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

SLIDE 1

Gains from Openness with Heterogenous Firms

Phemelo Tamasiga Gerald Willmann

Bielefeld University

June 25, 2014

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 1 / 33

SLIDE 2

Overview

1

Introduction

2

Model

3

Measure of gains from Trade

4

Conclusion

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 2 / 33

SLIDE 3

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

utflows 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))

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 3 / 33

SLIDE 4

Introduction

Research Question

Are total gains from openness underestimated by omission 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 Current resuslt: Gains from Openness Gj = 1 − (λj)− 1

ε

Cj = 1 −

λex

j − 1

ε + (Rη(σ−1)

j

− 1)

(σ−1)−ε (σ−1)ε λfdi

j − 1

ε

Phemelo Tamasiga, Gerald Willmann

Gains from Openness June 25, 2014 4 / 33

SLIDE 5

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. Romondo(2008), variant of Eaton and Kortum, in which there are no trade flows. 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. Melitz and Redding(2014)New trade models different welfare implications.

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 5 / 33

SLIDE 6

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 H + 1 sectors, sector 0 produces a homogeneous good with 1 unit of labour per unit output, Sectors h ≥ 1 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

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 6 / 33

SLIDE 7

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−βh

H

h=1
ω∈Ωh

qh(ω)

σh−1 σh dω

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)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 7 / 33

SLIDE 8

Model

Production

Firms in country i can enter the domestic market by paying fixed costs of entry fEi > 0 which is thereafter sunk. Expectation of future positive profits is the only motivation for firms to pay these sunk costs. Exporting firm costs Exporting firms pay additional fixed (f ex

ij

> 0= for each export

destination. These marginal costs are given by,

C ex

ij

= wiτij ϕij (3)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 8 / 33

SLIDE 9

Model

production continued...

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 η η wiτij 1 − η 1−η (4) Mode of Supply decisions A firm will serve a foreign country if the operating profits are sufficient to cover fixed costs. A firm can choose to supply foreign markets via exports or set up FDI plants in foreign markets.

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 9 / 33

SLIDE 10

Model

production continued...

If firm chooses to supply foreign market via export, profits are given by: πex

ij = βPσ−1 j

ρwiτij)1−σ ϕ 1−σ Yj σ fex (5) accesing foreign markets via FDI gives the following profits πfdi

ij

= βPσ−1

j

ρwη

j (wiηij)1−η

ϕ 1−σ Yj σ ffdi (6) Cutoff Productivities From zero profit condition, we get cutoff productivies for export and FDI

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 10 / 33

SLIDE 11

Model

production continued...

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)η(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 ffdiRη(σ−1) ij

> fexτ η(σ−1)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 11 / 33

SLIDE 12

Model

Entry and Exit

Timing Firms are identical prior to entry and must pay a xed investment cost fE to enter. Upon entry, firms draw their initial productivity level, ϕ from a common distribution g(ϕ) = k(ϕmin)kϕ−(k+1) with positive support

ver (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.

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 12 / 33

SLIDE 13

Model

Entry and Exit continued

Pareto Distribution Good approximation of the upper tail of distribution of firm sizes (Simon and Bonini,1958). key feature 1: when truncated the random variable retains a Pareto distribution with the same shape parameter k. If entry is subject to an endogenous productivity cutoff, the distribution of the technologies that make the cut remains Pareto key feature 2: Pareto distributed random variable power functions are themselves Pareto distributed. Individual prices have a Pareto distribution, with a constant elasticity

f demand, so do sales, hence firm size and variable profits are Pareto

distributed.

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 13 / 33

SLIDE 14

Model

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)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 14 / 33

SLIDE 15

Model

Entry and Exit continued...

Free Entry Condition Expectation of future profits must be equal to the fixed costs or that the probability of successful entry multiplied by average profits conditional on successful entry equal fixed costs v(ϕ) =

∞

t=0

(1 − δ)π = [1 − G(ϕ∗)]π δ − fe (12) Where the average revenues and profits across all domestic firms earned from both domestic, export and FDI revenues are given as: r = πiD ˜ (ϕ) + nθexrex ˜ (ϕ) + nθfdirfdi ˜ (ϕ) (13)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 15 / 33

SLIDE 16

Model

Entry and Exit continued...

Taking into account the zero profit condition the previous equation becomes, r = σ(π + fiD + nθexfex + nθfdiffdi) (14) π = πiD ˜ (ϕ) + nθexπex ˜ (ϕ) + nθfdiπfdi ˜ (ϕ) (15) These average Profits pin down the equilibrium mass of incumbent firms given as M = R r = L σ(π + fe + nθexfex + nθfdiffdi) (16)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 16 / 33

SLIDE 17

Model

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 (17) 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

(18) P = M

1 1−σ p(

ϕ), W = M

1 σ−1 ρ

ϕ

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 17 / 33

SLIDE 18

Model

Aggregation continued...

Trade only Price Index Pex

j

= G(ϕ∗

fdi) − G(ϕ∗ ex)

1 − G(ϕ∗

i )

Nex

ij

  

ϕfdi

ij

ϕex

ij

ϕσ−1( σ σ − 1wijτij)1−σdG(ϕij)   

1 1−σ

(19) Evaluating the integral and substituting for cutoff productivities P−k

j

= Mij k k − σ + 1 1 Yj 1−

k σ−1

ϕk

min

σ

σ − 1wiτij −k σwjf ex

ij )

1−

k σ−1

(20)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 18 / 33

SLIDE 19

Model

Aggregation continued...

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)η(σ−1) − 1](wijτij)1−σdG(ϕij)    

1 1−σ

(21)

Evaluating the integral and substituting for cutoff productivities

P−k

j

= Mij k k − σ + 1 1 Yj 1−

k σ−1

ϕk

min

σ

σ − 1 wiτij −k σwj( ffdi − fex (ℜτij)η(σ−1) − 1 ) 1−

k σ−1

(22)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 19 / 33

SLIDE 20

Model

Aggregation continued...

Aggregate price Index price Index

P1−σ

ij

= G(ϕ∗

fdi) − G(ϕ∗ ex)

1 − G(ϕ∗

i )

Mex

ij

   

∞

ϕex

ij

ϕσ−1( σ σ − 1 wijτij)1−σdG(ϕij)     + 1 − G(ϕ∗

fdi)

1 − G(ϕ∗

i ) Nfdi ij

   

∞

ϕfdi

ij

ϕσ−1( σ σ − 1 )1−σ[(ℜijτij)η(σ−1) − 1](wijτij)1−σdG(ϕij)     Evaluating the Integral and substituting for the cut off productivities P−k

j

= Mij k k − σ + 1 1 Yj 1−

k σ−1

σ σ − 1 (wiτij) −k (σwj)1−

k σ−1

f (ex

ij )1−

k σ−1 + (

ffdi − fex (ℜτij)η(σ−1) − 1 )1−

k σ−1

Phemelo Tamasiga, Gerald Willmann

Gains from Openness June 25, 2014 20 / 33

SLIDE 21

Model

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 )

   (23) 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

(24) The effect of trade costs on export sales also yields the extensive and intensive margins as dlnX ex

ij

dlnτij = − (σ − 1)

intensive

− (k − σ + 1)

extensive

(25)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 21 / 33

SLIDE 22

Model

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

(26)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 22 / 33

SLIDE 23

Model

Aggregation continued...

Effect of an increase in variable trade barriers on total affiliate sales can be decomposed into intensive and extensive margin dlnX fdi

ij

dlnτij = − (1 − η)(σ − 1)

intensive

− (k − σ + 1)χfdi

extensive

(27) Where χfdi is defined as the elasticity of FDI cutoff to variable trade barriers. χfdi = (Rijτij)η(σ−1)(η − 1) − 1 (Rijτij)η(σ−1) − 1 (28)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 23 / 33

SLIDE 24

Measure of gains from Trade

Definition of gains from openness

Gains from openess equals the (absolute value of) the percentage change in real income associated with moving one country from the current, observed trade and fdi equilibrium to a counterfactual equilibrium We are interested in the effects of trade and FDI on the welfare measure. 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

(29) welfare depends on real labour income derived from export and foreign multinational affiliates

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 24 / 33

SLIDE 25

Measure of gains from Trade

ACR express country j welfare as a function of the share of 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 changes in Wj can be inferred from changes in bilateral trade and income expenditures alone.

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 25 / 33

SLIDE 26

Measure of gains from Trade

Expenditure shares

Trade expediture share λex

ij =

X ex

ij

v

Xvj = ϕ∗

ii

ϕ∗

ij

k Niwifijex

σk k−σ+1

v

ϕ∗

ii

ϕ∗

vj

k Niwifvjex

σk k−σ+1

(30) Insert the equilibrium mass of firms and export cutoff productivty: λex

ij =

(Li/fiE)ϕk

miniw − kσ−(σ−1)

σ−1

i

(τij)−kf

1−

k σ−1

ijex

v

(Lvj/fvE)ϕk

minv w −

kσ−(σ−1)

σ−1

v

(τvj)−kf

1−

k σ−1

vjex

(31)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 26 / 33

SLIDE 27

Measure of gains from Trade

Expenditure shares(Continued)

FDI expediture share λfdi

ij

= X fdi

ij

v

Xvj = ϕ∗

ii

ϕ∗

ij

k Niwi(fijfdi − fijex)

σk k−σ+1

v

ϕ∗

ii

ϕ∗

vj

k Niwi(fvjfdi − fvjex)

σk k−σ+1

(32) Insert the equilibrium mass of firms and FDI cutoff productivty:

λfdi

ij

= (Li/fiE)ϕk

mini w − kσ−(σ−1)

σ−1

i

(τij)−kf

1−

k σ−1

ijex

(ℜvjτij)η(σ−1) − 1)1−

k σ−1

v

(Lvj/fvE)ϕk

minv w − kσ−(σ−1)

σ−1

v

(τvj)−kf

1−

k σ−1

vjex

(ℜvjτvj)η(σ−1) − 1)1−

k σ−1

(33)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 27 / 33

SLIDE 28

Measure of gains from Trade

Welfare derivation

Knowing a country’s domestic share of trade and FDI and shape parameter of the productivity distribution k is sufficient to determine welfare gains from openness. To achieve this, write the export(FDI) price index as a function of country j’s share of trade(FDI) with itself, its wage, labour allocation and parameters. Welfare derived from Trade

Pex

j

−k =

i

(Li/fE )ϕk

mini w−k i

(τij)−kf

1−

k σ−1

ex

wex

j

Y ex

j

1−

k σ−1

σ σ − 1 −k σ−

k σ−1

σ − 1 k − σ + 1 (34)

We use the expression of country j’s expenditure with itself, λex

jj and

the expression for income derived from export sales, Y ex

j

= wex

j Lex j

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 28 / 33

SLIDE 29

Measure of gains from Trade

Welfare derivation (Continued)

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

− 1

k

(35)

We summarize the welfare gains from trade, measured as the welfare ratio between the open and closed economies(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

jex

(36) The change in real income derived from trade associated with a change in the country’s expenditures on domestic goods.

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 29 / 33

SLIDE 30

Measure of gains from Trade

Welfare derived from FDI

Pfdi

j

−k =

i

(Li/fiE)ϕk

mini w −k i

(τij)−k[(Rijτij)µ(σ−1) − 1]−(1−

k σ−1)

(ffdi − fex)1−

k σ−1

w fdi

j

Y fdi

j

1−

k σ−1

σ σ − 1 −k σ−

k σ−1

σ − 1 k − σ + 1

Now we use the expression of country j’s expenditure with itself, λfdi

jj

and the expression for income derived from FDI, Y fdi

j

= wfdi

j

Lfdi

j

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

1

k

(Lfdi

j )

1 σ−1 [Rη(σ−1)

j

− 1]

(σ−1)−k (σ−1)k

λfdi

jj

− 1

k

W fdi

j

= [ ˆ Rη(σ−1)

jj

− 1]

(σ−1)−k (σ−1)k

λ

− 1

k

jfdi

(37)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 30 / 33

SLIDE 31

Measure of gains from Trade

Gains from Openness

Wj

=

W ex

j

+ W fdi

j

= λex

j − 1

ε + (Rη(σ−1)

j

− 1)

(σ−1)−ε (σ−1)ε λfdi

j − 1

ε

Country j’s gains from openness Cj is the absolute value of the percentage change in real income associated with moving to the counterfactual equilibrium: Cj = 1 −

λex

j − 1

ε + (Rη(σ−1)

j

− 1)

(σ−1)−ε (σ−1)ε λfdi

j − 1

ε

(38)

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 31 / 33

SLIDE 32

Conclusion

Summary

We have revisited the welfare gains from trade in the presence of FDI. Gains from openness are underestimated by a trade only model: FDI provides an addition source of gains to trade gains.

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 32 / 33

SLIDE 33

Conclusion

Thank you

Phemelo Tamasiga, Gerald Willmann Gains from Openness June 25, 2014 33 / 33