝑝, we can model he subs i u ion e ec s be ween household consump ion
o domes ic and o eign goods. To do so, we model 𝜙𝜙𝑐𝑐,𝑡𝑡
𝑝𝑝 as a unc ion o he ela i e p ices. We can
ep esen his ela ionship as ollows:
ln(𝜙𝜙𝑐𝑐,𝑡𝑡
𝑝𝑝) = 𝛽𝛽0𝑐𝑐𝑝𝑝+𝛽𝛽1𝑐𝑐𝑝𝑝∗ln (𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑝𝑝) (equa ion 51)
The pa ame e 𝛽𝛽1𝑐𝑐𝑝𝑝, es ima ed ia OLS, cap u es he elas ici y o subs i u ion be ween domes ic and
impo ed goods.36 The es ima es o he impo elas ici ies associa ed wi h he 7 p oduc ypes a e
p esen ed in able 9 whe e he highes elas ici y is obse ed o Mea p oduc s.
36 In con as o equa ion 50 and 42 he impo elas ici ies o inal consump ion p esen ed in equa ion 51 a e es ima ed
using OLS on agg ega ed consump ion da a. As a esul , he i ed alues will be able o ma ch he obse ed da a and we
do no include any adjus men e m.
46
di idends (𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), income on o he in es men s (𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), and e ained ea nings on FDI
(𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). Finally, we also accoun o ne o he cu en ans e s ecei ed (𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶).
We can now calcula e he disposable income o he non- inancial co po a ions (𝑌𝑌𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) by
sub ac ing income axes paid by he non- inancial co po a ions (𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) as ollows:
𝑌𝑌𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 59b)
Following he de ini ion in he na ional accoun s, he sa ings equa ion o non- inancial i ms (𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶)
is ep esen ed as ollows: 𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 60)
NFC sec o spends a pa o i s sa ings on in es men (𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), co e ing changes in in en o ies,
acquisi ion and disposals o non-p oduced non- inancial asse s43 (𝐼𝐼𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), and o he capi al
ans e s (𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). The e o e, we can sub ac hese lows om sa ings, and calcula e ne balance
(o sec o al balance):
𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 61)
A posi i e (nega i e) ne balance, e lec ing a su plus (de ici ), implies ha he sec o is spending
less (mo e) han i s income. We now ocus on he e ical consis ency o he TFM, o which we
need o desc ibe how he esul an su plus is spen o , in he case o a de ici , how i is inanced.
This equi es speci ying he inancial aspec s o he sec o which includes he accumula ion o
inancial asse s.
As we speci y how ne lending (whe he posi i e o nega i e) a ec s he accumula ion o inancial
asse s, we also desc ibe he s eps and assump ions used o ensu e ha sec o al balance (o ne
lending in equa ion 61) equa es inancial balance. In o he wo ds, we speci y how ne lending
(whe he posi i e o nega i e) a ec s he accumula ion o inancial asse s. We s a by de ining he
inancial ne lending (o inancial balance) as ollows:
𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 62)
whe e 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 deno es he inancial balance, which is equal o he sum o (ne ) ansac ions
associa ed wi h gold (gold is only ele an o he inancial co po a ions and ROW), deposi s
43 Non-p oduced non- inancial asse s e e o asse s ha ha e no been p oduced bu ha e economic alue and can be
owned o exchanged. These asse s include na u al esou ces, con ac s, licenses, e c., as well as o he in angible asse s.

47
(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶), secu i ies (𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶), loans (𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶), equi ies (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶), insu ance/ ech.
ese es (𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶), inancial de i a i es (𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶), and ade c edi s (𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶). No e
ha he ne ansac ion linked o each inancial s ock is compu ed as he ansac ion ela ed o he
accumula ion o a inancial asse (which is an ou low o pu chasing a inancial asse ) minus he
ansac ion ela ed o he liabili y o ha asse (which is an in low ep esen ing sou ces o unding).
To p o ide an o e iew o he balance shee , we can calcula e he inancial ne weal h (𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶)
as ollows:
𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶
+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 63)
Financial ne weal h is he sum o ne deposi s (𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), secu i ies (𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), loans
(𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), equi ies (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), insu ance/ ech. ese es (𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), inancial de i a i es
(𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶), and ade c edi s (𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶). No e ha no a ions used o ne inancial s ocks a e
dis inguished om ne inancial ansac ions as he o me include “ ” in he subsc ip .
A his poin , one can p oceed o modelling each inancial s ock included in equa ion 63. I he e a e
k numbe o inancial s ocks, one app oach is o model a maximum o k-1 s ocks and ea he las
inancial asse as a esidual. Fo simpli ica ion, we choose o only model ne loans (o business
c edi ) o i ms while ea ing o he inancial s ocks as exogenous. The unc ional o m o he
equa ion de e mining he demand o loans is ep esen ed as ollows:
�𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶
𝐾𝐾𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 �= 0.26∗∗∗+ 0.28∗∗�𝐼𝐼𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶
𝐶𝐶𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶�−2.11∗∗∗𝑝𝑝𝑡𝑡−1
𝐿𝐿𝐶𝐶𝑉𝑉 (equa ion 64)
equa ion 64 s a es ha loan o capi al a io depends posi i ely on in es men o sa ings a io �𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝑁𝑁
𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝑁𝑁�
and nega i ely on in e es a e. The in ui ion is ha in es men in excess o sa ings, is pa ly
inanced h ough loans. Mo eo e , an inc ease in he cos o bo owing ( ep esen ed by in e es a e
on loans) will lowe he demand o loans.
A e endogenizing he s ock o loans, we can use he change in s ock o loans o de e mine loan
ansac ions using he accoun ing iden i y exp essed as ollows:
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 65)
whe e 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 ep esen s he s ock e alua ions ( ea ed as exogenous), Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 he change in
he s ock o loans, and 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 is he ansac ion o loans.
48
While ea ing o he inancial s ocks as exogenous, we can desc ibe he accoun ing iden i ies o
show hei e olu ion o e ime. This is done by adding he ne ansac ions and ne e-e alua ions o
he las yea s s ock o he ne inancial asse :
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 66)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 67)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 68)
𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 69)
whe e NSEC ep esen s ne s ock o secu i ies, NINSU ep esen s ne s ock o insu ance and
pensions, NDERV ep esen s he ne s ock o de i a i es, and NTCRED ep esen s he ne s ock o
ade c edi s. No e ha no a ions o ansac ions and e alua ions pe aining o each o he inancial
s ock a e dis inguished by using subsc ip s and , espec i ely. In he abo e se o equa ions, o
each inancial s ock, we can see ha when cu en ansac ions and e alua ions a e added o he
pas alue o a inancial s ock, we ge he p esen alue o he inancial s ock. In o he wo ds,
changes in he alue o a inancial s ock can occu o only wo easons, i.e., new ansac ions and
e alua ions.
We a e now le wi h wo inancial s ocks namely equi ies and deposi s. Rega ding equi ies, we
assume ha he s ock ma ke is demand-d i en in a sense ha new equi ies issued by non- inancial
co po a ions equal he demand o equi ies om o he sec o s. This ela ionship is cap u ed in
equa ion 70a as ollows:
𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=−�𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅� (equa ion 70a)
whe e he ansac ions pe aining o he supply o equi ies by NFC is deno ed by 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶, which is
equal o he collec i e demand o equi ies by o he sec o s, gi en by he sum o he ansac ions o
equi ies by households (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻), inancial co po a ions (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶), go e nmen (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺), and es
o he wo ld (𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅). This implies ha he ne s ock o equi ies ( ep esen ing a liabili y) o NFC
equals he sum o he ne s ock o equi ies ( ep esen ing asse s) o o he sec o s:
𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 70b)
To ensu e ha sec o al balance (o ne lending in equa ion 61) equa es inancial balance in equa ion
62, we ea one inancial s ock, namely deposi s, as esiduals, which in his case should be de ined
as ollows:
49
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 −(𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶) (equa ion 71a)
No e ha we include an ex a adjus men e m 𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 o accoun o he small disc epancy be ween
inancial ne lending (𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) and ne lending (𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶) p esen in he published da a. Like o he
inancial s ocks, we ea s ock e alua ions o deposi s as exogenous, and can show ha he s ock
o deposi s e ol es acco ding o equa ion 71b:
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 (equa ion 71b)
This comple es he desc ip ion o how he balance shee o NFC sec o is ela ed o he eal side o
he economy. While holding he es o he inancial s ocks exogenous, we ha e modeled wo main
sou ces o unds: issuing equi ies and secu ing loans. We now p oceed o discussing he income and
inancial aspec s o he household sec o .
5.3.2. Households
We s a by desc ibing he compu a ion o income o he household sec o . The majo sou ce o
household income akes he o m o labou income sha e (wages), paid by he NFC. Fi s , we de ine
he o al amoun o wages paid by he NFC sec o as he sum o all wages paid by he nine
indus ies:
𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=�𝑊𝑊𝑡𝑡𝑢𝑢
9
𝑢𝑢=1 (equa ion 72a)
We know ha a small ac ion o wo ke s employed by he NFC sec o is o eign labou . The e o e,
we can sub ac wages paid o non- esiden s om he o al wages in equa ion 66a, he esul an o
which will gi e us wages paid o domes ic households. This calcula ion is ca ied ou in equa ion
66b below: 𝑊𝑊𝑡𝑡𝐻𝐻= 𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶−𝑊𝑊𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 (equa ion 72b)
Whe e 𝑊𝑊𝑡𝑡𝐻𝐻 ep esen s wages ecei ed by he household sec o and 𝑊𝑊𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅 deno es wages paid o
o eign labou .
We can now calcula e he ne income ecei ed by households (𝑌𝑌𝑡𝑡𝐻𝐻) as ollows:
𝑌𝑌𝑡𝑡𝐻𝐻=𝐵𝐵2𝑡𝑡𝐻𝐻+𝑊𝑊𝑡𝑡𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝐻𝐻+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝐻𝐻−𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡
𝐻𝐻
+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻 (equa ion 73a)
50
Households income consis s o a ious income ypes: g oss ope a ing su plus ecei ed by
households is deno ed by (𝐵𝐵2𝑡𝑡𝐻𝐻), wages a e deno ed by (𝑊𝑊𝑡𝑡𝐻𝐻), ne income ecei ed on inancial
s ocks (𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻,𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻,𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝐻𝐻,𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝐻𝐻), social bene i s ecei ed (𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡
𝐻𝐻), and ne o he
cu en ans e s (𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻) and inally we deduc social con ibu ions paid (𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡
𝐻𝐻).
By sub ac ing income axes om ne income ecei ed by households (𝑌𝑌𝑡𝑡𝐻𝐻), we can calcula e he
disposable income o households:
𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻=𝑌𝑌𝑡𝑡𝐻𝐻−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝐻𝐻 (equa ion 73b)
We can now calcula e household sa ings by sub ac ing agg ega e p i a e consump ion (𝐶𝐶𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎) and
adjus ing o pension sa ings (𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡𝑎𝑎𝑑𝑑𝑗𝑗), which is a pa o household sa ings (𝐶𝐶𝑡𝑡𝐻𝐻), bu a e no
accessible o consump ion as hey a e placed in pension unds.
𝐶𝐶𝑡𝑡𝐻𝐻=𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻−𝐶𝐶𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎+𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡𝑎𝑎𝑑𝑑𝑗𝑗 (equa ion 74)
We can hen calcula e he ne lending (o sec o al balance) o he household sec o :
𝐼𝐼𝐿𝐿𝑡𝑡𝐻𝐻=𝐶𝐶𝑡𝑡𝐻𝐻−𝐼𝐼𝑡𝑡𝐻𝐻−Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝐻𝐻−𝐼𝐼𝑃𝑃𝑡𝑡𝐻𝐻−𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻 (equa ion 75)
whe e 𝐼𝐼𝑡𝑡𝐻𝐻 deno es household in es men , 𝐼𝐼𝑃𝑃𝑡𝑡𝐻𝐻 deno es ansac ions pe aining o he acquisi ion and
disposal o non-p oduced non- inancial asse s (such as na u al esou ces, con ac s, licences, e c.),
and 𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻 deno es o he capi al ans e s.
We now ocus on modeling he inancial side o households, whe e we oughly ollow he same
app oach as o non- inancial co po a ions. Fi s , we de ine he equa ion o inancial balance:
𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻
+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻 (equa ion 76)
whe e 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝐻𝐻 is he ne lending, de e mined by ne ansac ions pe aining o a ious inancial asse s.
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻 deno es ansac ion ela ed o deposi s, 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻 deno es ansac ions ela ed o
secu i ies, 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻 ep esen s loan ansac ions, 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻 deno es ansac ions ela ed o
insu ance and pensions, 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻 deno es ansac ions ela ed o de i a es, and 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻
deno es ansac ions ela ed o ade c edi s.
We now de ine he inancial ne weal h o he households as ollows:
51
𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐻𝐻
+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐻𝐻 (equa ion 77)
𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝐻𝐻 is he inancial ne weal h, de e mined by he ne alue o he inancial s ocks on he
balance shee o households.
Fo he household sec o , we endogenies wo inancial s ocks, which cons i u e a signi ican po ion
o he balance shee . On he asse side, we model equi ies endogenously, whe eas on he liabili y
side, we model loans endogenously. To model equi ies, we i s de ine a a iable, equi y o weal h
a io, ep esen ing he sha e o ne equi ies o o al inancial weal h in he p e ious pe iod.
𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻=�𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐻𝐻−𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡−1
𝐻𝐻� (equa ion 78a)
Following he in ui ion o Tobins po olio heo y, which has now become a well-in eg a ed pa o
he s ock- low consis en models, we assume ha he sha e o equi y in he inancial weal h o
households pa ly depends on he a e o e u n associa ed wi h equi ies.44 The speci ic unc ional
o m o he es ima ed equa ion is ep esen ed as ollows:
Δ𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻= 0.33∗Δ𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1
𝐻𝐻+ 0.060Δ�𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡−1
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡−1
𝐻𝐻�
𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−2
𝐻𝐻−0.18𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1
𝐻𝐻
+ 0.10∗�𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡−2
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡−2
𝐻𝐻�
𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−3
𝐻𝐻 (equa ion 78b)
The es ima es imply ha an inc ease in he e u n on equi y will inc ease he sha e o equi ies in he
weal h o mula ion. This is ound o be he case bo h in he sho - un and long- un. The in e cep
(0.063) can be in e p e ed as cap u ing he sha e o equi ies in weal h ha is no dependen on he
a e o e u n associa ed wi h equi ies. We can use he es ima ed sha e in equa ion 78b o calcula e
ne equi ies held by he household as ollows:
𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐻𝐻=𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻∗𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡−1
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻 (equa ion 78c)
The es ima ed s ock alue in equa ion 78c is hen used o de e mine he ansac ions o equi ies
(while ea ing he e alua ions o equi ies as exogenous):
𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻=Δ𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐻𝐻−𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻 (equa ion 78d)
44 He e we use a di e en a e o e u n compa ed o he di idend a e calcula e in appendix 8.3. The a e used in
equa ion 78b only ocus on he household sec o and u he mo e includes he e-e alua ions. Fo equi ies, he e-
e alua ions seem o be an impo an aspec in de e mining demand, whe eas we include his in he a e o e u n.

52
To endogenies household loans, we i s de ine he a io o loans o disposable income.45
𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻=�−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻
𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻� (equa ion 79a)
We assume his a io is posi i ely in luenced by in es men and nega i ely in luenced by he cos o
he loan, ep esen ed by he in e es a e on he loan. The es ima ed unc ional o m o his
ela ionship is gi en by equa ion 79b:
𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻= 0.91∗∗∗𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1+ 2.28∗∗∗�𝐼𝐼𝑡𝑡𝐻𝐻
𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻�−0.31𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉−0.37∗∗∗𝑃𝑃2016 (equa ion 79b)
We can use he es ima ed sha e om equa ion 79b o calcula e he s ock o loans held by he
household sec o as ollows: 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻=−𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻∗𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻 (equa ion 79c)
The s ock alue in equa ion 79c is hen used o de e mine he ansac ions o loans (while ea ing
he e alua ions o loans as exogenous):
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻=Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻 (equa ion 79d)
To ensu e ha sec o al balance o he household sec o equa es i s inancial balance, we again ea
deposi s, as esiduals, which in his case should be de ined as ollows:
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻=𝐼𝐼𝐿𝐿𝑡𝑡𝐻𝐻+𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝐻𝐻−(𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻
+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻) (equa ion 80a)
He e, again, we include an adjus men e m 𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝐻𝐻 o cap u e disc epancies be ween ne lending
and inancial balance in he published s a is ics.
The ansac ion da a on deposi s can be used o de e mine he s ock o deposi s o he households
(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝐻𝐻) while ea ing e alua ions as exogenous:
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻 (equa ion 80b)
The emaining inancial asse s on he balance shee o he households a e exogenously de e mined;
hese inancial s ocks e ol e as ollows:
45 We mul iply he a io by -1 as households only ha e loans as liabili ies, whe eas he ne loans a e nega i e.
53
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐻𝐻=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻 (equa ion 81)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝐻𝐻=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻 (equa ion 82)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻 (equa ion 83)
𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐻𝐻=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻 (equa ion 84)
The iden i ies in he abo e se o equa ions ha e he same in ui ion as discussed ea lie in he case
o NFC. Tha is, when cu en ansac ions and e alua ions a e added o he pas alue o a
inancial s ock, we ge he p esen alue o he inancial s ock.
This comple es he desc ip ion o he ac o s in luencing households balance shee in ou model. To
sum-up, o he household sec o , we ha e modeled wo inancial s ocks namely equi ies (asse s)
and loans (liabili ies); bo h collec i ely cons i u e a subs an ial po ion o he households balance
shee . In he nex , we discuss he ole o inancial co po a ions.
5.3.3. Financial co po a ions
We i s de ine he income o inancial co po a ions. Using he de ini ion o ne income p esen ed in
sec ion 4.2.1 and appendix 8.3 we can calcula e he income ecei ed by he inancial sec o (𝑌𝑌𝑡𝑡𝑁𝑁𝐶𝐶)
using he ollowing iden i y:
𝑌𝑌𝑡𝑡𝑁𝑁𝐶𝐶=𝐵𝐵2𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑁𝑁𝐶𝐶+𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶−𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶
+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶 (equa ion 85a)
The income consis s o a ious lows: g oss ope a ing su plus (𝐵𝐵2𝑡𝑡𝑁𝑁𝐶𝐶), ne income on inancial
asse s (𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶,𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶,𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑁𝑁𝐶𝐶,𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑁𝑁𝐶𝐶), social con ibu ions ecei ed (𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶), and ne
o he cu en ans e s (𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶). Finally, we sub ac social bene i s paid (𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶) o compu e ne
income.
By sub ac ing axes om ne income, we can compu e disposable income as ollows:
𝑌𝑌𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶=𝑌𝑌𝑡𝑡𝑁𝑁𝐶𝐶−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝑁𝑁𝐶𝐶 (equa ion 85b)
We can now calcula e he sa ings o he inancial co po a ions, which equi es adjus ing ne
disposable income o lows pe aining o pensions. The sa ing iden i y o he inancial co po a ions
can be p esen ed as ollows:
𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶=𝑌𝑌𝑃𝑃𝑁𝑁𝐶𝐶−𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡𝑎𝑎𝑑𝑑𝑗𝑗 (equa ion 86)
54
No e ha he pension deduc ions om he income o inancial co po a ions a e, in u n, ecei ed by
he households (𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡𝑎𝑎𝑑𝑑𝑗𝑗), as was shown in he sa ings equa ion o he household sec o (see
equa ion 74).
We can calcula e he ne lending o he inancial co po a ions using he same se -up as be o e:
𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝐶𝐶=𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶−𝐼𝐼𝑡𝑡𝑁𝑁𝐶𝐶−Δ𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶−𝐼𝐼𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶−𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶 (equa ion 87)
Focusing on he inancial aspec s o he sec o , we can calcula e he inancial ne lending as ollows:
𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶
+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 (equa ion 88)
whe e 𝑃𝑃𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝐶𝐶 is he inancial balance which, by de ini ion, is equal o he sum o ne ansac ions
associa ed wi h each inancial s ock. The only addi ional ansac ion is ela ed o he acquisi ion o
sale o gold deno ed by 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶.
We can now de ine he ne inancial weal h ( ep esen ing he ne alue o he inancial balance
shee ) o he inancial sec o as ollows:
𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶
+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶 (equa ion 89)
We assume ha inancial co po a ions clea he ma ke o deposi s, loans, insu ance, and
de i a i es. Thus, we can w i e:
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅� (equa ion 90)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅� (equa ion 91)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅� (equa ion 92)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅� (equa ion 93)
Using he ansac ions in he abo e se o equa ions, we can de e mine he alue o each inancial
s ock as ollows: 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶 (equa ion 94)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶 (equa ion 95)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶 (equa ion 96)
55
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶 (equa ion 97)
To ensu e consis ency be ween sec o al balance (equa ion 87) and inancial balance (equa ion 88),
we model ne ansac ions o secu i ies as a esidual:
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =𝐼𝐼𝐿𝐿𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝑁𝑁𝐶𝐶 −(𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶
+ 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶) (equa ion 98)
Using he ansac ions o secu i ies in equa ion 98, we can de ine he e olu ion o ne s ock o
secu i ies o e ime as ollows:
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶 (equa ion 99)
We a e now le wi h wo inancial s ocks on he balance shee s o inancial co po a ions, gold
ese es and he ne s ock o ade c edi s. These wo inancial s ocks a e assumed o be ully
exogenous and a e gi en by he ollowing equa ions:
𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶 (equa ion 100)
𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶 (equa ion 101)
This concludes he ac o s in he balance shee o he inancial co po a ions. To sum-up, he main
ole o his sec o is o clea he ma ke o deposi s, loans, insu ance, and de i a i es in he model.
In he ollowing, we desc ibe he income and inancial aspec s o he go e nmen sec o .
5.3.4. Go e nmen
The main income ecei ed by he go e nmen sec o is axes, his includes commodi y axes, alue
added axes, o he p oduc ion axes, and impo du ies paid by each indus y. To calcula e he o al
axes paid o he go e nmen , we ake he sum o di e en axes ac oss indus ies and he inal
demand componen s.
𝐶𝐶𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢
9
𝑢𝑢=1 +𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐺𝐺𝑃𝑃𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡+𝐼𝐼𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝑋𝑋𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 102a)
𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢
9
𝑢𝑢=1 +𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐺𝐺𝑃𝑃𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝑋𝑋𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 102b)
𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑃𝑃𝑉𝑉𝑃𝑃𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 (equa ion 102c)
62
We endogenize he ene gy used by households using a linea ela ionship be ween ene gy used and
domes ic consump ion. This ela ionship is exp essed in equa ion 132:
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝐻𝐻=𝑃𝑃𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻∗𝑐𝑐𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 (equa ion 132)
We use he di e ence be ween o al ene gy usage and o al ene gy supply, o calcula e he change in
ene gy in en o ies as ollows:
𝐼𝐼𝑖𝑖𝑖𝑖𝑃𝑃𝑟𝑟𝑠𝑠𝑡𝑡𝑎𝑎,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸= 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 −𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 133)
Un o una ely, he s ock alues o hese in en o ies a e no a ailable o ou sample, he e o e we
se he s a ing s ock alue o ze o in he i s pe iod o he sample wi h changes in his s ock being
de ined as: 𝐼𝐼𝑖𝑖𝑖𝑖𝑡𝑡𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸=𝐼𝐼𝑖𝑖𝑖𝑖𝑡𝑡−1
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸+𝐼𝐼𝑖𝑖𝑖𝑖𝑃𝑃𝑟𝑟𝑠𝑠𝑡𝑡𝑎𝑎,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸 (equa ion 134)
We now ocus on ene gy ese es a ailable in he economy. The e a e wo ene gy ese es in
Denma k: C ude oil (𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡
𝑎𝑎𝑗𝑗 ) and Na u al gas ex ac ed (𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡
𝑎𝑎𝑗𝑗 ). The da a on hese ese es
is measu ed in m3 and Nm3, bu we con e hem o gigajoules o i he ene gy usage and supply
accoun s. Fo con e sions, we use he con e sion a es p esen ed in he annual epo s by he
Danish ene gy agency. I can be shown ha he ese es o c ude oil and na u al gas e ol e
acco ding o he ollowing equa ions:51
𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡
𝑎𝑎𝑗𝑗 =𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗 −�𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡−1
𝑢𝑢
9
𝑢𝑢=1 + 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗 (equa ion 135a)
𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡
𝑎𝑎𝑗𝑗 =𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗 −�𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑟𝑟𝑐𝑐𝑡𝑡𝑝𝑝,𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡−1
𝑢𝑢
9
𝑢𝑢=1 +𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗 (equa ion 135b)
In he abo e se o equa ions, 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡
𝑎𝑎𝑗𝑗 and 𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡
𝑎𝑎𝑗𝑗 a e he opening s ocks o c ude oil and
na u al gas. These ene gy ese es will deple e o e ime depending on he pace o ex ac ions,
which in u n, depends on he demand o hese ype o ene gies; he ex ac ion o c ude oil is
deno ed by ∑𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑢𝑢,𝑡𝑡−1
𝑐𝑐𝑢𝑢𝑝𝑝
9𝑢𝑢=1 and he ex ac ion o na u al gas is deno ed by ∑𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑟𝑟𝑐𝑐𝑡𝑡𝑝𝑝,𝑢𝑢,𝑡𝑡−1
𝑐𝑐𝑢𝑢𝑝𝑝
9𝑢𝑢=1 .
51 Supply da a o c ude oil and na u al gas ma ches closely wi h he p oduc ion da a o c ude oil and na u al gas
ese es p o ided by he Danish ene gy agency o oil and gas ese es in Denma k. The e o e, we assume ha
domes ic supply da a om S a is ics Denma k shows how much oil and gas is p oduced/ex ac ed om he oil and gas
ese es. The eby he es o he da a is consis en wi h consump ion and use da a also used om S a is ics Denma k.

63
New disco e ies o ese es o e alua ions a e added o he exis ing s ocks, cap u ed by he e ms
𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗 o c ude oil, and 𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗 o na u al gas.52
5.4.2. Emissions
We now p esen a de ailed assessmen o GHG emissions in he economy. In ou analysis, we begin
by ca ego izing emissions based on economic ac i i y. In his ega d, we dis inguish emissions
gene a ed in he p oduc ion p ocess om hose gene a ed by household consump ion.
A e wa ds, bo h sou ces o emissions (i.e., p oduc ion and consump ion- ela ed emissions) a e
u he classi ied in o wo ypes: i) Ene gy-Rela ed Emissions (Di ec Emissions), which a e
emissions caused by he use o ene gy sou ces, such as emissions esul ing om bu ning ossil uels
like coal, oil, o na u al gas; and ii) O he p oduc ion ela ed Emissions (Indi ec Emissions),
which a e emissions associa ed wi h economic ac i i ies no di ec ly caused by ene gy usage, e.g.,
emissions om was e managemen p ac ices o me hane emissions by li es ock.
No e ha emissions o igina ing om he a o emen ioned ac i i ies can ake he o m o speci ic
gases. As men ioned in sec ion 4.3.2, we include he ollowing ypes o emissions: ca bon dioxide
(CO2), ni ous oxide (N2O), me hane (CH4), sul u hexa luo ide (SF6), pe luo oca bons (PFC),
and hyd o luo oca bons (HFC).53 These o ms o emissions a e la e used o calcula e he CO2-
equi alen measu e.54
In wha ollows, i is help ul o unde s and he dis inc ion be ween he sou ces o emissions
(gene a ed by 4 ypes o economic ac i i y) and he o ms hey ake (6 o ms o GHG emissions as
discussed abo e). In he ollowing sec ions, we will i s examine he di ec and indi ec emissions
p oduced du ing he p ocess o p oduc ion. A e wa d, we will add ess he di ec and indi ec
emissions esul ing om households’ consump ion.
A. Di ec Ene gy-Rela ed Emissions o domes ic p oduc ion
Following he app oach o Beck and Dahl (2020), we calcula e emission coe icien s linked o each
ene gy ype o each indus y. To ha end, we use a da ase linking emissions o he use o speci ic
52 As da a on c ude oil and na u al gas ese es we e inconsis en in 2006, 2014 and 2015, p obably as a esul o
ounding e o s, we ha e adjus ed he da a o 𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗 by + 1 m3 in 2006, +1 m3 in 2014, and by -1 m3 in 2015,
he eby making he da a consis en . Fo na u al gas (𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗 .), we +1 Nm3 in 1997, - 1 Nm3 in 2006, + 1 Nm3 in
2012.
53 SF6, PFC, and HFC a e no emi ed as a esul o using ene gy, whe eas hey only occu o he ca ego y “un ela ed o
ene gy”.
54 The model can be ex ended o include addi ional emission ypes, Da a om Denma k s a is ics allow us o include 15
ypes o emissions.
64
ene gy ypes o each indus y. The emission coe icien in he case o di ec emissions o each
indus y is calcula ed as ollows:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑡𝑡
𝑢𝑢
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝑢𝑢 (equa ion 136a)
whe e 𝑖𝑖 de e mines indus y, 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼 de e mines he ype o emissions (e.g. CO2, N20, and so
on), and 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌 de e mines ene gy ype (e.g. C ude oil, Oil p oduc s, and so on). To gi e an
example, he ene gy coe icien ela ing he usage o oil p oduc s (OilP) o ca bon dioxide emissions
(CO2) in he ag icul u e indus y is calcula ed as ollows:
𝐶𝐶𝑃𝑃2𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐶𝐶𝑖𝑖𝑠𝑠𝑃𝑃,𝑉𝑉𝐺𝐺𝑃𝑃𝐼𝐼=𝐶𝐶𝑃𝑃2𝐶𝐶𝑖𝑖𝑠𝑠𝑃𝑃,𝑡𝑡
𝑉𝑉𝐺𝐺𝑃𝑃𝐼𝐼
𝑃𝑃𝑖𝑖𝑠𝑠𝑃𝑃𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝑉𝑉𝐺𝐺𝑃𝑃𝐼𝐼 (equa ion 136b)
whe e 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼=𝐶𝐶𝑃𝑃2, 𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌=𝑃𝑃𝑖𝑖𝑠𝑠𝑃𝑃, and 𝑖𝑖=𝑉𝑉𝐺𝐺𝑅𝑅𝐼𝐼.
Since we ha e emissions ela ed o each o he 21 ene gy ypes, we can ake he sum ac oss he
ene gy ypes o each indus y o calcula e he o al di ec ene gy- ela ed emissions o each
indi idual indus y.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝑢𝑢=�𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝑢𝑢∗𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢
21
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸=1 (equa ion 136c)
No e ha he a ailable da a used o es ima e emission coe icien is a ailable un il 2017. Since, ou
sample ex ends o 2019, we assume he same emission coe icien s om 2017-2019.
B. Indi ec emissions o domes ic p oduc ion
To es ima e indi ec emissions ela ed o p oduc ion, we calcula e emission coe icien s using o al
p oduc ion o a gi en indus y.55 The calcula ion o emission coe icien s in his case is gi en by:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑢𝑢=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝑢𝑢
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑢𝑢 (equa ion 137a)
Again, using 𝑖𝑖 as he no a ion o indus ies, and 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼 as he no a ion o emission ype.
Using ou calcula ed emission coe icien in equa ion 137a, he o al indi ec emission o each
indus y is gi en by:
55 This is simila o he me hods used in he G eenREFORM model by he DREAM g oup.
65
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝑢𝑢=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑢𝑢∗𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑡𝑡𝑢𝑢 (equa ion 137b)
By agg ega ing equa ion 136c and 137b, we can calcula e he o al emission (incl. di ec and
indi ec ) o each indus y as ollows:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡
𝑢𝑢=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝑢𝑢+𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝑢𝑢 (equa ion 138)
C. Di ec Ene gy-Rela ed Emissions o households consump ion
To calcula e di ec ene gy- ela ed emissions o he household sec o , we ollow he same p ocedu e
as was ollowed o indus ies. In his case, he emission coe icien s linked o he use o each
ene gy ype is gi en by:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻𝐻𝐻=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑡𝑡
𝐻𝐻𝐻𝐻
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝐻𝐻𝐻𝐻 (equa ion 139a)
The emission coe icien s in equa ion 139a a e used o calcula e di ec ene gy- ela ed emissions o
he household sec o ollowing he same app oach as o indus ies in equa ion 136a. Again, we can
ake he sum ac oss he ene gy ypes o calcula e he o al di ec ene gy- ela ed emission o he
household sec o as ollows:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝐻𝐻=�𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝐻𝐻∗𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻
21
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸=1 (equa ion 139b)
D. Indi ec emissions o households consump ion
To es ima e indi ec emission o he household sec o , we calcula e emission coe icien s using
domes ic consump ion. The emission coe icien s in his case a e gi en by:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝐻𝐻=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝐻𝐻
𝑐𝑐𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 (equa ion 140a)
The emissions coe icien s om equa ion 140a a e hen used o es ima e he indi ec emissions
associa ed wi h consump ion:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝐻𝐻=𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝐻𝐻∗𝑐𝑐𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 (equa ion 140b)
By agg ega ing equa ion 139b and 140b, we can ind he o al emissions gene a ed by households
consump ion as ollows:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡
𝐻𝐻= 𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝐻𝐻+𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝐻𝐻 (equa ion 141)
66
We can now ind he o al emission o each emission ype in he en i e economy by agg ega ing
equa ion 138 and 141. Tha is, we add he o al emissions om he 9 indus ies oge he wi h
emissions om households:
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 +𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡
𝐻𝐻𝐻𝐻 (equa ion 142)
As we now ha e o al emissions o each o he 6 emission ypes, we can now con e each o m o
emission in o CO2 equi alen using he commonly used GWP con e sion a es. Mo e speci ically,
o CO2, SF6, PFC, and HFC he con e sion a e is 1 as hey a e al eady measu ed in CO2-
equi elan s; o CH4 he con e sion a e is 25, and o N2O he con e sion a e is 298. We calcula e
he CO2-equi elan emissions (CO2E) i s a an indus y le el:
𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑢𝑢=𝐶𝐶𝑃𝑃2𝑡𝑡𝑢𝑢+𝐶𝐶𝑃𝑃6𝑡𝑡𝑢𝑢+𝑃𝑃𝑃𝑃𝐶𝐶𝑡𝑡𝑢𝑢+𝐻𝐻𝑃𝑃𝐶𝐶𝑡𝑡𝑢𝑢+25 ∗𝐶𝐶𝐻𝐻4𝑡𝑡𝑢𝑢+298 ∗𝐼𝐼2𝑃𝑃𝑡𝑡𝑢𝑢 (equa ion 143a)
And o he en i e economy:
𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=𝐶𝐶𝑃𝑃2𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝐶𝐶𝑃𝑃6𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝑃𝑃𝑃𝑃𝐶𝐶𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝐻𝐻𝑃𝑃𝐶𝐶𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+25 ∗𝐶𝐶𝐻𝐻4𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+298
∗𝐼𝐼2𝑃𝑃𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 (equa ion 143b)
This comple es he desc ip ion o he en i onmen al block o he model, whe e we ha e modelled
he nexus be ween ene gy, emissions and economic ac i i y. We now p oceed o discussing an
impo an policy a iable, en i onmen al axes, ha is ecen ly ecei ing a lo o a en ion in he
discussions ela ed o clima e a ge s.
5.4.3. En i onmen al axes
In sec ion 5.1.2, we isola ed en i onmen al axes om he es o o he p oduc ion axes (see
equa ion 12). In equa ion 144a we assume en i onmen al axes o be dependen on CO2E emissions
o he indus y as ollows:56
𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢=𝐶𝐶𝑃𝑃2𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑢𝑢∗𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑢𝑢 (equa ion 144a)
We use an exogenously calcula ed ax a e o each indus y 𝑖𝑖 (𝐶𝐶𝑃𝑃2𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑢𝑢), which is calcula ed
ou side he model using he ollowing equa ion:
56 Equa ion 144a ela es CO2-equi elen emissions di ec ly o he en i onmen al axes paid by a gi en indus y. In
eali y, mos en i onmen al axes a e paid using ene gy ela ed axes whe e a speci ic ax a e is pu on ene gy usage. In
his cu en e sion o he model, we ely on he simple se -up o equa ion 144a whe eas his should be modeled in
mo e de ail in u u e e sions.
67
𝐶𝐶𝑃𝑃2𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑢𝑢=𝑉𝑉𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑐𝑐,𝑝𝑝𝑑𝑑𝑠𝑠𝑠𝑠𝑢𝑢𝑡𝑡𝑖𝑖𝑑𝑑𝑢𝑢
𝑢𝑢
𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑢𝑢 (equa ion 144b)
This comple es he en i onmen al aspec s o he model and also he en i e model desc ip ion. We
a e now eady o e alua e he model, a e which we will pe o m h ee simple scena ios.
6. Model e alua ion
To e alua e he model, we pe o m wo s anda d checks. Fi s , we nume ically sol e he model o
es ablish a baseline, he esul s o which a e compa ed wi h he obse ed da a. Second, we analyse
he esponse o he model o se e al shocks o analyse whe he o no he model is capable o
cap u ing he s ylised ac s. This s ep is also c ucial o unde s anding he di e en ansmission
mechanisms embedded in he model.
Figu e 2 shows he p edic ion o he model o eal p oduc ion o domes ic indus ies in domes ic
cu ency. The model decen ly cap u es he o e all endency and luc ua ion wi hin each o he nine
indus ies.
Figu e 2: To al eal p oduc ion o domes ic indus ies
Figu e 3 shows he de elopmen o eal GDP (including i s componen s) and employmen . Again,
we can see ha he model cap u es he de elopmen o key mac oeconomic a iables. The e a e

68
some episodes o di e gences be ween he model p edic ions and o iginal da a o employmen , bu
he model pe o ms ai ly well in cap u ing bo h he long un endency as well as cyclical
mo emen s.
Figu e 3: GDP componen s and employmen
We now p esen he model pe o mance ela ed o he en i onmen al aspec s o he model. Figu e 4
shows he model p edic ion o o al CO2 equi alen emissions associa ed wi h he 6 emission ypes.
The p edic ion o he model o emissions is consis en wi h he o iginal da a; i decen ly cap u es
bo h he end and luc ua ions. We can conclude ha he model pe o ms easonably well in
cap u ing he de elopmen in key a iables ela ed o he economy and en i onmen .
69
Figu e 4: Emissions
To ensu e ha ou model ul ils he p ope ies o a s ock- low-consis en model, we need o ensu e
ha each inancial asse has a coun e pa y, and ha each ansac ion has an o igin and a des ina ion.
Fi s , o ensu e consis ency in inancial asse s, we need o check ha ne holdings o inancial s ocks
ac oss he ins i u ional sec o s sum o ze o, implying ha he holding o e e y inancial asse has a
coun e pa y, o pu di e en ly, someone’s inancial asse is someone’s inancial liabili y. In
p inciple, one can pe o m his check on each inancial s ock, bu in p ac ice, pe o ming he check
on he ne holding o secu i ies will su ice in ou case. The eason is ha ansac ions ela ed o
secu i ies by he es o he wo ld (𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅) a e no included as an equa ion in he model, as his
is ou edundan equa ion. All o he inancial s ocks and hei ela ed ansac ions, h ough speci ic
accoun ing iden i ies, a e ied ac oss he sec o s h ough explici equa ions in he model. The e o e,
i ne holdings o secu i ies ac oss he sec o s sum o ze o, we can sa ely conclude ha he model
ul ils he equi emen o s ock consis ency. Second, we need o ensu e ha he sum o ne lendings
(o inancial balances) ac oss sec o s sum o ze o, meaning ha a sec o ’s de ici is inanced by
o he sec o s’ su plus. A e ca ying ou he a o emen ioned- es s, we ind ha bo h condi ions a e
ul illed, and he model is s ock- low-consis en .
6.1. In oducing h ee simple scena ios
We now analyse he esponse o he model o a ious ypes o shocks ela ed o mone a y and iscal
policy. Fi s , we in oduce a mone a y policy shock, in which we pe manen ly inc ease he in e es
a es on loans, deposi s and bonds by 2 pe cen age poin s. Second, we in oduce 2 ypes o iscal
policy shocks as ollows: i) public spending shock, whe e we pe manen ly inc ease go e nmen
70
consump ion by 5% in he bigges indus y (ca ego ised as “o he indus ies”), and ii) ca bon ax
shock, in which we pe manen ly inc ease he ca bon ax a e in he ag icul u al indus y.
The e ec s o he shocks a e p esen ed as de ia ions om he baseline. No e ha hese shocks a e
in oduced independen ly o each o he in he baseline in 2010. Fo ins ance, when we in oduce a
ca bon ax shock o he model, we do no in oduce any o he shock in he same scena io.
6.1.1. A shock o in e es a es
The e ec s o a con ac iona y mone a y policy shock on g oss domes ic p oduc (GDP)
componen s a e isualised in Figu e 5. Following a mone a y policy shock, GDP con ac s by abou
0.8% ela i e o he baseline alue; his de elopmen is mainly d i en by a all in consump ion
(which educes by 2.1%). The main mechanism is ha highe in e es a es lowe disposable
income, which causes inal consump ion o all. The o e all con ac ion in he economy also has he
e ec o lowe ing in es men and employmen ; ade balance sligh ly imp o es as impo s con ac
sha ply whe eas expo s emain una ec ed.
Figu e 5: Change in GDP componen s
In Figu e 6, we show he e ec s o he shock on eal p oduc ion along wi h some o he key
componen s o each indus y. We can obse e ha an inc ease in in e es a e has he e ec o
lowe ing eal p oduc ion ac oss all indus ies. The main ansmission channel is ha he all in inal
consump ion lowe s p oduc ion, which in u n, educes in e media e consump ion. The educ ion in
in e media e consump ion ein o ces he educ ion in o al p oduc ion. I is in e es ing o no e ha
he e ec s o he shock on o al p oduc ion ac oss he indus ies a e he e ogenous (i.e., inancial
71
co po a ions expe ience a la ge d op in eal p oduc ion compa ed o o he indus ies), bu he
e ec s o he shock on inal consump ion a e homogenous, i.e., he inal consump ion o he goods
supplied by each indus y alls wi h he same magni ude. The eason is ha income shocks (in his
case induced by highe in e es a es) a ec he inal consump ion p opo ionally. The he e ogenous
esponse o o al p oduc ion ac oss he indus ies is pa ly d i en by hei sales o inpu s o o he
indus ies (which in u n, depend on he p oduc ion equi emen o he indus y) and pa ly by he
di e ence in weigh s o he unde lying componen s o o al p oduc ion.
Figu e 6: Changes in eal p oduc ion o indus ies
We now p oceed o discussing he e ec s o iscal shocks in ou model.
6.1.2. A shock o go e nmen spending
We in oduce a go e nmen spending shock, cha ac e ized by a 5% inc ease in go e nmen
consump ion o inal goods supplied by indus y no. 9 called “o he indus ies”. In igu e 7, we
depic he e ec s o his shock on GDP, along wi h se e al key mac oeconomic componen s. We
can see ha he shock igge s expansiona y economic e ec s; speci ically, we obse e an inc ease
in inal consump ion and eal in es men s, e lec ing he posi i e spillo e e ec s o highe
go e nmen demand on p i a e sec o ac i i y. Mo eo e , we ind he iscal mul iplie o his shock
o be a ound 1.14.
78
While building he model s uc u e, mos o he model pa ame e s we e es ima ed using annual ime
se ies da a om 1995 o 2019. To assess model alidi y, we pe o med wo s anda d checks. Fi s ,
we nume ically sol ed he model o es ablish a baseline, he esul s o which we e compa ed wi h
he obse ed da a. We ound ha he model decen ly cap u ed he o e all endency and luc ua ion
in key a iables ela ed o economic ac i i y and en i onmen . Second, we analysed he esponse o
he model o a a ie y o shocks ela ed o mone a y and iscal policy. We ound ha he model
e ec i ely cap u es he s ylized ac s and ha hese shocks a ec he economy h ough mul iple
channels, which a e impo an in policy making. We belie e, ou model in his pape will se e as a
ounda ion, which can be ex ended in a a ie y o ways. The model has he po en ial o o e a
easonable assessmen o he clima e policies o he ele an s akeholde s.
Re e ences
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Be g, M., Ha ley, B., & Rich e s, O. (2015). A s ock- low consis en inpu –ou pu model wi h
applica ions o ene gy p ice shocks, in e es a es, and hea emissions. New jou nal o
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s ock‐ low consis en model o he Danish economy. Me oeconomica, 73(1), 144-197.
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h ps://www.ens.dk.
Denma k s a is ics (DST). (2021). Annual Sec o Accoun s In en o y.
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s abili y in a s ock- low consis en model. Jou nal o Financial S abili y, 54, 100872.
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Membe S a es doing? Clima e ac ion in Denma k (PE 679.106). Eu opean Union. Re ie ed om
h ps://clima e.ec.eu opa.eu/eu-ac ion/clima e-s a egies- a ge s/p og ess-clima e-ac ion_en.
Feens a, R. C., Luck, P., Obs eld, M., & Russ, K. N. (2018). In sea ch o he A ming on
elas ici y. Re iew o Economics and S a is ics, 100(1), 135-150.

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Feyen, E. H., U z, R. J., Zucca di Hue as, I. E., Bogdan, O., & Moon, J. (2020). Mac o- inancial
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Mone a y Fund.
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8. Appendix:
8.1. Indus y s a is ics
The indus y le el da a impo ed om S a is ics Denma k includes a o al o 117 indus ies. In his pape , we
agg ega e hese 117 indus ies o 9 o ob ain a simple ep esen a ion o he economy. The 9 indus ies a e
p esen ed below oge he wi h key en i onmen al and economic s a is ics.59
Table A1: Indus y s a is ics
8.2. Dis ibu ion o g oss ope a ing su plus and mixed income (B2)
This appendix will p o ide a desc ip ion on how we make he ansi ion om indus y o sec o al
le el in he model using g oss ope a ing su plus as he combining a iable. The main eason ha we
need o make his ansi ion is ha no all en ies below g oss su plus in he TFM ( able 4) a e
a ailable a an indus ial le el.
The mos app op ia e poin o ansi ioning om indus y o sec o al accoun s is a he g oss
ope a ing su plus and mixed income (B2), as his is he inal en y e lec ed in he inpu -ou pu
ables (see Table 2). The objec i e is o ensu e a consis en ansi ion by aligning obse ed da a o
B2 a bo h he indus y and sec o al le els. A common p ac ice in he S ock-Flow-Consis en
li e a u e is o assume ha he non- inancial co po a ions sec o collec s he en i e g oss ope a ing
su plus, which is hen dis ibu ed o he household, go e nmen , and inancial co po a ion sec o s
59 The “O he ene gy in ensi e” indus y includes indus ies ha a e no pa o he ene gy p oduc ion and supply, bu
s ill egula ed by he ETS p og am.
81
using exogenous sha es. This me hod could be easily inco po a ed in o he cu en model by
summing he o al g oss ope a ing su plus o mixed income ac oss indus ies and hen alloca ing i
acco ding o hese sec o al sha es. This app oach assumes ha all indus ies a e equally linked o
he ou domes ic sec o s based on exogenous sha es, which diminishes he alue o including
indus ial agg ega ion in he model. Fo ins ance, conside he impac o a ca bon ax on he
ag icul u al indus y, which educes g oss ope a ing su plus. I we ail o accoun o he ac ha
his indus y is p edominan ly "owned" by he household sec o (67%) and ins ead use agg ega e
sec o al sha es, whe e he household sec o holds a weigh o jus 21%, we will unde es ima e he
e ec on he household balance shee .
To calcula e hese sha es a he indus y le el, we ely on he indus y by sec o ma ix p o ided by
S a is ics Denma k (DST 2021), which de ails he indus ial con ibu ions o sec o al accoun s based
on g oss alue added (GVA) in 2016. This ma ix helps us es ima e how g oss ope a ing su plus and
mixed income should be alloca ed among he ou domes ic sec o s ac oss he nine indus ies. The
p ocess in ol es he ollowing s eps:
1. Wi hin each indus y we calcula e he weigh o NFCs, FCs, households, and he
go e nmen o each ow in he ma ix o indus y by sec o .
2. As he ma ix o indus y by sec o is disagg ega ed in o mo e han 90 indus ies, we use
g oss ope a ing su plus and mixed income o each indus y o make a weigh ed a e age o
he sha es a he 9-indus y le el used in his pape .60
3. As hese sha es a e calcula ed based on 2016 da a, hey ha e mos likely changed since
1998, in which we s a he simula ion o he model. To ake his in o accoun , we include a
end calcula ed om he sec o al o o al g oss ope a ing su plus and mixed income and
apply his end on he indus y le el sha es calcula ed in s ep 2.
4. Las ly, we calcula e an adjus men e m o conside disc epancies be ween ou es ima ed
sec o al g oss ope a ing su plus and mixed income a iables, based on he i s 3 s eps, and
obse ed g oss ope a ing su plus and mixed income o each sec o .
These s eps esul in equa ion 57a-57d in which g oss ope a ing su plus and mixed income a e
calcula ed o he household, go e nmen , inancial co po a ions, and non- inancial co po a ions. In
he able below, we show he es ima ed sha es o 2016.
Table A2: Sec o al weigh s by indus y
60 In he cu en e sion o he model, we only use he 2016 alues o B2 o make his agg ega ion.
82
To gi e an example, o g oss ope a ing su plus in he ag icul u al indus y, 67% will be associa ed
wi h he household sec o , while 33% will be associa ed wi h he non- inancial co po a ion sec o .
Fo he Mining indus y, g oss ope a ing su plus will be associa ed only wi h he non- inancial
co po a ion sec o . As no g oss ope a ing su plus should be los while making his ansi ion, all
ows sum o 1.
Las ly, in igu e A1 we show he magni ude o he adjus men e ms (calcula ed in s ep 4) ela i e o
he obse ed alue o g oss ope a ing su plus. The adjus men e ms o he inancial co po a ions
and go e nmen sec o a e close o 0. The eason o he unde shoo ing o g oss ope a ing su plus
o he household sec o (as he adjus men e m is posi i e) and he o e shoo ing o non- inancial
co po a ions g oss ope a ing su plus, a e o be ound in he ma ix o indus y by sec o s.61 A
majo i y o indus ies show ha household con ibu e by 0.0% o o al g oss ope a ing su plus
wi hin a speci ic indus y. When his no a ion is used, i means ha he ac ual alue is be ween 0.0%
and 0.05%.62
61 The le el o adjus men in he household and non- inancial co po a ion sec o is almos equal in absolu e alues.
62 In cases whe e he ue alue is 0%, he en y is emp y.
83
Figu e A1: Adjus men e ms ela i e o obse ed alues
8.3. Calcula ion o inancial lows
In his appendix, we calcula e h ee ypes o a es o e u ns:63 i) i s , we calcula e 3 di e en
in e es a es ( ela ed o deposi s, secu i ies, loans, and o he accoun s), which will de e mine he ne
in e es income deno ed by NINT, ii) second, we calcula e he a e o e u n on equi y holdings,
which de e mines he low associa ed wi h equi ies (mos ly di idends) deno ed by NDIV, and iii)
hi d, we calcula e he a e o e u n on o he in es men income ( ela ed o pension and insu ances),
which de e mines he low called NOIR. No e ha he income low ela ed o ein es ed ea nings on
FDI exp esses he ope a ing su plus o he o eign di ec in es men co po a ions. This is no ela ed
o any o he inancial asse s in he TFM.64
Following s anda d accoun ing, we know ha paymen lows in he cu en pe iod depends on he
s ock o las pe iod and he a e o e u ns om he las pe iod. This ela ionship, exp essed in equa ion
A1, is used o calcula e ou a es o e u ns:
63 We use unconsolida ed da a o calcula e he a es o e u ns in he model.
64 Ren is de ined as income ecei ed by he owne o a na u al esou ce and is simply included as a low wi hou
associa ing i o any ype o a e o e u n.

84
𝑓𝑓𝑠𝑠𝑝𝑝𝑤𝑤𝑡𝑡=𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑡𝑡−1∗𝑠𝑠𝑡𝑡𝑝𝑝𝑐𝑐𝑘𝑘𝑡𝑡−1⟺𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑡𝑡−1=𝑓𝑓𝑠𝑠𝑝𝑝𝑤𝑤𝑡𝑡
𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑡𝑡−1 (equa ion A1)
Focusing on in e es a e calcula ions, i s we calcula e he in e es a e on secu i ies, assuming he
a e o e u n on secu i ies o be he same domes ically and ab oad. The e o e, we calcula e he in e es
a e on secu i ies (𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶) as he mean o he a e in Denma k and ECB as ollows:
𝑝𝑝𝑡𝑡−1
𝐶𝐶𝐸𝐸𝐶𝐶= 0.5 ∗ 𝑖𝑖_𝑠𝑠𝑖𝑖𝑐𝑐𝑡𝑡−1
𝑃𝑃𝐷𝐷 + 0.5 ∗ 𝑖𝑖_𝑠𝑠𝑖𝑖𝑐𝑐𝑡𝑡−1
𝐸𝐸𝐶𝐶𝐸𝐸 (equa ion A2)
By mul iplying his a e o e u n wi h he s ock o secu i ies in he las pe iod, we ge he in e es
paymen ela ed o secu i ies. The in e es paymen on secu i ies is hen sub ac ed om he o e all
in e es paymen , he esul an o which is used o calcula e in e es a e on deposi s and loans.
To calcula e he in e es a e on deposi s (𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃𝐶𝐶) paid by he inancial co po a ions, we ake he o al
ne in e es paid by inancial co po a ions, om which we sub ac in e es paymen s on secu i ies
issued by he inancial co po a ions. The esul an is di ided wi h he s ock o deposi s ( ep esen ing
a liabili y) o he inancial co po a ions in he las pe iod. This calcula ion can be exp essed as
ollows:
𝑝𝑝𝑡𝑡−1
𝑃𝑃𝐸𝐸𝑃𝑃𝐶𝐶=𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑝𝑝𝑖𝑖𝑠𝑠𝑡𝑡 𝑝𝑝𝑎𝑎𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡−(𝑝𝑝𝑡𝑡−1
𝐶𝐶𝐸𝐸𝐶𝐶∗𝑠𝑠𝑖𝑖𝑐𝑐𝑠𝑠𝑡𝑡−1
𝑁𝑁𝐶𝐶,𝐿𝐿)
𝑝𝑝𝑖𝑖𝑝𝑝𝑝𝑝𝑠𝑠𝑖𝑖𝑡𝑡𝑠𝑠 𝑖𝑖𝑖𝑖 𝑃𝑃𝐶𝐶𝑡𝑡−1 (equa ion A3a)
whe e 𝑝𝑝𝑡𝑡−1
𝐶𝐶𝐸𝐸𝐶𝐶∗𝑠𝑠𝑖𝑖𝑐𝑐𝑠𝑠𝑡𝑡−1
𝑁𝑁𝐶𝐶,𝐿𝐿is he in e es paymen s o inancial co po a ions on hei issued secu i ies.
To calcula e he in e es a e on loans 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉, we use he same app oach, i.e., we ake he o al ne
in e es ecei ed by inancial co po a ions, om which we sub ac in e es income ecei ed on
secu i ies owned by he inancial co po a ions, which is hen di ided wi h he s ock o loans (which
ep esen s an asse ) issued by inancial co po a ions in he las pe iod. This is gi en by equa ion 8b
as ollows:
𝑝𝑝𝑡𝑡−1
𝐿𝐿𝐶𝐶𝑉𝑉=𝑖𝑖𝑖𝑖𝑡𝑡𝑖𝑖𝑝𝑝𝑖𝑖𝑠𝑠𝑡𝑡 𝑝𝑝𝑖𝑖𝑐𝑐𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡−(𝑝𝑝𝑡𝑡−1
𝐶𝐶𝐸𝐸𝐶𝐶∗𝑠𝑠𝑖𝑖𝑐𝑐𝑠𝑠𝑡𝑡−1
𝑁𝑁𝐶𝐶,𝑉𝑉)
𝐿𝐿𝑝𝑝𝑎𝑎𝑖𝑖 𝑃𝑃𝐶𝐶𝑡𝑡−1 (equa ion A3b)
whe e 𝑝𝑝𝑡𝑡−1
𝐶𝐶𝐸𝐸𝐶𝐶∗𝑠𝑠𝑖𝑖𝑐𝑐𝑠𝑠𝑡𝑡−1
𝑁𝑁𝐶𝐶,𝑉𝑉 deno es in e es paymen s ecei ed by inancial co po a ions on holding
secu i ies as inancial asse s.
Once in e es a es on in e es bea ing s ocks a e compu ed, we can show ha he ne in e es
paymen s (NINT) o sec o 𝑠𝑠 a e gi en by he ollowing equa ion:
85
𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝐶𝐶=𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐶𝐶)+𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐶𝐶+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉
∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐶𝐶 (equa ion A4)
No e ha he a e o e u n on h ee inancial s ocks namely, ne deposi s (NDEPO), ne de i a i es
(NDERV), and ne ade c edi s (NTCRED), is he same as deno ed by in e es a e 𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃. The ne
s ock o secu i ies (NSEC) and ne s ock o loans (NLOA) a e linked o hei co esponding a e o
e u ns deno ed (𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶) and 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉, espec i ely.
The e u n on equi ies (𝑝𝑝𝑡𝑡𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃) is also calcula ed using equa ion A1. This calcula ion is exp essed in
equa ion A5 as ollows:
𝑝𝑝𝑡𝑡−1
𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃=𝑝𝑝𝑖𝑖𝑖𝑖𝑖𝑖𝑝𝑝𝑖𝑖𝑖𝑖𝑝𝑝𝑠𝑠 𝑝𝑝𝑎𝑎𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡
𝑖𝑖𝑒𝑒𝑠𝑠𝑖𝑖𝑡𝑡𝑖𝑖𝑖𝑖𝑠𝑠 𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡−1 (equa ion A5a)
We can now de e mine ne income ecei ed om di idend paymen s o sec o 𝑠𝑠 as ollows:
𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝐶𝐶= 𝑝𝑝𝑡𝑡𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝐶𝐶 (equa ion A5b)
whe e NEQ ep esen s he ne s ock o equi ies.
Simila ly, he a e o e u n o insu ance and pensions (𝑝𝑝𝑡𝑡𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼) is gi en by:
𝑝𝑝𝑡𝑡−1
𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼=𝑝𝑝𝑖𝑖𝑡𝑡𝑠𝑠𝑝𝑝𝑖𝑖 𝑝𝑝𝑎𝑎𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡
𝑖𝑖𝑖𝑖𝑠𝑠𝑠𝑠𝑝𝑝𝑎𝑎𝑖𝑖𝑐𝑐𝑖𝑖𝑠𝑠 𝑖𝑖𝑠𝑠𝑠𝑠𝑠𝑠𝑖𝑖𝑝𝑝 𝑏𝑏𝑦𝑦 𝑃𝑃𝐶𝐶𝑡𝑡−1 (equa ion A6a)
We can use he a e o e u n 𝑝𝑝𝑡𝑡𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼 o calcula e he income associa ed wi h ne insu ance paymen s
o sec o 𝑠𝑠 as ollows: 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝐶𝐶=𝑝𝑝𝑡𝑡𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝐶𝐶 (equa ion A6b)
whe e NINSU ep esen s he ne s ock o insu ance and pensions.
This concludes he p esen a ion o indus y and sec o al le el a iables used wi hin he model. In
he nex sec ion we ins ead ocus on en i onmen al da a used in he model.
8.4. Subs i u ion be ween consump ion p oduc s
In his appendix, we show he wo subs i u ion e ec s modelled o inal consump ion. The wo
e ec s a e i) subs i u ion be ween p oduc ypes, ii) subs i u ion be ween domes ically and o eign
p oduced p oduc s.
86
Subs i u ion be ween p oduc ypes
To allow o subs i u ion be ween p oduc ypes, we endogenize he sha es
γ
𝑡𝑡 𝑐𝑐𝑝𝑝(used in equa ion 19)
ollowing a simila me hod as used in he G eenREFORM and ADAM models, which includes a
nes ed s uc u e. In ou model, he i s nes includes a choice be ween indus y speci ic consump ion
p oduc s (𝑐𝑐𝑡𝑡𝑐𝑐𝑝𝑝𝑟𝑟𝑐𝑐) and ood p oduc s (𝑐𝑐𝑡𝑡110+ 𝑐𝑐𝑡𝑡120+ 𝑐𝑐𝑡𝑡130+𝑐𝑐𝑡𝑡140+𝑐𝑐𝑡𝑡160+𝑐𝑐𝑡𝑡180). In he second nes ,
consume s choose be ween he six di e en ood p oduc s. The nes ed s uc u e can be modelled as
ollows:65
γ
𝑡𝑡𝑐𝑐𝑢𝑢𝑝𝑝𝑢𝑢𝑠𝑠 =𝜃𝜃𝑐𝑐𝑝𝑝𝑟𝑟𝑐𝑐∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑑𝑑𝑡𝑡ℎ,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1
(Equa ion A7. )
γ
𝑡𝑡𝑐𝑐110 =𝜃𝜃110∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡110,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equa ion A8. )
γ
𝑡𝑡𝑐𝑐120 =𝜃𝜃120∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡120,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equa ion A9. )
γ
𝑡𝑡𝑐𝑐130 =𝜃𝜃130∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡130,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equa ion A10. )
γ
𝑡𝑡𝑐𝑐140 =𝜃𝜃140∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡140,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equa ion A11.)
γ
𝑡𝑡𝑐𝑐160 =𝜃𝜃160∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡160,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equa ion A12. )
γ
𝑡𝑡𝑐𝑐180 =𝜃𝜃180∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡180,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑡𝑡𝑡𝑡
𝑝𝑝𝑝𝑝𝑐𝑐𝑑𝑑𝑢𝑢𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 �𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1 (Equa ion A13. )
Se e al pa ame e s go in o he equa ions abo e. S a ing wi h 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡2 and 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡1 hese ep esen he
elas ici y o subs i u ion in he wo nes s. We se 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡2= 0.8 and 𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡1= 0.2 which is sligh ly
lowe compa ed o he pa ame e s used by G eenREFORM who use a di e en disagg ega ion o he
consume baske . Las ly, he pa ame e s 𝜃𝜃𝑡𝑡𝑐𝑐𝑝𝑝𝑟𝑟𝑐𝑐,𝜃𝜃110,𝜃𝜃120,𝜃𝜃130,𝜃𝜃140,𝜃𝜃160, and 𝜃𝜃180 a e calib a ed o
ma ch he s a ing alue o each co esponding sha e. Equa ion A.7-A.13 includes se e al p ice
65 To ensu e consis ency, we model he sha e
γ
𝑡𝑡𝑐𝑐𝑢𝑢𝑝𝑝𝑢𝑢𝑠𝑠 as a esidual, o ensu e ha he sum o he sha es always sum o 1.
87
de la o s, all o hem adjus ed o he ax a e.66 Fi s , we de ine se en p ice de la o s; one o each
p oduc ype: 67
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐=⎝
⎜
⎛
𝐶𝐶𝑡𝑡𝑝𝑝
∑𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢
9𝑢𝑢=1 + ∑𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢
9𝑢𝑢=1 +𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢𝑢𝑢 𝑝𝑝
𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢𝑢𝑢⎠
⎟
⎞
∗�1 + 𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑝𝑝� (Equa ion A14. )
The eby each o he 7 p oduc ypes 𝑝𝑝 a e a unc ion o he p oduce p ice indexes o he 9 domes ic
indus ies (𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢) as well as he en o eign p ice indexes (𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢,𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢𝑢𝑢). As he consume is aced wi h
he p ice a e axes, we mul iply on he a e age ax- a e o a gi en p oduc (𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑝𝑝). The a e age
ax- a e is modelled as ollows:
𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑝𝑝=�𝐶𝐶𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝+𝐶𝐶𝑠𝑠𝑡𝑡𝑡𝑡𝑡𝑡,𝑡𝑡
𝑝𝑝+𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑝𝑝�
𝐶𝐶𝑡𝑡𝑝𝑝 (Equa ion A15. )
Whe e 𝐶𝐶𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝 de ines impo du ies, 𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑝𝑝 de ines commodi y axes, and 𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑝𝑝 de ines alue added
axes all associa ed wi h consump ion o p oduc ype 𝑝𝑝.
Besides om he 7 p ice indexes o each o he 7 p oduc ypes (𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐), we need wo agg ega e
p ice indexes, one o he en i e consump ion (𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐), and one o consump ion o ood p oduc s
(𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐). We ollow he same app oach as in equa ion (𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐) bu agg ega e ac oss he
ele an p oduc ypes 𝑝𝑝. The same goes o he a e age ax a e.
The eby, we ha e he 9 p ice indexes o di e en consump ion goods and baske s used in equa ion
A7-A13. In he ollowing we ocus on he second subs i u ion e ec .
Subs i u ion be ween domes ic and o eign p oduc s
To allow subs i u ion be ween domes ic and o eign p oduc s, we need o calcula e a domes ic and
o eign p ice index o each p oduc ype p. Fo each o he 7 p oduc ypes in he consump ion baske
he p ice de la o is calcula ed as ollows:
66 We can use his ax-adjus ed de la o o go om nominal alue plus axes o eal- alues wi hou axes.
𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝∗𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐=𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝+𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑝𝑝+𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑝𝑝+𝐶𝐶𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝
67 We include hese ax a es wi hin he consume p ice indexes, as hese a es a e included wi hin he inal p ice paid by
he consume . Also, his allows us o implemen ca bon axes on he consume s o di e en p oduc ypes o u u e
analysis.
94
𝑀𝑀𝑖𝑖𝑢𝑢𝑣𝑣𝑟𝑟𝑢𝑢𝑡𝑡,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =�𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 + 𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
(M.21)
𝑀𝑀𝑎𝑎𝑑𝑑𝑣𝑣
𝑡𝑡𝑑𝑑𝑡𝑡 =�𝐺𝐺𝑃𝑃𝑉𝑉𝑖𝑖𝑑𝑑
𝑢𝑢
9
𝑢𝑢=1 +𝐺𝐺𝑃𝑃𝑉𝑉𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
(M.22)
𝑀𝑀𝑐𝑐𝑡𝑡𝑑𝑑𝑡𝑡=�𝑋𝑋𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 + 𝑋𝑋𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
(M.23)
Final demand componen s
lnΔ(𝑐𝑐
𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡)= 0.37∗∗ 𝑠𝑠𝑖𝑖Δ𝑦𝑦𝑝𝑝
𝑡𝑡
𝐻𝐻−0.30∗∗∗ 𝑠𝑠𝑖𝑖 𝑐𝑐
𝑡𝑡−1
𝑡𝑡𝑑𝑑𝑡𝑡+ 0.29∗∗∗ln 𝑦𝑦𝑝𝑝
𝑡𝑡−1
𝐻𝐻+
0.01 ln 𝑓𝑓𝑖𝑖𝑤𝑤𝑡𝑡−1
𝐻𝐻−0.002∗∗ 𝑉𝑉𝑝𝑝𝑖𝑖𝑖𝑖𝑝𝑝
(M.24)
𝑐𝑐𝑡𝑡
𝑝𝑝
=
γ
𝑡𝑡
𝑐𝑐𝑝𝑝
∗𝑐𝑐𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
(M.25)
γ
𝑡𝑡𝑐𝑐𝑢𝑢𝑝𝑝𝑢𝑢𝑠𝑠 =𝜃𝜃𝑑𝑑𝑡𝑡ℎ∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑑𝑑𝑡𝑡ℎ,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1
(M.26)
γ
𝑡𝑡𝑐𝑐110 =𝜃𝜃110∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡110,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2
∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1
(M.27)
γ
𝑡𝑡𝑐𝑐120 =𝜃𝜃120∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡120,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2
∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �
𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1
(M.28)
γ
𝑡𝑡𝑐𝑐130 =𝜃𝜃130∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡130,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1
(M.29)
γ
𝑡𝑡𝑐𝑐140 =𝜃𝜃140∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡140,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2
∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1
(M.30)
γ
𝑡𝑡𝑐𝑐160 =𝜃𝜃160∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡160,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2
∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1
(M.31)
γ
𝑡𝑡𝑐𝑐180 =𝜃𝜃180∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡180,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐�𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡2
∗�𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡𝑎𝑎𝑐𝑐
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑡𝑡𝑎𝑎𝑐𝑐 �𝜎𝜎
𝑖𝑖𝑢𝑢𝑢𝑢𝑡𝑡1
(M.32)
𝑐𝑐
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝= (1 −𝜙𝜙
𝑐𝑐,𝑡𝑡
𝑝𝑝)∗𝑐𝑐
𝑡𝑡
𝑝𝑝
(M.33)
𝑐𝑐
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝= (𝜙𝜙
𝑐𝑐,𝑡𝑡
𝑝𝑝)∗𝑐𝑐
𝑡𝑡
𝑝𝑝
(M.34)
ln(𝜙𝜙𝑐𝑐,𝑡𝑡
𝑝𝑝
) = 𝛽𝛽0
𝑐𝑐𝑝𝑝
+𝛽𝛽1
𝑐𝑐𝑝𝑝
∗ln (𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡
𝑝𝑝
) + 𝑎𝑎𝑝𝑝𝑗𝑗𝜙𝜙,𝑡𝑡
𝑝𝑝
(M.35)
𝑐𝑐
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝=𝜆𝜆
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝∗𝑐𝑐
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝
(M.36)

95
𝑐𝑐
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝=𝜆𝜆
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝∗𝑐𝑐
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝
(M.37)
𝑐𝑐
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝=𝛾𝛾
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝∗𝑐𝑐
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝
(M.38)
𝐶𝐶
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝=𝑐𝑐
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝∗𝑝𝑝𝑦𝑦
𝑡𝑡
𝑢𝑢
(M.39)
𝐶𝐶
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝=𝑐𝑐
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝∗𝑝𝑝𝑚𝑚
𝑡𝑡
𝑢𝑢
(M.40)
𝐶𝐶
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝=𝑐𝑐
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝∗𝑝𝑝𝑚𝑚
𝑡𝑡
𝑢𝑢𝑢𝑢
𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝=�𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
9
𝑢𝑢=1
(M.41)
𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝=�𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
9
𝑢𝑢=1 +𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢𝑢𝑢 𝑝𝑝
(M.42)
𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝=�𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
9
𝑢𝑢=1
(M.43)
𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝=�𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
9
𝑢𝑢=1 +𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢𝑢𝑢 𝑝𝑝
(M.44)
𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢=�𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1
(M.45)
𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢=�𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1
(M.46)
𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢𝑢𝑢=�𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1
(M.47)
𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢=�𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1
(M.48)
𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢=�𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1
(M.49)
𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢𝑢𝑢=�𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢𝑢𝑢 𝑝𝑝
7
𝑝𝑝=1
(M.50)
𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑐𝑐𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1
(M.51)
96
𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑐𝑐𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1
(M.52)
𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1
(M.53)
𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1
(M.54)
𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1
(M.55)
𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡= 1.8∗∗∗Δln �
𝑦𝑦
𝑡𝑡−1
𝑘𝑘𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶�−0.09∗∗∗ln(𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡−1
𝑡𝑡𝑑𝑑𝑡𝑡)+ 1.42∗∗∗ 𝑝𝑝𝑠𝑠𝑡𝑡−1
(M.56)
𝑖𝑖𝑖𝑖𝑖𝑖
𝑡𝑡
𝑢𝑢=𝜆𝜆
𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢∗𝑖𝑖𝑖𝑖𝑖𝑖
𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
(M.57)
𝑖𝑖𝑖𝑖𝑖𝑖
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
=𝛾𝛾
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣 ∗𝑖𝑖𝑖𝑖𝑖𝑖
𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
=�1−𝜙𝜙𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢
�∗𝑖𝑖𝑖𝑖𝑖𝑖𝑡𝑡
𝑢𝑢
(M.58)
𝑖𝑖𝑖𝑖𝑖𝑖
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢=�𝜙𝜙
𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢�∗𝑖𝑖𝑖𝑖𝑖𝑖
𝑡𝑡
𝑢𝑢
(M.59)
𝐼𝐼𝐼𝐼𝑉𝑉
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑖𝑖𝑖𝑖𝑖𝑖
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦
𝑡𝑡
𝑢𝑢
(M.60)
𝐼𝐼𝐼𝐼𝑉𝑉
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑖𝑖𝑖𝑖𝑖𝑖
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑚𝑚
𝑡𝑡
𝑢𝑢
(M.61)
𝐼𝐼𝐼𝐼𝑉𝑉
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
=𝑖𝑖𝑖𝑖𝑖𝑖
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝∗𝑝𝑝𝑚𝑚
𝑡𝑡
𝑢𝑢𝑢𝑢
(M.62)
𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.63)
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.64)
𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐼𝐼𝐼𝐼𝑉𝑉𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.65)
𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝐼𝐼𝐼𝐼𝑉𝑉𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.66)
ln �
𝑥𝑥
𝑡𝑡
𝑢𝑢
𝑚𝑚𝑡𝑡𝑢𝑢∗�=
α
0
𝑢𝑢+
α
1𝑢𝑢∗ln(𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡−1
𝑢𝑢)+𝑎𝑎𝑝𝑝𝑗𝑗𝑐𝑐,𝑡𝑡
𝑢𝑢
(M.67)
𝑥𝑥
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=�1−𝜙𝜙
𝑐𝑐,𝑡𝑡
𝑢𝑢�∗𝑥𝑥
𝑡𝑡
𝑢𝑢
(M.68)
𝑥𝑥
𝑑𝑑,𝑡𝑡
𝑢𝑢=�𝜙𝜙
𝑐𝑐,𝑡𝑡
𝑢𝑢�∗𝑥𝑥
𝑡𝑡
𝑢𝑢
(M.69)
97
𝑋𝑋
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑥𝑥
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑦𝑦
𝑡𝑡
𝑢𝑢
(M.70)
𝑋𝑋
𝑑𝑑,𝑡𝑡
𝑢𝑢=𝑥𝑥
𝑑𝑑,𝑡𝑡
𝑢𝑢∗𝑝𝑝𝑚𝑚
𝑡𝑡
𝑢𝑢
(M.71)
𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑥𝑥𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.72)
𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑥𝑥𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.73)
𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 = �𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.74)
𝑋𝑋𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡= �𝑋𝑋𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.75)
Labo ma ke and p ices
𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢 = (1 + 𝜇𝜇𝑡𝑡𝑢𝑢)∗
𝐶𝐶𝑃𝑃𝐶𝐶𝑉𝑉
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢
(M.76)
𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑢𝑢=𝑥𝑥𝑝𝑝𝑡𝑡∗
𝑝𝑝𝑦𝑦
𝑡𝑡
𝑢𝑢
𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢
(M.77)
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝,𝑡𝑡𝑎𝑎𝑐𝑐=⎝
⎜
⎛
𝐶𝐶𝑡𝑡𝑝𝑝
∑𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢
9𝑢𝑢=1 + ∑𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢
9𝑢𝑢=1 +𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢𝑢𝑢 𝑝𝑝
𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢𝑢𝑢⎠
⎟
⎞
∗�1 + 𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑝𝑝�
(M.78)
𝑡𝑡𝑎𝑎𝑥𝑥𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑝𝑝=�𝐶𝐶𝑖𝑖𝑑𝑑𝑑𝑑,𝑡𝑡
𝑝𝑝
+𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑝𝑝
+𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑝𝑝
�
𝐶𝐶𝑡𝑡𝑝𝑝
(M.79)
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖𝑡𝑡𝑝𝑝=⎝
⎜
⎛
𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝
∑𝐶𝐶𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
𝑝𝑝𝑦𝑦𝑡𝑡𝑢𝑢
9𝑢𝑢=1 ⎠
⎟
⎞
(M.80)
𝑝𝑝𝑚𝑚𝑡𝑡𝑝𝑝=⎝
⎜
⎛
𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡,𝑝𝑝
∑𝐶𝐶𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢
9𝑢𝑢=1 ⎠
⎟
⎞
(M.81)
𝑝𝑝𝑖𝑖𝑝𝑝𝑡𝑡𝑝𝑝=𝑥𝑥𝑝𝑝𝑡𝑡∗
𝑝𝑝𝑝𝑝𝑐𝑐𝑝𝑝𝑖𝑖
𝑡𝑡
𝑝𝑝
𝑝𝑝𝑚𝑚𝑡𝑡𝑝𝑝
(M.82)
98
𝑉𝑉𝑀𝑀𝑃𝑃𝑡𝑡𝑢𝑢=
𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑡𝑡
𝑢𝑢
𝑎𝑎𝑡𝑡𝑢𝑢
(M.83)
𝑈𝑈𝐼𝐼𝑉𝑉𝑀𝑀𝑃𝑃𝑡𝑡=𝐿𝐿𝑃𝑃𝑡𝑡− �𝑉𝑉𝑀𝑀𝑃𝑃𝑡𝑡𝑢𝑢
9
𝑢𝑢=1
(M.84)
𝑈𝑈𝑅𝑅𝑡𝑡=
𝑈𝑈𝐼𝐼𝑉𝑉𝑀𝑀𝑃𝑃
𝑡𝑡
𝐿𝐿𝑃𝑃𝑡𝑡
(M.85)
𝑊𝑊
𝑡𝑡
𝑢𝑢=𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖
𝑡𝑡
𝑢𝑢∗𝑉𝑉𝑀𝑀𝑃𝑃
𝑡𝑡
𝑢𝑢
(M.86)
𝑠𝑠𝑖𝑖Δ�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖
𝑡𝑡
𝑎𝑎𝑟𝑟𝑢𝑢�
= 0.24∗∗∗+ 0.78∗∗∗𝑠𝑠𝑖𝑖Δ�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−2
𝑎𝑎𝑟𝑟𝑢𝑢�
+ 0.08∗∗𝑠𝑠𝑖𝑖Δ�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−2
𝑎𝑎𝑟𝑟𝑢𝑢,𝑉𝑉�−0.15∗∗ln�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−1
𝑎𝑎𝑟𝑟𝑢𝑢�
+ 0.09∗ln�𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−2
𝑎𝑎𝑟𝑟𝑢𝑢,𝑉𝑉�+ 0.28∗∗∗ln(𝑎𝑎𝑡𝑡−1)
(M.87)
𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡
𝑎𝑎𝑟𝑟𝑢𝑢,𝑉𝑉
=𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖𝑡𝑡−1
𝑎𝑎𝑟𝑟𝑢𝑢
∗
(
1 + 𝜋𝜋𝑡𝑡−1
)
(M.88)
ln (𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖
𝑡𝑡
𝑢𝑢) =
ω
0
+
ω
1
ln (𝑊𝑊𝑎𝑎𝑔𝑔𝑖𝑖
𝑡𝑡
𝑎𝑎𝑟𝑟𝑢𝑢)
(M.89)
II.) Sec o al le el equa ions
Non- inancial co po a ions
𝐵𝐵2𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎=�𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢
9
𝑢𝑢=1
(M.90)
𝐵𝐵2𝑁𝑁𝑁𝑁𝐶𝐶=𝐵𝐵2
𝑡𝑡
𝑎𝑎𝑎𝑎𝑎𝑎−(𝐵𝐵2𝐻𝐻+𝐵𝐵2𝑁𝑁𝐶𝐶+𝐵𝐵2𝐺𝐺)
(M.91)
𝐼𝐼𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
=𝐼𝐼𝑡𝑡
𝑎𝑎𝑎𝑎𝑎𝑎
−
(
𝐼𝐼𝑡𝑡
𝐻𝐻
+𝐼𝐼𝑡𝑡
𝑁𝑁𝐶𝐶
+𝐼𝐼𝑡𝑡
𝐺𝐺)
(M.92)
𝑌𝑌
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌
𝑡𝑡
−(𝐵𝐵2
𝑡𝑡
𝑎𝑎𝑎𝑎𝑎𝑎−𝐵𝐵2
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶)−�𝐼𝐼𝑉𝑉𝑎𝑎𝑥𝑥
𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑,𝑡𝑡
+ 𝑃𝑃𝑃𝑃𝑉𝑉
𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡�−𝑊𝑊
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶
+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶
(M.93)
𝑌𝑌𝑃𝑃
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.94)
𝐶𝐶
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝑌𝑌𝑃𝑃
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.95)
𝐼𝐼𝐿𝐿
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐶𝐶
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝑃𝑃
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶−𝐶𝐶𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.96)
𝑃𝑃𝐼𝐼𝐿𝐿
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.97)
𝑃𝑃𝐼𝐼𝑊𝑊
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶
(M.98)
�
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
𝐾𝐾𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶 �= 0.26∗∗∗+ 0.28∗∗�
𝐼𝐼
𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶
𝐶𝐶𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶�−2.11∗∗∗𝑝𝑝𝑡𝑡−1
𝐿𝐿𝐶𝐶𝑉𝑉
(M.99)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.100)
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.101)
99
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.102)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.103)
𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.104)
𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=−�𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅�
(M.105)
𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑄𝑄
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.106)
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝐿𝐿
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿
𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶 −(𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶)
(M.107)
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡−1
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.108)
𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝑝𝑝
𝑡𝑡
𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶)
+𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶
(M.109)
𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶= 𝑝𝑝
𝑡𝑡
𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.110)
𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶=𝑝𝑝
𝑡𝑡
𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.111)
Households
𝐵𝐵2𝑡𝑡𝐻𝐻=�𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢∗𝐶𝐶𝐻𝐻,𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1 + adj H
(M.112)
𝐼𝐼𝑡𝑡𝐻𝐻=�𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎∗𝐶𝐶𝐻𝐻,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣
9
𝑢𝑢=1
(M.113)
𝑊𝑊𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶=�𝑊𝑊𝑡𝑡𝑢𝑢
9
𝑢𝑢=1
(M.114)
𝑊𝑊
𝑡𝑡
𝐻𝐻= 𝑊𝑊
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶−𝑊𝑊
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.115)
𝑌𝑌
𝑡𝑡
𝐻𝐻=𝐵𝐵2
𝑡𝑡
𝐻𝐻+𝑊𝑊
𝑡𝑡
𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉
𝑡𝑡
𝐻𝐻+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉
𝑡𝑡
𝐻𝐻+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅
𝑡𝑡
𝐻𝐻+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼
𝑡𝑡
𝐻𝐻
−𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡
𝐻𝐻+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝐻𝐻
(M.116)
𝑌𝑌𝑃𝑃
𝑡𝑡
𝐻𝐻=𝑌𝑌
𝑡𝑡
𝐻𝐻−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝐻𝐻
(M.117)
𝐶𝐶𝑡𝑡𝐻𝐻=𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻−𝐶𝐶𝑡𝑡
𝑎𝑎𝑎𝑎𝑎𝑎
+𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡
𝑎𝑎𝑑𝑑𝑗𝑗
(M.118)
𝐼𝐼𝐿𝐿
𝑡𝑡
𝐻𝐻=𝐶𝐶
𝑡𝑡
𝐻𝐻−𝐼𝐼
𝑡𝑡
𝐻𝐻−𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉
𝑡𝑡
𝐻𝐻−𝐼𝐼𝑃𝑃
𝑡𝑡
𝐻𝐻−𝐶𝐶𝑉𝑉
𝑡𝑡
𝐻𝐻
(M.119)
𝑃𝑃𝐼𝐼𝐿𝐿
𝑡𝑡
𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻
+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝐻𝐻
(M.120)
𝑃𝑃𝐼𝐼𝑊𝑊
𝑡𝑡
𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝐻𝐻
+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐻𝐻
(M.121)
𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻=�
𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝐻𝐻−𝐼𝐼𝑉𝑉𝑄𝑄
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
𝑃𝑃𝐼𝐼𝑊𝑊𝑡𝑡−1
𝐻𝐻�
(M.122)

100
Δ𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻= 0.33∗Δ𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1
𝐻𝐻+ 0.060Δ�𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡−1
𝐻𝐻
+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡−1
𝐻𝐻
�
𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−2
𝐻𝐻
−0.18𝑉𝑉𝑄𝑄𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1
𝐻𝐻+ 0.10∗�𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡−2
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑝𝑝𝑣𝑣,𝑡𝑡−2
𝐻𝐻�
𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡−3
𝐻𝐻
(M.123)
𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝐻𝐻=𝑉𝑉𝑄𝑄
𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻∗𝑃𝑃𝐼𝐼𝑊𝑊
𝑡𝑡−1
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
(M.124)
𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻=Δ𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝐻𝐻−𝐼𝐼𝑉𝑉𝑄𝑄
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
(M.125)
𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻=�−
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝐻𝐻
𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻�
(M.126)
𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻= 0.91∗∗∗𝐿𝐿𝑃𝑃𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡−1+ 2.28∗∗∗�
𝐼𝐼
𝑡𝑡
𝐻𝐻
𝑌𝑌𝑃𝑃𝑡𝑡𝐻𝐻�−0.31𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉
−0.37∗∗∗𝑃𝑃2016
(M.127)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝐻𝐻=−𝐿𝐿𝑃𝑃𝑉𝑉
𝑝𝑝𝑎𝑎𝑡𝑡𝑖𝑖𝑑𝑑,𝑡𝑡
𝐻𝐻∗𝑌𝑌𝑃𝑃
𝑡𝑡
𝐻𝐻
(M.128)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻=Δ𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝐻𝐻−𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
(M.129)
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻=𝐼𝐼𝐿𝐿
𝑡𝑡
𝐻𝐻+𝐼𝐼𝐿𝐿
𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝐻𝐻−(𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻
+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻)
(M.130)
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
(M.131)
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝐻𝐻=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
(M.132)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝐻𝐻=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
(M.133)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝐻𝐻=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
(M.134)
𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝐻𝐻=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡−1
𝐻𝐻+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐻𝐻
(M.135)
𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉
𝑡𝑡
𝐻𝐻=𝑝𝑝
𝑡𝑡
𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝐻𝐻+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝐻𝐻+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝐻𝐻)+𝑝𝑝
𝑡𝑡
𝐶𝐶𝐸𝐸𝐶𝐶
∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐻𝐻+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐻𝐻
(M.136)
𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉
𝑡𝑡
𝐻𝐻= 𝑝𝑝
𝑡𝑡
𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝐻𝐻
(M.137)
𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅
𝑡𝑡
𝐻𝐻=𝑝𝑝
𝑡𝑡
𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝐻𝐻
(M.138)
Financial co po a ions
𝐵𝐵2𝑡𝑡𝑁𝑁𝐶𝐶=�𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢∗𝐶𝐶𝑁𝑁𝐶𝐶,𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1 + adj FC
(M.135)
(M.139)
𝐼𝐼𝑡𝑡𝑁𝑁𝐶𝐶=�𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎∗𝐶𝐶𝑁𝑁𝐶𝐶,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣
9
𝑢𝑢=1
(M.140)
𝑌𝑌
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐵𝐵2
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼
𝑡𝑡
𝑁𝑁𝐶𝐶
+𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶−𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶
(M.141)
𝑌𝑌𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶=𝑌𝑌
𝑡𝑡
𝑁𝑁𝐶𝐶−𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑁𝑁𝐶𝐶
(M.142)
101
𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶=𝑌𝑌𝑃𝑃𝑁𝑁𝐶𝐶−𝑃𝑃𝑉𝑉𝐼𝐼𝑡𝑡
𝑎𝑎𝑑𝑑𝑗𝑗
(M.143)
𝐼𝐼𝐿𝐿
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐶𝐶
𝑡𝑡
𝑁𝑁𝐶𝐶−𝐼𝐼
𝑡𝑡
𝑁𝑁𝐶𝐶−𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶−𝐼𝐼𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶−𝐶𝐶𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶
(M.144)
𝑃𝑃𝐼𝐼𝐿𝐿
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶
+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶
(M.145)
𝑃𝑃𝐼𝐼𝑊𝑊
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶
+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑁𝑁𝐶𝐶
(M.146)
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺
+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅�
(M.147)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶
=−�𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻
+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺
+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
�
(M.148)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺
+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅�
(M.149)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =−�𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺
+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅�
(M.150)
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶
(M.151)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶
(M.152)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶
(M.153)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶
(M.154)
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 =𝐼𝐼𝐿𝐿
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝐿𝐿
𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝑁𝑁𝐶𝐶 −(𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶
+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶
+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶)
(M.155)
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶
(M.156)
𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶
(M.157)
𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶=𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡−1
𝑁𝑁𝐶𝐶 + 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝐶𝐶 +𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑁𝑁𝐶𝐶
(M.158)
𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶=𝑝𝑝
𝑡𝑡
𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝑁𝑁𝐶𝐶)+𝑝𝑝
𝑡𝑡
𝐶𝐶𝐸𝐸𝐶𝐶
∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑁𝑁𝐶𝐶+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑁𝑁𝐶𝐶
(M.159)
𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉
𝑡𝑡
𝑁𝑁𝐶𝐶= 𝑝𝑝
𝑡𝑡
𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝑁𝑁𝐶𝐶
(M.160)
𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅
𝑡𝑡
𝑁𝑁𝐶𝐶=𝑝𝑝
𝑡𝑡
𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝑁𝑁𝐶𝐶
(M.161)
Go e nmen
𝐵𝐵2𝑡𝑡𝐺𝐺=�𝑃𝑃𝑅𝑅𝑃𝑃𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑢𝑢∗𝐶𝐶𝐺𝐺,𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢
9
𝑢𝑢=1 + adj G
(M.162)
𝐼𝐼𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉=�𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎∗𝐶𝐶𝐺𝐺𝐶𝐶𝑉𝑉,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣
9
𝑢𝑢=1
(M.163)
102
𝐶𝐶𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝐶𝐶𝑉𝑉𝑡𝑡𝑢𝑢
9
𝑢𝑢=1 +𝐶𝐶𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐺𝐺𝑃𝑃𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡+𝐼𝐼𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
+𝑋𝑋𝑐𝑐𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
(M.164)
𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑢𝑢
9
𝑢𝑢=1 +𝐶𝐶𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐺𝐺𝑃𝑃𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
+𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝑋𝑋𝑉𝑉𝑉𝑉𝑉𝑉,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
(M.165)
𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡=�𝑃𝑃𝑉𝑉𝑃𝑃𝑡𝑡𝑎𝑎𝑐𝑐,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1
(M.166)
𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 =�𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡
𝑢𝑢
9
𝑢𝑢=1 +𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡
𝐶𝐶+𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉 +𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡
𝐼𝐼𝑁𝑁𝑉𝑉 +𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡
𝑋𝑋
(M.167)
𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑
=𝐶𝐶𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝑉𝑉𝑉𝑉𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡+𝑀𝑀𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
(M.168)
𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋
𝑝𝑝,𝑡𝑡
=𝑀𝑀
𝑑𝑑𝑢𝑢𝑡𝑡𝑑𝑑,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡 +𝑃𝑃𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋
𝑝𝑝
(M.169)
𝐼𝐼𝐼𝐼𝑀𝑀𝑉𝑉𝑎𝑎𝑥𝑥
𝑡𝑡
=𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋
𝑝𝑝
−𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋
𝑝𝑝
(M.170)
𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝐻𝐻= 0.36 ∗𝑌𝑌
𝑡𝑡
𝐻𝐻
(M.171)
𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶= 0.12 ∗𝑌𝑌
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
(M.172)
𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑁𝑁𝐶𝐶= 0.08 ∗𝑌𝑌
𝑡𝑡
𝑁𝑁𝐶𝐶
(M.173)
𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡=𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝐻𝐻+𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑁𝑁𝐶𝐶+𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.174)
𝑌𝑌𝑃𝑃𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉
=𝐵𝐵2𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉
+𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑
+ 𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑
+𝐼𝐼𝐼𝐼𝑀𝑀𝑉𝑉𝑎𝑎𝑥𝑥𝑡𝑡
+𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉,𝑝𝑝+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉
+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉−𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉
(M.175)
𝐶𝐶𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉
=𝑌𝑌𝑃𝑃𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉
−𝐺𝐺𝑡𝑡
𝑎𝑎𝑎𝑎𝑎𝑎
(M.176)
𝐼𝐼𝐿𝐿
𝑡𝑡
𝐺𝐺=𝐶𝐶
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉−𝐼𝐼
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉−𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝐼𝐼𝑉𝑉
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉−𝐼𝐼𝑃𝑃
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉−𝐶𝐶𝑉𝑉
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉
(M.177)
𝑃𝑃𝐼𝐼𝐿𝐿
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐺𝐺𝐶𝐶𝑉𝑉
+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝
𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝐺𝐺𝐶𝐶𝑉𝑉
(M.178)
𝑃𝑃𝐼𝐼𝑊𝑊
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝐺𝐺𝐶𝐶𝑉𝑉
+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝐺𝐺𝐶𝐶𝑉𝑉
(M.179)
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺=𝐼𝐼𝐿𝐿
𝑡𝑡
𝐺𝐺+𝐼𝐼𝐿𝐿
𝑎𝑎𝑑𝑑𝑗𝑗,𝑡𝑡
𝐺𝐺−(𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡,𝑡𝑡𝑝𝑝
𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺
+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺
+ 𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺)
(M.180)
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝐺𝐺=𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡−1
𝐺𝐺+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐺𝐺
(M.181)
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝐺𝐺=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡−1
𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐺𝐺
(M.182)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝐺𝐺=𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡−1
𝐺𝐺+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐺𝐺
(M.183)
103
𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝐺𝐺=𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡−1
𝐺𝐺+ 𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+𝐼𝐼𝑉𝑉𝑄𝑄
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐺𝐺
(M.184)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝐺𝐺=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡−1
𝐺𝐺+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐺𝐺
(M.185)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝐺𝐺=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡−1
𝐺𝐺+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐺𝐺
(M.186)
𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡
𝐺𝐺=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡−1
𝐺𝐺+ 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐺𝐺
(M.187)
𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝐺𝐺=𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡−1
𝐺𝐺+ 𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+𝐼𝐼𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝐺𝐺
(M.188)
𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉
𝑡𝑡
𝐺𝐺=𝑝𝑝
𝑡𝑡
𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝐺𝐺+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝐺𝐺+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝐺𝐺)+𝑝𝑝
𝑡𝑡
𝐶𝐶𝐸𝐸𝐶𝐶
∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝐺𝐺+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝐺𝐺
(M.189)
𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉
𝑡𝑡
𝐺𝐺= 𝑝𝑝
𝑡𝑡
𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝐺𝐺
(M.190)
𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅
𝑡𝑡
𝐺𝐺=𝑝𝑝
𝑡𝑡
𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼∗𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝐺𝐺
(M.191)
Res o he wo ld
𝑌𝑌𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝑀𝑀
𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡−𝑋𝑋
𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡+𝑊𝑊
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅−(𝐼𝐼𝐼𝐼𝑀𝑀𝑉𝑉𝑎𝑎𝑥𝑥
𝑡𝑡
+𝐼𝐼𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅)
+𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝐼𝐼𝑅𝑅𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅
+𝐼𝐼𝑅𝑅𝑉𝑉𝑃𝑃𝑃𝑃𝐼𝐼𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐶𝐶𝐶𝐶𝑃𝑃𝐼𝐼𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅−𝐼𝐼𝐶𝐶𝐵𝐵𝑉𝑉𝐼𝐼𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
+𝑃𝑃𝐶𝐶𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅
(M.192)
𝐼𝐼𝐿𝐿
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝑌𝑌𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅−𝐶𝐶𝑉𝑉
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅−𝐼𝐼𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.193)
𝑃𝑃𝐼𝐼𝐿𝐿
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡,𝑡𝑡𝑝𝑝
𝑃𝑃𝐶𝐶𝑅𝑅
+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡,𝑡𝑡𝑝𝑝
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡,𝑡𝑡𝑝𝑝
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡,𝑡𝑡𝑝𝑝
𝑃𝑃𝐶𝐶𝑅𝑅
+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡,𝑡𝑡𝑝𝑝
𝑃𝑃𝐶𝐶𝑅𝑅
(M.194)
𝑃𝑃𝐼𝐼𝑊𝑊
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
+𝐼𝐼𝑉𝑉𝑄𝑄𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅
+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅
(M.195)
𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=−�𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺+ 𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅�
(M.196)
𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
=−�𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑁𝑁𝑁𝑁𝐶𝐶
+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐻𝐻
+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝐺𝐺
+ 𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅�
(M.197)
𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡−1
𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.198)
𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡−1
𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.199)
𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡−1
𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑉𝑉𝑄𝑄
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.200)
𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡−1
𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐼𝐼𝐼𝐼𝐶𝐶𝑈𝑈
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.201)
𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡−1
𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.202)
𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡−1
𝑃𝑃𝐶𝐶𝑅𝑅+ 𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑡𝑡𝑝𝑝,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝐺𝐺𝑃𝑃𝐿𝐿𝑃𝑃
𝑝𝑝𝑣𝑣,𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.203)
𝐼𝐼𝐼𝐼𝐼𝐼𝑉𝑉
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅=𝑝𝑝
𝑡𝑡
𝑃𝑃𝐸𝐸𝑃𝑃∗(𝐼𝐼𝑃𝑃𝑉𝑉𝑃𝑃𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑃𝑃𝑉𝑉𝑅𝑅𝑉𝑉
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅+𝐼𝐼𝑉𝑉𝐶𝐶𝑅𝑅𝑉𝑉𝑃𝑃
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅)
+𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶∗𝐼𝐼𝐶𝐶𝑉𝑉𝐶𝐶𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅+ 𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉∗𝐼𝐼𝐿𝐿𝑃𝑃𝑉𝑉𝑡𝑡𝑃𝑃𝐶𝐶𝑅𝑅
(M.204)
𝐼𝐼𝑃𝑃𝐼𝐼𝑉𝑉
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅= 𝑝𝑝
𝑡𝑡
𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃∗𝐼𝐼𝑉𝑉𝑄𝑄
𝑡𝑡
𝑃𝑃𝐶𝐶𝑅𝑅
(M.205)
110
To al ne p oduc ion axes
𝐼𝐼𝑉𝑉𝑉𝑉𝑋𝑋
𝑡𝑡𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑
To al ne o he p oduc ion axes
𝑃𝑃𝑃𝑃𝑉𝑉𝑡𝑡𝑝𝑝𝑝𝑝𝑑𝑑𝑑𝑑
To al ne impo axes
𝐼𝐼𝐼𝐼𝑀𝑀𝑉𝑉𝑎𝑎𝑥𝑥𝑡𝑡
Impo axes ecei ed by Denma k
𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋𝑝𝑝,𝑡𝑡
Impo axes paid by Denma k
𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋𝑝𝑝,𝑡𝑡
O he ne impo axes paid by Denma k.
𝑃𝑃𝐼𝐼𝑀𝑀𝑉𝑉𝑉𝑉𝑋𝑋𝑝𝑝,𝑡𝑡
In e es a e on secu i ies
𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶
In e es a e on deposi s
𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃𝐶𝐶
In e es a e on loans
𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉
In e es a e on di idends
𝑝𝑝𝑡𝑡𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃
In e es a e on pensions and insu ance
𝑝𝑝𝑡𝑡𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼
Sec o al eal capi al s ock
𝑘𝑘𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶,𝑘𝑘𝑡𝑡𝐻𝐻,𝑘𝑘𝑡𝑡𝑁𝑁𝐶𝐶,𝑘𝑘𝑡𝑡𝐺𝐺
Sec o al nominal capi al s ock
𝐾𝐾𝑡𝑡𝑁𝑁𝑁𝑁𝐶𝐶,𝐾𝐾𝑡𝑡𝐻𝐻,𝐾𝐾𝑡𝑡𝑁𝑁𝐶𝐶,𝐾𝐾𝑡𝑡𝐺𝐺
capaci y u iliza ion a e
𝑠𝑠𝑡𝑡
En i onmen al a iables
no a ion
Ene gy supply in indus y n.
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡
𝑢𝑢
Ene gy supply impo ed.
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡
𝐸𝐸
Ene gy supply in he o m o was e.
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡
𝑅𝑅𝑎𝑎𝑐𝑐𝑡𝑡𝑟𝑟
Ene gy supply in he o m o enewable ene gy.
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡
𝑃𝑃𝐸𝐸
To al ene gy supply
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡
𝑡𝑡𝑑𝑑𝑡𝑡
Ene gy usage in indus y n.
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝑢𝑢
Ene gy expo ed o usage ou side Denma k
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝑋𝑋
Dis ibu ion losses ela ed o ene gy usage.
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝑃𝑃𝐿𝐿
Ene gy usage by households.
𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝐻𝐻𝐻𝐻
Change in in en o ies o ene gy ypes.
𝐼𝐼𝑖𝑖𝑖𝑖𝑃𝑃𝑟𝑟𝑠𝑠𝑡𝑡𝑎𝑎,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸
In en o y s ock o ene gy.
𝐼𝐼𝑖𝑖𝑖𝑖𝑡𝑡𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸
New disco e ies o c ude oil ese es.
𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠
𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗
S ock o c ude oil ese e.
𝐶𝐶𝑝𝑝𝑖𝑖𝑠𝑠
𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡
𝑎𝑎𝑗𝑗
New disco e ies o na u al gas o ex ac ion ese es.
𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠
𝑑𝑑𝑡𝑡𝑐𝑐,𝑡𝑡−1
𝑎𝑎𝑗𝑗
S ock o na u al gas o ex ac ion ese e.
𝐼𝐼𝑉𝑉𝑔𝑔𝑎𝑎𝑠𝑠
𝑝𝑝𝑟𝑟𝑐𝑐,𝑡𝑡
𝑎𝑎𝑗𝑗
Emissions
Emission o indus y n di ec ly ela ed o ene gy.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝑢𝑢
Emission o indus y n un ela ed o ene gy.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝑢𝑢
To al emissions o indus y n (bo h di ec and indi ec )
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡
𝑢𝑢
Emissions o households di ec ly ela ed o ene gy.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝐻𝐻𝐻𝐻
Emissions o households un ela ed o ene gy.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑡𝑡
𝐻𝐻𝐻𝐻
To al emissions o households.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑑𝑑𝑡𝑡,𝑡𝑡
𝐻𝐻𝐻𝐻
To al emissions in he Danish economy
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡
CO2-equi elan emissions o each indus y n.
𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑢𝑢
To al CO2-equi elan emissions in he Danish economy.
𝐶𝐶𝑃𝑃2𝑉𝑉𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡
No e: The no a ion o ene gy (𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌) co e s he 21 ypes o ene gy (Coil (c ude oil), Oilp: Oil p oduc s), Re G
(Refine y gas), GasT (Gasoline o anspo a ion), FGas (je uel), FGasBunk (Je uel bunke ed), DieT (Diesel o
anspo a ion), Die TBunk (Diesel o anspo a ion - bunke ed), NGasEx (Na u al gas ex ac ion), NGasCons (Na u al
gas consump ion – incl. ci y gas), CC (coal and smoke), Was e (Was e), RE (Renewable ene gy), S aw (S aw), FW
(Fi ewood and wood chips), WP (wood pelle s), BioG (Bio gas), BBB (Biodiesel, bioe hanol and bio oil), El (elec ici y),
DHea (Dis ic hea ).).

111
The no a ion o emissions (𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼) co e s he 6 ypes o emissions (CO2 (ca bon dioxide), N2O (ni ous oxide),
CH4 (me hane), SF6 (sul u hexafluo ide), PFC (pe fluo oca bons), and HFC (Hyd ofluo oca bons))
The no a ion o indus ies (n) co e s he ollowing indus ies: Ag icul u al, Fo es y, Fishe y, Mining, Manu ac u ing o
ood, Ene gy supply and efine ies, O he ene gy in ensi e indus ies, Financial co po a ions, O he indus ies.
Pa ame e s
No a ion
Economic pa ame e s
Technical coe icien ela ing ou pu o indus y n o inpu s
bough by indus y n in indus y i.
𝑎𝑎
𝑡𝑡
𝑖𝑖 𝑢𝑢
Impo sha e o indus y n.
𝜙𝜙𝑧𝑧,𝑡𝑡
𝑖𝑖 𝑢𝑢
Impo sha e o in es men p oduc s o indus y n.
𝜙𝜙𝐼𝐼𝑁𝑁𝑉𝑉,𝑡𝑡
𝑢𝑢
Impo sha e o expo s o indus y n.
𝜙𝜙𝑋𝑋,𝑡𝑡
𝑢𝑢
In e cep in he equa ion o impo sha es o p oduc
ype p in inal consump ion.
𝛽𝛽0
𝑐𝑐𝑝𝑝
In e cep in he equa ion o impo sha es o p oduc
ype p o indus ies.
𝛽𝛽0𝑧𝑧
𝑖𝑖 𝑖𝑖
Impo elas ici y o inal consump ion in p oduc ype p.
𝛽𝛽1𝑐𝑐𝑝𝑝
Impo elas ici y o inpu s p oduced by indus y n.
𝛽𝛽1𝑧𝑧𝑖𝑖
Wage p emium o indus y n.
ω
0
𝑢𝑢
Wage ba gaining pa ame e o indus y n.
ω
1𝑢𝑢
Sha e o p oduc p supplied by domes ic indus y n o inal
consump ion
𝜆𝜆
𝑑𝑑𝑑𝑑𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
Sha e o p oduc p supplied by o eign indus y n o inal
consump ion
𝜆𝜆
𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢 𝑝𝑝
Sha e o in es men p oduc s bough om indus y n.
𝜆𝜆𝑖𝑖𝑢𝑢𝑣𝑣,𝑡𝑡
𝑢𝑢
Sha e o unspeci ied impo s o o al p oduc ion in indus y
n.
𝛾𝛾
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑢𝑢
Sha e o unspeci ied impo s o o al p oduc ion o inal
good p.
𝛾𝛾
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑝𝑝
Sha e o unspeci ied impo s o o al in es men s.
𝛾𝛾
𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣
Pa ame e se o ma ch i s obse a ion in consump ion
sha e
γ
𝒕𝒕
𝒄𝒄𝒑𝒑 .
𝜃𝜃𝑝𝑝
Ra e o subs i u ion o consump ion in nes 1.
𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡1
Ra e o subs i u ion o consump ion in nes 2
𝜎𝜎𝑢𝑢𝑟𝑟𝑐𝑐𝑡𝑡2
In e cep in expo equa ion. Se o ma ch s a ing alue o
𝒙𝒙𝒕𝒕𝒏𝒏
𝒅𝒅𝒕𝒕
𝒏𝒏∗ o indus y n.
α
0
𝑢𝑢
Expo elas ici y o indus y n.
α
1𝑢𝑢
In e es a e on deposi s
𝑝𝑝𝑡𝑡𝑃𝑃𝐸𝐸𝑃𝑃
In e es a e on secu i ies
𝑝𝑝𝑡𝑡𝐶𝐶𝐸𝐸𝐶𝐶
In e es a e on loans
𝑝𝑝𝑡𝑡𝐿𝐿𝐶𝐶𝑉𝑉
In e es a e on di idends
𝑝𝑝𝑡𝑡𝑃𝑃𝐼𝐼𝑉𝑉𝑃𝑃
In e es a e on insu ance, pension, and s anda dized
gua an ee schemes.
𝑝𝑝
𝑡𝑡
𝐼𝐼𝑁𝑁𝐶𝐶𝐼𝐼
P ice index o impo in indus y n.
𝑝𝑝𝑚𝑚𝑡𝑡𝑢𝑢
P ice index o unspeci ied impo s.
𝑝𝑝𝑚𝑚𝑢𝑢𝑖𝑖𝑑𝑑,𝑡𝑡
Ma k-up a e o indus y n.
𝜇𝜇𝑡𝑡𝑢𝑢
Sha e o indus y n g oss ope a ing su plus and mixed
income associa ed wi h he household sec o .
𝐶𝐶𝐻𝐻,𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢
112
Sha e o indus y n g oss ope a ing su plus and mixed
income associa ed wi h he inancial co po a ion sec o .
𝐶𝐶𝑁𝑁𝐶𝐶,𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢
Sha e o indus y n g oss ope a ing su plus and mixed
income associa ed wi h he go e nmen sec o .
𝐶𝐶𝐺𝐺,𝑡𝑡
𝑝𝑝𝑝𝑝𝑑𝑑𝑝𝑝𝑖𝑖𝑡𝑡,𝑢𝑢
Sha e dis ibu ing o al in es men s o he household
sec o .
𝐶𝐶
𝐻𝐻,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣
Sha e dis ibu ing o al in es men s o he inancial
co po a ion sec o .
𝐶𝐶𝑁𝑁𝐶𝐶,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣
Sha e dis ibu ing o al in es men s o he go e nmen
sec o .
𝐶𝐶
𝐺𝐺,𝑡𝑡
𝑖𝑖𝑢𝑢𝑣𝑣
Adjus men e m used in impo equa ion o indus ies
𝑎𝑎𝑝𝑝𝑗𝑗𝜙𝜙,𝑡𝑡
𝑢𝑢
Adjus men e m used o impo equa ion o inal
consump ion p oduc s.
𝑎𝑎𝑝𝑝𝑗𝑗
𝜙𝜙,𝑡𝑡
𝑝𝑝
Adjus men e m used in expo equa ion o indus ies.
𝑎𝑎𝑝𝑝𝑗𝑗𝑐𝑐,𝑡𝑡
𝑢𝑢
Adjus men e m used in he ansi ion o p o i s om
indus y o sec o al le el.
adj
H
Adjus men e m used in he ansi ion o p o i s om
indus y o sec o al le el
adj
FC
Adjus men e m used in he ansi ion o p o i s om
indus y o sec o al le el
adj
G
En i onmen al pa ame e s
Ene gy supply coe icien o indus y n.
𝑃𝑃𝑐𝑐𝑢𝑢𝑝𝑝,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢
Ene gy usage coe icien o indus y n.
𝑃𝑃𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢
Ene gy usage coe icien o households.
𝑃𝑃
𝑢𝑢𝑐𝑐𝑟𝑟,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻𝐻𝐻
Emission coe icien o emissions di ec ly om ene gy
usage in indus y n.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼
𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝑢𝑢
Emission coe icien o emissions no di ec ly om ene gy
usage in indus y n.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼
𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝑢𝑢
Emission coe icien o emissions di ec ly om ene gy
usage by households.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼
𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐸𝐸𝑁𝑁𝐸𝐸𝑃𝑃𝐺𝐺𝐸𝐸,𝐻𝐻𝐻𝐻
Emission coe icien o emissions no di ec ly om ene gy
usage by he households.
𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼
𝑐𝑐𝑑𝑑𝑟𝑟𝑝𝑝,𝑡𝑡
𝐼𝐼𝑁𝑁𝑃𝑃𝐼𝐼𝑃𝑃𝐸𝐸𝐶𝐶𝑉𝑉,𝐻𝐻𝐻𝐻
CO2-equi elan ax a e o each indus y n.
𝐶𝐶𝑃𝑃2𝑉𝑉𝑝𝑝𝑎𝑎𝑡𝑡𝑟𝑟,𝑡𝑡
𝑢𝑢
No e: The no a ion o ene gy (𝑉𝑉𝐼𝐼𝑉𝑉𝑅𝑅𝐺𝐺𝑌𝑌) co e s he 21 ypes o ene gy (Coil (c ude oil), Oilp: Oil p oduc s), Re G
(Refine y gas), GasT (Gasoline o anspo a ion), FGas (je uel), FGasBunk (Je uel bunke ed), DieT (Diesel o
anspo a ion), Die TBunk (Diesel o anspo a ion - bunke ed), NGasEx (Na u al gas ex ac ion), NGasCons (Na u al
gas consump ion – incl. ci y gas), CC (coal and smoke), Was e (Was e), RE (Renewable ene gy), S aw (S aw), FW
(Fi ewood and wood chips), WP (wood pelle s), BioG (Bio gas), BBB (Biodiesel, bioe hanol and bio oil), El (elec ici y),
DHea (Dis ic hea ).).
The no a ion o emissions (𝑉𝑉𝑀𝑀𝐼𝐼𝐶𝐶𝐶𝐶𝐼𝐼𝑃𝑃𝐼𝐼) co e s he 6 ypes o emissions (CO2 (ca bon dioxide), N2O (ni ous oxide),
CH4 (me hane), SF6 (sul u hexafluo ide), PFC (pe fluo oca bons), and HFC (Hyd ofluo oca bons))
The no a ion o indus ies (n) co e s he ollowing indus ies: Ag icul u al, Fo es y, Fishe y, Mining, Manu ac u ing o
ood, Ene gy supply and efine ies, O he ene gy in ensi e indus ies, Financial co po a ions, O he indus ies.
The no a ion o p oduc ypes (p) co e s he ollowing p oduc s: b ead (𝑐𝑐𝑡𝑡110), mea (𝑐𝑐𝑡𝑡120), ish (𝑐𝑐𝑡𝑡130), dai y (𝑐𝑐𝑡𝑡140),
ui s and ege ables (𝑐𝑐𝑡𝑡160), o he ood p oduc s (𝑐𝑐𝑡𝑡180), and inally indus y speci ic p oduc s (𝑐𝑐𝑡𝑡𝑐𝑐𝑝𝑝𝑟𝑟𝑐𝑐).
Imp in
Publishe
Mac oeconomic Policy Ins i u e (IMK) o Hans-Böckle -Founda ion, Geo g-Glock-S . 18,
40474 Düsseldo , Con ac : mm@boeckle .de, h ps://www. mm-mac o.ne
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