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Lecture 2c
THE GRAVITY MODEL
By Carlos Llano,
References for the topic:
• UNCTAD: https://vi.unctad.org/tpa/web/docs/vol1/ch3.pdf
• Head, K. and Mayer, T., (2014). Gravity Equations: Workhorse, Toolkit, and
Cookbook. Chapter 3 in Gopinath, G, E. Helpman and K. Rogoff (eds), vol. 4 of the
Handbook of International Economics, Elsevier: 131–-195.
• Feenstra, Advanced International Economics, Chapter 5, 2004.
• Steven Brakman, Peter A.G. van Bergeijk. (2009?): The Gravity Model in
International Trade: Advances and Applications
1
Index
1.
2.
3.
4.
Introduction
The gravity model
Applications
Practice
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1. Introduction
The law of gravity states that the force of gravity between
two objects depends on the product of their masses and
the square of the distance between them (Baldwin y
Taglioni, 2006):
M1 * M 2
FG12  G
Dist 122
Dist12
M1
M2
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•
1. Introduction
The “gravity equation” is a metaphor with physics:
X ij  K
•
Yi Y j
Tij
The bilateral trade flow intensity between two specific geographical areas
(i-j, countries / regions), is positively correlated with the emission and
absorption capacity of the points of origin and destination, and inversely
proportional to the cost of interaction between the two points.
–
–
–
Yi = Emission capacity of exporting area. Proxy: Gross Output or GDP.
Yj = Absorption capacity of importing area: Proxy: Gross Output or GDP.
Tij= The cost of interaction. Proxy: physical distance, traveling time…
ln X ij  k   ln Yi   ln Y j   ln Tij   ij
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•
•
•
•
1. Introduction
The gravity equation has been widely used to model all
kind of interactions in space that can be explained from
the interplay of the attraction and repulsion forces.
There are many applications in the fields of trade,
transport and immigration.
The use of “the gravity equation” is dated in the 50’ in the
field of regional science, geography and urban planning:
Wilson, Cesario, Isard…;
In economics, Timbergen (1962) is usually reported as
the first author using it.
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•
•
•
1. Introduction
The gravity model has been described as: “the backbone of
empirical international trade analysis”.
It has shown a great list of achievements in applied work, but it
has been criticized for many years for its “lack of theoretical
base”.
Milestones in the development of modern “gravity equation”:
1.
Anderson (1979): “Theoretical Foundation for the Gravity Equation”,
American Economic Review, 1979, 69, 106-116.
2.
1995: Trefler and “the missing trade”;
3.
2004: Anderson and van Wincoop (2004): “Gravity with gravitas: a solution to
the border puzzle”, AER, 93, 170-192
4.
2008: HMR (2008); Chaney (2008)…
5.
Recent Reviews:
1.
UNCTAD: https://vi.unctad.org/tpa/web/docs/vol1/ch3.pdf
2.
Head, K. and Mayer, T., (2014). Gravity Equations: Workhorse, Toolkit, and
Cookbook. Chapter 3 in Gopinath, G, E. Helpman and K. Rogoff (eds), vol. 4 of the
6
Handbook of International Economics, Elsevier: 131–-195.
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Gravity with exogenous prices (Feenstra, 2004)
• DS Monopolistic Competition model between N countries
and K products.
• Exogenous prices (no transport costs)
• Preferences
– Identical and homothetic demand between countries
– Therefore, the demand of products from i consumed in j is
proportional to the j’s GDP
K
i
i
Y

Y
– The GDP in i:
k
k 1
– The GDP in the World:
N
Y W  Y i
i 1
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Gravity with exogenous prices (Feenstra, 2004)
• J country's participation in global spending:
• With the assumptions that all countries produce different
goods and have an identical and homothetic demand, exports
of product k from i to j are:
•
sj 
Yi
YW
X kij  s jYki
Adding to all products exported:
K
K
Y jY i
k 1
k 1
YW
X ij   X kij s j Yki s jY i 
 s j s i Y W  s i Y j  X ji
• Then calculate the volume of trade between i and j:
X ij  s jY i 
X ji  siY j 
Y jY i
YW
Y iY j
YW
 2
V  X  X  W
Y

ji
ij
 i j
Y Y


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Example: Helpman, 1987
The effect of the economic size of countries
• The relative volume of trade within a region (group of countries)
depends on the relative size of the countries in that region.
• The smaller the disparity between the economic size of the countries
within a region (the larger the similarity) the larger the ratio between
trade/GDP in that region.
 2
V  X  X  W
Y

ji
ij
 i j
Y Y


Y A  Y i Y j
YA
A
s  W
Y
Yi
iA
s  A
Y
ji
ij
VA X X
iA jA A
A
iA 2 

 2 s s s  s 1   s 
A
A
Y
Y
 iA

 
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Gravity with endogenous prices (Feenstra, 2004)
• Let’s consider the situation where a country i have to
decide how to import from a country j:
• The representative consumer in country j maximizes a
CES utility function subject to a budget constraint
σ= elasticity of substitution(> 1); N = # of products from i)
qij

 1  1

 N
max   N i cij
c ij
 i 1
N
• There are iceberg transportation costs, so prices differ
between countries (cif vs fob prices):
• Exports from country i to country j are:
• The income of country i is equal to the sum of
expenditures in products imported from country i:
N p q
i 1
i




 Yj
ij ij
pij   ij pi
X ij  N i pij qij
N
Yi   X ij
j 1
1
• CES preferences imply that exports from i to j are:
  ij pi 

X ij  N i 
 P 
 j 
Yj
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The relative price issue in the gravity model
• Do trade flows between i and j depend only on bilateral trade
costs, regardless of the level of trade costs that prevails
among other bilateral flows?
• If trade costs between i and j decrease, are affected trade
flows between other countries?
• If the costs of bilateral trade in other flows decrease, how is
affected the trade flows between the rest?
• The answer to these questions requires some economic
theory:
– Adding micro-foundations expect to get something like a gravity equation,
but in response to the problem of relative prices
– Anderson and van Wincoop, (2004): model “gravity with gravitas"
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The Gravity Model a la
Anderson and van Winkoop, 2004
1 k
Yi E   
X 


Y k   ik Pjk 
k
k
ij
Outward multilateral resistance
Inward multilateral resistance
 
k 1 k
i
P 
k 1 k
j
k
j
k
ij
1 k
C 
  
  j 1  
 P 
k 1 k
C 
  ij 
 i 1  k 
  i 
k
ij
k
j
E kj
Yk
Yi k
Yk
• The impact of trade costs on exports from i to j is complex because it
depends on a first-order (or direct) and second-order effects (as
reflected in the multilateral resistance terms)
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Part I: Do we really Know that the WTO increase
trade. Rose, 1994; 2004.
Rose, 1994:
1. Gravity model (50 years,
175 countries).
2. Little evidence about
countries joining or
belonging to the
GATT/WTO have a
different trade patterns
from outsiders.
3. Generalized System of
Preference (GSP) seems
to have a strong effect.
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Rose, 1994:
1. Gravity model (50
years, 175
countries).
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Rose, 1994:
1. Gravity model (50 years,
175 countries).
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Part II. The Border Effect. US-Canada
 Border effect is considered as one of the main puzzles of international
macroeconomics (Obstfeld & Rogoff, 2000).
 McCallum(1995) found that a Canadian province trades 22 times more
with another Canadian province than with any State from US,
controlling by size and distance.
 Then, a number of
authors have tried to
estimate similar effects in
other countries…
 …Using alternative
specifications, and
looking for different
explanations…
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Part II. The Border Effect. US-Canada
 External border effect: how many times a region trades more
with another region of the same country than with any other
(non-adjacent) region from another country.
 Helliwell (1996, 1998), Anderson and van Wincoop (2003),…
 Internal border effect (home bias): how many times a region
trades more with itself than with another (non-adjacent)
region of the same country.
 Canada: Helliwell (1997);
 US: Wolf (2000), Hillberry and Hummels (2003; 2008), Millimet and Osang
(2006), …
 Others: Combes et al. (2005, France), Djankow & Freund (2000, USSR),
Poncet (2003, China); Daumal & Zignago (2005, Brazil);
 Spain: Requena & Llano (2009), Garmendia et al (2012).
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Part II. The Border Effect. US-Canada
How can we explain the puzzle?
1.
External barriers to trade (tariffs and non-tariff barriers…).
2.
Endogenous responses: agglomeration economies…
3.
Information barriers (Rauch, 2001)
4.
Social and Business Networks (Combes et al, 2005)
5.
Elasticity of substitution + heterogeneity of firms (Evans, 2003;
Chaney, 2008)
6.
Misspecification of the model (Anderson & van Wincoop, 2003 …)
7.
Spatial aggregation artefact & mismeasurement of distance:
•
Imputed intra-national trade/distance (Head&Mayer, 2000; 2002)
•
Non-linear relationship between distance and trade (Hillberry and
Hummels, 2008; Llano-Verduras et al, 2011)
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Part II. The Border Effect. US-Canada
Papers
Sectors
Period
Ext. Border
No
No
No
No
Yes
1988
1988-1990
1993
1991-1996
1997
22
22
20
15-10
11
No
No
1982-1994
1996
1979-1990
1983-1990
10-2.6
13
1996. Wei
1997 Helliwell
Spatial units
Region-to-Region
Canada-United State
Canada-United State
Canada-United State
Canada-United State
United States (Wolf, 1997,2000)
Country-to-Country
OCDE
OCDE
2000 Nitsch
EU-10
No
EU-9
Yes
1976-1995
30-11
EU-12
EU-7
Yes
Yes
1993-1995
1996
13
6
1995. McCallum
1996. Helliwell
1998. Hillbery
2001 Helliwell
2002 Head & Mayer
2000 Head & Mayer
2004. Chen
7-10
Region-to-country
1999. Anderson & Smith
2005. Gil et al.
2003. Minondo
2007. Helble
2010.Requena &Llano
2010. Ghemawat et al.
2011. Llano et al.
Canada-United State
Spain (17 regions), Rest of Spain and OECD-27
País Vasco, Rest of Spain, 201 countries
France, EU-14; Germany, EU-14
Spain (17 regions) OECD-28
Cataluña, Rest of Spain, OECD
Spain (17 regions; 50 Provinces, OECD)
No
No
No
No
Yes
Yes
No
1995-1998
1993-1999
2002
1995 & 00
1995-2006
2000 & 05
12
21
20-26
8; 3
13
55
40 19
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(Anderson and van Wincoop, 2004), Feenstra, 2004
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Part III. The Border Effect. Spain
1. Gil et al (2005):
1. The Spanish CCAA trade between them is 20 times the trade with
the bordering CCAA.
2. Llano-Verduras et al (2011):
1. The Spanish border effect decrease to a factor of 5 when using
provinces instead of regions.
3. Garmendia et al (2012): Internal-border-provinces.
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Interregional trade of goods. 2005. Largest Interregional commodity flows
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ASTURIAS
GALICIA
P.VASCO
1.9%
CANTABRIA
RIOJA
CASTILLA-LEÓN
NAVARRA
ARAGON
2.8%
CATALUÑA
2.9%
MADRID
COM. VALENCIANA
1.9%
BALEARES
CASTILLA-LA MANCHA
EXTREMADURA
2%
1.9%
% REGIONAL GVA
ANDALUCIA
SPAIN
19
9,5
1,9
POPULATION %
MURCIA
/ NATIONAL GVA
13 ,6
5 ,8
3 ,4
1 ,8
0 ,2
a
a
a
a
a
19 ,1
13 ,6
5 ,8
3 ,4
1 ,8
(2)
(3)
(4)
(5)
(4)
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Computer Lab
http://www.uam.es/carlos.llano/master_ec_intern/gravity_border_lab.zip
http://www.uam.es/carlos.llano/master_ec_intern/Chapter_5.zip
http://www.uam.es/carlos.llano/master_ec_intern/Chapter_5_full.zip
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(Anderson and van Wincoop, 2004), Feenstra, 2004
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