Introduction The EK model Empirical Applications Conclusion Appendix
Lecture 6: Technology, Geography and Trade
Gregory [email protected]
Isabelle Mé[email protected]
International TradeUniversité Paris-Saclay Master in Economics, 2nd year.
16 November 2016
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Introduction The EK model Empirical Applications Conclusion Appendix
Introduction
Ricardo and HO theories (Lectures 2-4) :I Specialization according to comparative advantageI Inter-industry trade between countries that differ in terms of
technologies (Ricardo) or endowments (HO)I Gains from trade due to a better allocation of resources
Limited empirical support (Lecture 5)I Missing features in HOV can partially explain poor empirical
performancesI In any case, the R2 of such regressions is small
No (explicit) role for geographyI Hardly reconcilable with the gravity equation.
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The gravity equation
Robust empirical model of bilateral trade in which size and distanceeffects enter multiplicatively :
Xij = G × Si ×Mj × dij
Workhorse econometric model of bilateral trade flows since Tinbergen(1962)
Rationalized in mainstream modeling frameworks under some -widelyused- parametric restrictions (See Lecture 10)
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Trade and the size of countries
Japanese exports in the EU Japan imports from the EUFigure 1: Trade is proportional to size
(a) Japan’s exports to EU, 2006 (b) Japan’s imports from EU, 2006
MLT
ESTCYP
LVA
LTUSVN
SVK
HUNCZE
PRT
FINIRLGRC
DNK
AUTPOL
SWE
BELNLD
ESP ITAFRA
GBRDEU
slope = 1.001fit = .85
.05
.1.5
15
10Ja
pan'
s 20
06 e
xpor
ts (G
RC =
1)
.05 .1 .5 1 5 10GDP (GRC = 1)
MLT
EST
CYP
LVA
LTU
SVN
SVK
HUNCZE
PRT
FIN
IRL
GRC
DNKAUT
POL
SWEBELNLD ESP
ITAFRAGBR
DEU
slope = 1.03fit = .75
.51
510
5010
0Ja
pan'
s 20
06 im
ports
(GRC
= 1
)
.05 .1 .5 1 5 10GDP (GRC = 1)
in concert to establish robustness. In recent years, estimation has become just a first step before a
deeper analysis of the implications of the results, notably in terms of welfare. We try to facilitate
diffusion of best-practice methods by illustrating their application in a step-by-step cookbook mode
of exposition.
1.1 Gravity features of trade data
Before considering theory, we use graphical displays to lay out the factual basis for taking gravity
equations seriously. The first key feature of trade data that mirrors the physical gravity equation
is that exports rise proportionately with the economic size of the destination and imports rise in
proportion to the size of the origin economy. Using GDP as the economy size measure, we illustrate
this proportionality using trade flows between Japan and the European Union. The idea is that the
European Union’s area is small enough and sufficiently far from Japan that differences in distance
to Japan can be ignored. Similarly because the EU is a customs union, each member applies the
same trade policies on Japanese imports. Japan does not share a language, religion, currency or
colonial history with any EU members either.
Figure 1 (a) shows Japan’s bilateral exports on the vertical axis and (b) shows its imports.
The horizontal axes of both figures show the GDP (using market exchange rates) of the EU trade
partner. The trade flows and GDPs are normalized by dividing by the corresponding value for
Greece (a mid-size economy).2 The lines show the predicted values from a simple regression of log
2The trade data come from DoTS and the GDPs come from WDI. The web appendix provides more informationon sources of gravity data.
3
Correlation between the Japan-EU trade and the size of partners. The x-axismeasure the GDP of each EU members, in relative terms with respect to theGreek one. The y-axis measure the size of Japanese exports in each country(left-hand side) a,d the volume of Japanese imports from each country (right-hand side), again expressed in relative terms with respect to Greece. Data arefor 2006. Source : Head & Mayer (2014).
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Trade and distance
French exports French importsFigure 2: Trade is inversely proportional to distance
(a) France’s exports (2006) (b) France’s imports (2006)
slope = -.683fit = .22
.005
.05
.1.5
15
10E
xpor
ts/P
artn
er's
GD
P (
%, l
og s
cale
)
500 1000 2000 5000 10000 20000Distance in kms
EU25
Euro
Colony
Francophone
other
slope = -.894fit = .2
.005
.05
.1.5
15
1025
Impo
rts/
Par
tner
's G
DP
(%
, log
sca
le)
500 1000 2000 5000 10000 20000Distance in kms
EU25
Euro
Colony
Francophone
other
trade flow on log GDP. For Japan’s exports, the GDP elasticity is 1.00 and it is 1.03 for Japan’s
imports. The near unit elasticity is not unique to the 2006 data. Over the decade 2000–2009, the
export elasticity averaged 0.98 and its confidence intervals always included 1.0. Import elasticities
averaged a somewhat higher 1.11 but the confidence intervals included 1.0 in every year except
2000 (when 10 of the EU25 had yet to join). The gravity equation is sometimes disparaged on
the grounds that any model of trade should exhibit size effects for the exporter and importer.
What these figures and regression results show is that the size relationship takes a relatively precise
form—one that is predicted by most, but not all, models.
Figure 2 illustrates the second key empirical relationship embodied in gravity equations—the
strong negative relationship between physical distance and trade. Since we have just seen that GDPs
enter gravity with a coefficient very close to one, one can pass GDP to the left-hand-side, and show
how bilateral imports or exports as a fraction of GDP varies with distance. Panels (a) and (b) of
Figure 2 graph recent export and import data from France. These panels show deviations from the
distance effect associated with Francophone countries, former colonies, and other members of the
EU or of the Eurozone. The graph expresses the “spirit” of gravity: it identifies deviations from
a benchmark taking into account GDP proportionality and systematic negative distance effects.
Those deviations have become the subject of many separate investigations.
This paper is mainly organized around topics with little attention paid to the chronology of
when ideas appeared in the literature. But we do not think the history of idea development should
be overlooked entirely. Therefore in the next section we give our account of how gravity equations
went from being nearly ignored by trade economists to becoming a focus of research published in
4
Correlation between the volume of trade and the distance between partners.The x-axis is the distance from France, expressed in kilometers. The x-axismeasures the size of French exports (left-hand side) and the size of Frenchimports (right-hand side), both expressed in relative terms with respect ot thedestination country’s GDP. Data are for 2006. Source : Head & Mayer (2014).
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The Eaton and Kortum (2002) Model
Eaton & Kortum (2002) : neoclassical trade model in whichI Comparative advantage arises randomlyI Technological advantage interacts with geography to shape
comparative advantageI Gravity equation arises structurally
The EK model has been used in quantitative exercises on :I gains from trade liberalization (e.g. zero MFN tariffs, NAFTA)I the importance/evolution of Ricardian comparative advantageI the fall in trade during the 2008-2009 recessionI the US trade deficit and exchange rate adjustmentI the volatility of trade and GDP...
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Outline of this Lecture
Detailed presentation of the Eaton-Kortum model
Some extensions
Estimation of Eaton-Kortum
Numerical applications
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The Eaton-Kortum model
See analytical details in EatonKortumAnalytics.pdf
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Main features
Ricardian model (differences in technology) with geography (barriersto trade).The model yields a gravity equation which relates bilateral tradevolumes to deviations from purchasing power parity, technology andgeographic barriers.The model can be estimated structurally.
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Assumptions
I countries (i = 1...I )Continuum of goods j ∈ [0, 1]
CES preferences in each country i :
Ui =
[∫ 1
0Qi (j)
σ−1σ dj
] σσ−1
demand
Goods produced with a bundle of inputs whose price is homogenouswithin countries ci (first taken as exogenous)Iceberg trade costs dni > 1. Without loss of generality dii = 1.Cross-border arbitrage implies : dni ≤ dnkdki
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Assumptions (ii)
Country i ’s efficiency in producing good j : zi (j)⇒ CIF price of good j produced in country i and sold in country n :
pni (j) =ci
zi (j)︸ ︷︷ ︸Unit cost
dni︸︷︷︸Trade barrier
optimal price
Perfect competition across suppliers⇒ Price actually paid in country n for good j :
pn(j) = min{pni (j); i = 1...I}
Note : most results continue to hold with Bertrand competition.
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Assumptions (iii)
Stochastic productivity : zi (j) is the realization of a random variableZi drawn from a country-specific probability distribution :
Fi (z) = Pr [Zi ≤ z ]
Productivity draws assumed independent across goods and countriesFi assumed to be Fréchet (Type II extreme value) : Fréchet
∀z > 0,Fi (z) = e−Tiz−θ
with Ti > 0 and θ > 0Note : the Fréchet distribution can be shown to be the outcome of a process of innovation and diffusion inwhich Ti is a national stock of ideas. See Eaton & Kortum (IER, 1999).
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Interpretation
Fi (z) = e−Tiz−θ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Benchmark in red. Doubling of Ti inblue / of θ in green
Ti captures absoluteadvantage. The higher Ti , thehigher that country’s mean z : iis more likely to draw a high zfor each product j .θ captures the extent ofcomparative advantage. Thehigher θ, the lower Var(z) :trade will be less driven bycomparative advantage.
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Price distribution
Distribution of prices offered by country i in country n :
Gni (p) ≡ Pr [Pni ≤ p] = 1− e−Ti (cidni )−θpθ
Country n’s actual distribution of prices :
Gn(p) ≡ Pr [Pn ≤ p]
= 1−∏i
[1− Gni (p)]
= 1− e−Φnpθ
where Φn ≡∑
i Ti (cidni )−θ
details
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Price distribution
Gn(p) = 1− e−Φnpθ , Φn ≡∑i
Ti (cidni )−θ
Distribution of prices governed byStates of technology around the world {Ti},
Input costs around the world {ci},Geographic barriers {dni}
- If dni = 1,∀n, i then Φn = Φ,∀n (Law of One Price)- If dni →∞,∀i then Φn = Tnc
−θn (Autarky)
⇒ Φn represents the strength of competition that any firm will encounterin country n
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Bilateral trade
Share of goods that n buys from i = Probability that i provides thelowest price good in country n :
πni =Xni
Xn
= Pr [pni (j) ≤ min{pns(j); s 6= i}]
=
∫ ∞0
∏s 6=i
[1− Gns(p)]dGni (p)
=Ti (cidni )
−θ
Φn
or in log :
lnXni = ln(Tic−θi
)︸ ︷︷ ︸Exporter FE
+ ln(XnΦ−1n
)︸ ︷︷ ︸Importer FE
−θ ln dni︸ ︷︷ ︸Gravity
⇒ Gravity-type equationG. Corcos & I. Méjean (Ecole polytechnique) International Trade: Lecture 6 16 / 52
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Bilateral trade (ii)
EK structural interpretation of the gravity equation :The trade barriers coefficient relates to heterogeneity in productivity :
⇒ The greater heterogeneity among producers of a commodity (lower θ),the stronger the cost advantage of the lowest cost supplier, the morelikely he remains the lowest cost supplier when trade costs increase.
⇒ Trade flows respond to geographic barriers at the extensive margin :As a source becomes more expensive or remote, it exports a narrowerrange of goods [as in Dornbusch et al. (1977)].
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Bilateral trade (iii)
Country i ’s normalized import share in country n :
Sni ≡Xni/Xn
Xii/Xi=
Φi
Φnd−θni =
(pidnipn
)−θAlways lower than one due to the triangle inequality (the maximumvalue for pn is pidni )As overall prices in market n fall relative to prices in market i(↑ pi/pn) or as n becomes more isolated from i (↑ dni ), i ’s normalizedshare in n declinesA higher θ means comparative advantage forces weaken relative totrade costs : normalized import shares become more elastic.
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General equilibrium solution
Suppose production is linear in labor (EK has intermediate inputs) :
ci = wi
⇒ Price levels as a function of wages :
pn = γ
[∑i
Ti (dniwi )−θ
]−1/θ
where γ ≡[Γ(θ+1−σ
θ
)]1/(1−σ)price index
⇒ Trade shares as a function of wages and prices :
Xni
Xn= Ti
(γdniwi
pn
)−θG. Corcos & I. Méjean (Ecole polytechnique) International Trade: Lecture 6 19 / 52
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General equilibrium solution
To close the model, one needs to solve for equilibrium wages acrosscountriesThis is the trickier part of the exercise ⇒ Numerical solutionsAdditional simplifying assumptions can help solve the model :Exogenous labor supply, Wages determined in the nonmanufacturingsector, Trade balance.
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Extensions : Multiple sectors
Costinot, Donaldson & Komunjer (2012) reinterpret EK’s model in thecontext of a multi-country, multi-sector worldK industries/goods in each country (k = 1, ...,K ). Within eachindustry, a continuum of varieties is produced according to thetechnology described above.With multiple sectors, Ti now has a sector dimension (but, crucially, θremains common to all countries and industries...) :
F ki (z) = e−T
ki z−θ
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Extensions : Multiple sectors (ii)
The model predicts trade patterns at the industry-country pair level.For any importer j and any pair of exporters i , i ′ 6= j , the ranking ofrelative fundamental productivities determines the ranking of exports :
T 1i
T 1i ′≤ ... ≤
TKi
TKi ′⇒
X 1ji
X 1ji ′≤ ... ≤
XKji
XKji ′
In a 2-country world without heterogeneity, that ranking would imply
z1i (j)
z1i ′(j)< ... <
zKi (j)
zKi ′ (j)
i would specialize in high-k goods and i ′ in low-k goods, just as inDornbusch et al. (1977).
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Extensions : Multiple sectors (iii)
In this model with stochastic (Fréchet) productivity differences, wehave :
T 1i
T 1i ′≤ ... ≤
TKi
TKi ′⇒
z1i (j)
z1i ′(j)� ... �
zKi (j)
zKi ′ (j)
where � denotes first-order stochastic dominance.Country i ′ is not expected to specialize in high k goods, but toproduce and export relatively more of these goods.Unlike Dornbusch et al. (1977) here we can predict trade patterns formore than 2 countries.
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Extensions : Imperfect Competition
Bernard, Eaton, Jensen & Kortum (2003) extend EK to allow forimperfect competition between varietiesWith imperfect competition, consumer prices are above marginal costsModel predicts a distribution of mark-ups in each market, that isbounded above by the Dixit-Stiglitz constant mark-upAdditional predictions on within-country heterogeneity in prices,productivities, etc
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Bringing the Model to the Data
The model can be estimated to quantitatively assess the role ofRicardian advantages in driving international trade.Structural parameters θ and {Ti} must be estimated.Once those parameters are estimated, it is possible to run variouscounterfactuals.
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Example : EK Estimation of θ
Bilateral trade in manufactures among 19 OECD countries in 1990(342 bilateral relationships Xni )Absorption of manufactures as a measure of Xn (STAN, OECD)Proxy for trade barriers :
- Distance and other geographic barriers- Retail price differentials measured at the product level (WB) :Interpreted as a sample of pi (j), used to calculate relative prices, whichare theoretically bounded above by bilateral trade costs :
lnpidnipn'=
max2j{rni (j)}mean{rni (j)}
= Dni
rni (j) = ln pn(j)− ln pi (j) relative price of commodity j⇒ exp(Dni ) price index in destination n that would prevail if everythingwas purchased from i , relative to the actual price index in n
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Estimating θ, EK Method 1
Normalized import shares and relative pricestechnology, geography, and trade 1755
Figure 2.—Trade and prices.
we use this value for ! in exploring counterfactuals. This value of ! implies astandard deviation in efficiency (for a given state of technology T ) of 15 percent.In Section 5 we pursue two alternative strategies for estimating !, but we firstcomplete the full description of the model.
4� equilibrium input costs
Our exposition so far has highlighted how trade flows relate to geographyand to prices, taking input costs ci as given. In any counterfactual experiment,however, adjustment of input costs to a new equilibrium is crucial.To close the model we decompose the input bundle into labor and intermedi-
ates. We then turn to the determination of prices of intermediates, given wages.Finally we model how wages are determined. Having completed the full model,we illustrate it with two special cases that yield simple closed-form solutions.
4�1� Production
We assume that production combines labor and intermediate inputs, withlabor having a constant share 2.28 Intermediates comprise the full set of goods
28 We ignore capital as an input to production and as a source of income, although our intermediateinputs play a similar role in the production function. Baxter (1992) shows how a model in whichcapital and labor serve as factors of production delivers Ricardian implications if the interest rate iscommon across countries.
Source : Eaton & Kortum, 2002. Unconditional correlation -0.4
Model : Xni/Xn
Xii/Xi=(
pi dnipn
)−θEstimated θ (method-of-moments) : θ =
∑n
∑i ln
Xni/XnXii/Xi∑
n
∑i [ln dni−ln Pi+ln Pn ]
⇒ θ = 8.28
→ Standard deviation in efficiency at given T= 15%
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Counterfactuals
Once estimated, the model can be used to run counterfactuals :What are the welfare gains from trade ? (Arkolakis et al, 2012)What is the impact of multilateral/unilateral tariff eliminations ?(Caliendo & Parro, 2015, Alvarez &Lucas 2007)How much does trade spread the benefit of local improvements intechnology ?By how much should US real wages fall to restore current accountbalance ? (Dekle et al. 2007)
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Application : Evaluating the gains from NAFTA
Caliendo & Parro (2015) use a variant of the Eaton-Kortum model toevaluate the trade and welfare impact of NAFTA.
NAFTA : A free trade area between the US, Mexico and Canada- Enhance trade within the area / Divert existing trade between the areaand the RoW
- Increase welfare : Access to cheaper consumption goods plus increasedcompetitiveness through a drop in input prices
→ Potentially important Ricardian gains since the 3 countries have verydifferent production structures
Main insights :I Important role of sectoral IO linkages to amplify the trade and welfare
effect of the partnership
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Theoretical framework
i. Multiple sectors :
Ui =K∏
k=1
Qkiαki ,
K∑k=1
αki = 1, Qk
i =
[∫ 1
0Qk
i (j)σk−1σk dj
] σk
σk−1
ii. Input-Output linkages :
cki = wγkii
K∏k ′=1
Pk ′i
γk,k′
i ,K∑
k=1
γk,k′
i = 1− γki
iii. Non tradable sectors :
dkni = +∞ for some k
iv. Sector-specific productivity distributions (Fréchet) :
F ki (z) = e−T
ki z−θk
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Analytical predictions
Equilibrium prices under perfect competition :
pkni (j) =cki
zki (j)dkni ⇒ Pk
n = Ak
[I∑
h=1
T kh
[ckh d
knh
]−θk]−1/θkExpenditure shares :
πkni = Pr [pkni (j) ≤ mins{pkns(j); s 6= i}]
=T ki
[cki d
kni
]−θk∑Ih=1 T
kh
[ckh d
knh
]−θkChanges in tariffs affect πkni directly (through dk
ni ) and indirectly(through the price of inputs encapsulated in cki )
GE solution under the assumption of balanced trade at the world level(but country-specific trade deficits) gives the vector of equilibriumwages w which is specific to a tariff vector
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Impact of trade liberalization
Equilibrium in relative changes implies :
lnwn
Pn
= −K∑
k=1
αkn
θkln πk
nn︸ ︷︷ ︸Final goods
−K∑
k=1
αkn
θk1− γk
n
γkn
ln πknn︸ ︷︷ ︸
Intermediate goods
−K∑
k=1
αkn
γknln
J∏l=1
(P ln/P
kn
)γ l,kn
︸ ︷︷ ︸Sectoral Linkages
ln πkni = −θk
[ln cki + ln dk
ni − ln Pkn
]where x = dx/x , {cki } and {Pk
n } are non-linear functions of {wn}and {dk
ni}Impact of trade liberalization on real wages can be summarized by theimpact it has on domestic shares ({πknn}) and sectoral price indices({Pk
n })
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Impact of trade liberalization (ii)
Trade liberalization increases real wages by reducing the sectoralshares of domestic consumption (ln πknn), i.e.
i. Giving consumers access to cheaper imported goodsii. Reducing the cost of same sector imported inputs (Only role of
intermediates if γkn 6= 1 and γk,kn = 1− γkniii. Reducing the cost of imported inputs for other sectors (when
γk,kn 6= 1− γkn )
Changes in real wages do not directly map into changes in welfare inthis model because of trade deficits (Dn) and tariff revenues (Rn) :
ln Wn = lnIn
Pn
=wnLnIn
lnwn
Pn
+Rn
Inln
Rn
Pn
+Dn
Inln
Dn
Pn
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Welfare Impact
Using the equilibrium conditions of the model :
lnIn
Pn
=I∑
h=1
K∑k=1
(E khn
Inln ckn −
Mknh
Inln ckh
)︸ ︷︷ ︸
Terms of trade
+I∑
h=1
K∑k=1
dknhM
knh
In
(ln Mk
nh − ln ckh)
︸ ︷︷ ︸Volume of trade
Terms of trade effect due to an increase in exporter prices relative tothe change in importer pricesVolume of trade effect due to the creation of additional trade flowsfollowing trade liberalization
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Empirical strategy
Calibration of the observed parameters :I {πk
ni} calibrated using trade and production dataI {αk
i } fitted to data on sectoral absorptionI {γki } and {γ
k,k′
i } fitted to IO tables
Estimation of the unobserved parameters {θk} :
lnX kniX
kimX
kmn
X kinX
kmiX
knm
= −θk lndknid
kimd
kmn
dkind
kmid
knm
ln dkni = ln(1 + τkni ) + νkni + µkn + δki + εkni , νkni = νkin
⇒ lnX kniX
kimX
kmn
X kinX
kmiX
knm
= −θk ln(1 + τkni )1 + τkim)(1 + τkmn)
(1 + τkin)(1 + τkmi )(1 + τknm)+ εknim
Use sectoral bilateral trade and tariff data
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Sectoral trade elasticities
Table 1. Dispersion-of-productivity estimatesFull sample 99% sample 97.5% sample
Sector θj s.e. N θj s.e. N θj s.e. NAgriculture 8.11 (1.86) 496 9.11 (2.01) 430 16.88 (2.36) 364Mining 15.72 (2.76) 296 13.53 (3.67) 178 17.39 (4.06) 152ManufacturingFood 2.55 (0.61) 495 2.62 (0.61) 429 2.46 (0.70) 352Textile 5.56 (1.14) 437 8.10 (1.28) 314 1.74 (1.73) 186Wood 10.83 (2.53) 315 11.50 (2.87) 191 11.22 (3.11) 148Paper 9.07 (1.69) 507 16.52 (2.65) 352 2.57 (2.88) 220Petroleum 51.08 (18.05) 91 64.85 (15.61) 86 61.25 (15.90) 80Chemicals 4.75 (1.77) 430 3.13 (1.78) 341 2.94 (2.34) 220Plastic 1.66 (1.41) 376 1.67 (2.23) 272 0.60 (2.11) 180Minerals 2.76 (1.44) 342 2.41 (1.60) 263 2.99 (1.88) 186Basic metals 7.99 (2.53) 388 3.28 (2.51) 288 -0.05 (2.82) 235Metal products 4.30 (2.15) 404 6.99 (2.12) 314 0.52 (3.02) 186Machinery n.e.c. 1.52 (1.81) 397 1.45 (2.80) 290 -2.82 (4.33) 186Office 12.79 (2.14) 306 12.95 (4.53) 126 11.47 (5.14) 62Electrical 10.60 (1.38) 343 12.91 (1.64) 269 3.37 (2.63) 177Communication 7.07 (1.72) 312 3.95 (1.77) 143 4.82 (1.83) 93Medical 8.98 (1.25) 383 8.71 (1.56) 237 1.97 (1.36) 94Auto 1.01 (0.80) 237 1.84 (0.92) 126 -3.06 (0.86) 59Other Transport 0.37 (1.08) 245 0.39 (1.08) 226 0.53 (1.15) 167Other 5.00 (0.92) 412 3.98 (1.08) 227 3.06 (0.83) 135
Test equal parameters F( 17, 7294) = 7.52 Prob > F = 0.00
Aggregate elasticity 4.55 (0.35) 7212 4.49 (0.39) 5102 3.29 (0.47) 3482
where εj = εjin− εjni+ εjhi− εjih+ εjnh− εjhn. Note that all the symmetric and asymmetric components of theiceberg trade costs cancel out. The terms κjni/κ
jin,κ
jih/κ
jhi, and κ
jhn/κ
jnh will cancel the symmetric bilateral
trade costs (νjni, νjih, and ν
jhn). The terms κ
jni/κ
jnh, κ
jih/κ
jin, and κ
jhn/κ
jhi cancel the importer fixed effects
(μjn,μji , and μ
jh); and the terms κ
jni/κ
jhi, κ
jih/κ
jnh, and κ
jhn/κ
jin cancel the exporter fixed effects (δ
ji , δ
jh, and
δjn). The only identification restriction is that εj is assumed to be orthogonal to tariffs.40
It is important to notice that our methodology is consistent with a wide class of gravity-trade models
and therefore the estimated trade cost elasticity from using this method does not depend on the underlying
microstructure assumed in the model. We estimate the dispersion-of-productivity parameter sector by sector
using the proposed specification (23) for 1993, the year before NAFTA was active.41 Table 1 presents the
(negative of the) estimates (θj) and heteroskedastic-robust standard errors. As we can see, the coefficients
have the correct sign and the magnitude of the estimates varies considerably across sectors. The estimates
40 Of course, as any estimation of trade elasticities from bilateral trade and tariff data, our method is subject to the endogenoustrade policy concern (Trefler 1993, and Baier and Bergstrand 2007). Still, our triple differencing might alleviate some of theseconcerns given that the estimates we obtain are comparable to the range of previous elasticity estimates done with differentmethods and different data.41We estimate (23) by OLS, dropping the observations with zeros. Zeros in the bilateral trade matrix are very frequent and
several studies are focused on understanding how robust the estimates of trade elasticities are if zeros are taken into account.For instance, Santos-Silva and Tenreyro (2010).
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Counterfactual analysis
i. Introduce the change in tariffs from 1993 to 2005 between NAFTAmembers, fix tariffs for the RoW to 1993 levels
ii. Introduce the change in tariffs from 1993 to 2005 between NAFTAmembers as well as observed changes in world tariffs
iii. Introduce the change in world tariffs from 1993 to 2005, fixing NAFTAtariffs to 1993 levels.
The difference between (ii) and (iii) measures gains from world tariffreductions with and without NAFTA.Note : In principle, trade liberalization affects trade deficits, which areexogenous in the model. This is a limit of the analysis.
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Pre-NAFTA tariffs
0
5
10
15
20
%
Applied tariff rates Mexico to USA (1993)
0
5
10
15
20
%
Applied tariff rates Canada to USA (1993)
0
5
10
15
20
%
Applied tariff rates Canada to Mexico (1993)
0
5
10
15
20
%
Applied tariff rates USA to Canada (1993)
0
5
10
15
20
%
Applied tariff rates USA to Mexico (1993)
0
5
10
15
20
%
Applied tariff rates Mexico to Canada (1993)
Source: UNCTAD TRAINS)
Fig. A.1. E ective applied tari rates before NAFTA
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Introduction The EK model Empirical Applications Conclusion Appendix
The role of intermediate goods and sectoral linkages
In 1993, the role of intermediate goods is already substantial...I Respectively 68, 61.5 and 64.6% of Mexico’s, Canada’s and the US
imports from non-NAFTA countries were intermediate goodsI Respectively 82.1, 72.3 and 72.8% of Mexico’s, Canada’s and the US
imports from NAFTA countries were intermediate goods
... As is the extent of cross-sectoral linkages :I In the IO Tables, the mean share of own-sector inputs is around 15-20%I More than 70% of intermediate consumption is addressed to other
sectorsI Average share of tradables in the production of non-tradables is 23%
for the US and 32% for Mexico / Average shares of non-tradables inthe production of tradables are 34% for the US and 26% for Mexico
G. Corcos & I. Méjean (Ecole polytechnique) International Trade: Lecture 6 39 / 52
Introduction The EK model Empirical Applications Conclusion Appendix
Welfare effect from NAFTA’s Tariff reductions
as a share of world GDP.
5.1 Trade and Welfare Effects from NAFTA’s Tariff Reductions
We now quantify the trade and welfare effects of NAFTA. Table 2 presents the welfare effects from
NAFTA’s tariff reductions while fixing the tariff to and from the rest of the world to the year 1993. Welfare
effects are calculated using (16) , and changes in real wages using (15) . As we can see, Mexico’s welfare
increases by 1.31%. The effects for Canada and the U.S. are smaller. Canada loses 0.06% while the U.S.
gains 0.08%. Still, we find that real wages increase for all NAFTA members and Mexico gains the most,
followed by Canada and the U.S.47
Table 2. Welfare effects from NAFTA’s tariff reductionsWelfare
Country Total Terms of trade Volume of Trade Real wagesMexico 1.31% -0.41% 1.72% 1.72%Canada -0.06% -0.11% 0.04% 0.32%U.S. 0.08% 0.04% 0.04% 0.11%
Decomposing the welfare effects into terms of trade and volume of trade underscores the sources of these
gains. The third column in Table 2 shows that the major source of gains are increases in volume of trade. The
welfare gains from trade creation for Mexico, Canada and the U.S. are 1.72%, 0.04% and 0.04% respectively.
We can look deeper and measure the extent to which the welfare effects are a result of trade creation with
NAFTA members vis-a-vis the rest of the world. This is done by applying the bilateral volume of trade
measures (18) defined before.
Table 3. Bilateral welfare effects from NAFTA’s tariff reductionsTerms of trade Volume of Trade
Country NAFTA Rest of the world NAFTA Rest of the worldMexico -0.39% -0.02% 1.80% -0.08%Canada -0.09% -0.02% 0.08% -0.04%U.S. 0.03% 0.01% 0.04% 0.00%
Column 3 in Table 3 shows that the trade created with NAFTA members is the single most important
contributor to the positive welfare effects. The figures are 1.80%, 0.08% and 0.04% for Mexico, Canada
and the U.S. respectively. This result unmasks an important channel by which NAFTA generated positive
welfare effects to all of its members, by creating more trade within the bloc. On the other hand, column 4
from Table 3 shows that the reduction in volume of trade with the rest of the world has a negative welfare
effect. This negative welfare effect, which we discuss further below, arises from NAFTA diverting trade from
countries outside of the agreement.47The welfare effects results in the model with trade deficits are very similar, 1.17%, -0.04% and 0.09% for Mexico, Canada
and the U.S. respectively. Appendix “Additional Results”, tables A.4 to A.7, includes this and additional results with tradedeficits and it shows that all the results in this section are robust to include trade deficits or not.
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Mexico gains the most, both in terms of welfare and in terms of realwages.Most important source of gains is increase in the volume of trade(mostly within NAFTA ; trade vis-à-vis the RoW decreases, tradediversion).US terms-of-trade improved, both vis-à-vis NAFTA members and theRoW.Welfare effects widely vary across sectors.
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Trade effect from NAFTA’s Tariff reductions
has a positive contribution to the welfare increase from volume of trade. Three sectors account for more than
50% of the sectoral contribution of Mexico’s and U.S.’s volume of trade. These are Textiles, Petroleum and
Electrical Machinery. For the case of Canada, the sectors that contribute the most are Textiles, Petroleum
and Auto. In general, volume of trade effects depend on the magnitude of the tariff reduction, the trade
elasticity, and the share of materials used in production and these factors weight differently for each of these
sectors. Textiles was the most protected sector by Mexico in the year 1993. Applied import tariffs were
on average 18%. So the large reduction in tariffs facilitates trade between members of NAFTA and results
in a significant contribution to the increase in volume of trade. Petroleum is a homogenous good sector.
As a consequence, small changes in import tariffs can have large trade effects since it is relatively easy to
substitute suppliers, as documented by its high import tariff trade elasticity (see Table 1). The average
import tariffs in Petroleum in the year 1993 across NAFTA members was 7%. Finally, NAFTA’s tariffs
reductions has important effects over the price of intermediate goods traded in some sectors compared to
others. This is particularly important for the sectors Electrical Machinery and Autos for reasons we discussed
in the previous paragraph. The reduction in trade prices in these sectors explains the increase in the volume
of trade effect.
Table 5. Trade effects from NAFTA’s tariff reductionsMexico Canada U.S.
Mexico’s imports - 116.60% 118.31%Canada’s imports 58.57% - 9.49%U.S.’s imports 109.54% 6.57% -
Table 5 presents aggregate trade effects from NAFTA. As we can see, NAFTA generated large aggregate
trade effects for all members. Mexico’s imports from NAFTA increased by more than 110% and equally so
across both partners. For the case of Canada, we find that the percentage increase in imports from Mexico
is more than five times larger than the percentage increase in imports from the U.S. This results reflect
that Mexico’s role as a supplier of intermediate goods to NAFTA members increased as a consequence of
NAFTA. In fact, this is even more evident when we look at the case of the U.S. imports. Imports from
Mexico increase more than 100% while from Canada only 6.57%. These figures reflect how interdependent
these economies become after the tariff reductions imposed by the agreement. In short, NAFTA strengthened
the trade dependence that these countries had before the agreement, and as a consequence Canada and the
U.S. source more goods from Mexico, while Mexico sources more goods from Canada and the U.S.
NAFTA also had an effect on sectoral specialization. Table 6 presents export shares by industry before
and after reducing NAFTA’s tariffs. First note that sectoral concentration varies considerably across sectors
and countries. Consider the case of Mexico before NAFTA, the year 1993. Three sectors account for 52.75%
of total exports. These sectors are Electrical Machinery, Autos and Mining. For the case of Canada, the
three sectors with the largest shares are Autos, Basic Metals and Mining, and account for 43.7% of total
exports. While for the U.S. the three largest sectors are Machinery, Chemicals, and Autos, and account for
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Large aggregate effects for all membersCanada and the US increased a lot their imports from Mexico : role asa supplier of intermediates to NAFTAStrong impact on the specialization of countries : Mexico becomesmore specialized
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Specialization due to NAFTA
28.57% of total exports. These figures reflect that Mexico was the country with the highest degree of sectoral
specialization while the U.S. the most diversified. In fact, the last row of the table presents the normalized
Herfindahl index (henceforth, HHI) and we make use of it as a measure of sectoral specialization. As we can
see, the HHI for Mexico was the largest and twice as large as the U.S. HHI, the smallest among all NAFTA
members. After NAFTA’s tariffs reductions we find that Mexico became more specialized while Canada and
the U.S. more diversified. In fact, Mexico’s share of exports from Electrical Machinery increase to 34.07%
and the three largest sectors account for 54.95% of total exports after NAFTA. This sectoral concentration
is reflected in Mexico’s HHI which increases to 0.138. On the other hand, the HHI indices of Canada and
the U.S. decrease.49
Table 6. Export shares by sector before and after NAFTA’s tariff reductionsMexico Canada United States
Sector Before After Before After Before AfterAgriculture 4.72% 3.03% 4.99% 5.04% 6.91% 6.35%Mining 15.53% 7.85% 8.99% 8.96% 1.72% 1.52%ManufacturingFood 2.33% 1.48% 4.82% 4.68% 5.09% 4.73%Textile 4.42% 6.92% 1.05% 1.49% 2.68% 3.49%Wood 0.59% 0.52% 8.12% 8.05% 2.02% 1.98%Paper 0.62% 0.51% 8.34% 8.44% 4.99% 4.89%Petroleum 1.62% 5.28% 0.59% 0.78% 4.30% 5.71%Chemicals 4.40% 2.53% 5.58% 5.40% 10.00% 9.25%Plastic 0.80% 0.48% 2.06% 2.06% 2.28% 2.43%Minerals 1.32% 0.84% 0.81% 0.78% 0.94% 0.92%Basic metals 3.24% 2.00% 10.29% 10.19% 3.05% 3.11%Metal products 1.22% 1.03% 1.47% 1.53% 2.23% 2.59%Machinery n.e.c. 4.30% 2.53% 4.69% 4.49% 10.37% 9.70%Office 3.34% 5.07% 2.44% 2.54% 7.70% 7.29%Electrical 20.79% 34.07% 2.50% 2.35% 6.07% 7.97%Communication 8.57% 7.08% 3.11% 3.02% 7.19% 6.81%Medical 2.48% 3.28% 0.98% 1.03% 5.16% 4.79%Auto 16.43% 13.05% 24.42% 24.07% 8.20% 8.09%Other Transport 0.28% 0.26% 3.21% 3.58% 7.32% 6.65%Other 3.02% 2.20% 1.55% 1.52% 1.77% 1.74%
Normalized Herfindahl 0.092 0.138 0.083 0.081 0.042 0.040
The rest of the world was hardly affected by NAFTA’s tariff reductions. Table A.3 in Appendix “Additional
Results”, which we do not include in the main text for brevity, presents the change in welfare, terms of trade
and volume of trade effects for the rest of the 28 countries in our sample. The effects are small. The two
countries most impacted are China and Korea and in both cases welfare falls by 0.03%. This is mostly due
to a reduction in the volume of trade for the case of China, and an equal reduction in the terms of trade and
volume of trade for the case of Korea. Looking at other countries we find that volumes of trade decreased49Many factors, besides NAFTA, could have influenced the pattern of sectoral specialization in the data. Still, the pattern of
sectoral specialization implied by the model from NAFTA’s tariff reductions for NAFTA members is in line with the observedpattern in the year 2005. In fact, the correlations are 0.59, 0.86, and 0.83 for Mexico, Canada, and the U.S. respectively.
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Introduction The EK model Empirical Applications Conclusion Appendix
Decomposition of trade and welfare effectswith no materials used in production (No materials), and with no I-O connections (No I-O).54 We calibrate
each of these models to the year 1993 and compute the welfare and trade responses from NAFTA’s tariff
reductions. Table 11 presents the simulated trade and welfare effects implied by the different models. The
first column shows the welfare effect from the one sector model. The second column presents the welfare
result for the no materials model, and the third column presents the welfare result for the no I-O model.
Table 11. Trade and welfare effects from NAFTA across different modelsWelfare Imports growth from NAFTA members
Multi sector Multi sectorCountry One sector No materials No I-O One sector No materials No I-O BenchmarkMexico 0.41% 0.50% 0.66% 60.99% 88.08% 98.96% 118.28%Canada -0.08% -0.03% -0.04% 5.98% 9.95% 10.14% 11.11%U.S. 0.05% 0.03% 0.04% 17.34% 26.91% 30.70% 40.52%
We find that for all models the welfare effects are smaller compared to the benchmark model. Still, in
all cases Mexico gains the most followed by the U.S. then Canada. The results from the one sector model
reflect the importance of accounting for sectoral heterogeneity. In fact, recent studies have emphasized
that the sectoral variation in trade elasticities is particularly important for the quantification of the welfare
gains.55 The calculations also show that intermediate goods amplify the welfare effects from tariff reductions.
Mexico’s figure increase from 0.50% to 0.66%, Canada’s deteriorate more from -0.03% to -0.04% and the
U.S. increase from 0.03% to 0.04% as we move from a model with no materials to a model with materials.
We also find that the model with input-output linkages amplifies the effects as well. If we compare the third
column on Table 11 to the results from the benchmark model, Table 2, we can clearly see that the welfare
effects are substantially larger for the countries that win and lower for the countries that loose.
Trade effects are also smaller across these models compared to the benchmark case. The last four columns of
Table 11 presents, for the case of Mexico, Canada and the U.S., the change in imports from NAFTA members
implied by the different models. As we can see, the trade effects are reduced substantially compared to the
benchmark case. In the one sector model, the trade responses are almost reduced by half. The intuition for
this result relates to the result on welfare. By averaging out the effects, a one sector model fails to capture
the large increase in trade flows from certain sectors. In fact, we know from tables 4 and 6 that NAFTA
generated very heterogenous responses across sectors. If we compare the results from column five to column
six we can see that adding intermediate goods increases the trade effects. The intuition for this result is
54The one sector model has one tradable sector and one non-tradable sector. Production uses materials from both sectors,(I-O). We agregate all sectoral data to calibrate the parameters and use the median tariff across sectors. We use our specification(23) to estimate an aggregate elasticity, the value is θ = 4.5. In the multi-sector model “No materials” there are no materialsused in production, γjn = 1, and as a result value added is equal to gross output. In the multi sector model “No I-O”, materialsare used in production, γjn < 1, but we zero out the off-diagonal elements of the I-O matrix. Firms can only use materialssourced from the same sector they operate, γj,jn = 1 − γjn. We use I-O tables for each country to calibrate γj,jn . For all cases,we first calibrate the model and then eliminate the observed aggregate trade deficits.55 In a recent study, Ossa (2012) shows that the heterogeneity in trade elasticities per se has an important effect on the
quantification of the welfare gains from trade. He shows this for the case of iceberg trade costs and by calculating welfare lossesfrom reverting to autarky.
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Welfare gains are always reduced in comparison to benchmark⇒ Trade in intermediates, Sectoral heterogeneity and Sectoral linkages all
matter
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Introduction The EK model Empirical Applications Conclusion Appendix
Concluding remarks
A very elegant way of introducing Ricardo into a multi-country andpossibly multi-sector modelAnalytics strongly rely on some assumptions : Fréchet distribution,Variance of productivities homogenous across industriesThe model can be parsimoniously calibrated and extended to bebrought to the data.Many empirical applications, such as the evaluation of tradeagreements.But results can be sensitive to how structural parameters areestimated... [more on this in Lectures 10-11]
G. Corcos & I. Méjean (Ecole polytechnique) International Trade: Lecture 6 44 / 52
Introduction The EK model Empirical Applications Conclusion Appendix
References
- Alvarez, F. & Lucas, R., 2007. "General equilibrium analysis of theEaton-Kortum model of international trade," Journal of MonetaryEconomics, vol. 54(6), pp. 1726-1768
- Arkolakis C., Costinot A., and Rodriguez-Clare A. 2012. “New Trade Models,Same Old Gains ?” American Economic Review, 102(1) : 94-130.
- Bernard, A., Eaton J., Jensen, B. & Kortum S., 2003. “Plants andProductivity in International Trade,” American Economic Review93(4) :1268-1290.
- Costinot, Donaldson & Komunjer, 2012, “What Goods Do Countries Trade ?A Quantitative Exploration of Ricardo’s Ideas”, Review of Economic Studies79(2) :581-608.
- Caliendo & Parro, 2015, “Estimates of the Trade and welfare Effects ofNAFTA,” Review of Economic Studies 82 (1) : 1-44
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Introduction The EK model Empirical Applications Conclusion Appendix
References
- Dekle R., J. Eaton & S. Kortum, 2007, "Unbalanced Trade", AmericanEconomic Review : Papers and Proceedings, Vol. 97, No. 2, pp. 351-355
- Eaton J. & Kortum S., 1997. “International technology diffusion : Theoryand measurement,” International Economic Review 40(3) : 537-570.
- Eaton J. & Kortum S., 2002, “Technology, Geography and Trade”,Econometrica 70(5) :1741-1779
- Eaton J. & Kortum S., 2012, “Putting Ricardo to Work”, Journal ofEconomic Perspectives 26(2) :65-90
- Head, K. & Mayer T., 2014, “Gravity Equations : Workhorse,Toolkit, andCookbook”, chapter 3 in Gopinath, G, E. Helpman and K. Rogoff (eds), vol.4 of the Handbook of International Economics, Elsevier : 131-195.
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Demand functions
Consumers solve :max{Qi (j)}j∈[0,1]
[∫ 10 Qi (j)
σ−1σ dj
] σσ−1
s.t.∫ 10 Pi (j)Qi (j)dj ≤ Ri
Solution of the maximization program is :
Qi (j) =
(Pi (j)
Pi
)−σ Ri
Pi
with Pi the ideal price index (Ri/Pi = Ui , ∀Ri ) :
Pi =
[∫ 1
0Pi (j)
1−σdj
] 11−σ
Back to assumptions
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Optimal Prices
Firms’ profit :
πi (j) =∑n
[pni (j)Qni (j)−
cizi (j)
dniQni (j)
]=∑n
πni (j)
Under perfect competition :
pni (j) =ci
zi (j)dni
andQin(j) = 0 if pin(j) > pn(j)/Qn(j) otherwise
Back to assumptions
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Introduction The EK model Empirical Applications Conclusion Appendix
Price distribution
pni (j) = cizi (j)
dni is the realization of a random variable Pni which cdfis :
Gni (p) = Pr [Pni ≤ p] = Pr
[Zi ≥
cidnip
]= 1− Fi
(cidnip
)= 1− e
−Ti
(ci dnip
)−θ
pn(j) = min{pni (j); i = 1...I} is the realization of a random variablePn = min{Pni ; i = 1...I} which cdf is :
Gn(p) = Pr [Pn ≤ p] = 1−I∏
i=1
Pr [Pni > p]
= 1−I∏
i=1
[1− Gni (p)] = 1− e−pθ∑I
i=1 Ti (cidni )−θ
Back to the model
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Price index
Cdf / pdf of consumption prices :
Fn(p) = 1− e−Φnpθ
and fn(p) = Φnθpθ−1e−Φnp
θ
Define : y = g(p) = pθ, then
Gn(y) = Fn(g−1(y)) and gn(y) = f (g−1(y))
∣∣∣∣∂g−1(y)
∂y
∣∣∣∣ = Φne−Φny
Thus the price index :
Pn =
[∫ 1
0pn(j)1−σdj
] 11−σ
=
[∫ 1
0y
1−σθ Φne
−Φnydy
] 11−σ
= Φ−1/θn
[∫ 1
0u
1−σθ e−udu
] 11−σ
where u = Φny
= Φ−1/θn
[Γ
(1− σθ− 1)] 1
1−σ
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Introduction The EK model Empirical Applications Conclusion Appendix
Fréchet distribution
Generalized extreme value distribution : A family of continuousprobability distributions used as an approximation to model themaxima of long (finite) sequences of random variablesCDF :
F (x ;µ, σ, ξ) = exp
{−[1 + ξ
(x − µσ
)]− 1ξ
}µ a location parameter, σ > 0 the scale parameter, ξ the shapeparameter
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Introduction The EK model Empirical Applications Conclusion Appendix
Fréchet distribution
In particular :I Gumbel or type I extreme value : ξ = 0
F (x ;µ, σ, 0) = exp
{−exp
[−x − µ
σ
]}, x ∈ R
I Frechet of type II extreme value : ξ = α−1 > 0
F (x ;µ, σ, ξ) =
{0, x ≤ µexp
{−[x−µσ
]−α}, x > µ
I Reversed Weibull or type III extreme value : ξ = −α−1 < 0
F (x ;µ, σ, ξ) =
{exp
{−[− x−µ
σ
]α}, x < µ
1, x ≥ µ
Back to the model
G. Corcos & I. Méjean (Ecole polytechnique) International Trade: Lecture 6 52 / 52