Gains from Openness with Heterogenous Firms Phemelo Tamasiga 1 Gerald - - PowerPoint PPT Presentation

Gains from Openness

Gains from Openness with Heterogenous Firms

Phemelo Tamasiga1 Gerald Willmann2

1Bielefeld Graduate School of Economics and Management, Germany 2Bielefeld University, Germany

June 30, 2015

Gains from Openness

Overview

Introduction Motivation Research Question Literature Model Assumptions Preferences and Demand Production Measure of gains from Trade Conclusion

Gains from Openness Introduction Motivation

◮ International trade research has devoted a lot of attention on

trade gains, less attention has been paid to measure gains. from FDI

Gains from Openness Introduction Motivation

◮ International trade research has devoted a lot of attention on

trade gains, less attention has been paid to measure gains. from FDI

◮ Arkolakis,derived gains from trade from the most commonly

used quantitative trade models defined as Gj = 1 − (λjj)− 1

ε

Gains from Openness Introduction Motivation

◮ International trade research has devoted a lot of attention on

trade gains, less attention has been paid to measure gains. from FDI

◮ Arkolakis,derived gains from trade from the most commonly

used quantitative trade models defined as Gj = 1 − (λjj)− 1

ε

◮ The derivation is based on the observed share of a country’s

trade with itself, λj, and the elasticity of imports with respect to variable trade costs, ε

Gains from Openness Introduction Motivation

◮ International trade research has devoted a lot of attention on

trade gains, less attention has been paid to measure gains. from FDI

◮ Arkolakis,derived gains from trade from the most commonly

used quantitative trade models defined as Gj = 1 − (λjj)− 1

ε

◮ The derivation is based on the observed share of a country’s

trade with itself, λj, and the elasticity of imports with respect to variable trade costs, ε

◮ In the first quarter of 2013, the magnitude of global FDI

inflows and outflows were 357 and 353 billion US dollars

• respectively. [OECD (2013) FDI statistics report]

Gains from Openness Introduction Motivation

◮ International trade research has devoted a lot of attention on

trade gains, less attention has been paid to measure gains. from FDI

◮ Arkolakis,derived gains from trade from the most commonly

used quantitative trade models defined as Gj = 1 − (λjj)− 1

ε

◮ The derivation is based on the observed share of a country’s

trade with itself, λj, and the elasticity of imports with respect to variable trade costs, ε

◮ In the first quarter of 2013, the magnitude of global FDI

inflows and outflows were 357 and 353 billion US dollars

• respectively. [OECD (2013) FDI statistics report]

◮ Multinationals comprise a substantial majority of U.S. trade,

roughly 90% of U.S. exports and imports (Bernard et al (2009))

Gains from Openness Introduction Research Question

◮ Are total gains from openness underestimated by

• mission of gains from FDI: To that effect how does the

welfare measure of trade [a’la Arkolakis et al(2012)] change with FDI(gains from openess measure)

◮ Result Preview Define country j’s gains from international

trade(openess) Gj(Cj), as the absolute value of the % change in real income associated with moving from an observed equilibrium to autarky

Gains from Trade Gains from Openness Gj = 1 − (λj)− 1

ε

Cj = 1 −

• λex

j − 1

ε + (Rµ(σ−1)

j

− 1)

(σ−1)−ε (σ−1)ε λfdi

j − 1

ε

Gains from Openness Introduction Research Question

Example: Trade Gains

◮ In 2000, US import penetration ratio (IPR) was 7% ◮ Share of demestic expenditures on domestic goods

λ = 1 − IPR = 0.93

◮ Anderson and Wincoop (2004) provide estimates of trade

elaticities, for US (-5,-10)

◮ Gains from trade USA: 0.7% − 1.4%

Gains from Openness Introduction Literature

Proximity concentration trade off

◮ Brainard(1997) presents a simple theory to understand the trade-off

between export and FDI.

◮ Markusen and Venables (2000)add factor endowment differences between

countries to this simple model.

◮ Helpman, Melitz and Yeaple (2004) add firm heterogeneity

Gains from Openness...?

◮ Eaton-Kortoum(2002), the only way of serving a foreign market is via

exporting.

◮ Ramondo Rodriguez-Clare(2009),Trade and multinational MP in an

Eaton and Kortum model.

◮ Arkolakis et al(2012)New trade models same old gains with average

sectoral elasticity.

◮ Ralph Ossa (2012) Average elasticity underestimates gains from trade,

different sectoral elasticities more trade gains.

Gains from Openness Model Assumptions

◮ Following Helpman et al (2004), there are N countries. ◮ Each country i is endowed with Li units of labour with wage

rate wi.

◮ Each country comprises 2 sectors, sector 0 produces a

homogeneous good with 1 unit of labour per unit output,

◮ H sectors produce differenciated products. ◮ The homogeneous good is freely traded with wage rate equal

to 1 this ensures factor price equalisation as long as each and every country produces it.

◮ An exogenous fraction of income h 1 − βh is spent on the

homogeneous sector and,

◮ βh is spent on the differentiated goods sector

Gains from Openness Model Preferences and Demand

◮ Preferences are a Cobb-Douglas aggregate of the

homogeneous good sector and differentiated traded goods

◮ CES across a continuum of differentiated goods in

h = 1, ..., H sectors, (Krugman, 1980) U = q1−β0

H

• h=1
• ωh∈Ω

qh(ω)

σh−1 σh

• σh

σh−1 βh

(1) where σ > 1 is the elasticity of substitution (ρ = σ−1

σ ) ◮ Utility maximization implies quantity demanded in county j of

good ω is qj(ω) = β pj(ω)−σ P1−σ

j

Yj (2)

Gains from Openness Model Production

◮ Exporting firm costs

Exporting firms pay fixed costs (f ex

ij

> 0) for each export

• destination. These marginal costs are given by,

C ex

ij

= wiτij ϕij (3)

◮ FDI firm costs

FDI firms pay fixed costs of FDI defined as f fdi

ij . FDI marginal

costs are : C fdi

ij

=

• 1

ϕfdi

ij

wj µ µ wiτij 1 − µ 1−µ (4)

Gains from Openness Model Production

Zero Profit Conditions

A firm will serve a foreign country if the operating profits are sufficient to cover fixed costs

◮ If firm chooses to supply foreign market via export, profits are

given by: πex

ij = 0 → βPσ−1 j

ρwiτij)1−σ ϕ 1−σ Yj σ = fex (5)

◮ accesing foreign markets via FDI gives the following profits

πfdi

ij

= 0 → βPσ−1

j

• ρwµ

j (wiηij)1−η

ϕ 1−σ Yj σ = ffdi (6)

Gains from Openness Model Production

Cutoff Productivities

From zero profit condition, we get cutoff productivies for export and FDI

◮ Export Productivity cutoff

˜ ϕex

ij = κ

f ex

ij

Yj

• 1

σ−1

P−1

j

wiτij (7) such that κ =

• σ

β

• 1

σ−1 ρ

◮ FDI Productivity cutoff

˜ ϕfdi

ij

= κ

• f fdi

ij

− f ex

ij

Yj[(Rijτij)µ(σ−1) − 1]

• 1

σ−1

P−1

j

wiτij (8) To ensure that the fdi cutoff productivity is higher than export productivity,i.e ϕfdi

ij

> ϕex

ij ,assume that

ffdiRµ(σ−1)

ij

> fexτ µ(σ−1)

Gains from Openness Model Production

Entry and Exit

Timing

◮ Upon entry, firms draw their initial productivity level, ϕ from

a common distribution g(ϕ) = k(ϕmin)kϕ−(k+1) with positive support over (0, ϕmax).and a continuous cumulative distribution G(ϕ) = 1 − ϕmini

ϕ

κ

◮ A firm drawing a low productivity ϕ may decide to

immediately exit and not produce.

◮ Produtivities are distributed Pareto ◮ Firms face a constant probability of a bad shock in every

period that would force them to δ exit.

Gains from Openness Model Production

Entry and Exit Continued

◮ Probability of entry in the home market, exporting

(conditional on successful entry)and into FDI are given by θiD = 1 − G(ϕ∗

i )

(9) θex = G(ϕ∗

fdi) − G(ϕ∗ ex)

1 − G(ϕ∗

i )

(10) θfdi = 1 − G(ϕ∗

fdi)

1 − G(ϕ∗

i )

(11)

Gains from Openness Model Production

Aggregation

◮ Let M be the equilibrium mass of incumbent firms in any

country,

◮ Mass of firms that enter foreign country via exports and FDI

Mex = θexM and Mfdi = θfdiM

◮ Total mass of varieties available to consumers in each country

is given by the total mass of firms competing in the country, M = M + nMex + nMfdi (12)

◮ Weighted productivity average

• ϕ = 1

M

• M

ϕσ−1

iD

+ nMexτ 1−σ ϕσ−1

ex

+ nMfdiτ (1−σ)(1−η) ϕσ−1

fdi

• 1

σ−1

(13) P = M

1 1−σ p(

ϕ), W = M

1 σ−1 ρ

ϕ

Gains from Openness Model Production

Aggregation continued...

◮ Trade only Price Index Pex

j

= G(ϕ∗

fdi) − G(ϕ∗ ex)

1 − G(ϕ∗

i )

Mex

ij

   

ϕfdi

ij

• ϕex

ij

ϕσ−1( σ σ − 1 wijτij)1−σdG(ϕij)    

1 1−σ

(14) ◮ FDI only Price Index Pfdi

ij

= 1 − G(ϕ∗

fdi)

1 − G(ϕ∗

i ) Mfdi ij

   

∞

• ϕfdi

ij

ϕσ−1( σ σ − 1 )1−σ[(ℜijτij)µ(σ−1) − 1](wijτij)1−σdG(ϕij)    

1

(15)

Gains from Openness Model Production

Aggregation continued...

◮ Trade Sales

X ex

ij

= G(ϕ∗

fdi) − G(ϕ∗ ex)

1 − G(ϕ∗

i )

Mex

ij

  

∞

• ϕex

ij

ϕσ−1( σ σ − 1wijτij)1−σβ Yj P1−σ

j

dG(ϕex

ij )

   (16) Evaluating the integral and substituting for productivity cutoffs we get X ex

ij

= ϕmin ϕex k Mex

ij

• extensive
• σk

k − σ + 1

• fexwj
• intensive

(17)

Gains from Openness Model Production

Aggregation continued...

◮ FDI Sales X fdi

ij

= 1 − G(ϕ∗

fdi)

1 − G(ϕ∗

i ) Mfdi ij ∞

• ϕfdi

ij

ϕσ−1( σ σ − 1 )1−σ[(ℜijτij)η(σ−1) − 1](wijτij)1−σ β Yj P1−σ

j

dG(ϕfdi

ij )

X fdi

ij

= ϕmin ϕfdi k Mfdi

ij

• extensive
• σk

k − σ + 1

• wj(ffdi − fex)
• intensive

(18)

Gains from Openness Measure of gains from Trade

Gains from openness

◮ ACR express country j trade gains as a function of the share

• f expenditure that falls on domestically produced

goods(which is equal to 1 minus the import penetration ratio. This share, λj under autarky is 1,therefore total size of gains from openness will be equal to 1 − λj

◮ Welfare is given by the per capita value of real income

accruing to consumers: Wj = Yj LjPj = wex

j

Pex

j

+ wfdi

j

Pfdi

j

(19)

◮ welfare depends on real labour income derived from export

and foreign multinational affiliates

Gains from Openness Measure of gains from Trade

Knowing a country’s domestic share of trade and FDI and shape parameter of the productivity distribution k is sufficient to determine gains from openness.

◮ Trade expediture share

λex

ij =

X ex

ij

• v

Xvj = ϕ∗

ii

ϕ∗

ij

k Miwifijex

σk k−σ+1

• v

ϕ∗

ii

ϕ∗

vj

k Miwifvjex

σk k−σ+1

(20)

◮ FDI expediture share

λfdi

ij

= X fdi

ij

• v

Xvj = ϕ∗

ii

ϕ∗

ij

k Miwi(fijfdi − fijex)

σk k−σ+1

• v

ϕ∗

ii

ϕ∗

vj

k Miwi(fvjfdi − fvjex)

σk k−σ+1

(21)

Gains from Openness Measure of gains from Trade

Derivation of Gains

◮ Trade Only Gains a’la Akorlakis et al(2012)

W ex

j

=

• w ex

j

Pex

j

• =
• σ

σ − 1 −k σ−

k σ−1

σ − 1 k − σ + 1ϕk

minj f 1−

k σ−1

ex

fE 1

k

(Lex

j )

1 σ−1

λex

jj

(22)

Gains from trade are given by,(the domestic trade shares in the closed economy are xed at λclosed = 1):

• W ex

j

= W open

j

W closed

j

= λ

− 1

k

jjex

(23)

Gains from Openness Measure of gains from Trade

◮ Welfare derived from FDI

W fdi

j

=

• w fdi

j

Pfdi

j

• =
• σ

σ − 1 −k σ−

k σ−1

σ − 1 k − σ + 1ϕk

minj (ffdi − fex)1−

k σ−1 f −1

jE

• k

(Lfdi

j )

1 σ−1 [Rµ(σ−1)

j

− 1]

(σ−1)−k (σ−1)k

• λfdi

jj

− 1

k

• W fdi

j

= [ ˆ Rµ(σ−1)

jj

− 1]

(σ−1)−k (σ−1)k

λ

− 1

k

jjfdi

(24)

Gains from Openness Measure of gains from Trade

◮ Gains from Openness

• Wj

=

• W ex

j

+ W fdi

j

= λex

jj − 1

ε + (Rµ(σ−1)

j

− 1)

(σ−1)−ε (σ−1)ε λfdi

jj − 1

ε

Country j’s gains from openness Cj is the absolute value

• f the percentage change in real income associated with

moving to the counterfactual equilibrium: Cj = 1 −

• λex

j − 1

ε + (Rµ(σ−1)

j

− 1)

(σ−1)−ε (σ−1)ε λfdi

j − 1

ε

• (25)

Gains from Openness Conclusion

Summary

◮ We have revisited the welfare gains from trade in the presence

• f FDI.

◮ Gains from openness are underestimated by a trade only

model: FDI provides an addition source of gains to trade gains.

Gains from Openness Conclusion

Thank you