introducing firm heterogeneity in a cge model for europe · 2018. 11. 9. · 2 introducing firm...

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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.

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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.

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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.

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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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%.

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Simulation Results – GDP Greece

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Simulation Results – GDP Greece

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Simulation Results – Entering Firms Greece

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Simulation Results – Domestic Firms Greece

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Simulation results – Dom Survival rate Greece

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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. (+)

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Simulation Results –Sector Productivity

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Spillovers

• Melitz EU GDP: • ∆ 4.34%

• Krugman EU GDP: • ∆ 4.75%

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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?

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Thank you!

•All comments are welcome.

•Email: Javier.BARBERO-JIMENEZ@ec.europa.eu

•Email: Francesco.DI-COMITE@ec.europa.eu

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