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The European Commission’s science and knowledge service
Joint Research Centre
Introducing Firm
Heterogeneity in a CGE Model
for Europe
2
Introducing Firm
Heterogeneity in a CGE
Model for Europe
Javier Barbero Jiménez
Francesco Di Comite
The views expressed are purely those of the authors and may not in any circumstances
be regarded as stating an official position of the European Commission.
The European Commission’s science and knowledge service
Joint Research Centre
3
Table of Contents
1. Background and motivation.
2. Trade theories in CGE.
3. The CGE model with heterogeneous firms.
• Trade module.
• General equilibrium.
4. Simulation example.
4
Background
• There is a growing need for place-based impact assessment of
public policies in the European Union.
• The available models for the EU:
• Identical firms.
• R&D at an aggregate level.
• Models:
• QUEST: DSGE. DG ECFIN.
• RHOMOLO: Regional CGE. Lecca et al. (2018).
• GEM-E3: Clean energy CGE. Carros et al. (2013).
5
Motivation
• Exploratory Research on heterogeneous firms general equilibrium
model (HETFIGE).
• Include in a modelling framework the empirical evidence that firms
have: • Different productivity
• Different sizes.
• Policy shocks may induce firms to relocate within an industry.
6
Firm Heterogeneity in one slide
• Model: Firms with higher productivity can produce and sell at lower
prices
𝑃𝑟𝑖𝑐𝑒 = 𝑀𝑎𝑟𝑘𝑈𝑝 ×𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡
𝑷𝒓𝒐𝒅𝒖𝒄𝒕𝒊𝒗𝒊𝒕𝒚
• Firms with: • Very low productivity: cannot survive and leave the market.
• Low productivity: operates only in domestic market.
• High productivity: export to foreign markets.
7
With Firm Heterogeneity
• The introduction of firm heterogeneity in a modelling framework
allow us to analyse:
• Within-industry relocation: firms increase or decrease their size, and
exit or enter the market.
• Evolution of firm productivity.
• Survival rate of firms.
• Shock to bilateral fixed trade costs.
8
Firm heterogeneity in CGE
• Balistreri and Rutherford (2013). Different sectors modelled
according to Armington (1969), Krugman (1980), or Melitz (2003)
trade theories.
• Balistreri, Hillberry and Rutherford (2011). Decomposition
algorithm: Melitz PE and Armington GE.
• Dixon, Jerie and Rimmer (2016): Armingon-Krugman-Melitz
Encompassing (AKME) model.
• Roson and Oyamada (2014). Multiple factors and intermediate
inputs.
• Akgul, Villoria and Hertel (2016). Firm heterogeneity in GTAP.
9
The HETFIGE model
• Geography: • Flexible: 28 European Countries – 267 NUTS 2 regions. (In Progress)
• Sectors: • Flexible: 10 NACE 2.0 sectors
• Temporal: • Base year: 2013.
• Recursive dynamics: 50 years.
• Coded in GAMS.
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Sectors NACE REV 2 Sectors Description
A Agriculture, Forestry and Fishing
B,D,E Mining and Quarrying + Electricity, Gas, Steam and Air Conditioning Supply + Water Supply;
Sewerage, Waste Management and Remediation Activities
C Manufacturing
F Construction
G-I Wholesale and Retail Trade; Repair of Motor Vehicles and Motorcycles + Transportation and
Storage + Accommodation and Food Service Activities
J Information and Communication
K-L Financial and Insurance Activities/ Real Estate Activities
M_N Professional, Scientific and Technical Activities + Administrative and Support Service Activities
O-Q Public Administration and Defence; Compulsory Social Security
+ Education + Human Health and Social Work Activities
R-U
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
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General Equilibrium
• Households: consume goods, pay taxes, receive transfers from
government, and save a fraction of the disposable income.
• Government: collect taxes on household income from labour, and
firms gross output. Expend their income in consumption, transfers
to household, and savings.
• Investment: Virtual investment agent that collect savings from
households, governments, and the rest of the world, and expend
then on investment goods. Savings driven investment.
• Firms: produce output using value added and intermediate inputs.
• Final demand: is the sum of household consumption, government
consumption, investment, and intermediate inputs.
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Production structure
Output
Value added
Capital Labour
Low Medium High
Intermediate Inputs
Sector 1 Sector 2 Sector 3
CET
13
Trade theories
• Armington (1969). Domestic commodities and commodities from
different countries are imperfect substitutes. Perfect competition.
• Krugman (1980). Consumers have Love-of-variety: each variety is
perceived as a different product. Monopolistic competition. Firm
homogeneity: same quantity, same productivity, and export to
every market.
• Melitz (2003). Love-of-variety. Monopolistic competition. Firms
have different productivities, produce different quantities, and
operate in different markets.
14
Heterogeneous Firms - Melitz
• 𝑀𝑟𝑖 firms enter the market by paying a fixed set-up cost of 𝐻𝑟𝑖
units of the composite input.
• The productivity of the firm is revealed and drawn from a
Pareto distribution.
• If productivity 𝜙𝑟𝑖 is lower than a threshold 𝜑𝑟𝑖𝑠∗ , the firm exit
the market as it is not able to make enough profits to repay the
fixed set-up cost.
• To operate in each trade link, firms have to pay a fixed
operating cost, and only firms with higher productivity export.
15
Trade theories Armington Krugman Melitz
Fixed set-up cost 0 Positive Positive
Fixed cost on each trade
link
0 0 Positive
Productivity of each firm Identical Identical Different
Market structure and
behaviour
Perfect
competition
Monopolistically
competition
Monopolistically
competition
Perceived elasticity of
demand
Infinity: ∞ Finite: 𝜎 Finite: 𝜎
Firm profits 0 Not 0 Not 0
Industry profits 0 0 0
Number of firms Exogenous Endogenous Endogenous
Firms exporting in a link All All Endogenous
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Price depending on trade theory
• Armington: no varieties.
• Krugman optimal price of the variety:
𝑝 𝑟𝑖𝑠 =𝜎𝑖
𝜎𝑖 − 1𝑐𝑟𝑖𝜏𝑟𝑖𝑠
• With all 𝑀𝑟𝑖 firms operating in all trade links.
• Melitz optimal price of the average variety:
𝑝 𝑟𝑖𝑠 =𝜎𝑖
𝜎𝑖 − 1
𝑐𝑟𝑖𝜏𝑟𝑖𝑠𝜑 𝑟𝑖𝑠
• With 𝑁𝑟𝑖𝑠 firms operating in the trade link from 𝑟 to 𝑠.
• With 𝜑 𝑟𝑖𝑠 being endogenous.
17
Heterogeneous Firms - Melitz
• Following Melitz (2003), the CES weighted average productivity:
𝜑 𝑟𝑖𝑠 = 𝑏𝑖𝛾𝑖
𝛾𝑖 − 𝜎𝑖 − 1
1 𝜎𝑖−1 𝑁𝑟𝑖𝑠𝑀𝑟𝑖
−1 𝛾𝑖
• This equations reveals one of the parametric restrictions of the
Melitz model given by the Pareto distribution:
γi > σi − 1
or, alternatively, γi
σi − 1> 1
• Shape parameter: 𝛾 • The lower 𝛾, the higher heterogeneity.
18
Trade – Number of Equations
Equations 28 EU Countries
268 NUTS-2
Armington 2 𝐼 × 𝑅 560 5,360
Krugman 2 𝐼 × 𝑅 × 𝑅 + 3 𝐼 + 𝑅 16,520 1,444,520
Melitz 4 𝐼 × 𝑅 × 𝑅 + 3 𝐼 + 𝑅 32,200 2,881,000
• R: number of regions.
• I: number of sectors. 𝐼 =10.
• The number of equations in a Melitz trade framework is around
double of Krugman trade framework.
19
Model Dynamics
• Private and public capital updates every period based on
depreciation rates and investment:
∆𝐾𝑎𝑝𝑆𝑡𝑜𝑐𝑘𝑟𝑖 = −𝛿𝑟𝑖𝐾𝑎𝑝𝑆𝑡𝑜𝑐𝑘𝑟𝑖 + 𝐼𝑛𝑣𝑒𝑠𝑡𝐾𝑟𝑖
• In steady state: 𝛿𝑟𝑖𝐾𝑎𝑝𝑆𝑡𝑜𝑐𝑘𝑟𝑖 = 𝐼𝑛𝑣𝑒𝑠𝑡𝐾𝑟𝑖
• Flexible wage setting of imperfect competition in the labour
market:
log 𝑟𝑤𝑎𝑔𝑒𝑟𝑙 = 𝑎𝑟𝑙 − 휀𝑟𝑙 log 𝑢𝑟𝑎𝑡𝑒𝑟𝑙 + 𝛼𝑟𝑙𝑟𝑤𝑎𝑔𝑒𝑟𝑙,𝑡−1
• If 𝛼𝑟𝑙 is equal to 1, a Philip curve is in operation.
20
Data
• NUTS 2 data comes from the regionalized Social Accounting
Matrices and Interregional trade data from Thissen M., Husby,
T., Ivanova, O. and Mandras G. (2018, forthcomming).
• Transport costs: two options • Calibrated from trade equations.
• Generalized Transport Cost (GTC): Persyn, Díaz-Lanchas and Barbero
(2018, forthcomming).
• Data on number of firms and survival rates is taken from the
EUROSTAT-OECD Business Demography Statistics.
21
Elasticity of substitution and Pareto shape
• Spearot (2016) estimates Pareto shapes using tariff data.
• Akgul, Villoria, and Hertel (2015) two step procedure:
• Extensive margin: Probit.
• Intensive margin: OLS with firm heterogeneity and sample
selection corrections.
• Erhardt (2017):
• Pareto shape: import demand elasticity from Kee et al. (2008)
• Elasticity of substitution: ratio of operating revenues to
operating profits. Bureau van Dijk’s Amadeus data base.
• GTAP-HET: 𝜎 = 3.75. 𝛾 = 2.89
22
Simulation Example - Shock
• Shock: Decrease of fixed set-up cost in Greece for two sectors: • B,D,E: Mining and Quarry + Electricity, Gas, Steam and Air Conditioning
Supply + Water Supply; Sewerage, Waste Management and Remediation
Activities …
• C: Manufacturing
• -3.85%.
23
Simulation Results – GDP Greece
24
Simulation Results – GDP Greece
25
Simulation Results – Entering Firms Greece
26
Simulation Results – Domestic Firms Greece
27
Simulation results – Dom Survival rate Greece
28
Average productivity in the sector
• Akgul et al. (2016) propose the following measure of average
productivity of all active firms in the sector:
Φ 𝑟𝑖 = 𝑁𝑟𝑖𝑠
𝑁𝑟𝑖𝑠′𝑠′𝑠
𝜙 𝑟𝑖𝑠𝜎𝑖−1
1𝜎𝑖−1
• Higher domestic competition: less productive firms exit. (+)
• New exporters emerge: • New exporters are less productive than existing. (-)
• Exporters become more important in weight. (+)
29
Simulation Results –Sector Productivity
30
Spillovers
• Melitz EU GDP: • ∆ 4.34%
• Krugman EU GDP: • ∆ 4.75%
31
Future developments
• Own estimation of elasticities of substitution.
• Innovation and R&D at the regional and sectoral level.
• Firm level innovation decision: • Binary: technology upgrading.
• Continuous.
• Dynamics based on Expectations?
33
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