D IVERSIFICATIONTHROUGH T RADE

D

T

Franceso Caselli Miklos Koren Milan Lisicky Silvana Tenreyro

January 2011

T

W

1 Substantial decline in output volatility in developed countries

in majority of developing countries

2 Large and widespread increase in trade openness

emergence of new trading partners (e.g. China and India)

3 Fast transmission of the current crisis, with the near collapse of trade

T

"

"

Openness to trade=⇒specialization=⇒increases volatility.

Implicit assumption: sector-specific shocks are the prevalent source of volatility.

But in volatility accounting, country-specific shocks (affecting all sectors) account for a large part of overall volatility.

Openness to trade may lead to sectoral specialization, but it may also help diversify country-specific shocks (both on demand and supply sides).

A

Increased trade openness brings about a larger pool of potential suppliers of input, and thus the potential for diversification of cost shocks.

the larger the pool of suppliers, the lower the impact of shocks affecting particular suppliers.

mitigation of supply shocks may also lead to more stable global demands.

Increased trade openness also means that a large shock to a particular country (e.g. US) can have a larger impact on other countries through stronger demand linkages.

Trade can mitigate the shock’s impact on the GDP of the country hit by the shock.

The model

C

F

Eaton-Kortum-Alvarez-Lucas’s Ricardian model of trade

N countries with immobile nonproduced equipped labour and produced good (used as intermediates and for direct consumption).

Efficiency varies across countries and goods; modeled as random variables drawn from a (known) distribution.

Constant returns to scale and perfect competition.

Output for a given country is deterministic; there is no aggregate volatility

Add country-specific shocks, which shift the distribution of efficiencies in a country

Output in a country becomes stochastic.

P

EK-AL

A

Buyers purchase individual goodsq(x)to maximize the CES:

q= Z ∞

0

q(x)^η−1η φ(x)dx _η−1^η α

(1)

φis the density of goods with technology x.

Technology forq(x)(per unit of L) is Cobb-Douglas:

q(x) =x^−θs(x)^βqm(x)^1−β (2)

i) drawsxare common to all producers; ii) CRS→p=mc; iii)x∼exp(λ) Price of bundle

p=

λ Z ∞

0

p(x)^1−ηe^−λxdx _1−η¹ α

(3)

Price of individual goods

p(x) =Bx^θw^βp^1−β (4)

M

-

q(x)can be traded internationally.

φ(x) =φ(x₁, ...,x_N)is the joint density of goods that have productivity drawsx = (x₁, ...,x_N)across N countries.

Draws independent across countries.

Delivering a tradable good from countryjto countryi results in 0< κ_ij ≤1 arriving at j (=1 ifi=j);κ_ij ≥κ_ikκ_kj,∀i,k,j.

P

The total output for use as input or consumption in countryi.

q_i = Z

R^N+

q_i(x)

η−1

η φ(x)dx

!_η−1^η

(5)

Price

p_i =AB





N

X

j=1

w_j^βp^1−β_j κ_ij

!^−1/θ λ_j





−θ

(6)

where:A(θ, η) = R∞

0 e^−zz^θ(1−η)dz_1−η¹ B=β^−β(1−β)^β−1

S

V

M

: S

1 p_i(w) =AB PN j=1

w_j^βpj(w)^1−β κij

−1/θ

λ_j

!−θ

;

2 d_ij(w) =

R

Bijpi(x)qi(x)φ(x)dx

p_iq_i = (AB)^−1/θ

w_j^βp_j(w)^1−β p_i(w)κ_ij

−1/θ

λ_j;

3 L_ip_iq_i =PN

j=1L_jp_jq_jd_ji(w) Y_i = L_iw_i

p_i =realGDP (7)

A

-

In EKAL,λ_j’s are deterministic, so GDP per capita is a deterministic constant for each countryj.

Assume now thatλj’s are subject to shocks

Higher realization ofλ_j leads to stochastically lower costsx in countryj and higherGDP_j

Stochasticity inλ_j imparts stochasticity inGDP_j.

Some Simple Analytical Results

L

GDP

A

GDP:

Y_i = L_iw_i

p_i = L_iw_i

(AB)^1/βλ^−θ/β_i w_i = (AB)^−1/βZ_i (8) where,Z_i ≡λ^θ/β_i ⁱL_i

Volatility

Var( ˆY_i) =Var( ˆZ_i) (9) xˆ≡ ^∆ln(x)_∆t

L

GDP

Y_i = (AB)^−1/βZ

β β+θ

i





N

X

j=1

Z

β θ+β

j





θ/β

(10)

Volatility:

Var( ˆY_i) =

β+θγ_i β+θ

2

Var( ˆZ_i) + θ

β+θ

2

PN

j6=iγ_i²Var( ˆZ_j) +2θ_(β+θ)^β+θγi2

PN

j6=iγ_jCov( ˆZ_j,Zˆ_i)

C

Productivity gain:

Y_i^T Y_i^A =

Z

β β+θ

i

PN

j=1Z

β β+θ

j

θ/β

Z_i =



1+Z

−β β+θ

i N

X

j6=i

Z

β β+θ

j





θ/β

>1

Gain higher

I the smaller the country:Z

−β β+θ

i

PZ

β β+θ

j

II the higher the importance of tradeables in production(1−β)

III the higher the scope of comparative advantageθ.

C

(

)

IfVar( ˆZ_i) =σandCov( ˆZ_i,Zˆ_j) =0 Var( ˆY_i^T) =σ





β+θγ_i β+θ

2

+ θ

β+θ 2 N

X

j6=i

γ_j²



 (11)

ThenVar( ˆY_i^A)>Var( ˆY_i^T)

Decline in volatility is higher the smaller the country (lowerγ_i) Results can be reversed if covariance are high and/or the volatility

Some Numerical Illustrations

E

Each period, drawλ= (λ₁, ..., λ_N)from a log-normal distribution with fixed mean and std deviation

ChooseA,B, θ, α, βas in AL

Time series, volatility and covariance:

S

1 Widespread decrease in international trade barriers

2 China joins the World

3 Crisis hits big country

C

"Barriers decrease":

LN=1;κ_ij,t =κ_tincreases over time fori6=j andκ_ii,t=1.

Same, butLN= (1,1,1,3,3).

"China joins": Same, butL_N = (1,1,1,3,3); andκi5,t =κ5j,t

smaller att =1.

"Crisis hit": lowλfor a big country;L_N = (1,1,1,3,3).

U

L_N =1;κij increases uniformly over time from 0.5 to 0.9 (κ_ii,t =1)

U

,

C

W

κ_ij increases uniformly but for a big country it increases more rapidly:

1−4=0.75→0.9, for the 5th moves 0.4→0.9. L=(1,1,1,3,3)

S

B

Counterfactual

C

C

C

Correlations:

magnitude of the change in volatility and the magnitude of the change in trade costs:0.70

change (absolute) in volatility and actual level of volatility:0.41 fall in volatility and size of the country:−0.21

C

When country-specific shocks are imperfectly correlated, trade can lead to lower volatility, particularly when

a country is small

the share of tradeables in the economy is big

trading partners are less volatile or the correlations are small.

A preliminary quantitative exercise shows sizeable decreases in volatility due to trade in small, open economies, but small changes in large countries.

The introduction of new trading partners:

1 increases the correlation of growth rates with the new partners

2 can decrease bilateral correlations among members of the "old"

group (US-Europe)