gravity rules - department of economics sciences...

Gravity rules

Thierry Mayer

Sciences-Po, CEPII, and CEPR.

Motivation

I Gravity rules in all cases to date.

I Xij = YiYj/dij is one of the most stable relationships ineconomics.

I The bad news: “To amaze your friends with anotherimportant trade effect, develop a new proxy for trade costsand use a really big dataset; success is not guaranteed, butyou’re likely to find significance (standard errors involve theinverse of the square root of number of observations) andyou’ll have loads of fun in any case.”

I The good news: we know why it works (much more than forZipf’s law for instance): most trade models require gravity towork.

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)

Trade is inversely proportional to distance

(a) Isard&Peck (1954) (b) Leamer&Levinsohn (1995)

Trade is inversely proportional to distance

(c) France’s exports (2006) (d) 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

... and yet

“If I had access to captive research assistance and funds,I could examine whether, for all conceivable combinationsof countries and distances among them, and for severaldifferent time periods, the premise [that proximityincreases trade] is valid. I do not, so I must rely on casualempiricism and a priori arguments...Borders [such as theone between Pakistan and India] can breed hostility andundermine trade, just as alliances between distantcountries with shared causes can promote trade... ...[Thepremise that distance reduces trade] does not have a firmempirical or conceptual basis.” Bhagwati (1993)

...there can be large deviations from gravity

(a) Pakistan’s exports (b) India’s exports

PAK-->IND

4

4

44

4

44

4

44

44

4

4

4

4

44

4

4

44 4

444

4

4

444

5

5

5

PAK-->GBR

.00

01

.00

1.0

1.0

5.1

.51

5

1950 1960 1970 1980 1990 2000

real/naive gravity-pred. trade

IND-->PAK

44

4

44

44

444

4

4 44

4

4

4

444

44444

4

4444

4

5

5

5

IND-->GBR

.00

1.0

1.0

5.1

.51

5

1950 1960 1970 1980 1990 2000

real/naive gravity-pred. trade

3 landmarks steps to recognition

Leamer and Levinshon (1995, HIE): gravity models “have producedsome of the clearest and most robust findings in economics. Butparadoxically they have had no effect on the subject ofinternational economics.”

... “Why don’t trade economists ‘admit’ the effect of distance intotheir thinking?”

One might add: “... still, 40 years after Isard and Peck?”

I Admission (1995): Gravity is one way to measure the largeamount of “missing trade” and explain it. LL (1995). Trefler(1995), McCallum (1995).

I The MR/fixed effects revolution (2002-2004): Gravityhas (many) micro-foundations + easy to do “structural”estimation. EK (2002), AvW (2003), Feenstra (2004),Redding and Venables (2004).

I Convergence with the het. firms lit. (2007-2008):Gravity compatible with new paradigm, new usage of the toolto measure the margins. BJRS (2007), HMR (2008), Chaney(2008), MO (2008).

Part I

Defining Gravity

Theoretical foundations

I 3 definitions

I The two traditional versions: NPD-AvW and MC-DSK.

I The new derivations with heterogeneities (consumers,comparative advantage, firms).

Defining gravity

3 definitions:

1. General structural gravity

2. Special structural gravity

3. Naive gravity

General structural gravity

Set of models that yield bilateral trade equations that can beexpressed as

Xni = GSiMnφni .

I Si : “capabilities” of exporter i

I Mn : characteristics of a country which make it a largeimporter.

I 0 ≤ φni ≤ 1 : bilateral accessability of destination market n toexporter i (combines trade costs with their respectiveelasticity).

Special structural gravitySubset of general structural gravity models in which bilateral tradeis given by

Xni =Yi

Ωi︸︷︷︸Si

Xn

Φn︸︷︷︸Mn

φni ,

where Yi =∑

n Xni is the value of production, Xi =∑

i Xni is thevalue of expenditure, and Ωi and Φn are “multilateral resistance”terms defined as

Φn =∑`

φn`Y`Ω`

and Ωi =∑`

φ`iX`Φ`

.

Requires:

1. Multiplicative allocation budget shares (πni = Xni/Xn):

πni =Siφni

Φn, where Φn =

∑`

S`φn`.

2. Market clearing:

Yi =∑n

Xni = Si

∑n

φniXn

Φn= SiΩi .

Naive gravity

Naive gravity equations express bilateral trade as

Xni = GY ai Y b

n φni

I Imposes the implausible restriction that φni is a constant.

I Baldwin and Taglioni (2007): omission of 1/(ΩiΦn) is the“gold medal mistake” of gravity equations, characterizingmost empirical work before Anderson and van Wincoop(2003).

Part II

The two traditional versions

NPD-AvW

Anderson (1979) / Anderson and van Wincoop (2003): As inArmington (1968), each country is the unique source of eachproduct (1 variety per country). Utility exhibits CES and tradecosts are iceberg (pni = piτni ):

Un =

(∑i

(Aiqni )σ−1σ

) σσ−1

. (1)

I Ai is a utility shifter (whose mnemonic could be“attractiveness”) can be interpreted as a monadic qualityshifter.

I Simple maximization of (1) under budgetary constraintprovides optimal demand for each variety, such that

Si = Aσ−1i w1−σi , φni = τ1−σni . (2)

MC-DSK

Dixit-Stiglitz-Krugman assumptions yield gravity (first seem to beBergstrand, 1985, Wei 1996 is clearer).

I Each country has Ni identical firms supplying one variety eachto the world from a home-country production site.

I Utility is symmetric (Ai = 1,∀i) and CES in terms of allN =

∑i Ni varieties available in the world.

I Standard CES derivation of optimal demand yields

Si = Niw1−σi , φni = τ1−σni . (3)

MC-DSK

I Only apparent difference compared to the NPD model is theNi term: monopolistic competition / perfect competition

I Note that prices are also different, because of differentmarkups.

I Can be derived for trade in intermediates using Ethier (1982)

Part III

Estimation methods

Remoteness

I A few studies have included proxies for 1/Ωi and 1/Φn andreferred to them as “remoteness.”

I Helliwell (1998) measures remoteness asREM1n =

∑i Distni/Yi . However, as Yi → 0, REM1

explodes.

I A better measure of remoteness isREM2n = (

∑i Yi/Distni )

−1.

I Supposing φni ∼ Dist−1ni and Xn = Yn, the correct Φn and Ωi

are ∑`

(Y`/Distn`)Ω−1` ,∑`

(Y`/Distn`)Φ−1` .

I Still far off the mark.

Iterative structural estimation

1. Assume initial values of Ωi = 1 and Φn = 1,

2. Estimate the vector of parameters determining φni ,

3. Use a “contraction mapping” algorithm to find fixed pointsfor Ωi and Φn given those parameters.

4. Run OLS using ln Xni − ln Yi − ln Xn + ln Ωi + ln Φni as thedependent variable. This gives a new set of φni parameterestimates.

5. Iterate until the parameter estimates stop changing.

Fixed effects estimation

Standard estimating procedure involves taking logs ofequation (12), obtaining

ln Xni = ln G + ln Si + ln Mn + lnφni . (4)

I Tradition = using log GDPs (and possibly other variables) asproxies for the ln Si and ln Mj : Gold medal mistake.

I Since Harrigan (1996) practice has been moving towards usingfixed effects for these terms instead.

I Note that it does not involve strong structural assumptions onthe underlying model. Only need general structural gravity toestimate φij consistently

I Furthermore, market-clearing does not affect the estimationprocedure.

I Can help control for country-specific patterns (entrepottrade...)

Cautions

I With panels, importer and exporter fixed effects should betime-varying as well.

I The same is true if the data pools over several industries.

I For panels of trade flows with a large number of years and/orindustries, computational issues → other methods.

I If the precise model underlying fixed effects estimation doesnot matter for φni coefficients, it does for Si and Mn

estimates.

I Silver medal mistake: averaging the reciprocal flows.

I Bronze medal mistake: deflating the flows. Gravity is anexpenditure function allocating nominal GDP into nominalimports.

FE estimation of distance coefficient

.6.8

11.

21.

41.

6di

stan

ce c

oeffi

cien

t

1960 1970 1980 1990 2000

FE estimation of colonial link coefficient

1.3

1.4

1.5

1.6

1.7

1.8

colo

nial

link

age

coef

ficie

nt

1960 1970 1980 1990 2000

FE estimation of common language coefficient

.3.4

.5.6

.7co

mm

on la

ngua

ge c

oeffi

cien

t

1960 1970 1980 1990 2000

Alternatives to fixed effects-1

I One can use the multiplicative structure of the gravity modelto get rid of trouble terms.

I Bilateral “relative” imports by country n from country i for agiven industry/year, odds specification (Head and Mayer,2000):

Xni

Xnn=

(Si

Sn

)(φniφnn

). (5)


I Relative prices, Ai and Ni are difficult to observe. Frictionspecification (Head and ries, 2001):

XniXin

XnnXii=

(φniφinφnnφii

). (6)

I Note that if φni = φin and φnn = φii = 1,

φni =

√XniXin

XnnXii. (7)

I Can be used as a measure of “trade costs”.


I Those manipulations can be done with any reference country(Martin et al. 2008):

Xni

Xnus=

(Ni

Nus

)(pi

pus

)1−σ ( φniφnus

).

I Also to get rid of exporter effects (Anderson and Marcouiller,2002):

Xius

Xnus=

(φiusφnus

)(Φn

Φi

)(Xi

Xn

).

Alternatives to fixed effects-3Possible to get rid of... everything (Tetrads method), Romalis(2008), Hallak (2004), Head et al. (2010)

I Divide Xni = GSiMnφni by a reference importer k:

Rink =Xni

Xki=

MnφniMkφki

.

I Mn/Mk problem =⇒ pick a reference exporter `:

R`nk =Xn`

Xk`=

Mnφn`Mkφk`

.

I Taking the ratio of ratios =⇒ tetradic term

ri`nk =Rink

R`nk=

Xni/Xki

Xn`/Xk`=φni/φkiφn`/φk`

.

ln ri`jk = lnφni − lnφki − lnφn` + lnφk`.

Monte Carlo study of different estimators

I Monte Carlo using special structural gravity as a DGP.

I We use actual data for 170 countries that have GDP,distance, and RTA data in 2006.

φni = exp(− ln Distni + 0.5RTAni )ηni .

I 2 types of missing values: suppress X % of observationsrandomly, or smallest X % of the initial set of export flows.

Abbrev. Description Introduced by

OLS Linear-in-logs with GDPs Tinbergen (1962)SILS Structurally Iterated Least Squares Anderson and van Wincoop (2003)∗

2WFE Two-way country fixed effects Harrigan (1996)DDM Double-Demeaning of LHS & RHS noneBVU Bonus Vetus OLS, simple avgs. Baier and Bergstrand (2010)BVW Bonus Vetus OLS, GDP-weighted Baier and Bergstrand (2009)Tetrads Ratios of reference exporter & importer Head et al. (2010)PPDV Poisson PMLE w/ country dummies Santos Silva and Tenreyro (2006)

Monte Carlo results

I OLS is a poor estimator under the structural gravity DGP:Gold Medal mistake is a problem.

I SILS is close from 2WFE (slightly less precise) and robust tomissings: not worth the computational effort?

I DDM is one of the worse estimators when there are largenumbers of non-random missing observations. BVU (related)appears to have better robustness properties.

I BVW: not robust to missing data and very imprecise (highstandard deviation of the coefficients).

I Tetrads: unbiased except when high numbers of randomlymissing observations. Very important to (2-way) cluster. Notadvisable now that 2WFE methods can handle large numbersof fixed effects.

I PPDV: mildly biased towards zero but very stable. Biasdepends on the variance parameter chosen for error term.

Part IV

The trade impact of Policy variables

Gravity/FEs for GATT/WTO effects (Rose, 04 AER)

Gravity/Odds results (Martin et al., 08 Restud)

Gravity/Tetrad results (Head et al., 10 JIE)


60+ years

.25

.5.7

51

1.25

Trad

e ra

tio

0 10 20 30 40 50 60Years since independence

Specification (1) OLS

60+ years

.25

.5.7

51

1.25

Trad

e ra

tio0 10 20 30 40 50 60

Years since independence

Specification (6) Average over 30 tetrads


Despite the fall, colonies remain important for trade:

1960 1970 1980 1990 2000

ratio

:FR

A/G

BR

(lo

g sc

ale)

1/20

1/10

1/5

1/2

1

2

5

10

20

50

GDP ratio (FRA/GBR)

Ivory Coast

Ghana

Gha

na in

depe

nden

t fro

m U

K

Ivor

y C

oast

inde

pend

ent f

rom

Fra

nce

Exports from (former) ColonyImports to (former) Colony

1960 1970 1980 1990 2000

ratio

:FR

A/G

BR

(lo

g sc

ale)

1/10001/500

1/2001/100

1/50

1/201/10

1/5

1/212

51020

50100200

5001000

GDP ratio

(FRA/GBR)

Reunion(France)

Mauritius

Mau

ritiu

s in

depe

nden

t fro

m U

K

Floored at 0.001Exports from (former) ColonyImports to (former) Colony

Standard gravity for RTAs (Frankel et al. 95, JDE)d. Frankel et al./Journal of Development Economics 47 (1995) 61-95

Table 2 Gravity model with western hemisphere broken into sub-regions (aggregate trade, 1965-1990) a

71

1965 1970 1975 1980 1985 1990

GNP 0.63 " (0.02)

GNP per capita 0.26 "

(0.O2)

Distance - 0.44 (0.04)

Adjacency 0.62 " (0.17)

EAEC 1.40 "

(0.29)

APEC 0.61 " (0.21)

EC 0.24 ##

(0.17) EFTA 0.04

(O.30)

NAFTA - 0 . 1 2

(0.63) M E R C O S U R - 0.18

(0.46) ANDEAN - 0.51

(0.39)

# Observations 1194

SEE 1.07 Adjusted R 2 0.68

0.64 * " 0.72 * ' 0.74 °

(0.02) (0.18) (0.02)

0.36 ' ' 0.27 " ° 0.29 '

(0.02) (0.02) (0.02)

- 0 . 5 3 ° " - 0 . 6 8 " ° - 0 . 5 6 (0.04) (0.05) (0.04)

0.58 ° " 0.45 " 0.68 "

(0.17) (0.19) (0.18)

1.71 * " 0.86 * " 0.78 " (0.29) (0.31) (0.27)

0.76 ' " 0.97 ° " 1.49 * (0.21) (0.22) (0.18)

0.11 - 0 . 0 6 0.21

(0.17) (0.18) (0.18)

0.07 0.01 0.58

(0.30) (0.32) (0.32) - 0.41 - 0.44 0.08

(0.64) (0.70) (0.71)

0.46 0.43 0.81 ##

(0.46) (0.50) (0.51)

- 0 . 1 3 1.15 * " 1.11 * "

(0.32) (0.35) (0.32)

1274 1453 1708

1.08 1.18 1.20

0.71 0.71 0.71

0.53 " ' 0.75 " "

(0.02) (0.01)

0.06 " ' 0.09 " *

(0.02) 0.02

' - 0 . 3 5 " " - 0 . 5 6 * " (0.05) (0.04)

0.85 * " 0.79 " "

(0.20) (0.16)

- 0 . 4 1 # 0.63 ' "

(0.28) (0.24)

1 . 5 8 " " 1 . 3 2 " "

(0.20) (0.17)

1.51 * ' 0.49 " "

(0.19) (0.16)

0.06 - 0.05 (0.36) (0.29)

- 0.58 0.05 (0.75) (0.63) 0.72 2.09 " *

(0.55) (0.46)

- 0.17 0.90 " * (0.59) (0.29)

1343 1573 1 . 2 8 1.08

0.51 0.77

a Standard errors, are in parentheses. ' " denotes significant at 1% level ( t >/2.576);

" denotes significant at 5% level ( t /> 1.96);

# denotes significant at 10% level ( t /> 1.645); ## denotes significant at 15% level (t >/1.44).

All variables except the dummies are in logarithms.

p o r t i o n a t e l y ( h o l d i n g G N P p e r c a p i t a c o n s t a n t ) . T h i s r e f l e c t s t h e f a m i l i a r p a t t e r n

t h a t s m a l l e c o n o m i e s t e n d to b e m o r e d e p e n d e n t o n i n t e r n a t i o n a l t r a d e t h a n l a r g e r ,

m o r e d i v e r s i f i e d , e c o n o m i e s .

2.2. Estimation o f trade-bloc effects

I f t h e r e w e r e n o t h i n g to t h e n o t i o n o f t r a d i n g b l o c s , t h e n t h e s e f o u r b a s i c

v a r i a b l e s m i g h t s o a k u p a l l t h e e x p l a n a t o r y p o w e r . T h e r e w o u l d b e n o t h i n g l e f t to

a t t r i b u t e t o a d u m m y v a r i a b l e r e p r e s e n t i n g w h e t h e r t w o t r a d i n g p a r t n e r s a r e b o t h

l o c a t e d i n t h e s a m e r e g i o n . In t h i s c a s e t h e l e v e l a n d t r e n d i n i n t r a - r e g i o n a l t r a d e

The problems with gravity results for the EC

I The typical coefficient in 1990 = 0.5: two EC countriestraded “only 65% more” (exp(.5) = 1.65).

I NAFTA insignificant / MERCOSUR and ANDEAN very large.Results are generally quite puzzling and counter-intuitive.

⇒ Is this coming from a problem in the methodology or does itmean that the EC did not have much of an effect?

Standard gravity results for the CU (Rose, 00 EP)

Source : Tableau 1, Rose (2000)

1970 1975 1980 1985 1990 Pooled

Currency Union γ .87

(.43)

1.28

(.41)

1.09

(.26)

1.40

(.27)

1.51

(.27)

1.21

(.14)

Exchange Rate Volatility δ -.062

(.012)

.001

(.008)

-.060

(.010)

-.028

(.005)

-.009

(.002)

-.017

(.002)

Output b1 .77

(.02)

.81

(.01)

.81

(.01)

.80

(.01)

.83

(.01)

.80

(.01)

Output/Capita b2 .65

(.03)

.66

(.03)

.61

(.02)

.66

(.02)

.73

(.02)

.66

(.01)

Distance b3 -1.09

(.05)

-1.15

(.04)

-1.03

(.04)

-1.05

(.04)

-1.12

(.04)

-1.09

(.02)

Contiguity b4 .48

(.21)

.36

(.19)

.73

(.18)

.52

(.18)

.63

(.18)

.53

(.08)

Language b5 .56

(.10)

.36

(.10)

.28

(.09)

.36

(.08)

.50

(.08)

.40

(.04)

FTA b6 .87

(.16)

1.02

(.21)

1.26

(.16)

1.21

(.17)

.67

(.14)

.99

(.08)

Same Nation b7 1.02

(.74)

1.37

(.59)

1.12

(.38)

1.36

(.64)

.88

(.52)

1.29

(.26)

Same Coloniser b8 .91

(.15)

.73

(.14)

.52

(.12)

.48

(.12)

.59

(.12)

.63

(.06)

Colonial Relationship b9 2.52

(.23)

2.40

(.19)

2.28

(.14)

2.05

(.14)

1.75

(.15)

2.20

(.07)

Number of Observations 4052 4474 5092 5091 4239 22,948

R2 .57 .59 .62 .65 .72 .63

RMSE 2.18 2.18 2.03 1.94 1.75 2.02

Note: OLS estimation; robust standard errors in parentheses.

Constant term (and year controls for pooled regression) not reported.

The CUs considered by Rose (2000)

THE EURO’S TRADE EFFECTS, RICHARD BALDWIN 14

the bilateral trade data from Rose (2000) summed across all of each nation’s trade partners. The results are displayed in Figure 2. The top panel shows all 141 nations with data. The bottom panel includes only nations that have openness ratios of less than 200% of GDP.

Table 1: The Rose Garden, currency unions considered in Rose (2000)

Hu Misc. b and Spoke arrangements Multilateral currency unions

√ Australia √ USA CFA √ IndiaChristmas Island American Samoa √ Bhutan √ Benin Cocos (Keeling) kina Faso arkIslands

Guam √ Bur √ Denm

Norfolk Island √ US Virgin Islands s √ Cameroon Faeroe Island√ Kiribati Puerto Rico √ Central African Republic √ Greenland √ Nauru Northern Mariana

Islands √ Chad Turkey

√ Tuvalu √ British Virgin Islands s N. s Comoro CypruTonga (pre ’75) Caicos √ Congo Singapore√ Turks &√ France √ Bahamas √ Cote d’Ivoire Brunei √ French Guyana (OD) l Guinea (post '84) Bermuda Equatoria Norway√ French Polynesia √ Liberia √ Gabon Svalbard√ Guadeloupe (OD) Marshall Islands ricaGuinea-Bissau South AfMartinique (OD) Micronesia √ Mali (post '84) Lesotho Mayotte Palau √ Niger Namibia √ New Caledonia (OT) d √ Panama √ Senegal Swazilan√ Reunion (OD) ados nd√ Barb √ Togo SwitzerlaAndorra √ Belize ECCA Liechtenstein √ St.Pierre & Miquelon

√ Britain √ Anguilla Spain

Wallis & FutuIslands

na Islands d Barbuda a √ Falkland √ Antigua an Andorr

Monaco √ Gibraltar √ Dominica Singapore√ New Zealand Guernsey √ Grenada Brunei √ Cook Islands Jersey √ Montserrat Italy√ Niue Isle of Man √ St. Kitts and Nevis San Marino Pitcairn Islands √ Saint Helena an √ St. Lucia VaticTokelau Scotland √ St.Vincent Morocco √ Ireland (pre '79) Western

Sahara Nindicates that the nation is include

otes: This lists all the pre-Eur nd CU-like monetary arrangements from 1970 o heck’ sign e (2000).

ely open nations that also share a currency with penness is so unusual that it is hard to see what is going on

ozone currency unions ad in the sample of Ros

nwards. A ‘c

Source: Rose (2000) appendix table and footnotes.

The top panel shows that there are some extremsome other nation.6 These nations’ owith the rest. There are 6 nations with openness above 200%, Bahamas (1400%), Singapore (750%), Liberia (600%), Bahrain (400%), Kiribati (370%) and Belgium-Luxembourg (320%). All but one of these is involved in a currency union. Eyeballing the list, it is clear that many of these are centres of transit trade. (For example, due to Singapore’s excellent port, shipping services, and lack of corruption, many East Asian exports to the US and Europe are transhipped via Singapore.)

The problems with gravity results for the CU

I The typical coefficient is way too large to be credible: two CUcountries traded (exp(1.21) = 3.35) times more.

I Can we extend those results for small very open economies tothe eurozone?

Meta-analysis of gravity coefficients

I Use Disdier and Head (2008) as a base + add other covariates+ update since 2005 (top5 + JIE + Restat) + add all priceelasticity gravity papers found.

All Gravity Structural GravityEstimates: median mean s.d. # median mean s.d. #

Origin GDP .97 .98 .42 700 .86 .74 .45 31Destination GDP .85 .84 .28 671 .67 .58 .41 29Distance -.89 -.93 .4 1835 -1.14 -1.1 .41 328Contiguity .49 .53 .57 1066 .52 .66 .65 266Common language .49 .54 .44 680 .33 .39 .29 205Colonial link .91 .92 .61 147 .84 .75 .49 60RTA/FTA .47 .59 .5 257 .28 .36 .42 108Common currency .87 .79 .48 104 .98 .86 .39 37Home 1.93 1.96 1.28 279 1.55 1.9 1.68 71

Notes: The number of estimates is 2511, obtained from 161 papers. Structural gravity refers hereto some use of country fixed effects or ratio-type method.

Price-shifter elasticities in gravity equationsI “Gravity-based” estimates: regressing bil. trade on measures

of bilateral trade costs or exporter “competitiveness” (wagesor productivity). Typical equation:

ln Xni = ln Si + ln Mn + εT ln τni .

Estimates: median mean s.d. #

Full sample: -4.76 -6.23 8.66 508

Estimation method:Naive gravity -2.66 -2.88 1.64 32Structural gravity

Country FEs -4.4 -5.19 6.59 347Ratios -7.07 -9.88 12.65 129

Identifying variable:Tariffs/Freight rates -5.51 -7.5 9.6 369Price/Wage/Exchange rate -1.23 -2.88 3.81 139

Notes: The number of statistically significant estimates is 508, obtainedfrom 19 papers.

Tariff-equivalence of different variables.

A simple calculation can tell us if “meta” estimates lookreasonable.

I Take βRTA = ρ. Then, ρ = εT (ln τMFNni − ln τRTAni )

I Denote t MFN tariffs removed by RTA, and ν the ad-valoremtariff-equivalent of remaining trade barriers: τMFN

ni = 1 + ν + tand τRTAni = 1 + ν.

⇒ t = (1 + ν)[exp(ρ/εT )− 1].

I Meta: ρ = 0.47 and tariff-based εT = 5.51, assuming ν = 0implies t = 8.9%.

I “Home” median coefficient is 1.93 ⇒ν = exp(1.93/5.51)− 1 = 42% ⇒ t = 12.6%.

I WDI: 3.83% = weighted world MFN tariff in 2011. In 2000,the world simple average MFN tariff is 12.8%.

PTI, MTI, and GETI

Suppose lnφni is linear in Bni with coefficient β. What is theimpact on trade of changing Bni to B ′ni?

I Partial Trade Impact:

PTIni = φ′ni/φni = exp[β(B ′ni − Bni )].

I Modular Trade Impact:

MTIni =X ′niXni

= exp[β(B ′ni − Bni )]︸︷︷︸PTI

× Ωi

Ω′i

Φn

Φ′n︸︷︷︸MR adj.

I General Equilibrium Trade Impact:

GETIni =X ′niXni

= exp[β(B ′ni − Bni )]︸︷︷︸PTI

× ΩiΦn

Ω′iΦ′n︸︷︷︸

MR adj.

×Y ′i X ′nYiXn︸︷︷︸

GDP adj.

=Yi Xn

Ωi Φn

φni

I GETInn combined with εT provide welfare change.

PTI, MTI, and GETI: GDP adj.

I Production: Yi = wiLi , with Li constant, wi = Yi .

I In general, Xn 6= Yn, because of trade deficits, denoted as Dn.Assume that deficit is exogenously given on a per capita basis,that is Dn = Lndn. With this assumption, Xn = wnLn(1 + dn),so that Xn = wn = Yn.

I When πni obeys special structural gravity,

πni =(Yi τni )

ε∑` πn`(Y`τn`)ε

. (8)

I Using the market clearing condition that Y ′i =∑

n π′niX′n, one

can solve for the changes in production of each origin country.

Yi =1

Yi

∑n

πniπni YnXn =1

Yi

∑n

πni Yεi φni∑

` πn`Yε` φn`

YnXn, (9)

PTI, MTI, GETI and welfare effects

The method involves four steps:

1. Estimate a gravity equation, with dummy Bni indicatingRTA/CU with coefficient β. If possible recover the tradeelasticity, ε, in this step or use a value from the literature.

2. PTIni = φni = exp(β) for the ni for whom Bni = 1 andφni = 1 for all other pairs. (MTIni uses φni in the fixed pointiteration for MR terms seen in SILS.)

3. Plug estimated φni into (9). Along Yi , Xn, and the πni matrixdefines a system of equations determining Y ε

i for each

country. Substitute the φni and Y εi into equation (8) to derive

the matrix of trade changes, πni . Iterate using a dampeningfactor until πni stops changing.

4. The GETI for each country pair is πni Yn. The welfare change

is π1/εnn .

PTI, MTI, GETI and welfare effects

I Use TradeProd data for 2000 (square mfg. trade andproduction data for 84 countries).

I Experiment: turn off variables.

I Use εT = 4.76 in GETI and welfare.

coeff PTI MTI GETI Welfaremembers: yes yes yes no yes no yes no

RTA/FTA .725 2.065 1.752 .931 1.673 .916 1.026 .996Common currency .344 1.41 1.33 1.001 1.296 1.001 1.012 .999Common language .801 2.229 2.051 .969 1.955 .98 1.01 .997Colonial link .962 2.616 2.478 .972 2.539 .983 1.004 .999Border Effect 3.028 20.648 7.246 .417 13.83 .644 .574 .

Notes: The MTI, GETI and Welfare are the median value of the real / counterfactual traderatio for countries relevant in the experiment.

Part V

Issues beyond the gold medal mistake

Beyond the gold medal mistake

The most important issues have all to do with endogeneity of theagreements / currency unions.

I Specification: the theory commands to put the relative priceterm, which is usually omitted.

I Reverse causality: it might be that RTAs/CUs are signed bycountry pairs that already trade a lot.

I Omitted Variable Bias: it might be that RTAs/CUs are signedby country pairs that have other characteristics that facilitatetrade: trust, peaceful relationships, common legal origins...

FEs do not solve all endogeneity issues of RTAs and CUs.

First improvements

I How to control for dyadic OVB?

I A natural way to control for omitted variables is to include adyadic fixed effect.

I Will control for anything that does not vary over time andaffects bilateral trade.

Results with dyadic FEs

I Glick and Rose (2002) introduce country-pair FEs and thecoefficient drops to 0.65, meaning that CUs tend to increasebilateral trade by around 90%.

I Carrere (2006) and Baier and Bergstrand (2007) do the samefor the RTA dummy and the results go the other way: frominsignificant to around 0.7!

Might be because CUs are adopted by remote countries, and RTAsby central ones.

RTA impact with dyadic FEs (BB07, JIE)

bilateral trade. In Section 5.4.3, we address “strict exogeneity” issues; we test for the possibility ofreverse causality by addressing the effect of future FTA dummies on current trade flows.

5.4.1. Accounting for multilateral price terms and unit income elasticitiesWhile the results in the previous section are encouraging, the gravity equation suggested by

recent formal theoretical developments— summarized in the system of Eqs. (2), (3.1),…, (3.N) inSection 2— suggests that one needs to account for the multilateral price variables and to scale theLHS trade flow variable by real GDPs. None of the four specifications in Table 4 accounts forthese two elements. First, accounting for the multilateral price variables in a panel contextsuggests estimating:

lnXijt ¼ b0 þ b1ðlnRGDPitÞ þ b2ðlnRGDPjtÞ þ b3ðlnDISTijÞ þ b4ðADJijÞþ b5ðLANGijÞ þ b6ðFTAijtÞ−lnP1−r

it −lnP1−rjt þ eijt ð10Þ

Furthermore, scaling the LHS variable by the product of real GDPs suggests estimating:

ln½Xijt=ðRGDPitRGDPjtÞ ¼ b0 þ b3ðlnDISTijÞ þ b4ðADJijÞ þ b5ðLANGijÞþ b6ðFTAijtÞ−lnP1−r

it −lnP1−rjt þ eijt ð11Þ

In a panel setting, the multilateral price variables would be time varying, and consequently theresults in specifications (1)–(4) in Table 4 may suffer from an omitted variables bias as a result ofignoring these time-varying terms — a dilemma that cannot be resolved by the use of bilateralfixed effects using the panel data in its current form.21 Moreover, the theoretical model in Eqs. (2),(3.1),…, (3.N) suggests that the coefficient estimates for the real GDP variables should be unity,even though using bilateral fixed effects in specifications (3) and (4) suggests income elasticitiesare significantly different from unity.

Table 4Panel gravity equations in levels using various specifications

Variable (1) No fixed or timeeffects

(2) With timeeffects

(3) With bilateral fixedeffects

(4) With time and bilateralfixed effects

ln RGDPi 0.95 (217.50) 0.97 (230.98) 0.71 (34.54) 1.27 (47.16)ln RGDPj 0.94 (224.99) 0.97 (235.43) 0.58 (26.57) 1.22 (41.60)ln DISTij −1.03 (−79.09) −1.01 (−78.60)ADJij 0.41 (8.23) 0.38 (7.28)LANGij 0.63 (19.06) 0.58 (17.73)FTAij 0.13 (3.73) 0.27 (7.19) 0.51 (10.74) 0.68 (14.27)RMSE 1.9270 1.8601Overall R2 0.6575 0.6809Within R2 0.2036 0.2268No. observations 47,081 47,081 47,081 47,081

t-statistics are in parentheses. The dependent variable is the (natural log of the) real bilateral trade flow from i to j.Coefficient estimates for various fixed/time effects are not reported for brevity.

21 Random effects estimation would not be of any use either, as theory suggests that the multilateral price terms and theFTA variable would be correlated.

17S.L. Baier, J.H. Bergstrand / Journal of International Economics xx (2006) xxx–xxx

ARTICLE IN PRESS

Identification and remaining issues with dyadic FEs

I An important point for the CU result is that all changes areidentified in entries or exits.

I It happens to be the case that there are many more exitsthan entries.

I What really matters is entry: Volker Nitsch finds that whilethe exits have a large trade drop / entries do NOT have asignificant trade rise.

I Also time-varying omitted variables are more likely for exits(political trouble / large divergence in inflation rates...): TheIrish example.

The real problem with endogeneity

Figure 4: UK’s share of Irish trade, 1924-98 (Thom and Walsh 2002).

Is instrumentation of the EC/CU dummy possible?

I A valid IV would have to be a variable that predicts CU orEC membership well, without a link to bilateral trade.

I Geographical proximity, common language, common border,former colonial status and the smallness and poorness of thenation, have been shown to affect probability to sign RTA orCU.

I But all of those also affect trade.

I The current estimates using IV are very disappointing

I The way forward might be to use financial variables for CUsand political variables for RTAs/CUs. Even better: naturalexperiments such as Franc CFA countries used by Frankel(2010).

Results with matching

I Last issue is that the CU pairs are very unusual countries.They are very small, and nearby a large country with whichthey trade a lot.

I The “experiment” of the CU is by no way random.

I This causes a selection problem, since those countries thatchoose to abandon their own currencies are also very open.

I The solution to this issue is matching: Find for each countrypair in the CU, the most proximate country pair that is not ina CU.

I Compares CU pairs with other small open economies, ratherthan with the universe of all countries.

I Results: CU augment trade by between 15 and 50%.

I In any case, it is crucial to be extremely cautious wheninterpreting this for the eurozone.

Results on the eurozone

I Micco, Stein and Ordonez (2003) and Flam and Nordstromimplement the state of the art technology of gravity equationwith the non-euro EU as a control group and find an order ofmagnitude of 6%-15%.

I The estimate is 28% with simple Rose-type gravity.

I No evidence of trade diversion.

gravity rules - department of economics sciences...

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