measuring the cost of a tariﬀ war: a suﬃcient …pages.iu.edu/~alashkar/trade_war_slides.pdfthis...

Measuring the Cost of a Tariff War:A Sufficient Statistics Approach

Ahmad Lashkaripour, Indiana University

EIIT 2019

1 / 44

Background

Thanks to the WTO, Tariffs were Declining ...

– Source: WORLD BANK2 / 44

But then the US-China Tariff War Escalated

3 / 44

A Full-Fledged Global Tariff War may be Imminent

Christine Lagarde (head of the IMF)

“[the escalating US-China tariff war] is thebiggest risk to global economic growth.”

– G7 Summit, June 2018

4 / 44

A “what if” Question Facing Policy-Makers

What is the “prospective” cost of a full-fledged tariff war?

– To answer this question, we need to determine the Nash tariff levels that will prevailin the event tariff war.

– Despite recent advances in quantitative trade theory, answering this questionremains to be difficult!

– Existing analyses:

1. aggregate the global economy into a small set of regions.

2. abstract from input-output (I-O) linkages.

5 / 44

This Paper

– I develop a new sufficient statistics methodology that measures the prospective costof a tariff war in one step as a function of

1. observables: trade shares + applied tariffs + I-O shares

2. estimable parameters: trade elasticities + markup wedges

– Main contribution:

– capitalizing on the computational efficiency of my S.S. approach, I quantify thecost of a tariff war for many countries and years (no need for aggregation!).

– I highlight how (i) I-O linkages and (ii) pre-existing market distortions amplify thecost of a tariff war.

6 / 44

New Findings

– Due to the rise of input-output linkages, the prospective cost of a global tariff warhas more-than-doubled over the past 15 years.

– Position in the global value chains matters as much as country size indetermining the winners/losers from a tariff war.

– The cost of a tariff war is driven by two distinctive factors

– standard trade reduction loss

– exacerbation of pre-existing market distortions

– Aggregating many countries into the RoW (and treating them as one taxingauthority) greatly overstates the cost of a tariff war.

7 / 44

New Findings




– standard trade reduction loss (Johnson (1953) and Gross (1983))

– exacerbation of pre-existing market distortions (perviously-overlooked)


7 / 44

New Findings




– standard trade reduction loss

– exacerbation of pre-existing market distortions


7 / 44

Theoritical Framework

Environment

– Many countries: i = 1,...,N

– Many industries: k = 1,..., K

– Labor is the sole factor of production

– Each country i is populated with Li units of labor, who can move freely acrossindustries but not across countries.

8 / 44

Demand-Side of Economy i

Representative consumer’s utility

Ui(Q1i, ...,QNi) =

K∏k=1

(

N∑j=1

Qρkji,k)

ei,kρk

– “ji, k” indexes exporter j×importer i×industry k

– Qji = {Qji,1, ...,Qji,K}

–∑K

k=1 ei,k = 1

9 / 44

Demand-Side of Economy i

– Representative consumer’s problem

maxQi

Ui(Q1i, ...,QNi)

s.t.∑k∈K

∑j∈C

Pji,kQji,k = Yi

– Standard CES demand function (ε = 1/ρ − 1):

Pji,kQji,k =P−εk

ji,k∑`∈C P−εk

`i,k

ei,kYi

10 / 44

Supply-Side of the Economy

Perfectly competitive price:

Pji,k = (1 + tji,k)︸︷︷︸tariff

× τji,kaj,k︸︷︷︸unit labor cost

× wj︸︷︷︸wage rate

– Structural parameters: τji,k, aj,k

– Endogenous variable: wj

– Policy instrument: tji,k

11 / 44

Equilibrium: Expenditure Shares

– Plugging Pji,k into the CES demand function, implies that the share expenditure on

variety ji, k is given by:

λji,k(t;w) =

[(1 + tji,k)τji,kaj,kwj

]−εk∑N`=1

[(1 + t`i,k)τ`i,ka`,kwj

]−εk

– w ≡ {wi} and t ≡ {tji,k}.

– Total expenditure is Xji,k = λji,kei,kYi.

12 / 44

Equilibrium: Definition

– For a given vector of tariffs, t, equilibrium is a vector of wages, w, that satisfybalanced trade condition:

N∑j=1

K∑k=1

11 + tji,k

λji,k(t;w)Yi(t;w) =N∑

j=1

K∑k=1

11 + tij,k

λij,k(t;w)Yj(t;w)

where

Yi(t;w) = wiLi +

N∑j=1

K∑k=1

(tji,k

1 + tji,kλji,k(t;w)Yi(t;w)

)︸︷︷︸

Tariff Revenue

, ∀i

– Since w = w(t) we can express all equilibrium variables as a function of onlyt—e.g., Yi(t) = Yi(t; w(t)).

Equilibrium: Definition

– For a given vector of tariffs, t, equilibrium is a vector of wages, w, that satisfybalanced trade condition:

N∑j=1

K∑k=1

11 + tji,k

λji,k(t;w)Yi(t;w) =N∑

j=1

K∑k=1

11 + tij,k

λij,k(t;w)Yj(t;w)

where

Yi(t;w) = wiLi +

N∑j=1

K∑k=1

(tji,k


)︸︷︷︸

Ri(t;w)

, ∀i

– Since w = w(t) we can express all equilibrium variables as a function of onlyt—e.g., Yi(t) = Yi(t; w(t)).

Welfare in Country i

– Total welfare in country i can be expressed as

Wi(t) =Yi(t)∏K

k=1 Pi,k(t)ei,k

where Pi,k(.) =(∑N

j=1

[aj,kτji,kwj,k

(1 + tji,k

) ]−εk)−1/εk

.

– In the event of a tariff war, country i sets ti to maximize welfare s.t. applied tariffs inthe rest of the world, t−i:

t∗i (t−i) = argmaxti

Wi(ti; t−i)

14 / 44

Nash Tariffs

Nash tariffs solve the following system of N(N − 1)K equationst1 = t∗1(t−1)

...

tN = t∗N(t−N)

.

– Standard approach to solving this system (Ossa, 2014):

1. start with an initial guess for t∗

2. update t∗ by performing N constrained global optimizations, each involving(N − 1)K tariff rates.

3. repeat until convergence.15 / 44

Alternative Approach to Determining Nash Tariffs

We can bypass the standard iterative optimization procedure by deriving asufficient statistics formula for t∗i (.).

16 / 44

Proposition 1.

Country i’s optimal import tariff is uniform and can be characterized as

1 + t∗i =1 +

∑j,i

∑k χij,kεk

(1 − λij,k

)∑j,i

∑k χij,kεk

(1 − λij,k

) ,

in terms of only (i) trade elasticities, εk; and (ii) observable export revenue shares,χij,k ≡ Xin,k/

∑`,i

∑k Xi`,k.

– Uniformity across industries is due to assuming a Ricardian production structure(Beshkar and Lashkaripour, 2019).

– Uniformity across exporters is due to the fact that to a first-order approximation,∂ ln Wi∂ ln w`

d ln w`d ln(1+tj)

= 0 if ` , j, i.

17 / 44

The Exact Hat-Algebra Methodology

– Hat-Algebra notation (for any variable x)

– x: observed (factual) level

– x′: counterfactual level

– x ≡ x′/x

– Combining the hat-algebra methodology with Proposition 1, we can solve for Nashtariffs and their welfare cost in one simple step as a function of two set of sufficientstatistics:

1. Observables: λji,k, ei,k, Yi, wiLi, tji,k

2. Trade elasticities: εk

18 / 44

Proposition 2.

Nash tariffs, {t∗i }, and their effect on wages, {wi}, and total income, {Yi}, can besolved as solution to the following system:

1 + t∗i =1+

∑j,i

∑k[ χij,k χij,kεk(1−λij,kλji,k)]∑

j,i∑

k[ χij,k χij,kεk(1−λij,kλij,k)]

χij,k χij,k =λij,kλij,kej,kYjYj/(1+t∗j )∑

n,i λin,kλin,ken,kYnYn/(1+t∗n)

λji,k =(

1+t∗i1+tji,k

wj

)−εkPεk

i,k

P−εki,k =

∑j

[(1+t∗i

1+tji,kwj

)−εkλji,k

]wiwiLi =

∑k∑

j

[1

1+t∗jλij,kλij,kej,kYjYj

]YiYi = wiwiLi +

∑k∑

j

(t∗i

1+t∗iλji,kλji,kei,kYiYi

),

19 / 44

Proposition 2.


1 + t∗i =1+

∑j,i

∑k[ χij,k χij,kεk(1−λij,kλji,k)]∑

j,i∑




λji,k =(

1+t∗i1+tji,k

wj

)−εkPεk

i,k

P−εki,k =

∑j

[(1+t∗i

1+tji,kwj

)−εkλji,k

]wiwiLi =

∑k∑

j

[1


]YiYi = wiwiLi +

∑k∑

j

(t∗i


).

20 / 44

Proposition 2.


1 + t∗i =1+

∑j,i

∑k[ χij,k χij,kεk(1−λij,kλij,k)]∑

j,i∑




λji,k =(

1+t∗i1+tji,k

wj

)−εkPεk

i,k

P−εki,k =

∑j

[(1+t∗i

1+tji,kwj

)−εkλji,k

]wiwiLi =

∑k∑

j

[1


]YiYi = wiwiLi +

∑k∑

j

(t∗i


)21 / 44

Let’s Put Proposition 2 in Perspective

– Standard Approach (Ossa ,2014)

– Solves Nash tariffs by performing an iterative global optimization procedure.

– Each iteration performs N optimizations with (N − 1)K + 2N free-movingvariables.

– New method based on Proposition 2

– Solve a system of 3N independent equations and 3N independent unknowns,only once.

22 / 44

Extensions

Accounting for Pre-Existing Market Distortions

– Suppose prices are given by

Pji,k = (1 + tji,k) (1 + µk) τji,kaj,k wj

where µk > 0 is a constant industry-level markup wedge.

– Good’s market clearing condition:

Yi(t;w) = wiLi + Πi +∑

j

∑k

(tji,k


)︸︷︷︸

Ri(t;w)

, ∀i

where Πi > 0 denotes total profits in market i. 23 / 44

Proposition 3.

Country i’s optimal import tariff is uniform and can be characterized as

1 + t∗i,k =

[ ∑j,i

∑g Xij,g

[1 + εg

(1 − λij,g

) ]∑j,i

∑k[Xij,gεg

(1 − λij,g

)+ Xji,kεkλii,s

] ] (1 + µk)(1 + εkλii,k

)1 + µk + εkλii,k

,

in terms of only (i) trade elasticities, εk and markup wedges, µk; as well as (ii)observable expenditure levels, λji,k and Xji,k.

– Optimal tariffs are higher in high-profit industries.

– Intuition: targeted tariffs can improve allocative inefficiency as a second bestpolicy (Lashkaripour & Lugovskyy, 2019)

24 / 44

Proposition 3.

Nash tariffs, {t∗i,k}, and their effect on wages, {wi}, and total income, {Yi}, can besolved as solution to the following system of 2N + KN equations and unknowns:

1 + t∗i,k =(1 + τ∗i

) [1+µk−εk λii,kλii,k

(1+µk)(1−εk λii,kλii,k)

]1 + τ∗i =

∑j,i

∑k Xij,kXij,k[1+εk(1−λij,kλji,k)]∑

j,i∑

k[Xij,kXij,kεk(1−λij,kλij,k)+Xji,kXji,kεk λii,sλii,s]

Xij,kXij,k = λij,kλij,k βj,kYjYj/(1 + t∗j,k)

Xji,kXji,k =∑

g

(µgεg λii,gλii,g

1+µg+εg λii,gλii,g

)Xji,kXji,k

λji,k =( 1+t∗i,k

1+tji,kwj

)−εk ˆPεki,k

ˆP−εki,k =

∑j

[( 1+t∗i,k1+tji,k

wj

)−εkλji,k

]wiwiLi =

∑k∑

j

[λij,kλij,k βj,kYjYj/(1 + t∗j,k)(1 + µk)

]ΠiΠi =

∑k∑

j

[µk λij,kλij,k βj,kYjYj/(1 + t∗j,k)(1 + µk)

]YiYi = wiwiLi + ΠiΠi +

∑k∑

j

( t∗i,k1+t∗i,k

λji,kλji,k βi,kYiYi

)

,

25 / 44

Proposition 3.

Nash tariffs, {t∗i,k}, and their effect on wages, {wi}, and total income, {Yi}, can besolved as solution to the following system of 2N + KN equations and unknowns:

1 + t∗i,k =(1 + τ∗i

) [1+µk−εk λii,kλii,k

(1+µk)(1−εk λii,kλii,k)

]1 + τ∗i =

∑j,i

∑k Xij,kXij,k[1+εk(1−λij,kλji,k)]∑

j,i∑

k[Xij,kXij,kεk(1−λij,kλij,k)+Xji,kXji,kεk λii,kλii,k]

Xij,kXij,k = λij,kλij,kej,kYjYj/(1 + t∗j,k)

Xji,kXji,k =∑

g

(µgεg λii,gλii,g

1+µg+εg λii,gλii,g

)Xji,kXji,k

λji,k =( 1+t∗i,k

1+tji,kwj

)−εk ˆPεki,k

ˆP−εki,k =

∑j

[( 1+t∗i,k1+tji,k

wj

)−εkλji,k

]wiwiLi =

∑k∑

j

[λij,kλij,kej,kYjYj/(1 + t∗j,k)(1 + µk)

]ΠiΠi =

∑k∑

j

[µk λij,kλij,kej,kYjYj/(1 + t∗j,k)(1 + µk)

]YiYi = wiwiLi + ΠiΠi +

∑k∑

j

( t∗i,k1+t∗i,k

λji,kλji,kei,kYiYi

)

,

26 / 44

Accounting for Input-Output Linkages

– Production combines labor with intermediate inputs.

– Competitive prices are given by:

Pji,k = (1 + tji,k) aji,k wγj,k

j

∏,g

Pαj,k(`,g)`j,g

where γj,k = 1 −∑

`,g αj,k (`, g) is the share of local labor in production.

– I assume that governments provide duty drawbacks, which is consistent with data.

– In the US duty drawbacks have been a part of the tariff scheme since 1789.

27 / 44

Reformulating the I-O Model

– The model with IO linkages is isomorphic to a model where only final goods

(indexed by F ) are traded, but the production of each final good employs labor from

various locations:

PFji,k = (1 + tji,k) aji,k

N∏`=1

wγj,k(`)`

– γj,k(`) is country `’s share in country j’s output, with∑N

`=1 γj,k(`) = 1

– γ ≡ [γj,k (`)]jk,` can be determined by using the global I-O matrix, α:

γ = (INK − α)−1γIK

28 / 44

Proposition 5.

Country i’s optimal import tariff is uniform and can be characterized

as1 + t∗i =∑

j,i∑

k φij,kεk(1−λij,k)1+

∑j,i

∑k φij,kεk(1−λij,k)

,in terms of only (i) reduced-form demand elasticities,

and (ii) observable “value-added” export shares, φij,k = γi,k(i)XF

ij,k/∑

j,i∑

g γi,g(i)XFij,g,where.

– Note: the uniformity of tariffs across industries is due to duty drawbacks.

29 / 44

Proposition 6.

Nash tariffs, {t∗i,k}, and their effect on wages, {wi}, and total income, {Yi}, can besolved as solution to the following system of 3N equations and unknowns:

1 + t∗i =1+

∑j,i

∑k

[φij,kφij,kεk(1−λ

F

ij,kλF

ij,k)]

∑j,i

∑k


F

ij,kλF

ij,k)]

φij,kφij,k =γi,k(i)λ

F

ij,kλF

ij,k βF

j,kYjYj/(1+t∗j )∑n,i

∑k γi,k(i)λ

F

in,kλF

in,k βF

n,kYnYn/(1+t∗n)

λFji,k =[

1+t∗i1+tji,k

∏` w

γj,k(`)`

]−εk(ˆPFi,k

) εk

ˆPFi,k =∑

j

( [1+t∗i

1+tji,k

∏` w

γj,k(`)`

]−εkλFji,k

)−1/εk

wiwiLi =∑

k∑

j

[λFij,kλ

F

ij,k βF

j,kYjYj/

(1 + t∗j

)]YiYi = wiwiLi +

∑k∑

j

(t∗i

1+t∗iλFji,kλ

F

ji,k βF

i,kYiYi

),

30 / 44

Proposition 6.

Nash tariffs, {t∗i,k}, and their effect on wages, {wi}, and total income, {Yi}, can besolved as solution to the following system of 3N equations and unknowns:

1 + t∗i =1+

∑j,i

∑k


F

ij,kλF

ij,k)]

∑j,i

∑k


F

ij,kλF

ij,k)]

φij,kφij,k =γi,k(i)λ

F

ij,kλF

ij,k βF

j,kYjYj/(1+t∗j )∑n,i

∑k γi,k(i)λ

F

in,k βF

n,k βF

n,kYnYn/(1+t∗n)

λFji,k =[

1+t∗i1+tji,k

∏` w

γj,k(`)`

]−εk(ˆPFi,k

) εk

ˆPFi,k =∑

j

( [1+t∗i

1+tji,k

∏` w

γj,k(`)`

]−εkλFji,k

)−1/εk

wiwiLi =∑

k∑

j

[λFij,kλ

F

ij,k βF

j,kYjYj/

(1 + t∗j

)]YiYi = wiwiLi +

∑k∑

j

(t∗i

1+t∗iλFji,kλ

F

ji,k βF

i,kYiYi

),

31 / 44

Some Intuition

The cost of a tariff war is driven by

1. pure trade reduction, the effect of which depends on a country’s position in theglobal value chain.

2. the exacerbation of pre-existing market distortions.

– output in high-µ is sub-optimal even w/o a tariff war

– tariff war occurs =⇒ it is optimal to target tariffs at high-µ industries.

– global output shrinks in high-µ industries =⇒ further efficiency loss!

32 / 44

Quantitative Implementation

Data Sources

WORLD INPUT-OUTPUT DATABASE (2000-2014)

– Industry-level expenditure by country of origin; input-output shares.

– 44 Countries + an aggregate of the rest of the world

– 56 Industries

UNCTAD-TRAINS Database

– Applied Tariffs (tji,k)

33 / 44

Results: Avg. Nash Tariff Rates

– Baseline model: 40.6%

– Model with market distortions: 35.4%

– Model with IO linkages: 53.5%

– In the tariff war that followed the Smoot-Hawley Tariff Act of 1930, Nash tariffswhere around 50%.

34 / 44

Results: Total Cost to Global GDP

– Baseline model: $1.3 trillion

– Model with market distortions: $1.4 trillion

– Model with IO linkages: $1.6 trillion

– The cost of a full-fledged tariff war is the equivalent of erasing South Korea from theglobal economy!

35 / 44

Results: Select Countries[]

Baseline Model Model w/ Distortions Model w/ IO Linkages

Country Nash Tariff %∆ Real GDP Nash Tariff %∆ Real GDP Nash Tariff %∆ Real GDP

CHN 41.0% -0.24% 42.1% -0.42% 42.7% -0.22%GRC 12.5% -2.88% 31.1% -2.33% 15.1% -5.79%NOR 17.1% -2.23% 34.5% -2.24% 91.7% 2.46%USA 39.2% -0.87% 36.8% -0.64% 45.9% -1.10%

Cross-national differences in welfare cost are driven by

– Pattern of specialization: high-ε vs. low-ε or high-µ vs. low-µ

– Position in the global value chain

36 / 44

Cost of a Tariff War over Time

37 / 44

Dependence of Global Value Chains

AUS

AUTBEL

BGR

BRA

CAN

CHECHN

CYP

CZE

DEU

DNKESP

EST

FINFRA

GBR

GRC

HRVHUN

IDNINDIRL

ITAJPN

KOR

LTU

LUX

LVA

MEX

MLT

NLDNOR

POLPRT

ROU

RUS

SVK

SVN

SWETUR

TWN

USA

−15

−10

−5

0

5

% L

oss

in R

eal

GD

P

.1 .2 .3 .4 .5 .6

Dependence on Imported Intermediates

38 / 44

The Cost of a US-China Tariff War

– Consider a full-fledged US-China tariff war, where the US and China impose Nashtariffs on each-other without raising tariffs on other partners.

– We can use the same “one step” methodology to analyze this scenario.

– Overall cost to the global economy: $34 billion, which is the equivalent ofParaguay’s GDP.

39 / 44

Some Countries Lose without Being Involved!

Main Losers Main Winners

Country∆Real GDP

(millions of dollars)Country

∆Real GDP(millions of dollars)

United States -$24,680 Mexico $2,028China -$15,774 India $678Australia -$58 Japan $581Ireland -$26 Canada $460

40 / 44

Aggregating Many Countries into the RoW is Problematic

BRA

CHN

DEU

FRA

GBR

IND

ITA

JPN

USA

−2.5

−1.5

−.5

No

n−

Ag

gre

gat

ed D

ata

(Bas

elin

e)

−2.5 −1.5 −.5

Data Aggregated to 9 Countries plus the ROW

– Intuition: aggregating many countries into the RoW artificially assigns a highmarket power to these countries =⇒ larger Nash tariffs by the RoW =⇒ greaterwelfare loss

41 / 44

Conclusions

1. A full-fledged tariff war can shave $1.6 trillion from global GDP.

2. The prospective cost of tariff war has more-than-doubled in the past fifteen years.

3. Small, downstream economies will be the biggest losers.

42 / 44

Thank You.

measuring the cost of a tariﬀ war: a suﬃcient …pages.iu.edu/~alashkar/trade_war_slides.pdfthis...

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