FIDELIO 3 manual : equations and data sources.
Date: 2019-03-08
Institutions: Joint Research Centre
Subjects: consumption, data collection, data processing, econometrics, economic consequence, environmental impact, impact study, production policy, research report, simulation, sustainable development

FIDELIO 3 manual: Equations and 
data sources 

Rocchi,  P.,  Salotti,  S.,  Reynès,  F.,  Hu, 
J.,  Bulavskaya,  T.,  Rueda  Cantuche, 
J.M., Valderas Jaramillo, J.M., Velázquez 
Afonso,  A.,  Amores,  A.F.,  Corsatea,  T. 

2019  

i 

EUR 29620 EN 

 
 
 
This publication is a Technical report by the Joint Research Centre (JRC), the European Commission’s science 
and  knowledge  service.  It  aims  to  provide  evidence-based  scientific  support  to  the  European  policymaking 
process. The scientific output expressed does not imply a policy position of the European Commission. Neither 
the  European Commission  nor  any  person  acting  on  behalf  of  the  Commission  is responsible for  the  use  that 
might be made of this publication. 

Note:  TNO  stands for  Netherlands Organisation for  Applied  Scientific Research.  JRC stands  for  Joint Research 
Centre. 

Contact information  
Name: José Manuel Rueda-Cantuche 
Address: Directorate B - Growth and Innovation, Unit B.5, JRC Seville 
Email: Josem.RCANTUCHE@ec.europa.eu 
Tel.: 0034954 488243 

EU Science Hub 
https://ec.europa.eu/jrc 

JRC115308 

EUR 29620 EN 

PDF 

ISBN 978-92-79-98872-1 

ISSN 1831-9424 

doi:10.2760/219417 

Luxembourg: Publications Office of the European Union, 2019 

© European Union, 2019 

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How  to  cite  this  report:  Rocchi,  P.,  Salotti,  S.,  Reynès,  F.,  Hu,  J.,  Bulavskaya,  T.,  Rueda  Cantuche,  J.M., 
Valderas  Jaramillo,  J.M.,  Velázquez  Afonso,  A.,  Amores,  A.F.,  Corsatea,  T.  (2019).  FIDELIO  3  manual: 
Equations  and  data  sources,  EUR  29620  EN,  Publications  Office  of  the  European  Union,  Luxembourg,  ISBN 
978-92-79-98872-1, doi:10.2760/219417, JRC115308.

All content © European Union 2019 

ii 

Preface 

The  following  technical  report  describes  the  structure,  the  equations  and  the  data  that  constitute 
the model FIDELIO 3.  

FIDELIO  is  a  multi-sectoral  model  developed  by  the  unit  B.5  of  the  Directorate  General  Joint 
Research Centre (JRC) — the circular economy and industrial leadership unit. The model is designed 
to evaluate sustainable production and consumption policies through a dynamic econometric input-
output model. It conducts scenario analysis on the costs and impacts of policy measures providing 
their economic — such as jobs, value added and investment — and environmental effects — such as 
resource use or air emissions. The model can be used for policy formulation and evaluation to assess 
sustainable production and consumption policies capturing both spillover and rebound effects, and 
quantifying  their  impacts  in  jobs,  growth,  energy savings,  investments,  resource  use,  air  emissions 
and trade balance. 

FIDELIO  3  was  preceded  by  two  previous  versions.  The  changes  introduced  in  the  subsequent 
versions  of  the  model  have  two  main  objectives.  The  first  one  is  to  increase  the  coverage  of  the 
model.  The  second  one  is  to  improve  the  efficiency  and  the  capacity  of  the  model  to  evaluate 
sustainable  production  and  consumption  policies.  FIDELIO  1  was  created  between  2009  and  2011 
through the collaboration of the JRC B.5 unit and the Austrian institute of economic research WIFO 
(Kratena et al., 2013). Next, between 2011 and 2015, the two institutions worked on a new version 
of  the  model,  FIDELIO  2,  which  included  more  countries,  an  update  of  the  data  and  the  model 
calibration, and some improvements of the environmental block (Kratena et al., 2017). FIDELIO 3 is 
the result of the collaboration of the unit B.5 of the JRC and the Dutch research organization TNO 
that took place in 2018 and 2019. This last version further improves the geographical coverage, both 
in terms of number of countries  and quality of  details  and it updates the calibration of the model 
using data for 2010. Finally, compared to the previous one, this version includes important changes 
to the production block.  

iii 

Acknowledgements 

We  would  like  to  thank  the  National  Statistical  Institute  of  Austria,  Belgium,  Czech  Republic, 
Denmark, Estonia, Finland, Germany, Hungary, Portugal, Slovakia,  Spain and Sweden, for providing 
confidential or unpublished data. 

Authors 

Rocchi, Paola (JRC) 
Salotti, Simone (JRC) 
Reynès, Frédéric (TNO) 
Hu, Jinxue (TNO) 
Bulavskaya, Tanya (TNO) 
Rueda Cantuche, José Manuel (JRC) 
Valderas Jaramillo, Juan Manuel (JRC) 
Velázquez Afonso, Agustín (JRC) 
Amores, Antonio F. (JRC) 
Corsatea, Teodora (JRC) 

iv 

 
 
 
List of acronyms and symbols 

B2A3N 
B2A3G 
BP 
CGE 
CH4 
CIF 
CO2 
CPA 
COICOP 
D1 
D11 
D12 
D29x39 
D4 
D5 
D61  
D62 
D7 
ELIOD 
FIDELIO 
FOB 
GRAS 
IEA 
IO 
ISIC Rev. 4 
ITTM 
NACE Rev. 2 
NPISH 
N2O 
P51C 
PP 
QAIDS 
TJ 
TlS 
TTM 
VA 
WIOD 
WIOT 
WS 

Net operating surplus 
Gross operating surplus 
Basic prices 
Computational general equilibrium model 
Methane 
Cost-insurance-freight prices 
Carbon dioxide 
Classification of products by activity 
Classification of individual consumption according to purpose 
Compensation of employees 
Wages 
Social security contributions 
Production taxes less subsidies 
Property income 
Taxes paid by households 
Social security contributions paid by employees 
Transfers received by households 
Other transfers 
Environmental and labour accounts linked to a global input-output database 
Fully Interregional dynamic econometric input-output model 
Free-on-board prices 
Generalized RAS method 
International energy agency 
Input-output 
International standard industrial classification, revision 4 
International transport and trade margins 
Statistical classification of economic activities, revision 2 
Non-profit institutions serving households 
Nitrous oxide 
Depreciation 
Purchaser prices 
Quasi-almost ideal demand system 
Tera-joules 
Taxes less subsidies 
Transport and trade margins 
Value added 
World input-output database 
World input-output tables 
Wage settings 

v 

 
 
 
 
vi 

 
Table of Contents 

Preface ....................................................................................................................................... iii 
List of acronyms and symbols ....................................................................................................... v 

1. Introduction: an overview of the model .................................................................................... 1 
2. The sets of FIDELIO ................................................................................................................... 4 
3. The equations of FIDELIO .......................................................................................................... 6 
3.1 The production block .................................................................................................................... 7 
3.1.1 The production function ........................................................................................................ 7 
3.1.2 Investment, the stock of capital, and inventories ............................................................... 11 
3.2 The household block ................................................................................................................... 12 
3.2.1 Household income and wealth ............................................................................................ 12 
3.2.2 Consumption of durables ..................................................................................................... 14 
3.2.3 Consumption of non-durables ............................................................................................. 15 
3.2.4 Non-profit institutions serving households ......................................................................... 17 
3.3 The government block ................................................................................................................ 18 
3.4 The trade block ........................................................................................................................... 19 
3.5 The relationship between BP and PP, and the calculation of GDP ............................................. 21 
3.6 The labour market ....................................................................................................................... 21 
3.7 The energy block ......................................................................................................................... 22 
3.8 The pricing system ...................................................................................................................... 24 
4 The data of FIDELIO ................................................................................................................. 26 
4.1 The IO dataset ............................................................................................................................. 26 
4.1.1 Supply, use, and trade.......................................................................................................... 26 
4.1.2 International trade and transport margins .......................................................................... 29 
4.1.3 The VA components ............................................................................................................. 30 
4.1.4 The investment data ............................................................................................................ 33 
4.2 The rest of the data: the household block .................................................................................. 34 
4.2.1 Household income, taxes, and transfers ............................................................................. 34 
4.2.2 Household consumption ...................................................................................................... 35 
4.2.3 Household stocks ................................................................................................................. 40 
4.3 The rest of the data: the government block ............................................................................... 41 
4.4 The rest of the data: the labour market ..................................................................................... 42 
4.5 The rest of the data: the energy block ........................................................................................ 43 
References ................................................................................................................................. 45 
List of Figures ............................................................................................................................. 46 
List of Tables .............................................................................................................................. 47 
Annexes..................................................................................................................................... 48 

vii 

 
 
 
 
 
 
 
 
 
viii 

 
 
 
1. Introduction: an overview of the model 

This  technical  report  illustrates  the  third  version  of  the  FIDELIO  (Fully  Interregional  Dynamic 
Econometric  Long-term  Input-Output)  model.  FIDELIO  is  a  multi-regional  model  that  has  several 
similarities  with  Computable  General  Equilibrium  (CGE)  model.  Compared  to  neoclassical  CGE 
models — which assume that the perfect flexibility of prices and quantities ensures the full use of 
the  factors  of  production  at  all  times  —  FIDELIO  integrates  some  new-Keynesian  features: 
consumption adjusts slowly to its optimal level according to an error correction model and wages do 
not  clear  the  labour  market.  The  assumptions  that  prices  do  not  clear  the  markets  and  market 
"imperfections"  exist  generate  the  dynamics  of  the  model1 that  is  solved  sequentially  (recursive 
dynamic).  In  addition,  FIDELIO  is  an  econometric  model  since  the  calibration  of  most  of  the 
behavioural  parameters  of  the  model  (dynamic  adjustment  lags  of  prices  and  quantities,  and 
elasticities) is based on econometric estimations. 

With respect to the geographical coverage, FIDELIO is a multi-regional input-output model including 
35  regions  (the  28  Member  States  plus  Brazil,  China,  India,  Japan,  Russia,  Turkey  and  the  United 
States), each of them disaggregated in 56 industries and products. The main bulk of the data used in 
the model comes from the international supply and use tables of the World Input-Output database 
(WIOD)  (2016  release,  the  data  refer  to  2010).  Additional  information  required  is  taken  from 
CEDEFOP, Eurostat data, OECD data, the POLES model, UNECE data, World Bank data, and data from 
National Statistical Institutes of Belgium, China, Czech Republic, Hungary, India, Slovakia, Turkey, and 
the United Kingdom. 

As a CGE model, in FIDELIO total supply equals total demand. Products flow among four main actors, 
each  of  them  constituting  a  block  in  the  model:  firms,  households,  the  government,  and  foreign 
countries  —  through  international  trade.  Firms  produce  total  supply.  Total  demand  has  seven 
components:  demand  for  intermediate  inputs,  investment  demand,  changes  in  inventories, 
household  consumption,  consumption  of  non-profit  institutions  serving  households  (NPISH), 
government consumption, and demand from abroad. To these four main blocks, the model adds a 
capital block and a labour block to describe the markets of primary inputs. Finally, an energy block 
describes  the  environmental  impact  of  production  and  consumption  in  terms  of  energy  use  and 
emissions. 

The  production  block  is  characterized  by  firms  that  adjust  their  production  to  satisfy  the  total 
demand as shown in Figure 1.2 To produce, firms use four production factors: capital, labour, energy 
intermediates,  and  non-energy  intermediates or materials.  The  production  function  that  describes 
firms'  choices  is  a  nested  CES  production  function  with  two  levels.  In  a  first  level,  firms  choose 
between  materials  and  non-materials,  which  is  the  composed  bundle  of  factors  made  of  capital, 
labour and energy inputs. Then, in a second  level  and depending on factor prices  and substitution 
elasticities, firms choose across capital, labour and energy. From these production choices the first 

1 Prices and quantities might be rigid in the short run and they adjust slowly over time towards their optimal 
level. Being dynamic, the neo-Keynesian models are better suited to analyse medium term phenomena and 
the transition to the long run. 
2 The diagrams of this Section are aimed at providing a first insight of the model and do not contain all the 
variables of the model and the links among them. 

1 

 
                                                           
component  of  the  total  demand  originate:  the  demand  of  energy  and  non-energy  intermediates. 
Other  two  components  of  final  demand  are  related  to  firms'  choices:  investment  and  inventories. 
FIDELIO  has  three  options  to  compute  firms'  investment,  one  for  which  relates  investment  to  the 
capital stock variation. Inventories are exogenous and are assumed to shrink rapidly after the base 
year. From the production processes, firms pay the cost of the other factors of production (labour 
and capital) to households and to the government. 

Figure 1  Production block in FIDELIO  

Households  receive  their  income  through  wages,  a  share  of  the  gross  operating  surplus,  and  the 
government transfers (see Figure 2).  

This income, after taxes,  is either used for consumption or saved. Household total consumption is 
another component of total demand, and depends not only on disposable income, but also on the 
financial assets and on the stock of durables goods (vehicles and houses) owned by households. The 
sum  of  these  three  components  is  called  in  FIDELIO  cash-in-hand.  Households  consume  durable 
products and non-durable products. Durable products are housing rents and vehicles. Non-durable 
products  are  appliances,  electricity,  heating,  fuel  for  private  transport,  public  transport,  food, 
clothing, furniture and equipment, health, communication, recreation and accommodation, financial 
services,  and  other.  For  almost  all  consumption  categories,  the  demand  is  characterized  through 
econometric estimations. In particular, the demand for housing, vehicles, and total non-durables is 
described  through  error  correction  models,  slowly  adjusting  to  its  optimal  level  (housing  rents  is 
then  a  constant  share  of  housing).  Within  total  non-durables,  the  consumption  of  appliances, 
electricity, fuel, and heating is also derived econometrically. Finally, the consumption of the bundle 
of  the  remaining  eight  commodities  is  computed  as  a  residual  —  as  the  difference  between  total 
non-durables  minus  appliances,  electricity,  fuel,  heating,  and  public  transport.  Each  of  these 
commodities is then defined through a quasi- almost ideal demand system (QAIDS).  

2 

TOTAL SUPPLY CES functionMaterialsK,L,ECapitalLabourEnergyTOTALDEMAND Gross Operating SurplusNet Operating SurplusDepreciationInvestment (1)InventoriesIntermediatedemandKLE-M nestK-L-E nestInvestment (2)Investment (3)K stock 
 
Another component of  total demand is the consumption of NPISH that is treated as exogenous in 
FIDELIO and set accordingly to the base year data. 

Figure 2  Household block in FIDELIO  

The government  (see  Figure  3)  raises its  revenue  towards six main sources: operating surplus that 
goes  to  the  government,  production  taxes,  taxes  less  subsidies  on  products,  social  security 
contributions  by  both  employers  and  employees,  and  taxes  on  household  income.  This  revenue  is 
then used to finance the  government  interest,  the government  capital formation,  the government 
transfers  to  the  households,  and  the  government  consumption  that  is  another  component  of  the 
total demand. The budget balance is calculated as the difference between government revenues and 
expenses, and it determines the variation in public debt. 

Figure 3  Government block in FIDELIO  

3 

WagesHouseholdoperatingsurplusGovernmenttransfersHousehold disposable incomeTOTALHOUSEHOLD CONSUMPTIONSavingsNet worthCASH-in-HANDKhouses (-1)K vehicles (-1)TOTAL NON-DURABLESVehiclesHousingTOTALDEMAND TOTAL DURABLESAppliancesElectricityHeatingFuel Public transportQAIDS  COMMODITIESFoodClothingFurniture and equipmentHealthCommunicationRecreation and accommodationFinancial servicesOtherNPISH  consumptionProduction taxesSocial security (firm)Social security (worker)Transfers to household GOVERMENT REVENUESGOVERNMENT EXPENSESGovernmentoperating surplusTaxes on products less subsidiesGovernment consumptionGovernment investmentInterest on debt Taxes on householdincomeTOTALDEMAND  
 
 
The last component of total demand is export (Figure 4). Bilateral export transactions are computed 
in  FIDELIO  as  the  mirror  flow  of  bilateral  imports.  Demand  for  imports  is  modelled  as  a  two-step 
procedure. First, the share of imports in total demand for each commodity is determined. Second, 
imports are then distributed to the country of origin. In each step Armington elasticities determine, 
respectively, the share of import over domestic demand and the share of each bilateral trade flow.  

Figure 4  Trade block in FIDELIO  

Looking at  the  labour market,  the  sectoral wages  are  derived from the so-called wages curve  that 
describes  the  responsiveness  of  individual  real  wages  to  the  changing  market  conditions,  in 
particular the unemployment rate. Wages influence employment through the labour demand, while 
labour supply is exogenous. 

Finally, the model includes also an energy block, where the monetary value of the energy consumed 
by firms and households is linked to energy consumption in tera-joules. This information is then used 
to  compute  emissions  of  carbon  dioxide,  methane,  and  nitrous  oxide  related  to  production  and 
consumption. 

The  aim  of  this  report  is  twofold.  First,  it  contains  all  the  equations  of  the  model;  second,  it 
illustrates the characteristics of the data used by FIDELIO. The remainder of the report is organised 
as follows. The next Section introduces the main sets used in FIDELIO in order for the reader to know 
the  scope  of  the  model  and  to  be  able  to  better  understand  the  dimensions  of  the  variables 
appearing in the model equations. Section 3 contains all the equations of the model, and Section 4 
describes the dataset.  

2. The sets of FIDELIO 

There  are  two  sets  for  the  countries  or  regions  (the  words  "region"  and  "country"  are  used 
interchangeably in this document) modelled in FIDELIO: R (region) and WR (world region),3 the only 

3 See Annex 1 for a list of the sets used in FIDELIO. 

4 

TOTAL DEMANDDemand for IMPORTEDgoodsDemand for DOMESTIC goodsDemand for goodsof country 1 Demand for goodsof country 2Demand for goodsof country n...EXPORTArmington elasticityArmington elasticity 
                                                           
difference being that the latter also contains the rest of the world, which is not explicitly modelled in 
FIDELIO but exists for trade data purposes. The 35 countries modelled in FIDELIO are the 28 member 
states of the EU plus Brazil, China, India, Japan, Russia, Turkey and the USA.4 

Since FIDELIO uses the data mostly taken from the WIOD project, there are 56 industries (indexed 
with S). Industries are classified under the statistical classification of economic activities NACE Rev. 
2,5 which is consistent with the International Standard Industrial Classification (ISIC) Rev. 4. Annex 2 
provides a list of all FIDELIO  industries. The aU (all Users) set contains all those  industries plus the 
following  six  final  demand  categories  (set  aC):  private  household  consumption,  government 
consumption, consumption of NPISH, investment, inventories and exports.  

In  the  model,  56  products  (including  services)  are  produced  (set  G),  classified  using  the  2008 
Classification of Products by Activity (CPA). Annex 3 provides a list of all FIDELIO CPA products.  For 
modelling purposes, such products can be divided into two different subsets: 

 
 

Energy (eG) and non-energy products (neG),  
Services used in international trade and transport (TIRS) and the rest of the products (nTIR).  

The private consumption categories, corresponding to the set CPC, differ from the CPA categories, as 
they are based on the COICOP classification6 and then bridged to the NACE Rev. 2 categories within 
the  model  according  to  bridge  matrices  calibrated  on  the  base  year  (2010)  data.  The  CPC  set 
contains  the  following  items:  rents,  vehicles,  appliances,  electricity,  heating,  fuel  for  private 
transport,  public  transport,  and  eight  items  that  in  the  model  are  treated  within  a  QAIDS. 
Collectively, these eight items are grouped under the QC set (standing for QAIDS Commodities) and 
recreation  and 
are: 
accommodation, financial services, and other. The three energy goods electricity, heating, and fuel 
for private transport are grouped under the CPEn set (standing for private consumption of energy). 
Annex 4 provides a list of the FIDELIO consumption products and the corresponding COICOP goods. 

furniture  and  equipment,  health,  communication, 

food,  clothing, 

There  are  five  components  of  value  added  (VA)  in  the  VAC  (value  added  components)  set:  wages, 
social security contributions, production taxes, depreciation, and operating surplus. As for the labour 
market, there are three skill levels (low, medium, and high). The labour skills (LS) set contains those 
three plus the "all" category, and the LSca (ca standing for calculations) only contains the three skill 
levels. 

In  the  energy  block  of  the  model  three  sets  are  used:  EnC  (that  stands  for  energy  carriers  and 
includes  coal,  oil,  gas,  renewables,  and  electricity  and  heating),  EnC_calc  (the  previous  one  not 
including the total), and EnCd (detailed energy carriers) for all the eleven energy carriers present in 
the  data  (diesel,  gasoline,  jet  fuel,  other  gas,  waste,  coal/coke/crude,  fuel  oil,  liquid  and  biofuels, 
electricity for heating production, renewables/nuclear, natural gas/lpg, and other sources). 

4 These countries represent roughly the 70% of the world GDP. 
5 NACE is an acronym for "Nomenclature statistique des activités économiques dans la Communauté 
européenne". 
6 Classification of Individual Consumption According to Purpose. 

5 

 
 
                                                           
3. The equations of FIDELIO 

FIDELIO is a demand-driven model, in the tradition of the input-output (IO) framework, and it seems 
appropriate to start from the equation7  for total demand for domestically produced goods by region 
and good: 8 

𝑎𝑈
 𝐺𝐷𝑡𝑜𝑡(𝑅, 𝐺) = ∑ 𝐺𝐷_𝐵𝑃(𝑅, 𝐺, 𝑎𝑈)

(1) 

where 𝐺𝐷𝑡𝑜𝑡 is the  total  demand  of  domestically  produced  goods,9 defined over  region  and  good, 
and  it  is  computed  as  the  sum  over  all  users  of  the  demand  for  domestically  produced  goods  by 
region, good and user, 𝐺𝐷_𝐵𝑃 , which in turn is defined as follows:  

𝐺𝐷_𝐵𝑃(𝑅, 𝐺, 𝑎𝑈) = 𝐺_𝐵𝑃(𝑅, 𝐺, 𝑎𝑈) − 𝑀(𝑅, 𝐺, 𝑎𝑈) 

(2) 

𝐺_𝐵𝑃 is  total  demand  in  basic  prices  (BP)  and 𝑀 represents  imports  in  cost-insurance-freight  (CIF) 
prices. Leaving aside the definition of imports for the moment (introduced in Subsection 3.4), total 
demand in BP is defined as follows: 

𝐺_𝐵𝑃(𝑅, 𝐺, 𝑎𝑈) = 𝐺_𝑃𝑃(𝑅, 𝐺, 𝑎𝑈) − 𝑇𝑙𝑆(𝑅, 𝐺, 𝑎𝑈) + 𝑇𝑇𝑀𝑟𝑒𝑐(𝑅, 𝐺, 𝑎𝑈) − 𝑇𝑇𝑀𝑝𝑎𝑖𝑑(𝑅, 𝐺, 𝑎𝑈)  (3) 

where 𝐺_𝑃𝑃 is the demand in purchaser prices (PP), 𝑇𝑙𝑆 is taxes less subsidies (TlS), 𝑇𝑇𝑀𝑟𝑒𝑐 is trade 
and  transport  margins  (TTM)  received,  and 𝑇𝑇𝑀𝑝𝑎𝑖𝑑 is  TTM  paid  (see  Subsection  3.5  for  more 
details on this). The total demand is composed by different parts, described in other Subsections of 
Section  3:  intermediate  demand  of  industries  (3.1),  final  demand  of  households  and  NPISH  (3.2), 
government consumption (3.3), investment and inventories (3.1), and exports (3.4).  

From total demand for domestically produced goods 𝐺𝐷𝑡𝑜𝑡, sectoral output 𝑄 is derived using the 
market shares 𝑀𝑘𝑡𝑆ℎ𝑎𝑟𝑒𝑠2010

𝑚𝑎𝑘𝑒 that is the industry shares in output of any good: 

𝑄(𝑅, 𝑆) = ∑ (𝑀𝑘𝑡𝑆ℎ𝑎𝑟𝑒𝑠2010

𝑚𝑎𝑘𝑒(𝑅, 𝐺, 𝑆) × 𝐺𝐷𝑡𝑜𝑡(𝑅, 𝐺) )

𝐺

The market shares are calibrated on the base year IO make (supply) table as follows: 

𝑀𝑘𝑡𝑆ℎ𝑎𝑟𝑒𝑠2010

𝑚𝑎𝑘𝑒(𝑅, 𝐺, 𝑆) =

𝐼𝑂_𝑀𝑎𝑘𝑒2010(𝑅,𝐺,𝑆)
𝑆
∑ 𝐼𝑂_𝑀𝑎𝑘𝑒2010(𝑅,𝐺,𝑆)

Where 𝐼𝑂_𝑀𝑎𝑘𝑒2010(𝑅, 𝐺, 𝑆) is the data obtained from the make matrix for 2010.10 

(4) 

(5) 

7 As explained in the introduction, FIDELIO is a recursive dynamic model solved sequentially every year. For 
simplicity, in the equations of this manual we omit the time index whenever the variables refer the current 
year. 
8 Note that flows refer to nominal flows (monetary transactions), and not real flows (quantities). 
9 Whenever a new variable is introduced in the manual, it is followed by its definition. Anyway, since not all 
variables are defined after every equations (but only the variable not already defined before), and in order to 
ease the reading, Annex 5 and 6 provide a complete list of endogenous and exogenous variables, respectively, 
and their definition.  
10 Annex 7 provides a list of the base year data used for calibrating some of the FIDELIO parameters, Annex 8 
provides a list of the calibrated parameters, Annex 9 provides a list of the parameters econometrically 
estimated, while Annex 10 provides a list of the parameters whose values have been taken from the literature. 

6 

 
 
 
 
 
  
 
  
                                                           
Table 1 shows the Austrian sectoral market shares of the first four commodities as a mean to quickly 
illustrate the data used in equation (5).11 

Table 1  Austrian market shares for the first four products 

R 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 

G 

CPA_A01 
CPA_A02 
CPA_A03 
CPA_B 
CPA_B 
CPA_B 
CPA_B 
CPA_B 
CPA_B 
CPA_B 
CPA_B 
CPA_B 
CPA_B 
CPA_B 

S 
A01 
A02 
A03 
A01 
B 
C20 
C23 
C24 
D35 
F 
G46 
G47 
H49 
H52 

1.000 
1.000 
1.000 
0.002 
0.898 
0.001 
0.058 
0.000 
0.001 
0.028 
0.002 
0.002 
0.006 
0.002 

3.1 The production block  

To  introduce  the  production  block,  Subsection  3.1.1  describes  the  production  function  used  in 
FIDELIO,  while  Subsection  3.1.2  focuses  on  how  investment,  capital  stock,  and  inventories  are 
characterized in FIDELIO.  

3.1.1 The production function 

FIDELIO  uses  a  nested  CES  production  function  with  four  factors  of  production:  capital,  labour, 
energy  intermediates  (CPA_B,  CPA_C19,  and  CPA_D35)  and  materials,  where  materials  equal  the 
non-energy intermediates.12  

The nested CES production function exhibits two levels, as shown in Figure 1. At the first level, firms 
minimize  costs  choosing  between  materials  and  an  aggregate  consisting  in  capital,  labour,  and 
energy  bundle  (KLE).    At  the  second  level,  the  aggregate  KLE  is  further  split  into  its  three 
components. 

The equations of the production function are now introduced in the following order. First, we show 
how  the  shares  of  factors  of  production  are  determined  in  FIDELIO.  Second,  we  explain  how  the 
shares'  parameters  of  the  production  function  are  calibrated  using  the  base  year  data.  Third,  we 
describe how the shares are then used to find the demands of factors. 

Looking at the shares of factors of production, let's first introduce the shares of the first level, that is 
the share of the bundle KLE and the materials share. 

11 Annex 11 provides a list of the abbreviations used to indicate the FIDELIO countries. 
12 Non-energy intermediates include all CPAs not included in energy intermediates. 

7 

2010makeMktShares 
 
 
 
                                                           
The KLE share 𝐾𝐿𝐸_𝑄 is determined as follows: 

𝐾𝐿𝐸_𝑄(𝑅, 𝑆) = 𝛼𝐾𝐿𝐸(𝑅, 𝑆) × (

𝑃_𝐾𝐿𝐸(𝑅,𝑆) 
𝑃𝑄(𝑅,𝑆)

1−𝜎𝐾𝐿𝐸_𝑀(𝑅,𝑆)
)

(6) 

Where 𝛼𝐾𝐿𝐸13 is the share parameter for the KLE bundle within the first (or KLE-M) nest,  𝑃_𝐾𝐿𝐸 is 
the  price  of  combined  capital,  energy,  and  labour  inputs, 𝑃𝑄 is  the  output  price,  and 𝜎𝐾𝐿𝐸_𝑀 is 
substitution elasticity between KLE and M elements. 

Similarly, the materials share in the first nest level 𝑆𝑀_𝑄 is given by:  

𝑆𝑀_𝑄(𝑅, 𝑆) = 𝛼𝑀(𝑅, 𝑆) × (

𝑃_𝑆𝑀(𝑅,𝑆)
𝑃𝑄(𝑅,𝑆)

1−𝜎𝐾𝐿𝐸_𝑀(𝑅,𝑆)
)

(7) 

𝛼𝑀 being the share parameter for materials within KLE-M nest, and 𝑃_𝑆𝑀 the price of the materials. 

The parameters 𝛼𝐾𝐿𝐸 and 𝛼𝑀 are calibrated to fit the base year data as described later. By default, 
the  substitution  elasticity 𝜎𝐾𝐿𝐸_𝑀 of  the  first  nest  is  set  equal  to  0,  assuming  no  substitution 
between  the  KLE  bundle  and  materials.  This  is  a  standard  assumption  in  the  modelling  literature 
generally  supported  by  empirical  evidences  (e.g.  GTAP  model)  since  intermediary  material 
consumption  are  products  incorporated  or  destroyed  during  the  production  process.  They  are 
therefore not substitutable to the other inputs.   

Once the KLE share and the materials share are determined, they are used to determine the shares 
of capital, energy, and labour in the second nest (or K-L-E) level. 

In particular, starting from capital, the capital share in the second nest level is: 

𝑆𝐶_𝑄(𝑅, 𝑆) = 𝐾𝐿𝐸_𝑄(𝑅, 𝑆) × 𝛼𝐶(𝑅, 𝑆) × (

𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅,𝑆,"𝐶𝑎𝑝𝑖𝑡𝑎𝑙")
𝑃_𝐾𝐿𝐸(𝑅,𝑆)×𝑓𝑝𝑟𝑜𝑑(𝑅,𝑆,"𝐶𝑎𝑝𝑖𝑡𝑎𝑙")

1−𝜎𝐾_𝐿_𝐸(𝑅,𝑆)
)

(8) 

𝛼𝐶 is  the  relative  share  parameter  of  capital,  and  it  is  calibrated  to  fit  the  base  year  data  as 
described  below.  𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐶𝑎𝑝𝑖𝑡𝑎𝑙")  is  the  price  of  capital.  𝑓𝑝𝑟𝑜𝑑(𝑅, 𝑆, "𝐶𝑎𝑝𝑖𝑡𝑎𝑙")  is  a 
parameter  of  capital  productivity,  and  by  default  is  set  equal  to  one.  Finally, 𝜎𝐾_𝐿_𝐸  is  the 
substitution elasticity between capital, labour, and energy. We set its value equal to 0.95 which is in 
line  with  the  calibration  of  other  CGE models  and  econometric  results.  In  the  empirical  literature, 
there  is  a  large  heterogeneity  across  estimations  that  comes  from  several  factors:  the  production 
function  specification  estimated  (e.g.  translog  versus  nested  CES,  structure  of  the  nest),  the 
estimation method, the countries and/or industries under consideration, the data period. Looking at 
the meta-analysis performed by Koetse et al. (2008), about 80% of the studies retained (all of them 
carried out before 2000 and most of them estimating a translog function) find that the elasticity of 
substitution between capital and energy is below one. The survey of Okawa and Ban (2008) reaches 
a  similar  conclusion  for  the  elasticity  of  substitution  between  capital,  energy  and  labour  although 
they point out that the Cobb–Douglas hypothesis (unit elasticity) is not rejected in certain studies. 

13 We define 𝛼𝐾𝐿𝐸 and 𝛼𝑀 as share parameters, because they are the parameters that define the share of the 
KLE bundle and the share of materials per unit of output. On the contrary, we define the three parameters 𝛼𝐶, 
𝛼𝐿 and 𝛼𝐸 as relative share parameters because they refer to the weight of each factor relative to the bundle 
KLE (in fact, their sum is equal to 1).  

8 

 
 
 
 
  
 
  
                                                           
Similarly, the equation that determines the labour share is: 

𝑆𝐿_𝑄(𝑅, 𝑆) = 𝐾𝐿𝐸_𝑄(𝑅, 𝑆) × 𝛼𝐿(𝑅, 𝑆) × (

𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅,𝑆,"𝐿")
𝑃_𝐾𝐿𝐸(𝑅,𝑆)×𝑓𝑝𝑟𝑜𝑑(𝑅,𝑆,"𝐿")

1−𝜎𝐾_𝐿_𝐸(𝑅,𝑆)
)

(9) 

where 𝛼𝐿 is the relative share of labour calibrated to fit the base year data, 𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐿") is the 
price of labour, and 𝑓𝑝𝑟𝑜𝑑(𝑅, 𝑆, "𝐿") is a parameter of labour productivity, set by default equal to 
one. 

Also the energy share is determined as: 

𝑆𝐸_𝑄(𝑅, 𝑆) = 𝐾𝐿𝐸_𝑄(𝑅, 𝑆) × 𝛼𝐸(𝑅, 𝑆) × (

𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅,𝑆,"𝐸")
𝑃_𝐾𝐿𝐸(𝑅,𝑆)×𝑓𝑝𝑟𝑜𝑑(𝑅,𝑆,"𝐸")

1−𝜎𝐾_𝐿_𝐸(𝑅,𝑆)
)

(10) 

being 𝛼𝐸 the relative share of energy calibrated to fit the base year data, 𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐸") is the 
price of energy, and 𝑓𝑝𝑟𝑜𝑑(𝑅, 𝑆, "𝐸") the parameter of energy productivity, set by default equal to 
one. 

As  previously  suggested,  all  parameters 𝛼 in  (6)  to  (10)  that  represent  the  relative  shares  of  the 
factors  of  production  are  calibrated  over  the  base  year  data.  FIDELIO  first  computes  the  share  of 
total intermediate inputs over the sectoral output as: 

𝑆_𝑄2010(𝑅, 𝑆) =

𝐺

∑ 𝐼𝑂_𝑈𝑠𝑒_𝑃𝑃2010(𝑅,𝐺,𝑆)
𝑄2010(𝑅,𝑆)

,  

(11) 

 where 𝐼𝑂_𝑈𝑠𝑒𝑃𝑃2010 is the use matrix for 2010, and 𝑄2010(𝑅, 𝑆) = ∑ 𝐼𝑂_𝑀𝑎𝑘𝑒2010

𝐺

(𝑅, 𝑆, 𝐺).  

Then,  the  share  of  energy  intermediate  𝑆𝐸_𝑄2010  and  the  share  of  materials  𝑆𝑀_𝑄2010  are 
calculated as follow: 

𝑆𝐸_𝑄2010(𝑅, 𝑆) =

𝑒𝐺

∑ 𝐼𝑂_𝑈𝑠𝑒_𝑃𝑃2010(𝑅,𝑒𝐺,𝑆)
𝑄2010(𝑅,𝑆)

𝑆𝑀_𝑄2010(𝑅, 𝑆) = 𝑆_𝑄2010(𝑅, 𝑆) − 𝑆𝐸_𝑄2010(𝑅, 𝑆)  

The labour share is calculated starting from VA data: 

𝑆𝐿_𝑄2010(𝑅, 𝑆) =

[𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅,𝑆,"Wages")+𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅,𝑆,"𝑆𝑜𝑐𝑆𝑒𝑐")]
𝑄2010(𝑅,𝑆)

(12) 

(13) 

(14) 

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅, 𝑆, "Wages")  being  the  wages  component 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅, 𝑆, "SocSec") data on social security contributions.  

in  VA 

from  2010  data,  and 

Lastly,  capital  in  FIDELIO  is  defined  as  a  residual:  VA  minus  labour  compensation  (including  gross 
operating surplus, production taxes minus subsidies, and depreciation). Its share over output Q is: 

𝑆𝐶_𝑄2010(𝑅, 𝑆) = 1 − 𝑆_𝑄2010(𝑅, 𝑆) − 𝑆𝐿_𝑄2010(𝑅, 𝑆)   

(15) 

From these shares, the relative share parameters for the KLE bundle (𝛼𝐾𝐿𝐸 ) and for materials (𝛼𝑀) 
within the first nest are: 

𝛼𝐾𝐿𝐸(𝑅, 𝑆) = 𝑆𝐶_𝑄2010(𝑅, 𝑆) + 𝑆𝐿_𝑄2010(𝑅, 𝑆) + 𝑆𝐸_𝑄2010(𝑅, 𝑆)   

(16) 

9 

 
 
 
 
 
 
 
  
 
 
   
 
 
𝛼𝑀(𝑅, 𝑆) = 1 − 𝛼𝐾𝐿𝐸 (𝑅, 𝑆)  

(17) 

The  relative  share  parameters  for  capital,  labour,  and  energy  within  the  second  nest  are, 
respectively: 

𝛼𝐶(𝑅, 𝑆) =

𝑆𝐶_𝑄2010(𝑅,𝑆)
𝛼𝐾𝐿𝐸(𝑅,𝑆)

𝛼𝐿(𝑅, 𝑆) =

𝑆𝐿_𝑄2010(𝑅,𝑆)
𝛼𝐾𝐿𝐸(𝑅,𝑆)

𝛼𝐸(𝑅, 𝑆) =

𝑆𝐸_𝑄2010(𝑅,𝑆)
𝛼𝐾𝐿𝐸(𝑅,𝑆)

(18) 

(19) 

(20) 

As  an  example,  Table  2  illustrates  the  factors  shares  from  the  base  year  data  for  the  first  eight 
industries with Austrian data and the relative shares.  

Table 2  Austrian factors shares for the first eight products 

R 

S 

𝑆𝐶_𝑄2010  𝑆𝐿_𝑄2010  𝑆𝐸_𝑄2010 

𝛼𝐾𝐿𝐸 

𝛼𝐶 

𝛼𝐿 

𝛼𝐸 

𝑆𝑀_𝑄2010 
𝛼𝑀 
(3) 
0.514 
0.492 
0.596 
0.280 
0.678 
0.612 
0.689 
0.629 

(2) 

(1) 

(4) 
0.370 
AUT  A01 
0.389 
AUT  A02 
0.264 
AUT  A03 
0.373 
AUT  B 
0.148 
AUT  C10-C12 
0.155 
AUT  C13-C15 
0.128 
AUT  C16 
AUT  C17 
0.140 
Note: Columns are related in the following ways: (7) =(4)+(5)+(6); (3)+(7)=1; (8)+(9)+(10)=1. 

(5) 
0.047 
0.093 
0.059 
0.142 
0.151 
0.213 
0.151 
0.148 

(6) 
0.069 
0.026 
0.081 
0.205 
0.024 
0.020 
0.032 
0.083 

(7) 
0.486 
0.508 
0.404 
0.720 
0.322 
0.388 
0.311 
0.371 

(8) 
0.761 
0.765 
0.654 
0.518 
0.459 
0.399 
0.411 
0.377 

(9) 
0.096 
0.183 
0.146 
0.197 
0.468 
0.548 
0.486 
0.399 

(10) 
0.143 
0.052 
0.200 
0.285 
0.073 
0.052 
0.103 
0.225 

Once the shares of the factors of production are determined, they are then used to find the demand 
of materials, capital, labour, and energy, via simple multiplication by output: 

𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠(𝑅, 𝑆) = 𝑆𝑀_𝑄(𝑅, 𝑆) × 𝑄(𝑅, 𝑆) 

𝐶𝑎𝑝𝑖𝑡𝑎𝑙(𝑅, 𝑆) = 𝑆𝐶_𝑄(𝑅, 𝑆) × 𝑄(𝑅, 𝑆) 

𝐿𝑎𝑏𝑜𝑢𝑟(𝑅, 𝑆) = 𝑆𝐿_𝑄(𝑅, 𝑆) × 𝑄(𝑅, 𝑆) 

𝐸𝑛𝑒𝑟𝑔𝑦(𝑅, 𝑆) = 𝑆𝐸_𝑄(𝑅, 𝑆) × 𝑄(𝑅, 𝑆),  

(21) 

(22) 

(23) 

(24) 

The demand for labour is then used to determine VA components related to labour, that is wages 
( 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Wages") )  and  social  security  contributions  ( 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "SocSec") ),  by 
multiplying the labour demand by the relative share of wages and social security contributions from 
2010 data: 

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Wages") = 𝐿𝑎𝑏𝑜𝑢𝑟(𝑅, 𝑆) ×

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅,𝑆,"𝑊𝑎𝑔𝑒𝑠")
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅,𝑆,"𝑊𝑎𝑔𝑒𝑠")+𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅,𝑆,"𝑆𝑜𝑐𝑆𝑒𝑐")

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "SocSec") = 𝐿𝑎𝑏𝑜𝑢𝑟(𝑅, 𝑆) − 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Wages")  

(25) 

(26) 

10 

 
 
 
   
 
   
 
   
 
 
 
 
 
 
  
 
The  rest  of  the  VA  components  are  also  found  via  multiplication  by  output.  Production  taxes  and 
depreciation are defined as: 

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "ProdTax") = 𝑄(𝑅, 𝑆) ×

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Depr") = 𝑄(𝑅, 𝑆) ×

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅,𝑆,"ProdTax")
𝑄2010(𝑅,𝑆)

,  

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅,𝑆,"Depr")
𝑄2010(𝑅,𝑆)

,  

(27) 

(28) 

where  𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅, 𝑆, "ProdTax")  are 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅, 𝑆, "Depr") the sectoral depreciation in 2010. 

the 

sectoral  production 

taxes 

in  2010  and 

Finally,  the  last  component  of  VA  is  the  operating  surplus  that  is  calculated  with  the  following 
equation: 

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "OpSur") = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙(𝑅, 𝑆) −
−𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "ProdTax") − 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Depr")

(29) 

Therefore, total VA is the sum of all its components:  

𝑉𝐴(𝑅, 𝑆) = 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Wages") + 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "SocSec") +
+𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "ProdTax") + 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Depr") + 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "OpSur")

(30) 

Finally,  the  demand  for  non-energy  intermediates  (or  materials)  and  for  energy  intermediates  are 
used to compute the commodity demand in PP for intermediate inputs in each industry as follows:  

𝐺_𝑃𝑃(𝑅, 𝐺, 𝑆) = 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠(𝑅, 𝑆) ×

𝐼𝑂_𝑈𝑆𝐸_𝑃𝑃2010(𝑅,𝑛𝑒𝐺,𝑆)
𝑛𝑒𝐺

𝐼𝑂_𝑈𝑆𝐸_𝑃𝑃2010(𝑅,𝑛𝑒𝐺,𝑆)

∑

+𝐸𝑛𝑒𝑟𝑔𝑦(𝑅, 𝑆) ×

𝐼𝑂_𝑈𝑆𝐸_𝑃𝑃2010(𝑅,𝑒𝐺,𝑆)
𝑒𝐺
∑ 𝐼𝑂_𝑈𝑆𝐸_𝑃𝑃2010(𝑅,𝑒𝐺,𝑆)

where the industry-good structures come from the base year data. 

+

(31) 

3.1.2 Investment, the stock of capital, and inventories 

At  the  moment,  in  FIDELIO  there  are  three  alternative  options  to  generate  investment.  As  a  first 
option, investment can be computed as a constant share of the gross operating surplus, which is the 
sum of operating surplus plus depreciation, as follows: 

𝐼_𝑃𝑃_𝐺𝑂𝑃(𝑅, 𝑆) = [𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "OpSur") + 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Depr")] × 𝐼𝑂_𝐼_𝐺𝑂𝑃2010(𝑅, 𝑆)   (32) 

where 𝐼𝑂_𝐼_𝐺𝑂𝑃2010 is the proportion of investment over gross operating surplus in the base year 
data.  

As a second option, the model derives sectoral investment as a share of the sectoral production in 
the following way:  

𝐼_𝑃𝑃_𝑄(𝑅, 𝑆) = 𝑄(𝑅, 𝑆) × 𝐼𝑂_𝐼_𝑄2010(𝑅, 𝑆),  

(33) 

where 𝐼𝑂_𝐼_𝑄2010 Q is the proportion of investment over output in the base year data.  

Finally, the third option relates investment to capital stock that is defined as follows: 

11 

 
 
 
 
  
 
 
  
 
  
 
 
 
𝐾𝑆𝑡𝑜𝑐𝑘(𝑅, 𝑆) = (

𝐶𝑎𝑝𝑖𝑡𝑎𝑙(𝑅,𝑆)−𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅,𝑆,"𝑃𝑟𝑜𝑑𝑇𝑎𝑥")
𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅,𝑆,"𝐶𝑎𝑝𝑖𝑡𝑎𝑙")

×

1
𝐾𝑅𝑒𝑚𝑢𝑛𝑒𝑟

),  

(34) 

where 𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝑐𝑎𝑝𝑖𝑡𝑎𝑙") is  the  capital  price  and 𝐾𝑅𝑒𝑚𝑢𝑛𝑒𝑟 is  a  parameter  that  represents 
the remuneration of capital and is set equal to 0.03 as in EXIOMOD.14 

Then, investment is calculated as: 

𝐼_𝑃𝑃_𝐾𝑆𝑡𝑜𝑐𝑘(𝑅, 𝑆) = 𝐾𝑆𝑡𝑜𝑐𝑘(𝑅, 𝑆) − 𝐾𝑆𝑡𝑜𝑐𝑘𝑡−1(𝑅, 𝑆) × (1 − 𝐷𝑒𝑝𝑟𝑅𝑎𝑡𝑒),  

(35) 

where DeprRate represents the depreciation rate of capital stock and by default is equal to 0.05.15  

The investment at a industry level is finally aggregated into the investment demand: 

𝐺_𝑃𝑃(𝑅, 𝐺, "𝐼𝑛𝑣") = ∑ 𝐼_𝑃𝑃(𝑅, 𝑆) × 𝐼𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑆)

𝑆

(36) 

where 𝐼_𝑃𝑃 can  result  from  equation  (32),  (33),or  (35).  IStruct2010  is  the  commodity  investment 
structure  by  industry: 𝐼𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑆) =

,  where 𝐼𝑛𝑣𝑀𝑎𝑡𝑟𝑖𝑥2010   is  the 

𝐼𝑛𝑣𝑀𝑎𝑡𝑟𝑖𝑥2010(𝑅,𝐺,𝑆)
𝐺
∑ 𝐼𝑛𝑣𝑀𝑎𝑡𝑟𝑖𝑥2010(𝑅,𝐺,𝑆)

matrix of investment data by industry and by good. 

In  FIDELIO,  inventories  are  exogenous  and  are  assumed  to  shrink  rapidly  after  the  base  year.  The 
equation governing inventories is the following: 

𝐺_𝑃𝑃(𝑅, 𝐺, "𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦") = 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦_𝑃𝑃2010(𝑅, 𝐺) × 0.9𝑖−1  

(37) 

where 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦_𝑃𝑃2010 is  the  commodity  demand  for  inventories  in  the  base  year  data  and  i  
starts from 1  in the first year  of the FIDELIO simulation and increases every year of the simulation 
— which typically goes from 2010 to 2050. 

3.2 The household block 

This  Subsection  describes  how  households  receive  their  income  through  different  sources 
(Subsection  3.2.1)  and  how  they  use  it  to consume durable  and  non-durable products  (Subsection 
3.2.2 and 3.2.3, respectively). Finally, Subsection 3.2.4 introduces the NPISH consumption.  

3.2.1 Household income and wealth 

The  main  concept  of  the  household  block  is  cash-in-hands,  CashHH.  This  is  defined  as  disposable 
income (𝑌𝐷), plus financial assets (𝑁𝑒𝑡𝑊𝑜𝑟𝑡ℎ𝐻𝐻) and vehicles and houses stocks (𝐾𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑠 and 
𝐾𝐻𝑜𝑢𝑠),  the  idea  being  that  households  not  only  consume  out  of  income,  but  also  out  of  their 
assets  (the  latter  is  commonly  known  as  the  wealth  effect  in  the  literature  on  consumption  and 
savings).  

14 http://owsgip.itc.utwente.nl/projects/complex/index.php/2-uncategorised/23-exiomod 
15 At the moment, this third method to compute investment is still a working process, so only the other two 
methods are used in FIDELIO. 

12 

 
 
 
 
  
 
 
 
                                                           
𝐶𝑎𝑠ℎ𝐻𝐻(𝑅) = 𝑌𝐷(𝑅) + 𝑁𝑒𝑡𝑊𝑜𝑟𝑡ℎ𝐻𝐻(𝑅) +
+𝐾𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑠𝑡−1(𝑅) × (1 − 𝛿𝑣𝑒ℎ) + 𝐾𝐻𝑜𝑢𝑠𝑡−1(𝑅) × (1 − 𝛿ℎ𝑜𝑢𝑠)

(38) 

where the depreciation rate for vehicles 𝛿𝑣𝑒ℎ is by default 0.08 and the depreciation rate for houses 
𝛿ℎ𝑜𝑢𝑠 0.015 (see Wilhelmsson, 2008).  

Households accumulate assets and liabilities which results in a certain net wealth (𝑁𝑒𝑡𝑊𝑜𝑟𝑡ℎ𝐻𝐻). 
Equation (39) explains how it evolves:  

𝑁𝑒𝑡𝑊𝑜𝑟𝑡ℎ𝐻𝐻(𝑅) = 𝑁𝑒𝑡𝑊𝑜𝑟𝑡ℎ𝐻𝐻𝑡−1(𝑅) + 𝑆𝑎𝑣𝐻𝐻(𝑅) +
−(1 − 𝜃) × [𝐶𝑃𝑔𝑓𝑐𝑓_ℎ𝑜𝑢𝑠𝑖𝑛𝑔(𝑅) + 𝐶𝑃𝐶𝑜𝑚(𝑅, "𝑉𝑒ℎ")]

(39) 

Household net wealth depends on past net wealth (𝑁𝑒𝑡𝑊𝑜𝑟𝑡ℎ𝐻𝐻𝑡−1), savings (𝑆𝑎𝑣𝐻𝐻), and new 
debt  represented  by  the  proportion  of  expenditure  in  housing  (𝐶𝑃𝑔𝑓𝑐𝑓_ℎ𝑜𝑢𝑠𝑖𝑛𝑔)  and  in  vehicles 
𝐶𝑃𝐶𝑜𝑚(𝑅, "𝑉𝑒ℎ") that  can  be  financed with  debt.  The  parameter 𝜃 in  equation  (39)  represents  in 
fact collaterals for household durables (and is set equal to 0.37). 

Equation  (40)  defines  household  savings  as  the  difference  between  disposable  income  and  total 
households consumption 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑇𝑜𝑡")  . 

𝑆𝑎𝑣𝐻𝐻(𝑅) = 𝑌𝐷(𝑅) − 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑇𝑜𝑡")  

Disposable income is an important component of cash-in-hands, and it is defined as follows: 

𝑌𝐷(𝑅) = ∑ 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Wages")

𝑆

− 𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒(𝑅) − 𝑌𝐷𝑇𝑎𝑥𝑒𝑠𝐻𝐻(𝑅) +

+𝑌𝐷𝑂𝑝𝑆𝑢𝑟𝐻𝐻(𝑅) + 𝑌𝐷𝑇𝑟𝑎𝑛(𝑅) + 𝑌𝐷𝑂𝑡ℎ𝑒𝑟𝑇𝑟𝑎𝑛(𝑅)

(40) 

(41) 

where 𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒 is  social  security  contributions  paid  by  workers, 𝑌𝐷𝑇𝑎𝑥𝑒𝑠𝐻𝐻 represents 
taxes  paid by households to the  government, 𝑌𝐷𝑂𝑝𝑆𝑢𝑟𝐻𝐻 is the share of gross operating surplus 
going  to  households,  and 𝑌𝐷𝑇𝑟𝑎𝑛 and 𝑌𝐷𝑂𝑡ℎ𝑒𝑟𝑇𝑟𝑎𝑛 are,  respectively,  transfers  paid  by  the 
government to households and other transfers. The equations below illustrate how these different 
components of disposable income are modelled.  

Social security contributions paid by workers are proportional to the labour demand: 

𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒(𝑅) = ∑ 𝐿𝑎𝑏𝑜𝑢𝑟(𝑅, 𝑆)

𝑆

×

𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒(𝑅)
𝑌𝐷𝑆𝑆𝑒𝑐2010
∑ 𝐿𝑎𝑏𝑜𝑢𝑟2010(𝑅,𝑆)

𝑆

(42) 

where 𝑌𝐷𝑆𝑆𝑒𝑐2010
Account data, and 𝐿𝑎𝑏𝑜𝑢𝑟2010 the labour cost in 2010 data. 

𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒 is the base year social security contributions paid by workers from National 

Taxes paid by households to the government are: 

𝑌𝐷𝑇𝑎𝑥𝑒𝑠𝐻𝐻(𝑅) = 𝐼𝑂_𝑇𝑎𝑥_𝐼𝑛𝑐2010(𝑅) ×

𝑆

× [∑ 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Wages")

− 𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒(𝑅) + 𝑌𝐷𝑂𝑝𝑆𝑢𝑟𝐻𝐻(𝑅)]

(43) 

𝐼𝑂_𝑇𝑎𝑥_𝐼𝑛𝑐2010  being  the 2010 ratio of household income taxes over  income  as calculated in the 
square brackets of equation (43). 

13 

 
 
  
 
 
  
 
 
 
 
 
 
 
 
Household operating surplus is calculated as a fixed share of the gross operating surplus based on 
the share in the base year data 𝐼𝑂_𝐻𝐻𝑆ℎ𝑂𝑝2010: 

𝑌𝐷𝑂𝑝𝑆𝑢𝑟𝐻𝐻(𝑅) = ∑ (𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Depr") + 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "OpSur")) ∗
∗ 𝐼𝑂_𝐻𝐻𝑆ℎ𝑂𝑝2010(𝑅)

𝑆

(44) 

being 𝐼𝑂_𝐻𝐻𝑆ℎ𝑂𝑝2010 the share of operating surplus that goes to households in the base year. 

Finally, 𝑌𝐷𝑇𝑟𝑎𝑛 and 𝑌𝐷𝑂𝑡ℎ𝑒𝑟𝑇𝑟𝑎𝑛 are exogenous and set to be equal to their 2010 values.  

3.2.2 Consumption of durables 

Households  use  their  income  and  wealth  to  finance  consumption.  FIDELIO  features  a  rich 
consumption block. The equations that rule the household consumption are mostly specified using 
the  error  correction  model.16 Error  correction  specifications  are  chosen  so  to  acknowledge  the 
importance of past consumption in shaping actual and future consumption. The model distinguishes 
between consumption of durable and non-durable commodities. 

There  are  two  categories  of  durables  in  FIDELIO:  houses  and  vehicles.  Household  expenditures  in 
houses depend on previous housing consumption, cash on hand,  and the collaterals for household 
durables, according to the following equation:  

𝑙𝑛(𝐶𝑃𝑔𝑓𝑐𝑓_ℎ𝑜𝑢𝑠𝑖𝑛𝑔(𝑅)) = 𝑙𝑛(𝐶𝑃𝑔𝑓𝑐𝑓_ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡−1(𝑅)) +

+𝑐4

ℎ𝑜𝑢 [𝑙𝑛(𝐶𝑃𝑔𝑓𝑐𝑓_ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡−1(𝑅)) + 𝑐5

ℎ𝑜𝑢 𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻𝑡−1(𝑅)) + 𝑐6

+𝑐2

ℎ𝑜𝑢[𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻(𝑅)) − 𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻𝑡−1(𝑅))] + 𝑐3

ℎ𝑜𝑢[θ(𝑅) − θ𝑡−1(𝑅)] +
ℎ𝑜𝑢 𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻𝑡−1(𝑅))𝑙𝑛 ( 𝐾𝐻𝑜𝑢𝑠𝑡−2(𝑅)

𝑁𝑢𝑚𝑏𝑒𝑟𝐻𝐻(𝑅)

) + 𝑐7

ℎ𝑜𝑢θ𝑡−1(𝑅)]

 (45) 

where  an  explanatory  variable  in  the  error  correction  term  is  the  stock  of  housing  per  household, 
being 𝑁𝑢𝑚𝑏𝑒𝑟𝐻𝐻 the number of households. The parameter θ stands for the part of investment in 
durables  that  cannot  be  financed  via  debt,  allowing  for  the  analysis  of  the  effects  of  credit 
constraints.  The  c  parameters  are  not  country-specific  and  come  from  panel  estimates.17 Their 
ℎ𝑜𝑢 = 0.04, 
ℎ𝑜𝑢 = −0.35, 𝑐4
values  are  the  following: 𝑐2
and 𝑐7

ℎ𝑜𝑢 = −0.18, 𝑐5

ℎ𝑜𝑢 = −1.42, 𝑐6

ℎ𝑜𝑢 = 0.90, 𝑐3

ℎ𝑜𝑢 = 0.12.  

The equation for expenditure in vehicles is the following:  

𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑉𝑒ℎ")) = 𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅, "𝑉𝑒ℎ")) +

+𝑐2

𝑣𝑒ℎ[𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻(𝑅)) − 𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻𝑡−1(𝑅))] + 𝑐3

𝑣𝑒ℎ[θ(𝑅) − θ𝑡−1(𝑅)] +

  (46) 

+𝑐4

𝑣𝑒ℎ[𝑙𝑛(𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑉𝑒ℎ")) − 𝑙𝑛(𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅, "𝑉𝑒ℎ"))] + 𝑐5

𝑣𝑒ℎ[𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅, "𝑉𝑒ℎ")) + 𝑐6

𝑣𝑒ℎ 𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻𝑡−1(𝑅))

+𝑐7

ℎ𝑜𝑢 𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻𝑡−1(𝑅))𝑙𝑛 ( 𝐾𝑉𝑒ℎ𝑡−2(𝑅)

𝑁𝑢𝑚𝑏𝑒𝑟𝐻𝐻(𝑅)

) + 𝑐8

ℎ𝑜𝑢θ𝑡−1(𝑅) + 𝑐9

ℎ𝑜𝑢 𝑙𝑛(𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅, "𝑉𝑒ℎ"))]

where 𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑉𝑒ℎ") is the price of vehicles. In this case, the parameters assume the following 
𝑣𝑒ℎ = −0.36 , 
𝑣𝑒ℎ = 0.43 , 𝑐3
values  (estimated  using  panel  data):  𝑐2
𝑣𝑒ℎ = 0.02, 𝑐8
𝑣𝑒ℎ = −0.81, 𝑐7
𝑐6

𝑣𝑒ℎ = 0.02 and 𝑐9

𝑣𝑒ℎ = 0.02 ,  𝑐4

𝑣𝑒ℎ = 0.91 , 𝑐5

𝑣𝑒ℎ = −0.86.  

16 The most part of the values of the parameters in the following equation have been estimated using panel 
estimates. 
17 Most coefficients governing household consumption are econometrically estimated. See Annex 9 for a list of 
the coefficients that have been estimated. 

14 

 
 
 
 
 
 
                                                           
And now for the rest of the equations of the household block. 

The stocks of houses and vehicles change according to the following relationships: 

𝐾𝐻𝑜𝑢𝑠(𝑅) = (1 − 𝛿ℎ𝑜𝑢𝑠) × 𝐾𝐻𝑜𝑢𝑠𝑡−1(𝑅) + 𝐶𝑃𝑔𝑓𝑐𝑓_ℎ𝑜𝑢𝑠𝑖𝑛𝑔(𝑅) 

𝐾𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑠(𝑅) = (1 − 𝛿𝑣𝑒ℎ𝑖𝑐𝑙𝑒𝑠) × 𝐾𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑠𝑡−1(𝑅) + 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑉𝑒ℎ") 

(47) 

(48) 

The  actual  durable  consumption  related  to  houses  takes  the  form  of  rents  (corresponding  in  the 
base year data to the sum of imputed rents, actual rents, expenditures for the maintenance of the 
dwelling, and water expenditure) which are derived from the housing stock: 

𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑅𝑒𝑛𝑡𝑠") = 𝐾𝐻𝑜𝑢𝑠𝑡−1(𝑅) × 𝑅𝑒𝑛𝑡_𝐻𝑜𝑢𝑠𝑒𝑠2010(𝑅) 

(49) 

where 𝑅𝑒𝑛𝑡_𝐻𝑜𝑢𝑠𝑒𝑠2010 is the ratio of rents over housing stock in the base year.  

Total consumption of durables is then calculated as follows: 

𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑇𝑜𝑡𝐷𝑢𝑟") = 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑅𝑒𝑛𝑡𝑠") + 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑉𝑒ℎ") 

(50) 

3.2.3 Consumption of non-durables 

Total consumption of non-durables, 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑁𝑜𝑛𝐷𝑢𝑟"), is derived as follows: 

𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑁𝑜𝑛𝐷𝑢𝑟")) = 𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅, "𝑁𝑜𝑛𝐷𝑢𝑟")) +

+𝑐2

𝑛𝑜𝑛𝑑[𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻(𝑅)) − 𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻𝑡−1(𝑅))] + 𝑐3

𝑛𝑜𝑛𝑑[𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅, "𝑁𝑜𝑛𝐷𝑢𝑟")) +

(51) 

+𝑐4

𝑛𝑜𝑛𝑑 𝑙𝑛(𝐶𝑎𝑠ℎ𝐻𝐻𝑡−1(𝑅)) + 𝑐5

𝑛𝑜𝑛𝑑 × θ𝑡−1(𝑅) × 𝑙𝑛(𝐶𝑃𝑔𝑓𝑐𝑓_ℎ𝑜𝑢𝑠𝑖𝑛𝑔𝑡−1(𝑅) + 𝐶𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅, "𝑉𝑒ℎ"))]

In  this  case,  the  parameters  assume  the  following  values  (estimated  using  panel  data): 𝑐2
0.23, 𝑐3
non-durable and durable consumption.  

𝑛𝑜𝑛𝑑 =
𝑛𝑜𝑛𝑑 = 0.01.  Total  consumption  is  simply  the  sum  of 

𝑛𝑜𝑛𝑑 = −0.82 and 𝑐5

𝑛𝑜𝑛𝑑 = −0.14, 𝑐4

Let us now lay out the equations related to the consumption of non-durable commodities. First of 
all,  appliances  are  treated  as  such  even  though  a  stock  of  appliances  also  exists  (𝐾𝐴𝑝𝑝𝑙)  which 
depreciates at the rate of 𝛿𝑎𝑝𝑝𝑙 = 0.07. The  consumption  of appliances  is treated differently from 
that of housing and vehicles for the impossibility to finance their purchases with debt. It depends on 
previous stock of appliances and on current appliances consumption 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐴𝑝𝑝𝑙"). 

𝐾𝐴𝑝𝑝𝑙(𝑅) = 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐴𝑝𝑝𝑙") + (1 − 𝛿𝑎𝑝𝑝𝑙) × 𝐾𝐴𝑝𝑝𝑙𝑡−1(𝑅) 

(52) 

The consumption of appliances works as follows: 

𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐴𝑝𝑝𝑙")) = 𝑐2

𝑎𝑝𝑝𝑙 × 𝑙𝑛(𝑃𝐴𝑝𝑝𝑙(𝑅)) + 𝑐3

𝑎𝑝𝑝𝑙 × 𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑁𝑜𝑛𝐷𝑢𝑟")) 

(53) 

where 𝑃𝐴𝑝𝑝𝑙 is  the  price  of  appliances,   𝑐2
data).  

𝑎𝑝𝑝𝑙 = 0.54,  and 𝑐3

𝑎𝑝𝑝𝑙 = 0.68 (estimated  using  panel 

As for the rest of non-durable goods and services, let us differentiate between and energy block and 
a non-energy one. The former includes consumption of electricity, fuel for private transport, heating 

15 

 
 
 
 
 
 
 
 
 
 
fuel, and public transportation services. The relevant equations for electricity consumption and for 
fuel consumption are as follows. 

+𝑐2

𝑒𝑙 × 𝑙𝑛(𝑃𝐸𝑙𝑒𝑐(𝑅) × 𝐸𝑓𝑓_𝐴𝑝𝑝𝑙(𝑅)) + 𝑐3

𝑒𝑙 × 𝑙𝑛 (

𝐶𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅,"𝐸𝑙𝑒𝑐")
𝐾𝐴𝑝𝑝𝑙𝑡−1(𝑅)

) + 𝑐4

𝑒𝑙 × 𝑙𝑛(𝐻𝑒𝑎𝑡𝐷𝐷𝑎𝑦2010(𝑅))

𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐸𝑙𝑒𝑐")) = 𝑙𝑛(𝐾𝐴𝑝𝑝𝑙 (𝑅)) +

𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐹𝑢𝑒𝑙")) = 𝑙𝑛(𝐾𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑠(𝑅)) +

+𝑐2

𝑓𝑢𝑒𝑙 × 𝑙𝑛(𝑃𝐹𝑢𝑒𝑙(𝑅) × 𝐸𝑓𝑓_𝑉𝑒ℎ(𝑅)) + 𝑐3

𝑓𝑢𝑒𝑙 × 𝑙𝑛 (

𝐶𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅,"𝑉𝑒ℎ")
𝐾𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑠𝑡−1(𝑅)

) + 𝑐4

𝑓𝑢𝑒𝑙 × 𝑙𝑛(𝑉𝑒ℎ𝑃𝑜𝑝2010(𝑅))

(54) 

(55) 

Where 𝑃𝐸𝑙𝑒𝑐 is the electricity price, 𝑃𝐹𝑢𝑒𝑙 the price of fuel; 𝐸𝑓𝑓_𝐴𝑝𝑝𝑙 and 𝐸𝑓𝑓_𝑉𝑒ℎ are exogenous 
indices  capturing  the  efficiency  of  appliances  and  vehicles,  respectively; 𝐻𝑒𝑎𝑡𝐷𝐷𝑎𝑦2010 stands  for 
heating degree days, a measurement designed to quantify the demand for energy needed to heat a 
𝑒𝑙 = 0.21, 
building;   𝑉𝑒ℎ𝑃𝑜𝑝2010 is  the  exogenous  number  of  vehicles  divided  by  population18; 𝑐2
𝑓𝑢𝑒𝑙 = −0.47  (estimated  using  panel 
𝑒𝑙 = 0.59 ,  𝑐4
𝑐3
data). 

𝑓𝑢𝑒𝑙 = 0.69 ,  and  𝑐4

𝑓𝑢𝑒𝑙 = 0.38 ,  𝑐3

𝑒𝑙 = 0.13 ,  𝑐2

Heating consumption and is defined as follows: 

𝑙𝑛(𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐻𝑒𝑎𝑡")) = 𝑙𝑛(𝐾𝐻𝑜𝑢𝑠(𝑅)) +

+𝑐2

ℎ𝑒𝑎𝑡 × 𝑙𝑛(𝑃𝐻𝑒𝑎𝑡(𝑅) × 𝐸𝑓𝑓_𝐻𝑒𝑎𝑡(𝑅)) + 𝑐3

ℎ𝑒𝑎𝑡 × 𝑙𝑛 (

𝐶𝑃𝐶𝑜𝑚𝑚𝑡−1(𝑅,"𝐻𝑒𝑎𝑡")
𝐾𝐻𝑜𝑢𝑠𝑡−1(𝑅)

) + 𝑐4

ℎ𝑒𝑎𝑡 × 𝑙𝑛(𝐻𝑒𝑎𝑡𝐷𝐷𝑎𝑦2010(𝑅))

(56) 

where 𝐸𝑓𝑓_𝐻𝑒𝑎𝑡 is  an  index  capturing  the  efficiency  of  heating,   𝑃𝐻𝑒𝑎𝑡 is  the  price  of  heating,  
ℎ𝑒𝑎𝑡 = 0.10, 𝑐3
𝑐2

ℎ𝑒𝑎𝑡 = 0.84, and 𝑐4

ℎ𝑒𝑎𝑡 = 0.46. 

Finally, the consumption of public transportation services is a fixed share of fuel consumption based 
on its share in 2010:  

𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑃𝑢𝑏𝑇𝑟𝑎𝑛") = 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐹𝑢𝑒𝑙") ×

𝐶𝑃𝐶𝑜𝑚𝑚2010(𝑅,"𝑃𝑢𝑏𝑇𝑟𝑎𝑛")
𝐶𝑃𝐶𝑜𝑚𝑚2010(𝑅,"𝐹𝑢𝑒𝑙")

(57) 

transportation 

Total  expenditure  on 
sum  of 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑃𝑢𝑏𝑇𝑟𝑎𝑛")  and  𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐹𝑢𝑒𝑙") .  Total  expenditure  on  energy  services, 
the  sum  of  𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑇𝑟𝑎𝑛") ,  𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐻𝑒𝑎𝑡")  and 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐸𝑛𝑒𝑟𝑔𝑦") , 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐸𝑙𝑒𝑐"). 

services,  𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑇𝑟𝑎𝑛") , 

the 

is 

is 

The set of non-durables consumption is completed by eight categories which work in FIDELIO within 
a  QAIDS.  The  categories  are  the  following:  food,  clothing,  furniture  and  equipment,  health, 
communication, recreation and accommodation, financial services, and other. Total consumption of 
these categories is the following: 

𝐶𝑃𝑄𝐴𝐼𝐷𝑆(𝑅) = 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑁𝑜𝑛𝐷𝑢𝑟") − 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐸𝑛𝑒𝑟𝑔𝑦") − 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐴𝑝𝑝𝑙") 

(58) 

First, the shares of the eight commodities are found as follows: 

18 Population data are taken from the UN projections, medium variant. Eurostat provides data for the number 
of vehicles for most of the European countries treated in FIDELIO. The average number of vehicles calculated 
with  these  data  is  used  to  fill  for  the  countries  for  which  no  data  are  available,  assuming  that  the  average 
number  of  vehicles is low for Brazil, China, and India, and high  for Denmark,  Japan and the USA, and in the 
middle for Russia. See Section 4 for more details on the data. 

16 

 
 
 
 
 
 
 
 
 
 
                                                           
𝑄𝐴𝐼𝐷𝑆𝑆ℎ𝑎𝑟𝑒(𝑅, 𝑄𝐶) = 𝑐1

𝑎𝑖𝑑𝑠(𝑅, 𝑄𝐶) × 𝑙𝑛 (

𝑃𝐶𝑜𝑚𝑚(𝑅,𝑄𝐶)
𝑃𝐶𝑃(𝑅)
𝑎𝑖𝑑𝑠(𝑅, 𝑄𝐶, 𝑄𝐶) × 𝑙𝑛(𝑃𝐶𝑜𝑚𝑚(𝑅, 𝑄𝐶))

𝑄𝐶
+ ∑ 𝑐𝑄𝐶

) +

(59) 

where 𝑃𝐶𝑜𝑚𝑚(𝑅, 𝑄𝐶) is the price of the QAIDS products, and 𝑃𝐶𝑃 is the consumer price index. 

The values of the estimated 𝑐1
are country-specific, and those related to Austria are shown in Table 3 as an example.  

𝑎𝑖𝑑𝑠 parameters of equation (59) for the eight commodities 

𝑎𝑖𝑑𝑠 and 𝑐𝑄𝐶

Table 3  Values of the caids parameters for Austria 

food 
cloth 
furn 
health 
comm 
recr 
fin 
other 

c1 
-0.098 
0.027 
0.038 
0.009 
-0.014 
0.054 
0.000 
-0.016 

food 
0.281 
0.024 
0.050 
0.009 
0.010 
0.010 
0.053 
-0.437 

cloth 

furn 

health 

comm 

recr 

fin 

other 

0.045 
0.007 
-0.002 
0.002 
0.050 
0.012 
-0.138 

0.002 
0.002 
0.021 
0.027 
0.010 
-0.119 

0.011 
0.001 
0.044 
0.005 
-0.070 

0.007 
0.127 
-0.005 
-0.163 

0.139 
0.014 
-0.409 

0.012 
-0.100 

1.437 

Then, the consumption in absolute value is derived by multiplying those shares for CPQAIDS: 

𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, 𝑄𝐶) = 𝐶𝑃𝑄𝐴𝐼𝐷𝑆(𝑅) × 𝑄𝑈𝐴𝐼𝐷𝑆𝑆ℎ𝑎𝑟𝑒(𝑅, 𝑄𝐶) 

(60) 

The only thing needed to get to total private consumption 𝐺_𝑃𝑃(𝑅, 𝐺, "𝐶𝑃") by region and by good 
is  now  a  matrix  bridging  the  consumption  categories  (see  the  CPC  set)  to  the  56  products  of  the 
NACE Rev. 2 classification. The bridge matrix 𝐶𝑃𝐵𝑟𝑖𝑑𝑔𝑒2010 is computed from CPC-NACE Rev. 2 data 
on household consumption for 2010, and is used in the following equation: 

𝐺_𝑃𝑃(𝑅, 𝐺, "𝐶𝑃") = ∑ (𝐶𝑃𝐵𝑟𝑖𝑑𝑔𝑒2010(𝑅, 𝐺, 𝐶𝑃𝐶) × 𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, 𝐶𝑃𝐶))

𝐶𝑃𝐶

(61) 

3.2.4 Non-profit institutions serving households 

The user NPISH is treated as exogenous in FIDELIO, and set according to the base year values of the 
relevant VA variables: 

𝑁𝑃𝐼𝑆𝐻(𝑅) = ∑ 𝑉𝐴(𝑅, 𝑆)

𝑆

×

Where 𝐼𝑂_𝑁𝑃𝐼𝑆𝐻2010 is NPISH consumption in 2010. 

𝐺

∑ 𝐼𝑂_𝑁𝑃𝐼𝑆𝐻2010(𝑅,𝐺)
∑ 𝑉𝐴2010(𝑅,𝑆)

𝑆

(62) 

The  WIOD  use  commodity  structure  of  2010 𝑈𝑠𝑒𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, "𝑁𝑃𝐼𝑆𝐻") is  used  to  derive  final 
demand by NPISH by region and good: 

𝐺_𝑃𝑃(𝑅, 𝐺, "𝑁𝑃𝐼𝑆𝐻") = 𝑁𝑃𝐼𝑆𝐻(𝑅) × 𝑈𝑠𝑒𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, "𝑁𝑃𝐼𝑆𝐻") 

(63) 

17 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
3.3 The government block 

Governmental total revenues are equal to the sum of operating surplus that goes to the government 
( 𝐺𝑜𝑣𝑂𝑝𝑆𝑢𝑟 ),  TlS  on  products  ( 𝐺𝑜𝑣𝑇𝑙𝑆 ),  production  taxes  ( 𝐺𝑜𝑣𝑃𝑟𝑜𝑑𝑇𝑎𝑥 ),  social  security 
contributions by both employers (𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑟) and employees (𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒), and taxes on 
household  income  (𝑌𝐷𝑇𝑎𝑥𝑒𝑠𝐻𝐻).  Governmental  total  revenues  are  therefore  equal  to  the 
following: 

𝐺𝑜𝑣𝑇𝑜𝑡𝑅𝑒𝑣(𝑅) = 𝐺𝑜𝑣𝑂𝑝𝑆𝑢𝑟(𝑅) + 𝐺𝑜𝑣𝑇𝑙𝑆(𝑅) + 𝐺𝑜𝑣𝑃𝑟𝑜𝑑𝑇𝑎𝑥(𝑅) +
+𝑌𝐷𝑇𝑎𝑥𝑒𝑠𝐻𝐻(𝑅) + 𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑟(𝑅) + 𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒(𝑅)

(64) 

The operating surplus going to the government is computed as a fixed  share of the total operating 
surplus based on the share in the base year data 𝐼𝑂_𝐺𝑜𝑣𝑆ℎ𝑂𝑝2010: 

𝐺𝑜𝑣𝑂𝑝𝑆𝑢𝑟(𝑅) = ∑ [𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "OpSur") + 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Depr")]

𝑆

× 𝐼𝑂_𝐺𝑜𝑣𝑆ℎ𝑂𝑝2010(𝑅)  (65) 

The government revenue from TlS is the sum over all users and products of TlS: 

𝑎𝑈
𝐺𝑜𝑣𝑇𝑙𝑆(𝑅) = ∑ ∑ 𝑇𝑙𝑆(𝑅, 𝐺, 𝑎𝑈)

𝐺

where TlS are defined as: 

𝑇𝑙𝑆(𝑅, 𝐺, 𝑎𝑈) = 𝐺_𝑃𝑃(𝑅, 𝐺, 𝑎𝑈) ×

𝐼𝑂_𝐶𝑜𝑚𝑚𝑇𝑙𝑆2010(𝑅,𝐺,𝑎𝑈)
1+𝐼𝑂_𝐶𝑜𝑚𝑚𝑇𝑙𝑆2010(𝑅,𝐺,𝑎𝑈)

(66) 

(67) 

where 𝐼𝑂_𝐶𝑜𝑚𝑚𝑇𝑙𝑆2010   is the proportion of TlS over the  use value  in basic prices  plus trade and 
transport margins in the base year. 

Another government revenue is the sum of production taxes:  

𝐺𝑜𝑣𝑃𝑟𝑜𝑑𝑇𝑎𝑥(𝑅) = ∑ 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "𝑃𝑟𝑜𝑑𝑇𝑎𝑥")

𝑆

(68) 

where production taxes are defined as a share of output 

𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆,"ProdTax") = 𝑄(𝑅, 𝑆) × 𝐼𝑂_𝑃𝑟𝑜𝑑𝑇𝑎𝑥𝑄2010(𝑅, 𝑆)  

(69) 

being the share 𝐼𝑂_𝑃𝑟𝑜𝑑𝑇𝑎𝑥𝑄2010(𝑅, 𝑆) is the proportion of production taxes over output Q in the 
base year data.  

Social 
security  paid  by 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "𝑆𝑜𝑐𝑆𝑒𝑐"): 

firms 

is 

the 

sum  over 

industries  of 

the  VA  component 

𝑆
𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑟(𝑅) = ∑ 𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "𝑆𝑜𝑐𝑆𝑒𝑐")

(70) 

The remaining two revenue sources are defined above as for equations (42) and (43). 

Government  total  expenditure  is  the  sum  of  the  government  interest  ( 𝐺𝑜𝑣𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 ),  the 
government transfers to the households (𝑌𝐷𝑇𝑟𝑎𝑛), the other transfers from the government to the 
households  (𝑌𝐷𝑂𝑡ℎ𝑒𝑟𝑇𝑟𝑎𝑛),  the  government  capital  formation  (𝐺𝑜𝑣𝑔𝑓𝑐𝑓),  and  the  government 
consumption (𝐺𝑜𝑣𝐶𝑜𝑛𝑠): 

18 

 
 
 
 
 
  
 
  
 
  
 
 
  
𝐺𝑜𝑣𝑇𝑜𝑡𝐸𝑥𝑝(𝑅) = 𝐺𝑜𝑣𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡(𝑅) + 𝑌𝐷𝑇𝑟𝑎𝑛(𝑅) + 𝑌𝐷𝑂𝑡ℎ𝑒𝑟𝑇𝑟𝑎𝑛(𝑅) +
+𝐺𝑜𝑣𝑔𝑓𝑐𝑓(𝑅) + 𝐺𝑜𝑣𝐶𝑜𝑛𝑠(𝑅)

(71) 

The various expenditures are defined as follows. The interest paid by the government is equal to the 
government debt 𝐺𝑜𝑣𝐷𝑒𝑏𝑡 times the interest rate 𝐺𝑜𝑣𝐼𝑛𝑡𝑅𝑎𝑡𝑒2010: 

𝐺𝑜𝑣𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡(𝑅) = 𝐺𝑜𝑣𝐷𝑒𝑏𝑡(𝑅) × 𝐺𝑜𝑣𝐼𝑛𝑡𝑅𝑎𝑡𝑒2010(𝑅) 

(72) 

The  two  transfer  components  (𝑌𝐷𝑇𝑟𝑎𝑛 and 𝑌𝐷𝑂𝑡ℎ𝑒𝑟𝑇𝑟𝑎𝑛)  are  exogenously  fixed  to  be  equal  to 
their base year values. Then, public investment is as follows: 

𝐺𝑜𝑣𝑔𝑓𝑐𝑓(𝑅) = 𝐺𝑜𝑣𝐶𝑜𝑛𝑠(𝑅) × 𝐺𝑜𝑣𝑆ℎ𝑎𝑟𝑒𝑔𝑓𝑐𝑓2010(𝑅) 

(73) 

where 𝐺𝑜𝑣𝑆ℎ𝑎𝑟𝑒𝑔𝑓𝑐𝑓2010 is the proportion of public investment over public consumption as in the 
base  year  data.  Finally,  government  consumption  can  be  computed  as  a  constant  share  of  VA  as 
follows: 

𝐺𝑜𝑣𝐶𝑜𝑛𝑠(𝑅) = ∑ 𝑉𝐴(𝑅, 𝑆)

𝑆

× 𝐼𝑂_𝐺𝑜𝑣𝐶𝑜𝑛𝑠𝑉𝐴2010(𝑅) 

(74) 

where 𝐼𝑂_𝐺𝑜𝑣𝐶𝑜𝑛𝑠𝑉𝐴2010 is the proportion of government consumption over total VA in the base 
year  data.  Alternatively,  it  can  be  made  endogenous  and  evolving  depending  on  an  exogenously 
determined  budget  balance  path.  The  model  includes  a  third  way  to  compute  government 
consumption, fixing exogenously its growth rate.19 In any case, government consumption by region 
and good is then derived using the WIOD commodity structure of demand in PP for the base year: 

𝐺_𝑃𝑃(𝑅, 𝐺, "𝐶𝐺") = 𝐺𝑜𝑣𝐶𝑜𝑛𝑠(𝑅) × 𝑈𝑠𝑒𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, "𝐶𝐺") 

(75) 

The budget balance is calculated as the difference between government revenues (𝐺𝑜𝑣𝑇𝑜𝑡𝑅𝑒𝑣) and 
expenses (𝐺𝑜𝑣𝑇𝑜𝑡𝐸𝑥𝑝): 

𝐺𝑜𝑣𝐵𝑑𝑔𝑡(𝑅) = 𝐺𝑜𝑣𝑇𝑜𝑡𝑅𝑒𝑣(𝑅) − 𝐺𝑜𝑣𝑇𝑜𝑡𝐸𝑥𝑝(𝑅) 

The level of public debt 𝐺𝑜𝑣𝐷𝑒𝑏𝑡  is also calculated in FIDELIO as illustrated below. 

𝐺𝑜𝑣𝐷𝑒𝑏𝑡(𝑅) = 𝐺𝑜𝑣𝐷𝑒𝑏𝑡𝑡−1(𝑅) − 𝐺𝑜𝑣𝐵𝑑𝑔𝑡(𝑅) 

(76) 

(77) 

3.4 The trade block 

Demand for imports is modelled as a two-step procedure (see Figure 4). First, the share of imports in 
total demand in BP for each commodity is determined. Second, the trade matrix is used to distribute 
imports to the country of origin. 

The share of imports is equal to the following: 

𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝐺, 𝑎𝑈) =

𝐼𝑂_𝑀2010(𝑅,𝐺,𝑎𝑈)
𝐼𝑂_𝑈𝑠𝑒𝐵𝑃2010(𝑅,𝐺,𝑎𝑈)

× (

𝑃𝐺𝑑𝑜𝑚(𝑅,𝐺,𝑎𝑈
𝑃𝑀(𝑅,𝐺,𝑎𝑈)

𝜎𝐴𝑟𝑚(𝑅,𝐺)
)

(78) 

19 This is the default option in the current version of FIDELIO. 

19 

 
 
 
 
 
 
 
 
 
 
 
 
                                                           
Where 𝐼𝑂_𝑀2010 are the imports by commodity and user for the base year, 𝐼𝑂_𝑈𝑠𝑒𝐵𝑃2010 the total 
base year use, 𝑃𝐺𝑑𝑜𝑚 is the domestic commodity price, and 𝑃𝑀 the import price.  𝜎𝐴𝑟𝑚  is the first 
nest  Armington  elasticity  for  private  consumption  taken  from  the  GTAP  model,20 determining  the 
domestic vs imported step.  

To derive imports, demand in BP and the endogenous import shares are used: 

𝑀(𝑅, 𝐺, 𝑎𝑈) = 𝐺_𝐵𝑃(𝑅, 𝐺, 𝑎𝑈) × 𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝐺, 𝑎𝑈) 

(79) 

Total imports by region and good are simply summed over users: 𝑀𝑡𝑜𝑡(𝑅, 𝐺) = ∑ 𝑀(𝑅, 𝐺, 𝑎𝑈)

.   

𝑎𝑈

The trade shares matrix 𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠 is the second nest of the demand for imports, distributing the 
demand for imports to the various trading partners. The equation is the following: 

𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠(𝑅, 𝑊𝑅, 𝐺) = 𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠2010(𝑅, 𝑊𝑅, 𝐺) × 𝑃𝐺𝑃𝑎𝑟𝑡𝑛𝑒𝑟𝑠(𝑅, 𝑊𝑅, 𝐺)−2𝜎𝐴𝑟𝑚(𝑅,𝐺) 

(80) 

where 𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠2010  is the base year import share by trading partner, and 𝑃𝐺𝑃𝑎𝑟𝑡𝑛𝑒𝑟𝑠 is the 
price of the imported products by trading partner.  

Then, the matrix of trade flows expressed in free-on-board (FOB) prices and in Unites States dollars 
is computed. We distinguish between the goods and services for which trade and transport margins 
are  paid  (nTIR  commodities)  and  the  services  used  to  carry  out  international  trade  and  transport 
(TIRS  commodities).  The  part  of  the  trade  matrix  related  to  the  nTIR  commodities  is  calculated  as 
follows: 

𝑇𝑟𝑎𝑑𝑒𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅) =

𝑀𝑡𝑜𝑡(𝑅,𝑛𝑇𝐼𝑅)×𝑋𝑅𝑎𝑡𝑒2010(𝑅)×𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠(𝑅,𝑊𝑅,𝑛𝑇𝐼𝑅)
1+𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝐶𝑜𝑠𝑡2010(𝑅,𝑊𝑅,𝑛𝑇𝐼𝑅)

(81) 

where 𝑋𝑅𝑎𝑡𝑒2010 is the exogenous exchange rate (from WIOD data),  while 𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝐶𝑜𝑠𝑡2010 refers 
to the international trade and transport margins expressed as % over imports in FOB. The part of the 
trade matrix containing the services used in international transport is as follows: 

𝑇𝑟𝑎𝑑𝑒𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑇𝐼𝑅𝑆) = 𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠(𝑅, 𝑊𝑅, 𝑇𝐼𝑅𝑆) ×
× [𝑀𝑡𝑜𝑡(𝑅, 𝑇𝐼𝑅𝑆) × 𝑋𝑅𝑎𝑡𝑒2010(𝑅) + ∑ 𝑇𝐼𝑅𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑇𝐼𝑅𝑆)
]

𝑊𝑅

(82) 

The  matrix  of  international  trade  and  transport  margins 𝑇𝐼𝑅𝑀𝑎𝑡𝑟𝑖𝑥 (difference  between  trade 
matrix  in  CIF  viewed  from  the  importer  point  of  view  and  trade  matrix  in  FOB  viewed  from  the 
exporter point of view) is obtained as follows: 

𝑇𝐼𝑅𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅) = 𝑇𝑟𝑎𝑑𝑒𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅) × 𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝐶𝑜𝑠𝑡𝑠2010(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅) 

(83) 

𝑇𝐼𝑅𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑇𝐼𝑅𝑆) = ∑

𝑛𝑇𝐼𝑅

[𝑇𝐼𝑅𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅) × 𝑇𝐼𝑅𝑆ℎ𝑎𝑟𝑒𝑠2010(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅𝑆, 𝑇𝐼𝑅𝑆)]

  (84) 

where 𝑇𝐼𝑅𝑆ℎ𝑎𝑟𝑒𝑠2010 redistributes over the TIRS commodities the transport costs based on the base 
year data. 

These imports-related variables are used to derive exports according to the following equation: 

𝐺_𝑃𝑃(𝑅, 𝐺, "𝑋") =

𝑅1

∑ 𝑇𝑟𝑎𝑑𝑒𝑀𝑎𝑡𝑟𝑖𝑥(𝑅1,𝑅,𝐺)
𝑋𝑅𝑎𝑡𝑒(𝑅)

+ 𝑋𝑅𝑜𝑤2010(𝑅, 𝐺) 

(85) 

20 https://www.gtap.agecon.purdue.edu/ 

20 

 
 
 
 
 
 
 
 
 
 
                                                           
where 𝑋𝑅𝑜𝑤2010 contains all exports of the FIDELIO countries to those not explicitly modelled into it 
based on 2010 data. 

3.5 The relationship between BP and PP, and the calculation of GDP 

Demand in BP is derived from demand in PP by subtracting TlS and TTM as shown by equation (3). 
TlS are defined in equation (67); regarding TTM the relevant equations are the following: 

𝑇𝑇𝑀𝑝𝑎𝑖𝑑(𝑅, 𝐺, 𝑎𝑈) = [𝐺_𝑃𝑃(𝑅, 𝐺, 𝑎𝑈) − 𝑇𝑙𝑆(𝑅, 𝐺, 𝑎𝑈)] × 𝑀𝑟𝑔𝑃𝑎𝑖𝑑2010(𝑅, 𝐺, 𝑎𝑈) 

(86) 

where 𝑀𝑟𝑔𝑃𝑎𝑖𝑑2010 is  calculated  as  TTM  divided  by  Use  values  in  PP  minus  TlS  when  TTM  are 
positive. If negative, then: 

𝑇𝑇𝑀𝑟𝑒𝑐(𝑅, 𝐺, 𝑎𝑈) = ∑ 𝑇𝑇𝑀𝑝𝑎𝑖𝑑(𝑅, 𝐺, 𝑎𝑈)

𝐺

× 𝑀𝑟𝑔𝑅𝑒𝑐2010(𝑅, 𝐺, 𝑎𝑈) 

(87) 

where 𝑀𝑟𝑔𝑅𝑒𝑐2010 is equal to  the  share of TTM received over the  total TTM paid in the  base year. 
Now all the necessary elements are defined in order to derive domestic demand by region, good and 
user, equation (2), and total demand in BP, equation (3).  

The  gross  domestic  product  (GDP)  is  calculated  in  two  alternative  ways  (which  yield  the  same 
values), either from VA or from final demand minus imports: 

𝐺𝐷𝑃(𝑅) = ∑ 𝑉𝐴(𝑅, 𝑆)

𝑆

𝑎𝑈

𝐺

+ ∑ ∑ 𝑇𝑙𝑆(𝑅, 𝐺, 𝑎𝑈))

𝐺
𝐺𝐷𝑃(𝑅) = ∑ ∑ 𝐺_𝑃𝑃(𝑅, 𝐺, 𝑎𝐶)

𝑎𝐶

𝑎𝑈

𝐺

− ∑ ∑ 𝑀(𝑅, 𝐺, 𝑎𝑈))

(88) 

(89) 

3.6 The labour market  

We assume that the wage equation is specified as a Wage Setting (WS) curve with a unit indexation 
of wages 𝑃𝐿  on the consumer price index 𝑃𝐶𝑃 and the productivity computed as real output over 

employment 

𝑄𝑟𝑒𝑎𝑙
𝐸𝑚𝑝𝑙

: 

𝑙𝑛(𝑃𝐿(𝑅,S,LSca)) = 𝑙𝑛(𝑃𝐶𝑃𝑡−1(𝑅)) + 𝑙𝑛 (

𝑄𝑟𝑒𝑎𝑙𝑡−1(𝑅,𝑆)
𝐸𝑚𝑝𝑙𝑡−1(𝑅,𝑆)

) + 𝛼1

𝑃𝐿 × 𝑈𝑛𝑒𝑚𝑝𝑅𝑎𝑡𝑒𝑡−1(𝑅) 

(90) 

Where 

by default takes the value of 0.5. Although WS curve estimations differ across empirical 

studies, this value corresponds to the average estimation on OECD countries found in Tyrvaïnen 
(1995) and Van der Horst (2002). The unemployment rate (𝑈𝑛𝑒𝑚𝑝𝑅𝑎𝑡𝑒) is calculated as follows: 

𝑈𝑛𝑒𝑚𝑝𝑅𝑎𝑡𝑒(𝑅, 𝐿𝑆) =

𝐿𝑆𝑢𝑝𝑝𝑙𝑦(𝑅,𝐿𝑆)−∑ 𝐸𝑚𝑝𝑙(𝑅,𝑆,𝐿𝑆)

𝑆

𝐿𝑆𝑢𝑝𝑝𝑙𝑦(𝑅,𝐿𝑆)

Labour supply is exogenous and equal to the following:  

𝐿𝑆𝑢𝑝𝑝𝑙𝑦(𝑅, 𝐿𝑆) = 𝑃𝑜𝑝(𝑅) × 𝐿𝑆𝑢𝑝𝑝𝑙𝑦𝑅𝑎𝑡𝑒2010(𝑅, 𝐿𝑆) 

(91) 

(92) 

Where 𝑃𝑜𝑝 is the  total  population  by country,  and 𝐿𝑆𝑢𝑝𝑝𝑙𝑦𝑅𝑎𝑡𝑒2010 the participation  rate  by  skill 
level (from base year data). 

21 

1PL 
 
 
 
 
 
 
 
 
 
 
 
 
Employment can be found with the following equation: 

𝐸𝑚𝑝𝑙(𝑅, 𝑆, 𝐿𝑆𝑐𝑎) =

𝑆𝑘𝑖𝑙𝑙𝑆ℎ𝑎𝑟𝑒𝑠2010(𝑅,𝑆,𝐿𝑆𝑐𝑎)×[𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅,𝑆,"𝑤𝑎𝑔𝑒𝑠" )+𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅,𝑆,"𝑆𝑜𝑐𝑆𝑒𝑐")]
𝑃𝐿(𝑅,𝑆,𝐿𝑆𝑐𝑎)

(93) 

Where 𝑆𝑘𝑖𝑙𝑙𝑆ℎ𝑎𝑟𝑒𝑠2010 are the shares of skill groups. 

And total employment is simply equal to: 𝐸𝑚𝑝𝑙(𝑅, 𝑆, "𝑎𝑙𝑙") = ∑

𝐿𝑆𝑐𝑎

𝐸𝑚𝑝𝑙(𝑅, 𝑆, 𝐿𝑆𝑐𝑎)
. 

3.7 The energy block 

The  real  value  of  the  energy  factors  calculated  in  the  production  block  is  linked  to  energy 
consumption in tera-joules (TJ) via fixed coefficients according to the following equation: 

𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽(𝑅, 𝑆) = 𝐼𝑂_𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽2010(𝑅, 𝑆) ×

𝐸𝑛𝑒𝑟𝑔𝑦(𝑅,𝑆)
𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅,𝑆,"𝐸")

(94) 

where 𝐼𝑂_𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽2010 is  the  inverse  of  the  average  price  of  energy,  computed  as  the  sectoral 
demand of energy in TJ over the sectoral demand of energy in values. 

Then, a variable called InputFuel is created in order to distribute the energy consumption across the 
eleven energy carriers (see the EnCd set) featured in FIDELIO: 

𝐼𝑛𝑝𝑢𝑡𝐹𝑢𝑒𝑙(𝑅, 𝑆, 𝐸𝑛𝐶𝑑) = 𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽(𝑅, 𝑆) ×
∑ [𝑅𝑒𝑎𝑙𝐸𝑛𝑆ℎ𝑎𝑟𝑒𝑠(𝑅, 𝑆, 𝐸𝑛𝐶) × 𝐵𝑟𝑖𝑑𝑔𝑒_𝐸𝑛𝐶𝑑2010(𝑅, 𝑆, 𝐸𝑛𝐶, 𝐸𝑛𝐶𝑑)]

𝐸𝑛𝐶

(95) 

where 𝐵𝑟𝑖𝑑𝑔𝑒_𝐸𝑛𝐶𝑑2010 is  a  fixed  bridge  matrix  whose  first  eleven  entries  for  four  Austrian 
industries are shown in Table 4 below. 

The exogenous energy shares used in equation (95) 𝑅𝑒𝑎𝑙𝐸𝑛𝑆ℎ𝑎𝑟𝑒𝑠 are calculated outside the model 
with all exogenous parameters using a translog framework taking into account the exogenous prices 
of  the  five  EnC  energy  carriers  and  a  number of  parameters  estimated econometrically.  The  same 
data are also used to calculate the exogenous price of the energy input 𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐸") used in 
equation (94).  

Table 4  First eleven entries of the EnC-EnCd bridge matrix 

R 

EnC 

EnCd 

Diesel 
AUT  Oil 
Gasoline 
AUT  Oil 
Jetfuel 
AUT  Oil 
Fueloil 
AUT  Oil 
Othgas 
AUT  Gas 
Liquid 
AUT  Gas 
Natgas 
AUT  Gas 
Coal 
Coal 
AUT 
ElHeat 
AUT 
Electr 
Renewables  Waste 
AUT 
Renewables 
AUT 

Renewables 

A01 
0.96 
0.00 
0.00 
0.04 
0.00 
0.53 
0.47 
1.00 
1.00 
0.00 
1.00 

A03 
0.00 
0.00 
0.00 
0.00 
0.00 
0.98 
0.02 
0.00 
0.00 
0.00 
0.00 

B 
0.92 
0.00 
0.00 
0.08 
0.00 
0.00 
1.00 
1.00 
1.00 
0.00 
1.00 

A02 
0.00 
0.00 
0.00 
0.00 
0.00 
1.00 
0.00 
0.00 
0.00 
0.00 
1.00 

22 

 
 
 
 
 
 
 
 
 
Carbon  dioxide  (CO2)  emissions  related  to  production  are  calculated  using  the 𝐼𝑛𝑝𝑢𝑡𝐹𝑢𝑒𝑙 variable 
and a set of fixed coefficients 𝐼𝑂𝐸𝑚_𝐶𝑂22010 calculated using Eurostat emissions data according to 
the following equation: 

𝐸𝑚_𝐶𝑂2(𝑅, 𝑆, 𝐸𝑛𝐶𝑑) = 𝐼𝑂𝐸𝑚_𝐶𝑂22010(𝑅, 𝑆, 𝐸𝑛𝐶𝑑) × 𝐼𝑛𝑝𝑢𝑡𝐹𝑢𝑒𝑙(𝑅, 𝑆, 𝐸𝑛𝐶𝑑) 

(96) 

Emissions of methane (CH4) and nitrous oxide (N2O) related to production are modelled in a simpler 
way, using output coefficients calculated with the base year data for emissions and output directly 
within the model: 

𝐸𝑚_𝐶𝐻4(𝑅, 𝑆) = 𝐼𝑂𝐸𝑚_𝐶𝐻42010(𝑅, 𝑆) ×

𝐸𝑚_𝑁2𝑂(𝑅, 𝑆) = 𝐼𝑂𝐸𝑚_𝑁2𝑂2010(𝑅, 𝑆) ×

𝑄(𝑅,𝑆)
𝑃𝑄(𝑅,𝑆)

𝑄(𝑅,𝑆)
𝑃𝑄(𝑅,𝑆)

(97) 

(98) 

Where 𝐼𝑂𝐸𝑚_𝐶𝐻42010 and 𝐼𝑂𝐸𝑚_𝑁2𝑂2010 are  respectively  the  fixed  emissions  coefficient  over 
output for CH4 and N2O for the base year data. 

CO2 emissions directly related to household consumption are also modelled in FIDELIO. Similarly to 
production-related  emissions,  household  energy  consumption  in  TJ  is  firstly  calculated  in  the 
following way:  

𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽𝐻𝐻(𝑅, 𝐶𝑃𝐸𝑛) = 𝐼𝑂_𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽𝐻𝐻2010(𝑅, 𝐶𝑃𝐸𝑛) ×

𝐶𝑃𝐶𝑜𝑚𝑚(𝑅,𝐶𝑃𝐸𝑛)
𝑃𝐶𝑃𝐸𝑛𝑒𝑟𝑔𝑦(𝑅,𝐶𝑃𝐸𝑛)

(99) 

𝑃𝐶𝑃𝐸𝑛𝑒𝑟𝑔𝑦(𝑅, 𝐶𝑃𝐸𝑛) is  the  price  of  energy  consumed  by  households  and  it  is  an  exogenous 
variable.  The  fixed  factor  relating  consumption  of  energy  goods  and  consumption  of  energy  in  TJ 
𝐼𝑂_𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽𝐻𝐻2010  (the inverse of the price of energy) is calculated using the base year data for 
those variables. The factors for the first eight countries of such matrix are shown in Table 5 below.  

Table 5  First eight entries of the IO_EnergyTJHH matrix 

R 
AUT 
BEL 
BGR 
BRA 
CHN 
CYP 
CZE 
DEN 

Heating 
42.85 
41.06 
42.80 
3.16 
0.22 
32.20 
1.71 
3.76 

Electricity 
42.85 
41.06 
42.80 
3.16 
0.22 
32.20 
1.71 
3.76 

Fuel 
10.61 
13.90 
9.83 
1.42 
0.06 
21.98 
1.26 
1.50 

CO2 emissions are then calculated thanks to one bridge matrix from consumption of energy goods to 
to  CO2  emissions  coefficients 
detailed  energy  carriers 
(𝐼𝑂𝐸𝑚_𝐶𝑂2𝐻𝐻2010)  computed  from  2010  emissions  data  by  detailed energy  carrier.  This  leads  to 
CO2 household emissions by region and by detailed energy carrier: 

( 𝐵𝑟𝑖𝑑𝑔𝑒_𝐸𝑛𝐶𝑑𝐻𝐻2010 )  and 

𝐶𝑃𝐸𝑛

= ∑

[𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽𝐻𝐻(𝑅, 𝐶𝑃𝐸𝑛) × 𝐵𝑟𝑖𝑑𝑔𝑒_𝐸𝑛𝐶𝑑𝐻𝐻2010(𝑅, 𝐶𝑃𝐸𝑛, 𝐸𝑛𝐶𝑑) × 𝐼𝑂𝐸𝑚_𝐶𝑂2𝐻𝐻2010(𝑅, 𝐸𝑛𝐶𝑑)]

𝐸𝑚_𝐶𝑂2𝐻𝐻(𝑅, 𝐸𝑛𝐶𝑑) =

(100) 

The Austrian numbers of the 𝐵𝑟𝑖𝑑𝑔𝑒_𝐸𝑛𝐶𝑑𝐻𝐻2010 matrix are contained in Table 6 below. 

23 

 
 
 
 
 
 
  
 
 
 
 
Table 6  Austrian bridge matrix between CPEn and the detailed energy carriers 

Heating 
0.000 
0.000 
0.000 
0.000 
0.000 
0.009 
0.185 
0.042 
0.361 
0.213 
0.189 

Fuel 
0.633 
0.367 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 

Electricity 
0.000 
0.000 
0.000 
0.000 
0.000 
0.009 
0.185 
0.042 
0.361 
0.213 
0.189 

Diesel 
Gasoline 
Jetfuel 
Othgas 
Waste 
Coal_coke_crude 
Fuel_oil 
Liquid_gaseous_biofuels 
Electr_heatprod 
Renewables_nuclear 
Natgas_lpg_othpetro 

3.8 The pricing system 

Almost all prices ultimately derive from the output prices 𝑃𝑄(𝑅, 𝑆). Also, all prices are normalized to 
unit value for the base year.  

 In  accordance  with  the  production  block,  the  price  of  output  is  based  on  the  CES  production 
structure: 

𝑃𝑄(𝑅, 𝑆) =   𝛼𝐾𝐿𝐸(𝑅, 𝑆) ×   (𝑃_𝐾𝐿𝐸(𝑅, 𝑆) )1−𝜎𝐾𝐿𝐸_𝑀(𝑅,𝑆) +
𝛼𝑀(𝑅, 𝑆) ×   (𝑃_𝑆𝑀(𝑅, 𝑆))1−𝜎𝐾𝐿𝐸_𝑀(𝑅,𝑆)

(101) 

The price of the combined capital, energy, and labour inputs (𝑃_𝐾𝐿𝐸) is defined as: 

𝑃_𝐾𝐿𝐸(𝑅, 𝑆) =   [𝛼𝐶(𝑅, 𝑆) ×   (

1−𝜎𝐾𝐿𝐸(𝑅,𝑆)
𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅,𝑆,"𝐶𝑎𝑝𝑖𝑡𝑎𝑙")
)

𝑓𝑝𝑟𝑜𝑑(𝑅,𝑆,"𝐶𝑎𝑝𝑖𝑡𝑎𝑙")

+

+𝛼𝐿(𝑅, 𝑆) ×   (

𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅,𝑆,"𝐿")

𝑓𝑝𝑟𝑜𝑑(𝑅,𝑆,"𝐿")

1−𝜎𝐾𝐿𝐸(𝑅,𝑆)
)

+ 𝛼𝐸(𝑅, 𝑆) ×   (

1−𝜎𝐾𝐿𝐸(𝑅,𝑆)
𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅,𝑆,"𝐸")
)

𝑓𝑝𝑟𝑜𝑑(𝑅,𝑆,"𝐸")

]

1
1−𝜎𝐾𝐿𝐸(𝑅,𝑆)

(102) 

While the price of combined imported and domestic materials (𝑃_𝑆𝑀) is: 

𝑃_𝑆𝑀(𝑅, 𝑆) = ∑

𝑛𝑒𝐺

𝑃𝑀(𝑅, 𝑛𝑒𝐺, 𝑆) × 𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝑛𝑒𝐺, 𝑆) ×

𝑛𝑒𝐺

+ ∑

𝑃𝐺𝑑𝑜𝑚(𝑅, 𝑛𝑒𝐺, 𝑆) × (1 − 𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝑛𝑒𝐺, 𝑆)) ×

𝐼𝑂_𝑈𝑆𝐸𝑃𝑃2010(𝑅,𝑛𝑒𝐺,𝑆)
𝑛𝑒𝐺

𝐼𝑂_𝑈𝑆𝐸𝑃𝑃2010(𝑅,𝑛𝑒𝐺,𝑆)

∑

𝐼𝑂_𝑈𝑆𝐸𝑃𝑃2010(𝑅,𝑛𝑒𝐺,𝑆)
𝑛𝑒𝐺

𝐼𝑂_𝑈𝑆𝐸𝑃𝑃2010(𝑅,𝑛𝑒𝐺,𝑆)

∑

+

(103) 

The price of domestic commodities is the weighted average of output prices, the weights being the 
industries' market shares: 

𝑃𝐺(𝑅, 𝐺) = ∑ 𝑃𝑄(𝑅, 𝑆) × 𝑀𝑘𝑡𝑆ℎ𝑎𝑟𝑒𝑠2010

𝑚𝑎𝑘𝑒(𝑅, 𝐺, 𝑆)

𝑆

The domestic price including margins and TlS is the following: 

𝑃𝐺𝑑𝑜𝑚(𝑅, 𝐺, 𝑎𝑈) = 𝑃𝐺(𝑅, 𝐺) × 𝐵𝑃𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑎𝑈) +
+𝑃𝑇𝑇𝑀(𝑅, 𝑎𝑈) × 𝑇𝑇𝑀𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑎𝑈)

(104) 

(105) 

where𝐵𝑃𝑆𝑡𝑟𝑢𝑐𝑡2010 and 𝑇𝑇𝑀𝑆𝑡𝑟𝑢𝑐𝑡2010 are the proportion of BP and TTM, respectively, calculated 
on the base year data. As for 𝑃𝑇𝑇𝑀, it is the price of TTM, and its equation is the following: 

24 

 
 
 
 
 
 
 
 
 
 
 
 
 
𝑃𝑇𝑇𝑀(𝑅, 𝑎𝑈) = ∑ 𝑇𝑇𝑀𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑎𝑈) × 𝑃𝐺(𝑅, 𝐺)

𝐺

(106) 

The  import  price  for  pairs  of  trading  partners  including  transit  costs  is  defined  by  the  following 
equation:  

𝑃𝐺𝑃𝑎𝑡𝑛𝑒𝑟𝑠(𝑅, 𝑅1, 𝐺) = 𝑃𝐺𝑑𝑜𝑚(𝑅1, 𝐺, "𝑋") 

As for the prices of the rest of the world, we assume that: 

𝑃𝐺𝑃𝑎𝑡𝑛𝑒𝑟𝑠(𝑅, "𝑅𝑂𝑊", 𝐺) =

𝑃𝐺𝑑𝑜𝑚("𝐵𝑅𝐴",𝐺,"𝑋")+𝑃𝐺𝑑𝑜𝑚("𝐼𝑁𝐷",𝐺,"𝑋")
2

Import prices at the border (CIF) are as follows: 

(107) 

(108) 

𝑃𝑀𝑐𝑖𝑓(𝑅, 𝐺) = ∑ [𝑃𝐺𝑃𝑎𝑟𝑡𝑛𝑒𝑟𝑠(𝑅, 𝑊𝑅, 𝐺) × 𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠(𝑅, 𝑊𝑅, 𝐺)]

𝑊𝑅

(109) 

Import prices in PP (including TlS and TTM) are as follows: 

𝑃𝑀(𝑅, 𝐺, 𝑎𝑈) = 𝑃𝑀𝑐𝑖𝑓(𝑅, 𝐺) × 𝐵𝑃𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑎𝑈) +
+𝑃𝑇𝑇𝑀(𝑅, 𝑎𝑈) × 𝑇𝑇𝑀𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑎𝑈)

The price of commodities is a weighted average of domestic and import prices: 

𝑃𝑈𝑠𝑒(𝑅, 𝐺, 𝑎𝑈) = 𝑃𝑀(𝑅, 𝐺, 𝑎𝑈) × 𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝐺, 𝑎𝑈) +
+𝑃𝐺𝑑𝑜𝑚(𝑅, 𝐺, 𝑎𝑈) × [1 − 𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝐺, 𝑎𝑈)]

The total costs for each user is then calculated as follows: 

𝑃𝑈𝑠𝑒𝑇𝑜𝑡(𝑅, 𝑎𝑈) =

𝐺

∑ 𝑃𝑈𝑠𝑒(𝑅,𝐺,𝑎𝑈)×𝐺_𝑃𝑃(𝑅,𝐺,𝑎𝑈)

𝐺

∑ 𝐺_𝑃𝑃(𝑅,𝐺,𝑎𝑈)

(110) 

(111) 

(112) 

The  consumer  price  is  PUseTot  for  the  household  industry:  PUseTot(R,"CP").  The  prices  of  the 
consumption commodities are found using the CPA-COICOP bridge: 

𝑃𝐶𝑜𝑚𝑚(𝑅, 𝐶𝑃𝐶) = ∑ {[𝑃𝐺𝑑𝑜𝑚(𝑅, 𝐺, "𝐶𝑃") × (1 − 𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝐺, "𝐶𝑃")) + 𝑃𝑀(𝑅, 𝐺, "𝐶𝑃") × (𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝐺, "𝐶𝑃"))] ×
× 𝐶𝑃𝐵𝑟𝑖𝑑𝑔𝑒2010(𝑅, 𝐺, 𝐶𝑃𝐶)}

 (113) 

𝐺

The  following  prices  are  exogenous  and  2010-2050  time  series  are  imported  and  used  in  FIDELIO: 
PElec,  PFuel,  and  PHeat  are  used  in  equations  (54),  (55),  and  (56),  respectively;  the  price  of  the 
energy  input  is  also  exogenous  and  derived  as  explained  in  Subsection  3.7.  The  prices  of  the 
production  inputs  are  illustrated  by  the  equations  below  (the  price  of  energy  is  missing  below 
because exogenously determined in the energy block as explained above). 

𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐶𝑎𝑝𝑖𝑡𝑎𝑙") = ∑ [𝑃𝑈𝑠𝑒(𝑅, 𝐺, "𝐼𝑛𝑣𝑒𝑠𝑡") × 𝐼𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑆)]

𝐺

𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐿") =

𝑃𝐿(𝑅,𝑆,"𝑎𝑙𝑙")
𝐵𝑎𝑠𝑒_𝑃𝐿(𝑅,𝑆,"𝑎𝑙𝑙")

(114) 

(115) 

where 𝐵𝑎𝑠𝑒_𝑃𝐿 is equal to the base year wage per hour in the baseline run, and then equal to the 
baseline 𝑃𝐿 in the simulation runs. The following equation defines 𝑃𝐿 for all workers: 

𝑃𝐿(𝑅, 𝑆, "𝑎𝑙𝑙") = ∑

𝐿𝑆𝑐𝑎

𝑃𝐿(𝑅, 𝑆, 𝐿𝑆𝑐𝑎) × 𝑆𝑘𝑖𝑙𝑙𝑆ℎ𝑎𝑟𝑒𝑠(𝑅, 𝑆, 𝐿𝑆𝑐𝑎)

(116) 

25 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4 The data of FIDELIO 

The bulk of the dataset of the third version of FIDELIO lies in the IO dataset coming from WIOD, as 
explained  in  Subsection  4.1.  The  rest  of  the  data  come  from  various  sources  as  explained  in 
Subsection 4.2. 

4.1 The IO dataset 

This Subsection describes the IO data. The main part comes from the WIOD dataset (2016 release, 
the  data  refer  to  2010),  in  particular  the  WIOD  international  supply  and  use  tables.  Other  WIOD 
tables, such as the national supply and use tables, are used to apply some required transformations. 
Whenever the WIOD database does not provide all the necessary information, other databases, such 
as Eurostat supply and use tables or OECD data were used, as described in the following Subsections. 
In  particular,  Subsection  4.1.1  describes  the  data  that  constitute  the  IO  core.  Subsection  4.1.2 
explores  the  issues  of  international  trade  and  transport  margins  (ITTM).  Finally  Subsection  4.1.3 
focuses on data about VA. 

4.1.1 Supply, use, and trade  

The main data coming from the WIOD international supply and use tables are contained in a matrix 
of entries by region, by industry and by commodity. These are data on supply, use, and trade. Supply 
data  are  used  to  fill  a  "Make"  column.  Use  data  provide  the  demand  values  in  PP  and  BP,  the 
difference  between  the  two  being  constituted  by  TlS  and  TTM.  Use  data  also  contain  information 
about international trade flows: one category of final users is exports by product. An imports ("M") 
column completes  the  matrix  with the  values  of  imported commodities.  Since  in  the  international 
use  table  imports  are  expressed  in  FOB  terms,  they are  re-expressed  in  cost-insurance-and-freight 
(CIF)  terms  adding  the  ITTM  to  the  value  of  imported  goods.21 WIOD  international  supply  and  use 
tables are used to produce those data, as well as the trade shares. Data are split in 56 products and 
56  activities,  expressed  in  millions  of  dollars  (exchange  rates  are  used  to  convert  those  into  own 
currencies). Table 7 contains the first eight entries of this part of the dataset. 

Table 7  First eight entries of the IO Make and Use data 

R 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 

G 
CPA_A01 
CPA_A02 
CPA_A03 
CPA_B 
CPA_C10-C12 
CPA_C13-C15 

aU 
A01 
A01 
A01 
A01 
A01 
A01 

Make 
5376.41 
0.00 
0.00 
3.90 
687.86 
0.00 

PP 
1298.39 
7.35 
0.00 
15.19 
640.91 
21.05 

TlS 
0.15 
-0.02 
0.00 
0.01 
1.09 
0.12 

TTM 
38.24 
1.62 
0.00 
3.10 
59.03 
4.82 

BP 
1260.00 
5.75 
0.00 
12.08 
580.79 
16.11 

M 
262.24 
1.50 
0.00 
10.96 
104.25 
16.11 

21 In  the  WIOD  international  use  table  ITTM  are  shown  as  a  separate  column.  To  get  consistency  between 
FIDELIO  data  and  FIDELIO  model  we  add  ITTM  to  the  value  of  exported  transport  and  trade  services 
(Subsection 4.1.2 describes how ITTM by product provided by WIOD are attributed to ITTM services).  

26 

 
 
 
                                                           
A01 
AUT 
AUT 
A01 
Note: imports are expressed in CIF. 

CPA_C16 
CPA_C17 

18.48 
0.00 

36.23 
11.44 

0.04 
0.01 

6.02 
2.37 

30.17 
9.06 

10.61 
5.08 

The exchange rates used are contained in Table 8 below: 

Table 8  Exchange rates used in FIDELIO 

AUT: 1.326 
BEL: 1.326 
BGR: 0.678 
BRA: 0.568 
CHN: 0.148 
CYP: 1.326 
CZE: 0.052 

DEU: 1.326 
DEN: 0.178 
ESP: 1.326 
EST: 1.328 
FIN: 1.326 
FRA: 1.326 
GBR: 1.546 

LTU: 1.327 
GRC: 1.326 
LUX: 1.326 
HRV: 0.182 
HUN: 0.005 
LVA: 1.330 
IND: 0.022  MLT: 1.326 
NLD: 1.326 
IRL: 1.326 
POL: 0.333 
ITA: 1.326 
PRT: 1.326 
JPN: 11.415 

ROU: 0.315 
RUS: 0.033 
SVK: 1.326 
SVN: 1.326 
SWE: 0.139 
TUR: 0.666 
USA: 1.00 

Note: US$ per unit of local currency. 

Two additional data sources are used in order to get TTM and TlS data: 

  WIOD national supply and use tables for the year 2010 (release 2016). These tables, available 
for  43  countries,  are  split  in  64  products  and  64  industries,  and  are  expressed  in  millions  of 
national  currencies  (except  for  Bulgaria,  Cyprus,  Estonia,  Greece,  Croatia,  Lithuania, 
Luxembourg, Latvia, Malta, Portugal, Romania, Slovak Republic, Slovenia that are expressed in 
dollars).  Countries  not  included  in  FIDELIO  are  aggregated  into  the  rest  of  the  world,  and 
industries and products are aggregated in order to match the 56 categories used in FIDELIO. 
EUROSTAT  tables  (use  table  at  PP  T1600,  use  table  at  BP  T1610,  TTM  table  T1620,  TlS  table 
T1630), with information for 28 European countries, split in 65 products and 65 activities. Data 
are in millions of euro. Once again, an aggregation of products and activities is needed in order 
to match the FIDELIO categories. 

 

The  procedure  for  the  EU  countries  is  as  follows.  For  TlS  and  TTM,  WIOD  national  supply  tables 
provide a column for TTM and a column for  TlS split by product, and national use tables provide a 
vector for TlS split by activity. Additionally, we use EUROSTAT TTM and TlS tables (T1620and T1630) 
that  offer  information  on  TTM  and  TlS  split  by  product  and  by  activity.  EUROSTAT  tables  do  not 
contain information on TTM for Croatia (Greece is used as a proxy). In order to compute TTM and TlS 
split by product and by activity, we compute the share of TTM (and  TlS) over total use, by product 
and by activity, using EUROSTAT data (use tables T1610, TTM tables T1620, and  TlS tables T1630). 
Then, we multiply the shares for the WIOD use, by product and by activity (from the national USE 
tables),  obtaining  in  this  way  a  matrix  of  TTM  and  a  matrix  of  TlS.  The  matrices  obtained  are  not 
consistent with the total TTM and TlS columns and the total TlS row provided by WIOD. So, for each 
country we run a GRAS (Generalized RAS) to adjust the matrix obtained to the total WIOD. 

Two problems arise from the applied procedure. First, for some countries, the GRAS procedure does 
not converge (Slovakia for TTM and Estonia, Greece, Malta, and Portugal for TlS). Other procedures 
were tested (such as applying a RAS considering the WIOD total TlS vector and column and the WIOD 
use  matrix;  or  estimating  the  TlS  matrix  using  the  WIOD  use  matrix  proportions;  or  adjusting  the 
WIOD total TlS row and the gross operating surplus), but no one was able to provide useful results. 
As a solution for these five tables we computed TTM or  TlS using only WIOD information, splitting 
the WIOD totals based on the use table structure. Second, as a result of the procedure used, for the 

27 

 
TTM products (such as CPA-G46, CPA-G47) the estimated TTM might be greater than the value in the 
use table in basic prices and opposite in sign, resulting in a negative use in PP.  As a solution we relax 
the WIOD totals by product to the extent necessary to avoid negative values in the use data in  PP. 
We keep fixed the total by activity, that is equal to zero in the case of TTM, and that determines the 
value added in the case of TlS. 

For non-EU countries we  apply  the same  procedure as for EU countries. Since EUROSTAT data are 
available only for EU countries, we use the average of the EU countries to get TTM and TlS shares by 
product and by activity. As for EU countries, these shares are multiplied for the WIOD use by product 
and by country (from the national USE tables), obtaining in this way a matrix of TTM and a matrix of 
TlS. Since these matrices have to be consistent with the total TTM and TlS columns and the total TlS 
row provided by WIOD, for each country we run a GRAS to adjust the matrix obtained.  

WIOD  data on  TlS  and TTM  is  not  complete  for  all non-EU countries. TTM  information  is  available 
only  for  Brazil  and  Turkey,  thus  these  are  the  only  countries  for  which  TTM  are  computed  at  the 
moment. These are the only countries that have complete information also for TlS. For three other 
countries,  India,  Russia,  and  USA,  only  the  row  vector  TlS  split  by  activity  in  the  USE  tables  is 
available, while the column vector of TlS split by product in the supply tables is missing. For these 
countries we compute the column vector of TlS split by product distributing the WIOD country-total 
TlS  using  the  EUROSTAT  proportions.  Due  to  data  availability,  for  Japan  and  China  there  is  no 
estimation of TTM and TlS.  

Trade  shares  are  computed  using  the  information  from  WIOD  international  use  tables  from which 
import data are taken. They show, for each product and each country, what share is imported from 
what trading partner. Shares sum to one across trading partners for each commodity. Table 9 shows 
the first eight entries of that matrix. 

Table 9  First eight entries of the trade shares matrix 

Importer 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 

Exporter 
AUT 
BEL 
BGR 
CYP 
CZE 
DEN 
DEU 
ESP 

G 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 

TradeShares 

 -    
 0.0322  
 0.0035  
 0.0008  
 0.0454  
 0.0031  
 0.2534  
 0.0651  

Finally, another piece of information related to trade is required to have consistent data on imports 
and exports. Imports are the total imports only of FIDELIO countries, while exports measure exports 
to  all  countries.  To  get  consistency  between  these  two  flows  it  is  necessary  to  introduce  an 
additional  variable  that  is  exports  to  the  rest  of  the  world.  Although  not  explicitly  modelled  in 
FIDELIO, exports to the rest of the world are added to the countries' mirror exports (exports derived 
from import data) in order to make sure that total exports (derived from import data) reflect actual 
total exports in the data. Exports to the rest of the world are also adjusted in order to include ITTM 
services.  

28 

 
 
The first eight entries of this matrix are shown in Table 10 below. 

Table 10  First eight entries of the matrix of exports to the rest of the World 

R 

AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 

G 

CPA_A01 
CPA_A02 
CPA_A03 
CPA_B 
CPA_C10-C12 
CPA_C13-C15 
CPA_C16 
CPA_C17 

Exports 
to RoW 
92 
11 
0 
116 
1148 
642 
672 
742 

4.1.2 International trade and transport margins 

Since  imports  data  in  the  international  use  table  are  expressed  in  FOB,  such  data  do  not  contain 
ITTM. For each country, the international use table makes available an ITTM vector by product and 
by origin country and an ITTM row by activity, but not split by origin country. In order to get to that 
level of disaggregation, and using the available information, first we need to estimate how ITTM are 
split  by  product/activity/origin  country,  and  second  to  estimate  how  ITTM  are  assigned  to  ITTM 
services (the TIRS set made by the CPA-G and CPA-H services). 

We apply the following procedure. As a first step, since in national use tables imports are expressed 
in  CIF,  from  the  difference  between  the  national  use  table  and  the  consolidated  international  use 
table  we  compute  a  matrix  of  ITTM  split  by  product  and  by  activity  for  each  WIOD  country.  The 
matrix obtained is not disaggregated by trading partner. To split the ITTM matrix by trading partner, 
for each country we use the horizontal structure of the consolidated ITTM matrix obtained, and the 
vector of ITTM split by product and by origin. Applying the structure to the WIOD total vector, for 
each country we disaggregate the ITTM matrix product/activity/origin country. For each country the 
sum of ITTM by activity (sum by column) obtained corresponds to the ITTM row by activity available 
in  the  WIOD  international  use  table.  The  obtained  ITTM  split  by  product  and  user  are  added  to 
import (to express them in CIF value) and to the total use vector at basic prices. 

Then, we need to distribute the ITTM obtained to the TTM services (CPA-G and CPA-H). To distribute 
them, the main  source  used  is  the  WIOD world  IO  table  (WIOT).  Since  WIOT  is  expressed  in  basic 
prices, the table allocates TTM imported by each trading partner to TTM services (CPA-G and CPA-H). 
We assume that ITTM services have the same distribution as TTM services. Applying this assumption, 
from WIOT table we compute the ITTM services distribution in two different ways. A first estimation 
assumes that all ITTM associated to goods imported from one trading partner are provided by that 
trading partner. Under this assumption we compute the ITTM services applying the TTM structure of 
each  trading  partner.  A  second  estimation  assumes  that  ITTM  associated  to  goods  imported  from 
one  trading  partner  might  be  provided  by  another  trading  partner.  Under  this  assumption  we 
compute  the  ITTM  services  applying  the  TTM  structure  computed  on  the  total  TTM  services 
imported by each country from all trading  partners. The estimated ITTM services are added to the 
export vector at basic prices. 

29 

 
 
The  same  structure  obtained  under  the  first  method  is  also  used  to  compute  the  TIR  shares  that 
show how ITTM associated to any goods are allocated to the different ITTM services (see Table 11 to 
understand how those data are organised). TIR shares are split by product and by origin country, as 
required in FIDELIO. Both ITTM by product and by industry and ITTM services  by industry are then 
used, jointly to TTM, to transform the USE vector from BP to PP. 

Table 11  First eight entries of the matrix splitting ITTM among the TIRS commodities 

Imp 
BEL 
BGR 
CYP 
CZE 
DEU 
DEN 
ESP 
EST 

Exp 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 

G 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 
CPA_A01 

CPA_G45  CPA_G46  CPA_G47  CPA_H49  CPA_H50  CPA_H51  CPA_H52  CPA_H53 
 0.001  
 0.003  
 0.017  
 0.001  
 0.000  
 0.001  
 0.000  
 0.002  

 0.001  
 0.003  
 0.001  
 0.002  
 0.002  
 0.002  
 0.001  
 0.002  

 0.020  
 0.031  
 0.021  
 0.032  
 0.031  
 0.030  
 0.030  
 0.033  

 0.001  
 0.008  
 0.004  
 0.006  
 0.008  
 0.006  
 0.000  
 0.006  

 0.022  
 0.050  
 0.026  
 0.053  
 0.058  
 0.048  
 0.051  
 0.052  

 0.314  
 0.783  
 0.480  
 0.795  
 0.700  
 0.840  
 0.760  
 0.784  

 0.094  
 0.024  
 0.070  
 0.041  
 0.055  
 0.021  
 0.025  
 0.049  

 0.547  
 0.099  
 0.382  
 0.071  
 0.146  
 0.052  
 0.132  
 0.072  

Finally, another input required is transit cost shares, computed as ITTM as % of imports expressed in 
FOB. Table 12 below shows the first eight entries of the ITTM as % of imports in FOB: 

Table 12  First eight entries of the transit cost shares matrix 

Importer 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 

Exporter 
BEL 
BEL 
BEL 
BEL 
BEL 
BEL 
BEL 
BEL 

G 
CPA_A01 
CPA_A02 
CPA_A03 
CPA_B 
CPA_C10-C12 
CPA_C13-C15 
CPA_C16 
CPA_C17 

Transit cost shares 
0.0360 
0.0434 
0.0874 
0.0396 
0.0572 
0.0460 
0.0535 
0.0448 

4.1.3 The VA components 

For EU countries, VA components are calculated using WIOD international use table and EUROSTAT 
use tables. WIOD does not split the total VA (available by activity) in its five components as required 
in  FIDELIO,  while  the  EUROSTAT  database  has  such  information.  In  order  to  calculate  the  FIDELIO 
data, the WIOD total VA by activity is taken from the international use tables (it is the same as in the 
national use  tables),  and it is split into the  five  components by applying the ratios computed with 
EUROSTAT  data  (EUROSTAT  components  are  taken  from  the  use  table  at  basic  prices  T1610; 
EUROSTAT  total  VA  is  taken  either  from  the  use  table  T1610  or  from  the  use  table  at  PP  T16 
depending on data availability for each country). For some countries, EUROSTAT data do not have all 
components.  For  Spain  and  France,  gross  operating  surplus  (B2A3G)  is  not  split  between  net 
operating  surplus  (B2A3N)  and  depreciation  (P51C).  For  France  and  Ireland,  Compensation  of 
employees  (D1)  is  not  split  between  wages  (D11)  and  social  security  contribution  (D12).  In  these 
cases we apply the average of the EU countries by activity to obtain the missing information. 

30 

 
 
 
Codes  reported  in  Table    13  are  used  in  the  discussion  below  for  the  sake  of  brevity.  For  non-EU 
countries, the total VA by activity comes once again from WIOD data. In order to split total VA in its 
components,  different  sources  are  used  depending  on  the  country.  The  main  databases  used  are 
OECD data, World Bank data, and data from National Statistical Institute for China, India, and Turkey. 
Please see below the country-specific details. 

Table 13  VA components and their codes 

VA components 
Production taxes less subsidies 
Depreciation (consumption of fixed capital) 
Net operating surplus 

Wages 
Social security contributions 

Code 
D29x39 
P51C 
B2A3N 
B2A3G 
D11 
D12 
D1 

Gross operating surplus 

Compensation of employees 

 

Brazil: 
  D29x39 by activity comes from OECD data for the year 2010 (Table 41: Use, Value added and 

its components, GFCF and assets by activity22); 

  P51C  by  activity  is  computed  using  the  indicator  provided  by  the  World  Bank  on 
consumption of fixed capital as % of gross national income for the year 2010.23 This indicator 
is used as a proxy of P51C as % of VA. The indicator is available only at the country level, and 
it has been applied to all industries by multiplying the country-level indicator by the total VA 
by activity; 

  B2A3N is computed as the difference between B2A3G and P51C. Data on B2A3G by activity 

come from OECD data for the year 2010 (Table 41); 

  D11 by activity comes from the same OECD data as D29x39. D12 by activity is computed as 
the difference between D1 and D11. D1 by activity is  again taken from the OECD table no. 
41.  
China: 
  D29x39  is  taken  from  the  Chinese  IO  table  disaggregated  in  41  activities  (the  table  was 

 

obtained from the National Bureau of Statistics of China); 

  P51C taken from Chinese IO table disaggregated in 41; 
  B2A3N is also taken from the Chinese IO table; 
 

since information is not available for D11, we apply the average of the shares of Russia and 
Brazil (by activity) to the total D1 of China (by activity). The same goes for D12. D1 by activity 
is again taken from the IO table for China.  

 

India: 
  D29x39  by  activity  comes  from  national  statistics  (Ministry  of  Statistics,  Government  of 

India: national Accounts24). Data are available for the years 2011-2012; 

  P51C by activity also comes from national statistics as D29x39; 

22 http://stats.oecd.org/index.aspx?DatasetCode=SNA_TABLE41 
23 http://data.worldbank.org/indicator/NY.ADJ.DKAP.GN.ZS?locations=IN-US-BR-CN 
24 http://mospi.nic.in/publication/national-accounts-statistics-2016 

31 

 
 
 
 
 
 
 
 
 
                                                           
  B2A3N by activity also comes from national statistics;  
 

since  information  is  not  available  for D11  and D12, we  apply  the  average  of  the  shares of 
Russia and Brazil (by activity) to the total D1of India (by activity). Data on D1 by activity are 
available from national statistics. 

 

Japan: 
  D29x39 by activity comes from OECD data for the year 2011 (Table 6A: Value added and its 

components by activity, ISIC rev425); 

  P51C by activity comes from the same OECD dataset as D29x39; 
  B2A3N by activity also comes from the OECD dataset above; 
  D11  is  computed  using  OECD  data  (Table  14A:  Non-financial  accounts  by  activity26).  The 
OECD non-financial accounts report D1 and D11 at the country level. These data are used to 
compute D11  as  a  share  of  D1 which  is then  applied  to  D1  data  by  activity  available  from 
table 6A of the OECD. D12 by activity is then computed as the difference between D1 and 
D11. 
Russia: 
  D29x39 by activity comes from OECD data for the year 2011 (Table 6: Value added and its 

 

components by activity, SNA9327); 

  P51C  by  activity  is  computed  using  information  on  consumption  of  fixed  capital  at  the 
country level for the year 2011 taken from OECD data (Table 2: Disposable income and net 
lending  -  net  borrowing28).  This  information  is  used  to  compute  the  share  of  P51C  over 
B2A3G  at  the  country  level  (B2A3G  comes  from  the  OECD  table  no. 6).  The  latter  share  is 
then applied to calculate P51C by activity using data on B2A3G by activity again taken from 
table 6 of the OECD; 

  B2A3N is computed as the difference between B2A3G and P51C;  
  D11 by activity also comes from the OECD table no. 6 for the year 2011. D12 by activity is 

computed as the difference between D1 and D11. D1 also comes from OECD table 6. 

 

Turkey: 
  D29x39 by activity comes from the Use table published by the Turkish Statistical Institute for 

the year;29 

  P51C by activity comes from the same source as D29x39. Note that depreciation is equal to 

zero with the exception of nine activities; 

  B2A3N by activity again comes from the same national data as above; 
  D11  is  computed  using  OECD  data  for  year  2011  (Table  6A,  as  for  Japan).  The  OECD  data 
reports D1 and D11 at the country level. These data are used to compute D11 as a share of 
D1, then applied to data on D1 by activity available from the Turkish national data. D12 by 
activity is computed as the difference between D1 and D11. 

  USA: 

  D29x39 by activity come from OECD data for the year 2011 (Table 41, as for Brazil); 
  P51C by activity comes from the same Table 41 by OECD; 

25 http://stats.oecd.org/index.aspx?DatasetCode=SNA_TABLE6A 
26 https://stats.oecd.org/Index.aspx?DataSetCode=SNA_TABLE14A 
27 http://stats.oecd.org/index.aspx?DatasetCode=SNA_TABLE6_SNA93 
28 https://stats.oecd.org/Index.aspx?DataSetCode=SNA_TABLE2 
29 http://www.turkstat.gov.tr/PreTablo.do?alt_id=1021 

32 

 
                                                           
  B2A3N by activity also comes from the OECD Table 41. data, year 2011; 
  D11 and D12 by activity again come from the same OECD table above; 

In order to illustrate the data, Table 14 shows the totals and the data for first eight industries for the 
case of Austria. 

Table 14  First eight entries of the VA components for Austria 

VAC 
R 
prodtax 
AUT 
depr 
AUT 
opsur 
AUT 
AUT  wages 
socsec 
AUT 

total 

3950 
51583 
67876 
114600 
24302 

A01 
-1605 
1626 
2348 
248 
52 

A02 
-87 
142 
816 
172 
36 

A03 
0 
10 
1 
2 
0 

B 
-8 
319 
543 
271 
54 

C10-C12 
43 
702 
1785 
2152 
425 

C13-C15 
-6 
163 
306 
530 
105 

C16 
32 
362 
548 
934 
180 

C17 
-6 
353 
481 
713 
164 

4.1.4 The investment data 

Three  main  databases  are  used  in  order  to  produce  the  investment  data  for  FIDELIO  by  country, 
industry, and good. The first one is the "nama_10_a64_p5" Eurostat dataset containing information 
on gross capital formation by industry and by country. The second is WIOD, used for the information 
on gross capital formation by commodity and by country. Finally, the investment matrices provided 
by Belgium, Czech Republic, Hungary, Slovakia, and the United Kingdom are used as bridge matrices 
for all the countries in FIDELIO. 

The  first  step  produces  a complete  investment  matrix  for  the  total  gross  capital  formation  ("Total 
fixed  assets  (gross)"  in  NACE  Rev.  2  code)  for  EU  countries  by  activity  from  the  file  source 
"nama_10_a64_p5"  which  only  contains  complete  information  for  14  countries  (Austria,  Belgium, 
Bulgaria,  Czech  Republic,  Denmark,  Finland,  Germany,  Greece,  Hungary,  Ireland,  Italy,  Portugal, 
Romania, and Slovakia). For the rest of the countries there is information by activity but only at the 
level of one-digit NACE Rev. 2 code (with the exception of Croatia and Sweden which only have total 
gross fixed capital formation available). Then, two different approaches were  used to  produce the 
data for  the 56 activities  for these  countries. For the  first  group (Cyprus, France,  Lithuania, Malta, 
Poland,  and  Spain),  the  shares  of  each  specific  activity  over  the  NACE  Rev.  2  one-digit  code  total 
were  created  by  identifying  similar  countries.30 Cyprus,  Malta,  and  Spain  were  estimated  with  the 
information available for Italy. Czech Republic was used for Lithuania and Poland, Portugal was used 
for  France.  For  the  second  group  (Croatia,  Estonia,  Latvia,  Luxembourg,  Netherland,  Slovenia,  and 
the United Kingdom), the shares of each specific activity were used with respect to the total at the 
level  of  one  digit  code  of  NACE  Rev.  2  of  the  total  assets  of  the  14  countries  that  have  complete 
information.  As  for  the  rest  of  the  8  countries  of  FIDELIO  3  (Brazil,  China,  India,  Japan,  Russia, 
Sweden,  Turkey,  and the Unites  States) that  only  have  the  total  amount of the  "Total  fixed  assets 
(gross)" without any breakdown by activity, information was estimated with the average information 
of the 27 countries previously calculated as explained above.  

30 See  methodology  for  identifying  similar  countries  in  "Annex  A.  Approach  to  identify  similar  countries"  in 
Montinari et al. (2016). 

33 

 
 
                                                           
The second step produces a complete  investment matrix  for P51G for the 35 countries of FIDELIO 
and for 56 commodities at purchases prices estimated from WIOD database. 

The  third  step  produces  a  bridge  matrix  to  estimate  all  matrices  of  each  country  for  P51G  by  56 
industries  and  by  56  commodities.  This  bridge  matrix  was  estimated  with  information  related  to 
gross fixed capital formation matrices available for Belgium, Czech Republic, Hungary, Slovakia, and 
the United Kingdom that have different dimension of industries and commodities. All of them relate 
to the year 2010, except for Slovakia, which is related to the year 2013. All these 5 matrices were 
standardized  for  56  industries  and  for  56  commodities  and  a  matrix  with  the  average  of  the  5 
countries was estimated. 

Therefore,  a  GRAS  process  was  implemented  using  the  result  for  gross  fixed  capital  formation  of 
each  country  related  to  the  vectors  of  the  56  industries  (Step  1)  and  the  vectors  of  the  56 
commodities (Step 2) combining with the bridge matrix of the step 3. For those countries that had 
information  of  gross  fixed  capital  formation  in  a  specific  commodity  if  the  bridge  matrix  does  not 
contain  information,  the  average  of  the  commodities  related  to  the  commodities  that  are  at  one 
digit level of the NACE Rev. 2 classification was applied.  

4.2 The rest of the data: the household block 

4.2.1 Household income, taxes, and transfers 

Most  of  the  variables  characterising  the  income  earned  by  households,  the  taxes  paid  and  the 
transfers  received  by  them  come  from  the  Eurostat  dataset  (nasa_10_nf_tr)  "Non-financial 
transactions of households and non-profit institutions serving households" for the EU28 countries, 
and from the OECD dataset (no. 13) "Simplified non-financial accounts" for the non-EU countries of 
the model.  We  now  introduce  all  the  variables  needed  in  order  to calculate  household  disposable 
income. 

The  data  for  household  labour  wages  are  taken  from  the  VA  data  above,  corresponding  to  D1. 
Operating  surplus  corresponds  to  B2A3G  (operating  surplus  and  mixed  income,  gross,  received  - 
SB2G_B3G  in the  OECD  dataset).  In  case of  missing data  (in  this  case,  for  Brazil,  India, Russia,  and 
Turkey), operating surplus is calculated as a proportion of operating surplus taken from the VA data, 
the  proportion  being  the  average  proportion  in  the  sample  (in  our  case,  0.65).  Property  income  is 
calculated using D4 (property income) by subtracting paid property income from received property 
income. The same is done with OECD data, subtracting SD4P from SD4R. 

Taxes paid by the households, correspond to D5 (current taxes on income, wealth, etc., paid - SD5P 
in  the  OECD  dataset).  In  case  of  missing  data  (in  this  case,  for  Brazil,  India,  Luxembourg,  Malta, 
Russia, and Turkey), operating surplus is calculated as a proportion of the sum of wages and social 
security contributions taken from the VA data, the proportion being the average proportion in the 
sample  (in  our  case,  0.10).  Transfers  received  by  the  households  come  from  D62  (social  benefits 
other than social transfers in kind, received minus paid - SD61R_SD62R in the OECD dataset). In case 
of missing data (in this case, for Brazil, India, Luxembourg, Malta, Russia, and Turkey), transfers are 

34 

 
 
 
calculated as a proportion of the sum of wages and social security contributions taken from the VA 
data, the proportion being the average proportion in the sample (in our case, 0.35). Other transfers 
are also considered: D7, again received minus paid (other current transfers - SD7R minus SD7P in the 
OECD  dataset).  Social  security  contributions  are  also  needed  in  order  to  calculate  household 
disposable  income.  Those  paid  by  the  employer  are  taken  from  the  VA  data  as  explained  above. 
Those paid by the employee, D61 (net social contributions, paid minus received  -  SD61P_SD62P in 
the OECD dataset). In case of missing data (in this case, for Brazil, India, Luxembourg, Malta, Russia, 
and  Turkey),  social  security  contributions  are  calculated  as  a  proportion  of  the  sum  of  wages  and 
social security contributions taken from the VA data, the proportion being the average proportion in 
the  sample  (in  our  case,  0.11).  Finally,  household  disposable  income  is  calculated  in  the  model 
according to equation (41) using the variables described so far.  

4.2.2 Household consumption 

Total consumption is equal to the sum over products of the Use data in PP. Household consumption 
in  FIDELIO  3  differentiates  between  durable  and  non-durable  commodities.  Most  of  the  relevant 
data  come  from  the  Eurostat  dataset  (nama_10_co3_p3)  "Final  consumption  expenditure  of 
households by consumption purpose - COICOP 3 digit" for the EU28 countries, and from the OECD 
dataset  (no.  5)  "Final  consumption  expenditure  of  households"  for  the  seven  non-EU  countries  of 
the model.  

The non-durable and non-energy part of the consumption block is organised in a QAIDS that includes 
the  eight  following  categories:  food,  clothing,  furniture  and  equipment,  health,  communication, 
recreation and accommodation, financial services, and other. They are constructed as follows. 

 
 
 

 
 
 

 
 

food is the sum of CP01 (food and non-alcoholic beverages) and CP021 (alcoholic beverages);  
clothing corresponds to CP03 (clothing and footwear); 
furniture and equipment is the sum of CP051 (furniture and furnishings, carpets and other floor 
coverings),  CP052  (household  textiles),  CP054  (glassware,  tableware  and  household  utensils), 
CP055 (tools and equipment for house and garden), and CP056 (goods and services for routine 
household maintenance); 
health corresponds to CP06 (health); 
communication corresponds to CP08 (communications); 
recreation and accommodation is the sum of CP094 (recreational and cultural services), CP111 
(catering services), and CP112 (accommodation services); 
financial services is the sum of CP125 (insurance) and CP126 (financial services n.e.c.); 
other is  a residual category made  up by  the  sum of CP022 (tobacco), CP023 (narcotics),  CP09 
(recreation and culture) excluding CP094, CP10 (education), and CP12 (miscellaneous goods and 
services) excluding CP125 and CP126. 

The non-durable energy commodities considered in FIDELIO 3 are the following: 

 

electricity and heating, corresponding to CP045 (electricity, gas and other fuels)  — due to the 
lack  of  data,  electricity  and  heating  values  are  obtained  by  simply  dividing  the  total  value  by 
two; 

35 

 
 
 
 

fuel for private transport, corresponding to CP072 (operation of personal transport equipment);  
public transport, corresponding to CP073 (transport services). 

A variable related to the consumption of electricity and heating is heating degree days, defined as:  
(18∘ − 𝑇𝑚) ∗ 𝑑 if 𝑇𝑚  is lower than or equal to 15˚C (the temperature below which buildings need to 
be heated), and nil if 𝑇𝑚 is greater than 15˚C. 𝑇𝑚 is the mean (𝑇𝑚𝑖𝑛 − 𝑇𝑚𝑎𝑥)/2 outdoor temperature 
over  a  period  of 𝑑 days.  The  main  source  for  this  type  of  variable  is  the  Eurostat  dataset 
(nrg_esdgr_a) "Heating degree-days by NUTS 2 regions - annual data", under "Energy statistics". As 
for  the  countries  not  included  in  this  dataset,  values  were  assigned  depending  on  the  average 
temperature (for example, Japan was assigned a value close to that of Turkey because the average 
temperature in the two countries is very similar — 11.15 and 11.10 respectively). Table 15 shows the 
heating degree days values used in FIDELIO 3. 

Table 15  Heating degree days (Hdd) in 2010 

R 
AUT 
BEL 
BRA 
BGR 
CHN 
HRV 
CYP 
CZE 
DEN 

Hdd 
R 
3301  EST 
2696  FIN 
400  FRA 
2403  DEU 
3200  GRC 
2316  HUN 
IND 
IRL 
ITA 

600 
3327 
3235 

R 
Hdd 
4302 
JPN 
5596  LVA 
2340  LTU 
3063  LUX 
1449  MLT 
2594  NLD 
400  POL 
2841  PRT 
1829  ROU 

Hdd 
R 
2390  RUS 
4161  SVK 
3931  SVN 
2967  ESP 
499  SWE 
2727  TUR 
3439  GBR 
1166  USA 
2773 

Hdd 
6000 
3160 
2774 
1686 
5291 
2389 
2990 
3050 

The  following  parameters  of  FIDELIO  3  also  affect  energy  consumption:  efficiency  of  vehicles, 
heating,  and  electricity.  They  refer  to  the  efficiency  of  private  transport  vehicles,  heating  systems 
and household appliances respectively, and data are taken from the EU Reference Scenario 2016 on 
energy,  transport  and  GHG  emissions  containing  trends  to  2050.31 Table  16  shows  the  first  four 
entries of each of those parameters. 

Table 16  First five entries of the three parameters for the efficiency of appliances and vehicles 

R 
AUT 
BEL 
BRA 
BGR 
AUT 
BEL 
BRA 
BGR 
AUT 
BEL 
BRA 
BGR 

Parameters 
efficiency_electricity 
efficiency_electricity 
efficiency_electricity 
efficiency_electricity 
efficiency_heating 
efficiency_heating 
efficiency_heating 
efficiency_heating 
efficiency_vehicles 
efficiency_vehicles 
efficiency_vehicles 
efficiency_vehicles 

2010 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 

2011 
0.98 
0.99 
0.99 
1.00 
0.98 
0.99 
0.99 
1.00 
0.98 
0.98 
0.99 
0.99 

2012 
0.97 
0.97 
0.98 
1.00 
0.97 
0.97 
0.98 
1.00 
0.97 
0.96 
0.98 
0.97 

2013 
0.95 
0.96 
0.97 
1.00 
0.95 
0.96 
0.97 
1.00 
0.95 
0.94 
0.97 
0.96 

2014 
0.93 
0.95 
0.96 
1.00 
0.93 
0.95 
0.96 
1.00 
0.93 
0.92 
0.96 
0.95 

31 Capros,  P.,  A.  De  Vita,  N.  Tasios,  P.  Siskos,  M.  Kannavou,  A.  Petropoulos,  S.  Evangelopoulou  et  al.  "EU 
Reference Scenario 2016-Energy, transport and GHG emissions Trends to 2050." (2016). 

36 

 
 
 
 
                                                           
Households in FIDELIO 3 can also spend for vehicles and housing, which are considered as durable 
goods  and  treated  differently  from  the  non-durable  ones.  Thus,  the  following  variables  are  also 
considered in the model: 

 

 

rents, corresponding to the sum of CP041 (actual rentals for housing), CP042 (imputed rentals 
for housing), CP043 (maintenance of the dwelling), and CP044 (water supply and miscellaneous 
services relating to the dwelling), corresponding to CP044;  
vehicles, corresponding to CP071 (purchase of vehicles).  

The number of households is a parameter used in the equations for the investment in housing and 
vehicles.  Data  for  such  parameter  are  obtained  starting  from  population  data. Population  is taken 
from the UN, which provides projections to 2050 (the medium variant ones are used in FIDELIO 3), 
and  by  dividing  population  by  the  average  size  of  the  household  in  each  country  the  number  of 
households is obtained. The average household size was calculated thanks to Eurostat data for the 
EU28 countries and for Turkey, and thanks to UNECE for the US and Russia (for such countries both 
population and number of households exist for 2010). Census data for the four other non-European 
countries were used to retrieve the average household size and perform the calculations needed to 
obtain the number of households from 2010 to 2050.  Table 17 shows the average household sizes 
used in FIDELIO. 

Table 17  Average household size in FIDELIO 

R 
AUT 
BEL 
BRA 
BGR 
CHN 
HRV 
CYP 
CZE 
DEN 

hh size 

R 
2.29  EST 
2.39  FIN 
3.30  FRA 
2.60  DEU 
3.05  GRC 
2.83  HUN 
IND 
3.92 
IRL 
2.34 
ITA 
2.39 

R 
hh size 
2.38 
JPN 
2.13  LVA 
2.29  LTU 
2.05  LUX 
2.55  MLT 
2.44  NLD 
4.18  POL 
2.74  PRT 
2.37  ROU 

hh size 

R 
2.39  RUS 
2.47  SVK 
2.27  SVN 
2.47  ESP 
2.88  SWE 
2.25  TUR 
2.84  GBR 
2.62  USA 
2.69 

hh size 
2.62 
3.01 
2.46 
2.58 
2.08 
3.72 
2.29 
2.61 

Finally,  households  can  also  buy  appliances,  which  although  durable,  are  not  considered  as  own 
houses and vehicles in the model because they cannot be used as collateral. The variable governing 
the consumption of appliances takes the value of CP053 (household appliances) in the base year. 

As stated above, durables are treated differently from the other consumption categories due to the 
fact  that  they  can  be  used  as  collateral,  and  stocks  are  built  through  investment.  Investment  in 
vehicles in the model is set to be equal to the expenditure in vehicles. As for investment in dwellings, 
the base year value of gfcf_housing is obtained as the difference between P51G (from the Eurostat 
nasa_10_nf_tr dataset "Non-financial transactions of households and non-profit institutions serving 
households") and the expenditure for vehicles.  

Table 18  below contains the consumption data for Austria used in FIDELIO. 2009 and 2010 values 
are used due to the fact that in some cases lagged values of the consumption variables are used (see 
the equations of the model in Section 3). 

37 

 
 
 
 
Table 18  Household consumption data for Austria 

R 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 

COICOP 
food 
clothing 
furn_eq 
health 
comm 
recr_acc 
fin_serv 
other 

2009 
17596 
9113 
8689 
5606 
3479 
24742 
7221 
23375 

2010 
COICOP 
17917  elec_heat 
fuel 
9554 
9006  publ_tran 
5816 
3294  vehicles 
25370  appliances 
7110  gfcf_houses 
24194 

rents 

2009 
6104 
10362 
3464 
26759 
5885 
1659 
9364 

2010 
6285 
11443 
3548 
27596 
5599 
1732 
10326 

For the variables for which official statistics do not contain data we have to use some assumptions in 
order to  assign the  base  year values. Mostly,  such  assumptions  are  related  to the  bridge  matrices 
between COICOP and CPA (the methods used to impute missing data include simple deduction by 
means of differences when possible, previous year structures when available, and closest structure 
according to the available data) as explained below. 

Given  the  structure  of  the  FIDELIO  3  model,  a  bridge  matrix  linking  consumption  expressed  in 
COICOP  terms  (even  though  organised  according  to  the  variables  of  the  model)  and  the  CPA2008 
commodities is needed. In order to achieve these bridge matrices, several steps were necessary. The 
COICOP vector for each country organised by consumption categories has been produced according 
to the description above. As for the CPA vector, data in PP are extracted from WIOD as explained in 
Subsection  4.1.  Since  it  is possible  that  national  total  COICOP  values  coming  from  Eurostat  do  not 
match  national  CPA  totals  in  WIOD,  COICOP  data  have  been  occasionally  adjusted  to  match  this 
total, leaving the COICOP national structure unaltered.  

Thus, it is necessary to build a bridge matrix between both vectors. The following strategy has been 
adopted  in  order  to  do  so.  For  the  following  countries  we  started  with  some  initial  COICOP-CPA 
conversion  matrices:  Austria,  Belgium,  Czech  Republic,  Denmark,32 Estonia,  Finland,  Germany, 
Portugal, Slovakia, Sweden, and the United Kingdom,33 whose national statistical offices provided us 
with their own estimated COICOP-CPA conversion matrices. These matrices are quite heterogeneous 
in terms of product and COICOP breakdown and in some cases refer to years different from 2010. 
The Danish and German conversion matrices are expressed in BP. Hence, an initial harmonisation of 
these matrices was conducted to meet our desired level of disaggregation in terms of COICOP (15 
categories) and CPA (56 products) and, when necessary, also conversion to PP. 

Then, these matrices were commonly almost coincident to our COICOP vectors. In these cases, the 
resulting  matrix  directly  becomes  the  final  conversion  matrix  for  these  countries,  inducing 
occasionally  adjustments  to  the  BP-PP  conversion  of  the  final  consumption  of  households  of  the 
WIOD vector. 

32 For Denmark, tables are publicly available online at:  https://www.dst.dk/ext/5198749172/0/inout/Excel-
files-with-IO-data-for-the-period-2006-2015-(69-industries)--zip. 
33 For United Kingdom, tables are publicly available online at: 
https://www.ons.gov.uk/economy/nationalaccounts/supplyandusetables/datasets/inputoutputsupplyanduset
ables. 

38 

 
 
 
 
 
                                                           
For  the  rest  of  countries  for  which  a  prior  matrix  is  not  available,  a  balancing  procedure  was 
conducted.  The  above  mentioned  available matrices  were  used  as  proxies  for the  missing  country 
priors. Also, the theoretical correspondence between CPA and COICOP classification was used as a 
potential prior. In the last case, where  the  convergence  procedure was hard to achieve,  a mixture 
between the selected prior and the theoretical correspondence was used. 

In order to select a prior for a country from the set of available conversion matrices, several criteria 
were  used.  Based  on  the  assumption  that  similar  COICOP  and/or  WIOD  structures  would  lead  to 
similar conversion patterns, the proximity between the consumption vectors for the countries with 
no  conversion  matrix  available  and  the  countries  with  conversion  matrices  available  was  analysed 
using  different  metrics  (SWAPE,  SMAPE,  and  correlation  coefficients).  Countries  with  the  most 
similar patterns of consumption were identified and then confronted with those resulting from other 
selection criteria such as GDP per capita similarity and geographical proximity. This led us to an initial 
choice for the prior matrix. In those cases where our set of criteria did not lead to a sound choice, 
the theoretical correspondence between CPA and COICOP classification was used as a prior. 

In a subsequent step, the internal consistency of the chosen prior matrix was analysed in terms of its 
compatibility  with  the  COICOP  and  the  WIOD  data.  This  process  permitted  to  highlight  several 
internal  inconsistencies  between  the  consumption  values  available  in  the  COICOP  vector  and  the 
WIOD  vector.  It  is  possible  to  find  several  groups  of  categories  where  the  COICOP  structure  and 
WIOD structure link can be considered a one-to-one relationship. For instance, it is quite common 
that in most of the priors that the transport services category (CP073) in FIDELIO 3 and the transport 
categories  in  the  CPA  vector  (H49,  H50  and  H51  according  to  the  CPA  classification)  are  linked. 
Hence  the  subtotals  for  these  categories  in  the  WIOD  vector  and  the  COICOP  vector  must  match, 
and  the  balancing  procedure  would  only  work  in  estimating  the  internal  breakdown  for  these 
categories  in  the  CPA  product  dimension,  leaving  the  aggregated  subtotal  unchanged.  It  is  quite 
common  that  these  subtotals  do  not  match,  which  makes  convergence  impossible.  In  these 
situations we had to opt to modify the value of the subtotal either in the COICOP vector or in the 
WIOD  vector.  In  general,  the  value  closest  to  the  original  source  (i.e.  the  value  with  fewer 
transformations  undergone  in  the  process)  was  usually  kept,  and  the  other  one  was  modified 
accordingly. These decisions have led to posterior refinements in the BP-PP conversion of the WIOD 
final  consumption of  household  vectors, or  in the  estimation of  the  COICOP  vectors  substructures 
when the available information was not enough to match the 14 categories of FIDELIO 3. 

In  other  situations,  the  chosen  prior  matrix  was  combined  with  the  theoretical  correspondence 
between COICOP and CPA categories matrix to build a mixture prior. This was the case when target 
vectors of COICOP and WIOD showed values for products and categories of products, and the prior 
matrix  showed  no  correspondences  at  all  among  them,  or  when  convergence  problems  induced 
large  changes  in  the  COICOP  and  WIOD  vectors  which  were  not  fully  justified  according  to  the 
reliability of both vectors.  

In  the  end,  35  COICOP-CPA  conversion  matrices  have  been  built,  one  for  every  country  in  the 
database of the FIDELIO 3 model, according to the base year 2010 figures. This process has led, as 
mentioned above, to several additional modifications of the COICOP and WIOD Final Consumption 
Households targets for the sake of coherence  and convergence  of the balancing procedure. These 
modifications  in  the  COICOP  target vectors  are mostly  negligible,  and  in  the worst  cases,  the  final 

39 

 
target  vectors  structure  differs  in  less  than  a  5%  of  the  original  target  vector  structure.  These 
changes  have  generally  contributed  more  to  modify  and  refine  our  initial  imputations  methods  of 
missing data, better than changing official figures from OECD or Eurostat, when available. Regarding 
the WIOD Final Consumption of Households vectors, the size of changes in terms of importance are 
aligned  to  the  size  of  the  described  COICOP  changes,  however  these  changes  have  contributed  to 
improve the change of valuation process in terms of coherence. 

Table  19  below  shows  as  an  example  how  food  consumption  is  translated  to  the  NACE  Rev.  2 
commodities in the case of Austria. 

Table 19  Austrian bridge to NACE Rev. 2 for food consumption 

R 
AUT 
AUT 
AUT 
AUT 
AUT 

G 
CPA_A01 
CPA_A02 
CPA_A03 
CPA_B 
CPA_C10-C12 

food 
0.12177 
0.00000 
0.00477 
0.00000 
0.87346 

4.2.3 Household stocks 

Household vehicles and housing stock data are scarce and it proved impossible to find a unique data 
source  capable  of  providing  data  for  a  substantial  number  of  countries  and  at  the  same  time 
ensuring a certain consistency in the values. Thus, a decision was taken to assume the value of the 
stocks  depending  on  the  flow  variables  related to  them.  Based on  the  depreciation  rates  used  for 
FIDELIO 2, the following assumptions were made: 

 
 
 

Stock of appliances =  1.00/0.07 = 14.29 times the yearly expenditure for appliances; 
Stock of vehicles =  1.00/0.08 = 12.50 times the yearly expenditure for vehicles; 
Stock of houses = 1.00/0.015 = 66.67 times the yearly rents. 

Although this procedure can certainly be seen as ad hoc, and numbers can be questioned, we stand 
ready  to  modify  the  numbers  resulting  from  it  should  actual  data  become  available.  Also,  the 
advantage of such a simple set of assumptions is that it can be  easily modified should we acquire 
reliable information on the stock-flow relationships for such variables.  

A series of stock variables are used in FIDELIO 3. As per equations  (38) and (39), the net wealth of 
households  (made  by  financial  assets  and  liabilities)  is  used  and  its  data  come  from  the  Eurostat 
dataset  (nasa_10_f_bs)  "Financial  balance  sheets  of households  and  non-profit  institutions  serving 
households" for the EU28 countries, and from the OECD dataset (no. 710) "Financial balance sheets - 
consolidated".  The  2010  stocks  of  own  housing  and  vehicles  are  calculated  as  their  yearly 
consumption  in  2010  divided  by  the  assumed  depreciation  rates  (0.015  and  0.08,  respectively). 
Then, the stocks  move  according to equations  (47)  and (48). Finally, cash-in-hands  is calculated as 
the sum of disposable income, net wealth, and durable stocks as per equation (38). 

40 

 
 
   
 
 
4.3 The rest of the data: the government block 

Both governmental revenues and expenditures are featured in the model. The main source of this 
type  of  data  not  already  taken  from  WIOD  is  the  Eurostat  dataset  (nasa_10_nf_tr)  "Non-financial 
transactions" of the government for the EU28 countries, and the OECD governmental accounts for 
the non-EU countries.  

Operating  surplus  is  B2A3G  (operating  surplus  and  mixed  income,  gross)  accruing  to  the 
government, and the base year value is taken from Eurostat data. In the model, as per equation (65), 
it is assumed to be equal to the base year proportion of total operating surplus (coming from the IO 
VA data).34 Taxes less subsidies come from the IO dataset. Taxes on production and employer social 
security contributions correspond to D29X39 and D12, respectively, from the IO VA data. Employee 
social security contributions are the same appearing in the household block as explained above. The 
same goes for taxes on income and wealth, that is the YDTaxesHH variable of the household block, 
equation  (43).  The  sum  of  these  revenues  is  collected  in  the  total  revenues  variable  according  to 
equation (64). 

As for the spending side, government consumption comes from the IO dataset. The interests paid on 
public  debt  come  from  the  Eurostat  table  gov_10a_main  (interest,  payable).35 Public  investment 
data also come from that same Eurostat dataset. Missing data are filled using the sample average 
proportion of public  investment with respect to government consumption to mimic equation  (73). 
Governmental  transfers  correspond  to  the  sum  of  governmental  transfers  and  other  transfers  to 
households  already  introduced  in  equation  (41)  whose  data  come  from  Eurostat  as  explained  in 
Subsection 4.2.1 above. All these expenditures are summed into government total expenditure. 

Then, the budget balance is calculated according to equation (76). The 2010 value of this variable is 
calculated  directly  into  the  model  using  base  year  data  for  all  revenues  and  expenditures.  A 
correction  factor  is  used when  government consumption  is  endogenised so  to  make  sure  that  the 
values  match with the  data  for  the  ratio  between  the  budget  balance  and  GDP.  The  latter  ratio  is 
exogenous when government consumption is endogenised, and it is assumed to go to zero (that is, it 
is assumed that all countries achieve a balanced budget) in 2020.  

Finally, governments accumulate public debt, whose base year data correspond to GD (government 
consolidated  gross  debt)  in  the  Eurostat  dataset  (gov_10dd_edpt1)  "Government  deficit/surplus, 
debt  and  associated  data".  Data  for  Turkey  come  from  the  OECD  dataset  (no.  750)  "General 
government debt - Maastricht". Data for the rest of the countries are taken from the World Bank. 
Table  20    below  contains  the  base  year  values  of  the  governmental  variables  for  Austria,  Belgium 
and Bulgaria to illustrate the data. 

Table 20  Values of the governmental variables for the base year for three countries 

Variables 

GovOpSur 
GovTlS 
GovProdTax 

AUT 
7986.6 
32309.7 
3945.8 

BEL 
8024.7 
38706.6 
-1662.4 

BGR 
2126.7 
9829.8 
-920.0 

34 For the countries for which there are no data, the sample average (7%) is assumed. 
35 Once again, the sample average of the rate of interest paid over debt is used to fill the cells for the countries 
for which data are missing. 

41 

 
                                                           
YDTaxesHH 
YDSSecemployer 
YDSSecemployee 
GovInterest 
YDTran 
YDOtherTran 
Govgfcf 
GovCons 
GovDebt 

31098.5 
24286.7 
23159.0 
8544.9 
59194.0 
2380.0 
9607.4 
60011.5 
243773.7 

45823.3 
50383.3 
23599.4 
13199.3 
69839.0 
1824.0 
8428.3 
86308.6 
364751.5 

2093.0 
3967.5 
24214.6 
531.6 
8950.0 
1678.0 
3428.9 
11690.5 
11692.8 

4.4 The rest of the data: the labour market 

Employment  by  country  and  industry  is taken  from the WIOD  social  accounts.  The  unemployment 
rates used for the base year are shown in Table 21 below and come from Eurostat for the European 
countries and from the World Bank for the non-European ones. 

Table 21  Base year unemployment rates 

R 
AUT 
BEL 
BRA 
BGR 
CHN 
HRV 
CYP 
CZE 
DEN 

unempRate 

R 
0.047  EST 
0.082  FIN 
0.067  FRA 
0.089  DEU 
0.029  GRC 
0.115  HUN 
IND 
0.060 
IRL 
0.071 
ITA 
0.074 

R 
unempRate 
0.167 
JPN 
0.083  LVA 
0.089  LTU 
0.064  LUX 
0.120  MLT 
0.112  NLD 
0.035  POL 
0.139  PRT 
0.078  ROU 

unempRate 

R 
0.050  RUS 
0.195  SVK 
0.178  SVN 
0.048  ESP 
0.068  SWE 
0.048  TUR 
0.096  GBR 
0.116  USA 
0.064 

unempRate 
0.073 
0.143 
0.072 
0.191 
0.086 
0.109 
0.078 
0.096 

The base year labour supply (by region and labour skill) is calculated using data on employment and 
unemployment  rate  as  per  equation  (91).  The  skill-specific  labour  force  participation  rates  are 
calculated using CEDEFOP data, population data and the labour supply as per equation (92). As for 
the non-European countries,  German rates are used to calculate  the labour supply  rates for Japan 
and  the  USA,  and  Romanian  ones  are  used  for  the  rest  (rates  are  rescaled  in  order  to  match  the 
actual labour supply numbers). Numbers for the first eight countries of the sample are contained in 
Table 22 below. 

Table 22  Labour supply rates for eight countries 

Country 
AUT 
BEL 
BGR 
BRA 
CHN 
CYP 
CZE 
DEN 

LSupplyRate("low") 
0.086 
0.100 
0.080 
0.132 
0.149 
0.092 
0.031 
0.142 

LSupplyRate("medium") 
0.329 
0.173 
0.326 
0.319 
0.359 
0.149 
0.396 
0.229 

LSupplyRate("high") 
0.098 
0.173 
0.139 
0.084 
0.095 
0.146 
0.091 
0.166 

42 

 
 
 
 
 
 
In  the  absence  of  data,  the  wage  shares  by  skill  are  simply  calculated  so  to  be  equal  to  the 
employment  shares: that  is,  if 20%  of the employed are  low-skill  workers, then  the  base  year  low 
skill's wage share is equal to 0.20.  

4.5 The rest of the data: the energy block 

The exogenous prices of electricity, fuel and heating used in the household block in equations (54), 
(55), and (56) are taken from the POLES model. Three scenarios are available, the default in FIDELIO 
being the first one: reference, INDCs, and 2 degrees. The final user prices for buildings (electricity, 
average price for heating, and road transport gasoline prices) are used. As for the calculation of the 
exogenous price of the energy input used in equation (95), the POLES final user prices of the industry 
are  used  for  the  five  energy  carriers:  coal,  oil,  gas,  renewables  (biomass  prices  are  used),  and 
electricity  and  heating  (electricity  prices  are  used).  Table  23    contains  the  2010-2015  prices  for 
Austria (reference scenario) to illustrate the data format. 

Table 23  Austrian energy prices 2010-2015 

R 

AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 
AUT 

Price 

PElec 
PFuel 
PHeat 
PCoal 
POil 
PGas 
PRenew 
PElHeat 

2010 

2011 

2012 

2013 

2014 

2015 

1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 
1.00 

0.98 
1.11 
1.04 
1.09 
1.22 
1.01 
1.15 
0.97 

0.96 
1.15 
1.07 
1.17 
1.34 
1.16 
1.24 
0.93 

0.98 
1.08 
1.04 
1.01 
1.18 
1.16 
1.08 
0.91 

0.94 
1.03 
1.01 
0.91 
1.09 
1.09 
0.99 
0.86 

0.93 
0.91 
0.96 
0.89 
0.70 
1.03 
0.81 
0.83 

CO2, CH4, and N2O emissions in tonne by region and by industry are taken from the env_ac_ainah_r2 
dataset published by Eurostat. 

The  energy  uses  expressed  in  physical  units  (TJ)  are  estimated  by  the  ELIOD 36 project.  The 
deliverable 6 of the ELIOD project estimated the energy uses in physical units for the period 2010-
2014  and  for  EU-28  Member  States,  USA  and  Japan.  The  series  are  consistent  with  NACE  Rev.2 
classification.  

The estimates of energy uses are based on the methodology developed by Genty et al. (2012) for the 
first  edition  of  the  WIOD  Energy  Accounts.  The  methodology  implied  that,  whenever  available, 
official energy use accounts were used as main data source (mainly occurring for countries such as 
Austria, Germany, Netherlands and Denmark). However, as national data were not available for all 
countries/years/industries/commodities, the energy accounts were estimated using the information 
from the energy balances of the International Energy Agency (IEA) further disaggregated/reallocated 
using the monetary information from the Supply and Use Tables of WIOD, and complemented with 
information  on  fuel  prices  (IEA),  on  car  shares  (ODYSSEE  database),  on  international  bunkering 
(EXIOPOL database) and on employment (KLEMS database).   

36 Environmental and Labour accounts linked to a global Input-Output Database. 

43 

 
 
 
                                                           
The estimation implied: 

 

 

a redefinition of the industrial boundaries through a technical redistribution of energy uses that 
reflects the energy mix of countries and  
a correction for the geographical mismatch between the territorial principle (on which energy 
balances are based) and the residence principle (on which energy accounts are based).  

The resulting energy use tables represent an equivalent Use tables for energy products in physical 
terms;  it  contains  the  energy  products  that  are  consumed  by  the  intermediate  consumption  and 
households within the national territory. The main concept covered is the gross energy use, which 
includes  the  energy  intermediate  consumption  of  energy  by  industries  and  allows  answering 
questions related to the energy mix and to the substitution of energy inputs in electricity production 
over time. The gross energy use is fully consistent with the National Accounts framework on which 
WIOD is based.  

The  Energy  Use  tables  take  the  form  of  matrices  of  entries  by  country,  by  industry,  by  energy 
commodity and by year.  

 
 

 

The geographical coverage has been recently increased to 43 WIOD countries. 
The industrial coverage is the same as the WIOD's Use tables in monetary terms, i.e. 64 NACE 
Rev. 2 industries.  
The  energy  commodity  coverage  is  reduced  to  11  from  the  26  carriers  present  for  the  first 
edition of the WIOD Energy Accounts (see Annex 12). 

Table 24 illustrates the 2010 Austrian energy uses for selected industries. 

Table 24  Austrian gross energy use by energy commodities for selected industries (TJ) 

L
E
S
E
I
  D
9.32 
- 
- 
2.73 

A01 
A02 
A03 
B 

C10_12 
C13_15 
C16 

2.77 
0.14 
2.54 

E
N
I
L
O
S
A
G
- 
- 
- 
0.01 

0.07 
0.02 
0.03 

L
E
U
F
T
E
J

- 
- 
- 
- 

- 
- 
- 

,
E
K
O
C

,
L
A
O
C

E
D
U
R
C
0.05 
- 
- 
0.00 

S
A
G
H
T
O
- 
- 
- 
- 

E
T
S
A
W
- 
- 
- 
- 

- 
- 
- 

0.01 
- 
0.69 

0.16 
- 
- 

S
U
O
E
S
A
G
D
U
Q
I
L

I

I

S
L
E
U
F
O
B
0.76 
0.10 
0.00 
0.02 

,

R
T
C
E
L
E

D
O
R
P
T
A
E
H
4.66 
- 
- 
4.74 

0.15 
0.02 
0.03 

8.69 
1.59 
7.85 

L
I
O
L
E
U
F

0.36 
- 
- 
0.24 

2.36 
0.37 
0.30 

S
E
L
B
A
W
E
N
E
R

R
A
E
L
C
U
N
6.09 
0.00 
- 
0.02 

0.30 
0.04 
14.94 

,

G
P
L
S
A
G
T
A
N

R
T
E
P
H
T
O

L
A
T
O
T

0.68  21.92 
0.11 
0.00 
0.00 
0.00 
5.99  13.75 
12.8

6  27.37 
1.87 
4.06 
3.03  29.40 

The energy use in physical terms together with energy expressed in monetary terms serves for the 
calculation of the inverse of energy price 𝐼𝑂_𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽2010 in equation (96). It also feeds into the 
disaggregation of the energy consumption over 11 carriers (equation 97). 

ELIOD energy and emission accounts are expected to be published in 2019. 

44 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
References 

Capros,  P.,  De  Vita,  A.,  Tasios,  N.,  Siskos,  P.,    Kannavou,  M.,  Petropoulos,  A.,  Evangelopoulou  S. 
(2016).  EU  Reference  Scenario  2016:  Energy,  transport  and  GHG  emissions  Trends  to  2050.   
Publications Office of the European Union, Luxembourg , doi: 10.2833/001137. 

Genty, A., Arto, I., Neuwahl, F. (2012). Final database of environmental Satellite accounts: technical 
report on their compilation. WIOD Documentation Deliverable 6. 

Koetse, M.  J.,  de  Groot,  H.  L.  F.,  Florax,  R.  J.  G. M. (2008)  Capital-energy  substitution and  shifts  in 
factor demand: A meta-analysis. Energy Economics 30 (5): 2236–2251. 

Kratena,  K.,  Streicher,  G.,  Temurshoev,  U.,  Amores,  A.F.,  Arto,  I.,  Mongelli,  I.,  Neuwahl,  F.,  Rueda-
Cantuche, J.M., Andreoni. V. (2013). FIDELIO 1: Fully Interregional Dynamic Econometric Long-term 
Input-Output  Model  for  the  EU27.  EUR  25985,  Publications  Office  of  the  European  Union, 
Luxembourg, doi:  10.2791/17619. 

Kratena, K., Streicher, G., Salotti, S., Sommer, M., Valderas Jaramillo, J. (2017). FIDELIO 2: Overview 
and  theoretical  foundations  of  the  second  version  of  the  Fully  Interregional  Dynamic  Econometric 
Long-term Input-Output model for the EU-27. EUR 28503, Publications Office of the European Union, 
Luxembourg, doi:  10.2760/313390. 

Okagawa,  A.,  Ban,  K.  (2008).  Estimation  of  substitution  elasticities  for  CGE  models.  Mimeo,  Osaka 
University : 1–18. 

Montinari,  L.,  Amores,  A.F.,  Rueda-Cantuche,  J.M.  (2016).  Fixed  capital  indicators  for  the  EU-28 
Member  States  (1995-2015):  Data  and  methodology  of  calculations.  Deliverable  C5.6  TIMESUT3 
Contract JRC Ref. 33324-2014-01. 

Tyrväinen,  T.  (1995). Real  wage  resistance  and  Unemployment :  Multivariate  Analysis  of 
Cointegration Relations in 10 OECD countries. OECD Jobs Study Working Paper Series 10. 

Van der Horst, A. (2002). Structural estimates of equilibrium unemployment in six OECD Economies. 
CPB Discussion Paper 19. 

Wilhelmsson, M., 2008. House price depreciation rates and level of maintenance. Journal of Housing 
Economics, 17 (1), 88-101. 

45 

 
 
 
 
 
 
 
List of Figures 

Figure 1  Production block in FIDELIO ..................................................................................................... 2 
Figure 2  Household block in FIDELIO ..................................................................................................... 3 
Figure 3  Government block in FIDELIO .................................................................................................. 3 
Figure 4  Trade block in FIDELIO ............................................................................................................. 4 

46 

 
 
 
 
 
List of Tables 

Table 1  Austrian market shares for the first four products ................................................................... 7 
Table 2  Austrian factors shares for the first eight products ................................................................ 10 
Table 3  Values of the caids parameters for Austria ............................................................................... 17 
Table 4  First eleven entries of the EnC-EnCd bridge matrix ................................................................ 22 
Table 5  First eight entries of the IO_EnergyTJHH matrix ..................................................................... 23 
Table 6  Austrian bridge matrix between CPEn and the detailed energy carriers ................................ 24 
Table 7  First eight entries of the IO Make and Use data ..................................................................... 26 
Table 8  Exchange rates used in FIDELIO .............................................................................................. 27 
Table 9  First eight entries of the trade shares matrix .......................................................................... 28 
Table 10  First eight entries of the matrix of exports to the rest of the World .................................... 29 
Table 11  First eight entries of the matrix splitting ITTM among the TIRS commodities ..................... 30 
Table 12  First eight entries of the transit cost shares matrix .............................................................. 30 
Table 13  VA components and their codes ........................................................................................... 31 
Table 14  First eight entries of the VA components for Austria ........................................................... 33 
Table 15  Heating degree days (Hdd) in 2010 ....................................................................................... 36 
Table 16  First five entries of the three parameters for the efficiency of appliances and vehicles ...... 36 
Table 17  Average household size in FIDELIO ....................................................................................... 37 
Table 18  Household consumption data for Austria ............................................................................. 38 
Table 19  Austrian bridge to NACE Rev. 2 for food consumption ......................................................... 40 
Table 20  Values of the governmental variables for the base year for three countries ....................... 41 
Table 21  Base year unemployment rates ............................................................................................ 42 
Table 22  Labour supply rates for eight countries ................................................................................ 42 
Table 23  Austrian energy prices 2010-2015 ........................................................................................ 43 
Table 24  Austrian gross energy use by energy commodities for selected industries (TJ) ................... 44 

47 

 
 
 
 
 
Annexes 

Annex 1 List of sets in FIDELIO 
Set 
aC (aU) 
aU 
CPC 
CPEn (CPC) 
eG (G) 
EnC 
EnCcalc (EnC) 
EnCd 
G 
LS 
LSca (LS) 
neG (G) 
nTIR (G) 
QC (CPC) 
R (WR) 
S (aU) 
TIRS (G) 
VAC 
WR 
Note: The table lists both sets and sub-sets.for sub-sets, the respective set is specified in parenthesis 

Description 
"All Category": Components of final demand  
"All Users": Economic agents in supply-use-scheme (industries plus final demand)  
"CP Commodity Groups": Commodities in private consumption block  
"CP Energy Commodities": Energy goods in private consumption block 
"Energy Good": Energy commodities  
"Energy Carriers": Five main energy carriers and total energy 
"Energy Carriers Calculation": Five main energy carriers 
"Energy Carriers _detail": Eleven energy carriers 
"Good": Commodities in the supply-use-scheme (2-digit NACE labels) 
"Labour Skills": three labour skill levels (low, medium, and high) and total labour 
"Labour Skills Calculation": three labour skill levels 
"Non-Energy Good": Non-energy commodities  
"Non-TIR": Goods and services NOT used in international trade and transport TIR  
"QAIDS Commodity": Commodities included in QAIDS-model  
"Region": Countries modelled in FIDELIO (EU28 + 7 nonEU)  
"Sector": Industries in the supply-use-scheme ("aU" without final demand)  
"TIR Services": Services used in international trade and transport (TIR)  
"VA Components": Components of value added  
"World region": Countries in FIDELIO (EU28 + 7 nonEU + ROW as a residual) 

48 

 
 
 
 
Annex 2 List of NACE Rev. 2 industries in FIDELIO 
Sector 
A01  
A02  
A03  
B  
C10T12  
C13T15  

Description 
Crop and animal production, hunting and related service activities 
Forestry and logging 
Fishing and aquaculture 
Mining and quarrying 
Manufacture of food products, beverages and tobacco products 
Manufacture of textiles, wearing apparel and leather products 
Manufacture of wood and of products of wood and cork, except furniture; manufacture of 
articles of straw and plaiting materials 
Manufacture of paper and paper products 
Printing and reproduction of recorded media 
Manufacture of coke and refined petroleum products 
Manufacture of chemicals and chemical products 
Manufacture of basic pharmaceutical products and pharmaceutical preparations 
Manufacture of rubber and plastic products 
Manufacture of other non-metallic mineral products 
Manufacture of basic metals 
Manufacture of fabricated metal products, except machinery and equipment 
Manufacture of computer, electronic and optical products 
Manufacture of electrical equipment 
Manufacture of machinery and equipment n.e.c. 
Manufacture of motor vehicles, trailers and semi-trailers 
Manufacture of other transport equipment 
Manufacture of furniture; other manufacturing 
Repair and installation of machinery and equipment 
Electricity, gas, steam and air conditioning supply 
Water collection, treatment and supply 
Sewerage;  waste  collection,  treatment  and  disposal  activities;  materials  recovery; 
remediation activities and other waste management services 
Construction 
Wholesale and retail trade and repair of motor vehicles and motorcycles 
Wholesale trade, except of motor vehicles and motorcycles 
Retail trade, except of motor vehicles and motorcycles 
Land transport and transport via pipelines 
Water transport 
Air transport 
Warehousing and support activities for transportation 
Postal and courier activities 
Accommodation; food and beverage service activities 
Publishing activities 
Motion  picture,  video  and  television  programme  production,  sound  recording  and  music 
publishing activities; programming and broadcasting activities 
Telecommunications 
Computer programming, consultancy and related activities; information service activities 
Financial service activities, except insurance and pension funding 
Insurance, reinsurance and pension funding, except compulsory social security 
Activities auxiliary to financial services and insurance activities 
Real estate activities 
Legal and accounting activities; activities of head offices; management consultancy activities 
Architectural and engineering activities; technical testing and analysis 
Scientific research and development 
Advertising and market research 
Other professional, scientific and technical activities; veterinary activities 
Administrative and support service activities 
Public administration and defence; compulsory social security 

49 

C16  
C17  
C18  
C19  
C20  
C21  
C22  
C23  
C24  
C25  
C26  
C27  
C28  
C29  
C30  
C31_32  
C33  
D35  
E36  

E37T39  
F  
G45  
G46  
G47  
H49  
H50  
H51  
H52  
H53  
I  
J58  

J59_60  
J61  
J62_63  
K64  
K65  
K66  
L68  
M69_70  
M71  
M72  
M73  
M74_75  
N 
O84  

 
(cont'd) 

Annex 2 List of NACE Rev. 2 industries in FIDELIO 
Sector 
P85  
Q 
R-S  
T  

Description 
Education 
Human health and social work activities 
Arts, entertainment and recreation.  Other service activities 
Activities  of  households  as  employers;  undifferentiated  goods  and  services  producing 
activities of households for own use 
Activities of extraterritorial organisations and bodies 

U  

50 

 
 
 
 
CPA_C17 
CPA_C18 
CPA_C19 
CPA_C20 
CPA_C21 
CPA_C22 
CPA_C23 
CPA_C24 
CPA_C25 
CPA_C26 
CPA_C27 
CPA_C28 
CPA_C29 
CPA_C30 
CPA_C31_C32 
CPA_C33 
CPA_D35 
CPA_E36 
CPA_E37-E39 

Annex 3 List of CPA 2008 products in FIDELIO 
Description 
Good 
Products of agriculture, hunting and related services 
CPA_A01 
Products of forestry, logging and related services 
CPA_A02 
Fish and other fishing products; aquaculture products; support services to fishing 
CPA_A03 
Mining and quarrying 
CPA_B 
Food products; Beverages; Tobacco products 
CPA_C10-C12 
Textiles; Wearing apparel; Leather and related products 
CPA_C13-C15 
Wood  and  of  products  of  wood  and  cork,  except  furniture;  articles  of  straw  and  plaiting 
CPA_C16 
materials 
Paper and paper products 
Printing and recording services 
Coke and refined petroleum products 
Chemicals and chemical products 
Basic pharmaceutical products and pharmaceutical preparations 
Rubber and plastic products 
Other non-metallic mineral products 
Basic metals 
Fabricated metal products, except machinery and equipment 
Computer, electronic and optical products 
Electrical equipment 
Machinery and equipment n.e.c. 
Motor vehicles, trailers and semi-trailers 
Other transport equipment 
Furniture; Other manufactured goods 
Repair and installation services of machinery and equipment 
Electricity, gas, steam and air conditioning 
Natural water; water treatment and supply services 
Sewerage  services;  sewage  sludge;  Waste  collection,  treatment  and  disposal  services; 
materials recovery services; Remediation services and other waste management services 
Construction and construction works 
Wholesale and retail trade and repair services of motor vehicles and motorcycles 
Wholesale trade services, except of motor vehicles and motorcycles 
Retail trade services, except of motor vehicles and motorcycles 
Land transport services and transport services via pipelines 
Water transport services 
Air transport services 
Warehousing and support services for transportation 
Postal and courier services 
Accommodation and food services 
Publishing services 
Motion picture, video and television programme production services, sound recording and 
music publishing; Programming and broadcasting services 
Telecommunications services 
Computer programming, consultancy and related services; Information services 
Financial services, except insurance and pension funding 
Insurance, reinsurance and pension funding services, except compulsory social security 
Services auxiliary to financial services and insurance services 
Real estate services 
Legal and accounting services; Services of head offices; management consulting services 
Architectural and engineering services; technical testing and analysis services 
Scientific research and development services 
Advertising and market research services 

CPA_J61 
CPA_J62_J63 
CPA_K64 
CPA_K65 
CPA_K66 
CPA_L68 
CPA_M69_M70 
CPA_M71 
CPA_M72 
CPA_M73 
CPA_M74_M75  Other professional, scientific and technical services; Veterinary services 
CPA_N 
CPA_O84 

CPA_F 
CPA_G45 
CPA_G46 
CPA_G47 
CPA_H49 
CPA_H50 
CPA_H51 
CPA_H52 
CPA_H53 
CPA_I 
CPA_J58 
CPA_J59_J60 

Administrative and support services 
Public administration and defence services; compulsory social security services 

51 

 
(cont'd) 

Annex 3 List of CPA 2008 products in FIDELIO 
Description 
Good 
Education services 
CPA_P85 
Human health and social work services 
CPA_Q 
Arts, entertainment, recreation and other services 
CPA_R_S 
Services of households as employers 
CPA_T 
Services provided by extraterritorial organisations and bodies 
CPA_U 

52 

 
 
 
 
Annex 4 List of FIDELIO private consumption products and corresponding COICOP goods 

1 

2 
3 

4 
5 
6 

7 

Private consumption 
products 
Food 

Clothing 
Furniture/equipment 

COICOP code 
CP01 
CO021 
CP03 
CP051 
CP052 
CP054 
CP055 
CP056 
CP06 
CP08 

Financial services 

Imputed rent 
Electricity/heating 

Health 
Communication 
Recreation, accommodation  CP094 
CP111 
CP112 
CP125 
CP126 
CP042 
CP45 
CP053 
CP071 
CP072 
CP073 
CP09 (no CP094) 
CP10 
CP12  
(no CP125&CP126) 
CP022 
CP023 

8 
9 
10  Appliances 
11  Vehicles 
12  Private transport 
13  Public transport 
14  Other 

COICOP product 
Food and non-alcoholic beverages 
Alcoholic beverages 
Clothing and footwear 
Furniture and furnishings 
Household textiles 
Glassware, tableware and household utensils 
Tools and equipment for house and garden 
Goods and services - household maintenance 
Health 
Communications 
Recreational and cultural services 
Catering services 
Accommodation services 
Insurance 
Financial services n.e.c. 
Imputed rentals for housing 
Electricity, gas and other fuels 
Household appliances 
Purchase of vehicles 
Operation of personal transport equipment 
Transport services 
Recreation and culture except services 
Education 
Restaurants and hotels 

Tobacco 
Narcotics 

53 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Annex 5 FIDELIO endogenous variables 
Variable 
𝐶𝑎𝑝𝑖𝑡𝑎𝑙(𝑅, 𝑆) 
𝐶𝑎𝑠ℎ𝐻𝐻(𝑅) 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐴𝑝𝑝𝑙") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, 𝐶𝑃𝐶) 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐸𝑙𝑒𝑐") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐸𝑛𝑒𝑟𝑔𝑦") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐹𝑢𝑒𝑙") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝐻𝑒𝑎𝑡") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑁𝑜𝑛𝐷𝑢𝑟") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑃𝑢𝑏𝑇𝑟𝑎𝑛") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑅𝑒𝑛𝑡𝑠") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑇𝑜𝑡") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑇𝑜𝑡𝐷𝑢𝑟") 
𝐶𝑃𝐶𝑜𝑚𝑚("𝑇𝑟𝑎𝑛") 
𝐶𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑉𝑒ℎ") 
𝐶𝑃𝑔𝑓𝑐𝑓_ℎ𝑜𝑢𝑠𝑖𝑛𝑔(𝑅) 
𝐶𝑃𝑄𝐴𝐼𝐷𝑆(𝑅) 

𝐸𝑚_𝐶𝐻4(𝑅, 𝑆) 
𝐸𝑚_𝐶𝑂2(𝑅, 𝑆, 𝐸𝑛𝐶𝑑) 
𝐸𝑚_𝐶𝑂2𝐻𝐻(𝑅, 𝐸𝑛𝐶𝑑) 
𝐸𝑚_𝑁2𝑂(𝑅, 𝑆) 
𝐸𝑚𝑝𝑙(𝑅, 𝑆, 𝐿𝑆) 
𝐸𝑛𝑒𝑟𝑔𝑦(𝑅, 𝑆) 
𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽(𝑅, 𝑆) 
𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽𝐻𝐻(𝑅, 𝑆) 
𝐺_𝐵𝑃(𝑅, 𝐺, 𝑎𝑈) 
𝐺_𝑃𝑃(𝑅, 𝐺, 𝑎𝑈) 
𝐺_𝑃𝑃(𝑅, 𝐺, "𝐶𝑃") 
𝐺_𝑃𝑃(𝑅, 𝐺, "𝐶𝐺") 
𝐺_𝑃𝑃(𝑅, 𝐺, "𝐼𝑛𝑣") 
𝐺_𝑃𝑃(𝑅, 𝐺, "𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦") 
𝐺_𝑃𝑃(𝑅, 𝐺, "𝑁𝑃𝐼𝑆𝐻") 
𝐺𝐷_𝐵𝑃(𝑅, 𝐺, 𝑎𝑈) 
𝐺𝐷𝑃(𝑅) 
𝐺𝐷𝑡𝑜𝑡(𝑅, 𝐺) 
𝐺𝑜𝑣𝐵𝑑𝑔𝑡(𝑅) 
𝐺𝑜𝑣𝐶𝑜𝑛𝑠(𝑅) 
𝐺𝑜𝑣𝐷𝑒𝑏𝑡(𝑅) 
𝐺𝑜𝑣𝑔𝑓𝑐𝑓(𝑅) 
𝐺𝑜𝑣𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡(𝑅) 
𝐺𝑜𝑣𝑂𝑝𝑆𝑢𝑟(𝑅) 
𝐺𝑜𝑣𝑃𝑟𝑜𝑑𝑇𝑎𝑥(𝑅) 
𝐺𝑜𝑣𝑇𝑙𝑆(𝑅) 
𝐺𝑜𝑣𝑇𝑜𝑡𝐸𝑥𝑝(𝑅) 
𝐺𝑜𝑣𝑇𝑜𝑡𝑅𝑒𝑣(𝑅) 
𝐼_𝑃𝑃_𝐺𝑂𝑃(𝑅, 𝑆) 
𝐼_𝑃𝑃_𝐾𝑆𝑡𝑜𝑐𝑘(𝑅, 𝑆) 
𝐼_𝑃𝑃_𝑄(𝑅, 𝑆) 
𝐼𝑛𝑝𝑢𝑡𝐹𝑢𝑒𝑙(𝑅, 𝑆, 𝐸𝑛𝐶𝑑) 
𝐾𝐴𝑝𝑝𝑙(𝑅) 
𝐾𝐻𝑜𝑢𝑠(𝑅) 
𝐾𝐿𝐸_𝑄(𝑅, 𝑆) 

Description 
Sectoral demand for capital 
Household cash-in-hands 
Household consumption of appliances 
Household consumption by commodity group (CPC categories) 
Household consumption of electricity 
Household consumption of energy services 
Household consumption of fuel 
Household consumption of heating 
Household total non-durables durable consumption 
Household consumption of public transport services 
Household durables consumption related to houses 
Household total consumption 
Household total durables consumption 
Household consumption of transport 
Household durables consumption related to vehicles 
Household expenditure in houses 
Household consumption in food, clothing, furniture and equipment, health, 
communication,  recreation  and  accommodation,  financial  services,  and 
other (QAIDS products) 
Sectoral CH4 emissions related to production 
Sectoral CO2 emissions related to energy consumption 
CO2 household emissions by region and by detailed energy carrier 
Sectoral N2O emissions related to production 
Employment 
Sectoral demand for energy intermediates 
Sectoral demand for energy in TJ 
Household demand for energy in TJ 
Demand for domestic and imported products in basic prices  
Demand for commodities in purchaser prices 
Household demand for commodities  
Government demand for commodities 
Investment demand for commodities 
Demand for inventories 
NPISH demand for commodities 
Demand for domestically produced goods by each user 
Gross domestic product 
Total demand for domestically produced goods 
Government budget balance 
Government consumption 
Government debt 
Government capital formation 
Interests paid by the government 
Share of gross operating surplus going to the government 
Production taxes paid by firms to the government 
Taxes less subsidies paid by firms to the government 
Government total expenditure 
Governmental total revenues 
Sectoral investment computed from gross operating surplus 
Sectoral investment computed from capital stock 
Sectoral investment computed from output 
Sectoral demand or energy carriers 
Household stock of appliances 
Household stock of houses 
KLE share in the first CES nest level 

54 

 
(cont'd) 

Annex 5 FIDELIO endogenous variables 
Variable 
𝐾𝑆𝑡𝑜𝑐𝑘(𝑅, 𝑆) 
𝐾𝑉𝑒ℎ𝑖𝑐𝑙𝑒𝑠(𝑅) 
𝐿𝑎𝑏𝑜𝑢𝑟(𝑅, 𝑆) 
𝐿𝑆𝑢𝑝𝑝𝑙𝑦(𝑅, 𝐿𝑆) 
𝑀(𝑅, 𝐺, 𝑎𝑈) 
𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠(𝑅, 𝑆) 
𝑀𝑆ℎ𝑎𝑟𝑒(𝑅, 𝐺, 𝑎𝑈) 
𝑀𝑡𝑜𝑡(𝑅, 𝐺) 
𝑁𝑒𝑡𝑊𝑜𝑟𝑡ℎ𝐻𝐻(𝑅) 
𝑁𝑃𝐼𝑆𝐻(𝑅) 
𝑃_𝐾𝐿𝐸(𝑅, 𝑆) 
𝑃_𝑆𝑀(𝑅, 𝑆) 
𝑃𝐴𝑝𝑝𝑙(𝑅) 
𝑃𝐶𝑜𝑚𝑚(𝑅, 𝑄𝐶) 
𝑃𝐶𝑜𝑚𝑚(𝑅, "𝑉𝑒ℎ") 
𝑃𝐶𝑃(𝑅) 
𝑃𝐺(𝑅, 𝐺) 
𝑃𝐺𝑑𝑜𝑚(𝑅, 𝐺, 𝑎𝑈) 
𝑃𝐺𝑃𝑎𝑟𝑡𝑛𝑒𝑟𝑠(𝑅, 𝑊𝑅, 𝐺) 
𝑃𝐺𝑃𝑎𝑡𝑛𝑒𝑟𝑠(𝑅, 𝑅1, 𝐺) 
𝑃𝐺𝑃𝑎𝑡𝑛𝑒𝑟𝑠(𝑅, "𝑅𝑂𝑊", 𝐺) 
𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐶𝑎𝑝𝑖𝑡𝑎𝑙") 
𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐸") 
𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐿") 
𝑃𝐿(𝑅,S,LSca) 
𝑃𝑀(𝑅, 𝐺, 𝑎𝑈) 
𝑃𝑀𝑐𝑖𝑓(𝑅, 𝐺) 
𝑃𝑄(𝑅, 𝑆) 
𝑃𝑇𝑇𝑀(𝑅, 𝑎𝑈) 
𝑃𝑈𝑠𝑒(𝑅, 𝐺, 𝑎𝑈) 
𝑄(𝑅, 𝑆) 
𝑄𝑟𝑒𝑎𝑙(𝑅, 𝑆) 
𝑄𝐴𝐼𝐷𝑆𝑆ℎ𝑎𝑟𝑒(𝑅, 𝑄𝐶) 
𝑆𝑎𝑣𝐻𝐻(𝑅) 
𝑆𝐶_𝑄(𝑅, 𝑆) 
𝑆𝐸_𝑄(𝑅, 𝑆) 
𝑆𝐿_𝑄(𝑅, 𝑆) 
𝑆𝑀_𝑄(𝑅, 𝑆) 
𝑇𝐼𝑅𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅) 
𝑇𝐼𝑅𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑇𝐼𝑅𝑆) 
𝑇𝑙𝑆(𝑅, 𝐺, 𝑎𝑈) 
𝑇𝑟𝑎𝑑𝑒𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅) 
𝑇𝑟𝑎𝑑𝑒𝑀𝑎𝑡𝑟𝑖𝑥(𝑅, 𝑊𝑅, 𝑇𝐼𝑅𝑆) 
𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠(𝑅, 𝑊𝑅, 𝐺) 
𝑇𝑇𝑀𝑝𝑎𝑖𝑑(𝑅, 𝐺, 𝑎𝑈) 
𝑇𝑇𝑀𝑟𝑒𝑐(𝑅, 𝐺, 𝑎𝑈) 
𝑈𝑛𝑒𝑚𝑝𝑅𝑎𝑡𝑒(𝑅, 𝐿𝑆) 
𝑉𝐴(𝑅, 𝑆) 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "𝐷𝑒𝑝𝑟") 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "𝑂𝑝𝑆𝑢𝑟") 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "𝑃𝑟𝑜𝑑𝑇𝑎𝑥") 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "SocSec") 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠(𝑅, 𝑆, "Wages") 
𝑌𝐷(𝑅) 

Description 
Capital stock 
Household stock of vehicles 
Sectoral demand for labour 
Labour supply 
Demand for imports in CIF prices 
Sectoral demand for materials 
Share of import over total demand 
Total import by region and good 
Household financial assets 
Consumption of non-profit institutions serving households 
Price of combined capital, energy, and labour inputs 
Price of the materials 
Price of appliances 
Price of the QAIDS products 
Price of private consumption by commodity group 
Consumer price index 
Domestic commodity price excluding TTM and TlS 
Domestic commodity price including TTM and TlS 
Price of imported products by trading partner (all countries) 
Price of imported products by trading partner (countries excluding ROW) 
Price of imported products by trading partner (only ROW) 
Price of capital 
Price of energy 
Price of labour 
Wages 
Import price including domestic margins and TlS 
Import price 
Output price 
Price of TTM 
Price of commodities 
Output by industry 
Real output by industry 
Shares of QAIDS commodities consumption 
Household savings 
Capital share in the second CES nest level 
Energy share in the second CES nest level 
Labour share in the second CES nest level 
Materials share in the first CES nest level 
Matrix of international trade and transport margins (nTIR products) 
Matrix of international trade and transport margins (TIRS products) 
Taxes less subsidies 
Trade matrix by trading partner related to nTIR commodities 
Trade matrix by trading partner related to TIRS commodities 
Import shares matrix by trading partner 
Transport and trade margins paid 
Transport and trade margins received 
Unemployment rate 
Sectoral value added 
Sectoral depreciation 
Sectoral net operating surplus 
Sectoral production taxes 
Sectoral social security contribution  
Sectoral wages  
Household disposable income 

55 

 
(cont'd) 

Annex 5 FIDELIO endogenous variables 
Variable 
𝑌𝐷𝑂𝑝𝑆𝑢𝑟𝐻𝐻(𝑅) 
𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒(𝑅) 
𝑌𝐷𝑆𝑆𝑒𝑐𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑟(𝑅) 
𝑌𝐷𝑇𝑎𝑥𝑒𝑠𝐻𝐻(𝑅) 
𝑌𝐷𝑇𝑟𝑎𝑛(𝑅) 
𝑌𝐷𝑂𝑡ℎ𝑒𝑟𝑇𝑟𝑎𝑛(𝑅) 

Description 
Share of gross operating surplus going to households 
Social security contributions paid by workers 
Social security contributions paid by firms 
Taxes paid by households to the government 
Transfers paid by the government to households 
Other transfers paid to households 

56 

 
 
 
 
Annex 6 FIDELIO exogenous variables 
Variable 
𝐸𝑓𝑓_𝐴𝑝𝑝𝑙(𝑅) 
𝐸𝑓𝑓_𝐻𝑒𝑎𝑡(𝑅) 
𝐸𝑓𝑓_𝑉𝑒ℎ(𝑅) 
𝑃𝐶𝑃𝐸𝑛𝑒𝑟𝑔𝑦(𝑅, 𝐶𝑃𝐸𝑛) 
𝑃𝐸𝑙𝑒𝑐(𝑅) 
𝑃𝐹𝑢𝑒𝑙(𝑅) 
𝑃𝐻𝑒𝑎𝑡(𝑅) 
𝑃𝐼𝑛𝑝𝑢𝑡𝑠(𝑅, 𝑆, "𝐸") 
𝑃𝑜𝑝(𝑅) 
𝑅𝑒𝑎𝑙𝐸𝑛𝑆ℎ𝑎𝑟𝑒𝑠(𝑅, 𝑆, 𝐸𝑛𝐶) 

Description 
Exogenous index capturing the efficiency of appliances 
Exogenous index capturing the efficiency of heating 
Exogenous index capturing the efficiency of vehicles 
Price of energy consumed by households 
Price of electricity 
Price of fuel 
Price of heating 
Price of energy 
Population 
Exogenous shares of the 5 main energy carriers 

57 

Annex 7 2010 data used to calibrate the FIDELIO parameters 
Parameter 
𝐶𝑃𝐶𝑜𝑚𝑚2010(𝑅, "𝐹𝑢𝑒𝑙") 
𝐶𝑃𝐶𝑜𝑚𝑚2010(𝑅, "𝑃𝑢𝑏𝑇𝑟𝑎𝑛") 
𝐺𝑜𝑣𝐼𝑛𝑡𝑅𝑎𝑡𝑒2010(𝑅) 
𝐼𝑂_𝑀2010(𝑅, 𝐺, 𝑎𝑈) 
𝐼𝑂_𝑀𝑎𝑘𝑒2010(𝑅, 𝐺, 𝑆) 
𝐼𝑂_𝑁𝑃𝐼𝑆𝐻2010(𝑅, 𝐺) 
𝐼𝑂_𝑈𝑠𝑒𝐵𝑃2010(𝑅, 𝐺, 𝑎𝑈) 
𝐼𝑂_𝑈𝑠𝑒_𝑃𝑃2010(𝑅, 𝐺, 𝑆) 
𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦_𝑃𝑃2010(𝑅, 𝐺) 
𝐼𝑛𝑣𝑀𝑎𝑡𝑟𝑖𝑥2010(𝑅, 𝐺, 𝑆) 
𝐿𝑎𝑏𝑜𝑢𝑟2010(𝑅, 𝑆) 
𝑁𝑢𝑚𝑏𝑒𝑟𝐻𝐻(𝑅) 
𝑄2010(𝑅, 𝑆) 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅, 𝑆, "Wages") 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅, 𝑆, "SocSec") 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅, 𝑆, "𝑃𝑟𝑜𝑑𝑇𝑎𝑥") 
𝑉𝐴𝑏𝑙𝑜𝑐𝑘𝑠2010(𝑅, 𝑆, "𝐷𝑒𝑝𝑟") 
𝑋𝑅𝑎𝑡𝑒2010(𝑅) 
𝑋𝑅𝑜𝑤2010(𝑅, 𝐺) 
𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒(R) 
𝑌𝐷𝑆𝑆𝑒𝑐2010
𝐻𝑒𝑎𝑡𝐷𝐷𝑎𝑦2010(𝑅) 
𝑉𝑒ℎ𝑃𝑜𝑝2010(𝑅) 

Description 
Household consumption of fuel 
Household consumption of public transport 
Interest rate paid by the government on the debt 
Imports by user in CIF prices 
Make matrix  
Consumption of non-profit institutions serving households 
Total use by user in basic prices 
Total use by industry in purchaser prices  
Commodity demand for inventories 
Matrix of investment by country, good, and industry 
Sectoral labour cost 
Number of households 
Sectoral output  
Sectoral wages  
Sectoral social security contribution  
Sectoral production taxes 
Sectoral depreciation 
Exchange rates from WIOD 
Export to the rest of the world 
Social security contributions paid by workers  
Measurement of heating degree days  
Average number of vehicles per person  

58 

 
 
 
 
Annex 8 FIDELIO calibrated parameters from 2010 data 
Parameter 
𝛼𝐶(𝑅, 𝑆) 
𝛼𝐿(𝑅, 𝑆) 
𝛼𝐸(𝑅, 𝑆) 
𝛼𝑀(𝑅, 𝑆) 
𝛼𝐾𝐿𝐸(𝑅, 𝑆) 
𝐶𝑃𝐵𝑟𝑖𝑑𝑔𝑒2010(𝑅, 𝐺, 𝐶𝑃𝐶) 

𝐵𝑟𝑖𝑑𝑔𝑒_𝐸𝑛𝐶𝑑2010(𝑅, 𝑆, 𝐸𝑛𝐶, 𝐸𝑛𝐶𝑑) 
𝐵𝑟𝑖𝑑𝑔𝑒_𝐸𝑛𝐶𝑑𝐻𝐻2010(𝑅, 𝐶𝑃𝐸𝑛, 𝐸𝑛𝐶𝑑) 

𝐵𝑃𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺) 
𝐺𝑜𝑣𝑆ℎ𝑎𝑟𝑒𝑔𝑓𝑐𝑓2010(𝑅) 
𝐼𝑂_𝐶𝑜𝑚𝑚𝑇𝑙𝑆2010(𝑅, 𝐺, 𝑎𝑈) 

𝐼𝑂_𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽2010(𝑅, 𝑆) 
𝐼𝑂_𝐸𝑛𝑒𝑟𝑔𝑦𝑇𝐽𝐻𝐻2010(𝑅, 𝐶𝑃𝐸𝑛) 
𝐼𝑂_𝐺𝑜𝑣𝐶𝑜𝑛𝑠𝑉𝐴2010(𝑅) 
𝐼𝑂_𝐺𝑜𝑣𝑆ℎ𝑂𝑝2010(𝑅) 

𝐼𝑂_𝐻𝐻𝑆ℎ𝑂𝑝2010(𝑅) 

𝐼𝑂_𝐼_𝐺𝑂𝑃2010(𝑅, 𝑆) 
𝐼𝑂_𝐼_𝑄2010(𝑅, 𝑆) 
𝐼𝑂_𝑃𝑟𝑜𝑑𝑇𝑎𝑥𝑄2010(𝑅, 𝑆) 
𝐼𝑂_𝑇𝑎𝑥_𝐼𝑛𝑐2010(𝑅) 
𝐼𝑂𝐸𝑚_𝐶𝐻42010(𝑅, 𝑆) 
𝐼𝑂𝐸𝑚_𝐶𝑂22010(𝑅, 𝑆, 𝐸𝑛𝐶𝑑) 
𝐼𝑂𝐸𝑚_𝐶𝑂2𝐻𝐻2010(𝑅, 𝐸𝑛𝐶𝑑) 
𝐼𝑂𝐸𝑚_𝑁2𝑂2010(𝑅, 𝑆) 
𝐼𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑆) 
𝐿𝑆𝑢𝑝𝑝𝑙𝑦𝑅𝑎𝑡𝑒2010(𝑅, 𝐿𝑆) 
𝑚𝑎𝑘𝑒(𝑅, 𝐺, 𝑆) 
𝑀𝑘𝑡𝑆ℎ𝑎𝑟𝑒𝑠2010
𝑀𝑟𝑔𝑃𝑎𝑖𝑑2010(𝑅, 𝐺, 𝑎𝑈) 

𝑀𝑟𝑔𝑅𝑒𝑐2010(𝑅, 𝐺, 𝑎𝑈) 
𝑂𝑝𝑆𝑢𝑟𝐻𝐻_𝐺2010(𝑅) 
𝑅𝑒𝑛𝑡_𝐻𝑜𝑢𝑠𝑒𝑠2010(𝑅) 
𝑆𝐸_𝑄2010(𝑅, 𝑆) 
𝑆𝐿_𝑄2010(𝑅, 𝑆) 
𝑆𝑘𝑖𝑙𝑙𝑆ℎ𝑎𝑟𝑒𝑠2010(𝑅, 𝑆, 𝐿𝑆𝑐𝑎) 
𝑆𝑀_𝑄2010(𝑅, 𝑆) 
𝑆_𝑄2010(𝑅, 𝑆) 
𝑆𝐶_𝑄2010(𝑅, 𝑆) 
𝑇𝑟𝑎𝑑𝑒𝑆ℎ𝑎𝑟𝑒𝑠2010(𝑅, 𝑊𝑅, 𝐺) 
𝑇𝐼𝑅𝑆ℎ𝑎𝑟𝑒𝑠2010(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅𝑆, 𝑇𝐼𝑅𝑆) 
𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝐶𝑜𝑠𝑡2010(𝑅, 𝑊𝑅, 𝑛𝑇𝐼𝑅) 

𝑇𝑇𝑀𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, 𝑎𝑈) 
𝑈𝑠𝑒𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, "𝐶𝐺") 
𝑈𝑠𝑒𝑆𝑡𝑟𝑢𝑐𝑡2010(𝑅, 𝐺, "𝑁𝑃𝐼𝑆𝐻") 

Description 
Relative share of capital in the second CES nest 
Relative share of labour in the second CES nest 
Relative share of energy in the second CES nest 
Relative share of materials in the first CES nest 
Relative share of the KLE bundle in the first CES nest 
Bridge matrix from CPC consumption categories to NACE Rev. 2 
consumption classification  
Bridge matrix from 5 to 11 sectoral energy carriers 
Bridge  matrix  from  3  household  energy  commodities    to  11 
energy carriers 
Proportion of BP over BP plus TTM 
Proportion of public investment over public consumption 
Proportion  of  taxes  less  subsidies  over  the  use  value  in  basic 
prices plus trade and transport margins 
Inverse of the price of energy for sectoral consumption 
Inverse of the price of energy for household consumption 
Proportion of government consumption over total VA 
Proportion  of  government  operating  surplus  over  gross 
operating surplus 
Proportion of household operating surplus over gross operating 
surplus 
Proportion of investment over gross operating surplus 
Proportion of investment over output 
Proportion of production taxes over output Q 
Ratio of household income taxes over income 
CH4missions coefficient  per sectoral unit of output 
CO2missions coefficient  per sectoral energy inputs  used 
CO2missions coefficient  per household energy use 
N2Omissions coefficient  per sectoral unit of output 
Commodity investment structure by industry  
Participation rate by skill level 
Sector shares in output of any good 
Trade and transport margins as a share of use (PP) minus taxes 
less subsidies 
Share of TTM received over the total TTM paid 
Share of operating surplus that goes to households  
Ratio of rents over housing stock 
Share of energy intermediates over sectoral production 
Share of labour over sectoral production 
Shares of skill groups 
Share of material intermediates over sectoral production 
Share of total intermediate inputs over sectoral production 
Share of capital over sectoral production 
Import share by trading partner 
Transport cost distribution over TIRS commodities 
International trade and transport margins expressed as % over 
imports in FOB 
Proportion of TTM over BP plus TTM 
Use table commodity structure of government  consumption 
Use table commodity structure of NPISH consumption 

59 

 
 
 
 
Annex 9 FIDELIO estimated parameters 
Parameter 
𝑎𝑖𝑑𝑠(𝑅, 𝑄𝐶)
𝑐1
𝑎𝑖𝑑𝑠(𝑅, 𝑄𝐶, 𝑄𝐶)
𝑐𝑄𝐶
𝑎𝑝𝑝𝑙
𝑐2
𝑎𝑝𝑝𝑙
𝑐3
𝑒𝑙
𝑐2
𝑒𝑙
𝑐3
𝑒𝑙
𝑐4
𝑓𝑢𝑒𝑙
𝑐2
𝑓𝑢𝑒𝑙
𝑐3
𝑓𝑢𝑒𝑙
𝑐4
ℎ𝑒𝑎𝑡
𝑐2
ℎ𝑒𝑎𝑡
𝑐3
ℎ𝑒𝑎𝑡
𝑐4
ℎ𝑜𝑢
𝑐2
ℎ𝑜𝑢
𝑐3
ℎ𝑜𝑢
𝑐4
ℎ𝑜𝑢
𝑐5
ℎ𝑜𝑢
𝑐6
ℎ𝑜𝑢
𝑐7
𝑛𝑜𝑛𝑑
𝑐2
𝑛𝑜𝑛𝑑
𝑐3
𝑛𝑜𝑛𝑑
𝑐4
𝑛𝑜𝑛𝑑
𝑐5
𝑣𝑒ℎ
𝑐2
𝑣𝑒ℎ
𝑐3
𝑣𝑒ℎ
𝑐4
𝑣𝑒ℎ
𝑐5
𝑣𝑒ℎ
𝑐6
𝑣𝑒ℎ
𝑐7
𝑣𝑒ℎ
𝑐8
𝑣𝑒ℎ
𝑐9

Description 
Parameter governing household consumption in QIDS products 
Parameter governing household consumption in QIDS products 
Parameter governing household consumption in appliances 
Parameter governing household consumption in appliances 
Parameter governing household consumption in electricity 
Parameter governing household consumption in electricity 
Parameter governing household consumption in electricity 
Parameter governing household consumption in fuel 
Parameter governing household consumption in fuel 
Parameter governing household consumption in fuel 
Parameter governing household consumption in heating 
Parameter governing household consumption in heating 
Parameter governing household consumption in heating 
Parameter governing household consumption in housing 
Parameter governing household consumption in housing 
Parameter governing household consumption in housing 
Parameter governing household consumption in housing 
Parameter governing household consumption in housing 
Parameter governing household consumption in housing 
Parameter governing household consumption in non-durables 
Parameter governing household consumption in non-durables 
Parameter governing household consumption in non-durables 
Parameter governing household consumption in non-durables 
Parameter governing household consumption in vehicles 
Parameter governing household consumption in vehicles 
Parameter governing household consumption in vehicles 
Parameter governing household consumption in vehicles 
Parameter governing household consumption in vehicles 
Parameter governing household consumption in vehicles 
Parameter governing household consumption in vehicles 
Parameter governing household consumption in vehicles 

Value 

 0.54 
 0.68 
 0.21 
 0.59 
 0.13 
 0.38 
 0.69 
-0.47 
 0.10 
 0.84 
 0.46 
 0.90 
-0.35 
-0.18 
-1.42 
 0.04 
 0.12 
 0.23 
-0.14 
-0.82 
 0.01 
 0.43 
 0.02 
 0.91 
-0.36 
-0.81 
 0.02 
 0.02 
 0.86 

60 

Annex 10 FIDELIO parameters from literature 
Parameter 
𝛿𝑎𝑝𝑝𝑙 
𝛿ℎ𝑜𝑢𝑠 
𝛿𝑣𝑒ℎ 
𝜃 
𝜎𝐾_𝐿_𝐸 
𝜎𝐾𝐿𝐸_𝑀 
𝜎𝐴𝑟𝑚(𝑅, 𝐺) 
𝐷𝑒𝑝𝑟𝑅𝑎𝑡𝑒 
𝑓𝑝𝑟𝑜𝑑(𝑅, 𝑆, "𝐶𝑎𝑝𝑖𝑡𝑎𝑙") 
𝑓𝑝𝑟𝑜𝑑(𝑅, 𝑆, "𝐿") 
𝑓𝑝𝑟𝑜𝑑(𝑅, 𝑆, "𝐸") 
𝐾𝑅𝑒𝑚𝑢𝑛𝑒𝑟 

Description 
Depreciation rate of appliances 
Depreciation rate of houses 
Depreciation rate of vehicles 
Collateral for household durables 
Substitution elasticity between capital, labour, and energy 
Substitution elasticity between KLE and materials 
Armington elasticitiy 
Depreciation rate of capital stock 
Parameter of capital productivity in the second CES nest 
Parameter of labour productivity in the second CES nest 
Parameter of energy productivity in the second CES nest 
Remuneration of capital 

Value 
0.07 
 0.015 
 0.08 
0.37 
0.95 
0 

0.05 
1 
1 
1 
0.03 

61 

Annex 11 FIDELIO countries and abbreviations 
Country 
European Countries 

Abbreviation 

Austria 
Belgium 
Bulgaria 
Croatia 
Cyprus 
Czech Republic 
Denmark 
Estonia 
Finland 
France 
Germany 
Greece 
Hungary 
Ireland 
Italy 
Latvia 
Lithuania 
Luxembourg 
Malta 
Netherlands 
Poland 
Portugal 
Romania 
Slovakia 
Slovenia 
Spain 
Sweden 
United Kingdom 
Non-European countries 

Brazil 
China 
India 
Japan 
Russia 
Turkey 
United States 
Rest of the world 

AUT 
BEL 
BGR 
HRV 
CYP 
CZE 
DEN 
EST 
FIN 
FRA 
DEU 
GRC 
HUN 
IRL 
ITA 
LVA 
LTU 
LUX 
MLT 
NLD 
POL 
PRT 
ROU 
SVK 
SVN 
ESP 
SWE 
GBR 

BRA 
CHN 
 IND 
JPN 
RUS 
TUR 
USA 
ZROW 

62 

Annex 12. Energy commodities (plus losses) in the WIOD satellite accounts 

WIOD Code 

IEA Code 

COAL 

Hard coal and derivatives 

Lignite and derivatives 

Coke 

HCOAL 

BCOAL 

COKE  

Crude oil, NGL and feedstocks 

CRUDE 

CRUDE & FEEDSTOCKS 

ANTCOAL + BITCOAL + COKCOAL + 
PATFUEL + SUBCOAL 
BKB + CAOLTAR + LIGNITE + PEAT 

GASCOKE + OVENCOKE 

CRUDEOIL + NGL + REFFEEDS +ADDITIVE 
+ NONCRUDE 

PETROLEUM PRODUCTS 

Diesel oil for road transport 

Motor gasoline 

DIESEL 

GASOLINE 

GASDIES(1)* 

MOTORGAS 

Jet fuel (kerosene and gasoline) 

JETFUEL 

AVGAS + JETGAS + JETKERO 

Light Fuel oil 

Heavy fuel oil 

Naphtha 

Other petroleum products 

GASES 

Natural gas 

Derived gas 

LFO 

HFO 

NAPHTA 

OTHPETRO 

NATGAS 

OTHGAS 

RENEWABLES & WASTES 

Industrial and municipal waste 

WASTE 

Biogasoline also including hydrated 
ethanol 
Biodiesel 

Biogas 

BIOGASOL 

BIODIESEL 

BIOGAS 

GASDIES(2)* 

RESFUEL 

NAPHTA 

BITUMEN + ETHANE + LPG + LUBRIC+ 
ONONSPEC + OTHKERO + PARWAX+ 
PETCOKE + REFINGAS + WHITESP 

NATGAS 

BLFURGS + COKEOVGS + GASWKSGS+ 
MANGAS + OXYSTGS 

INDWASTE + MUNWASTEN 
+MUNWASTER 
BIOGASOL + OBIOLIQ 

BIODIESEL 

GBIOMASS 

Other combustible renewables 

OTHRENEW 

CHARCOAL + RENEWNS + SBIOMASS 

ELECTRICITY & HEAT 

Electricity 

Heat 

Nuclear 

Hydroelectric 

Geothermal 

Solar 

Wind power 

Other sources 

LOSSES 

ELECTR 

HEATPROD 

NUCLEAR 

HYDRO 

GEOTHERM 

SOLAR 

WIND 

OTHSOURC 

ELECTR 

HEAT + HEATNS 

NUCLEAR 

HYDRO 

GEOTHERM 

SOLARPV + SOLARTH 

WIND 

BOILER + CHEMHEAT + HEATPUMP 
+OTHER + TIDE 

Distribution losses 

LOSS 

DISTLOSS 

63 

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