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Lecture 8
THE GRAVITY MODEL
By Carlos Llano,
References for the slides:
• Feenstra, Advanced International Economics. Ariel Economía, 2000.
• Francisco Requena. Seminar given at the MEI-UAM in 2010.
• Web de Tierry Mayer, http://team.univ-paris1.fr/teamperso/mayer/thierry.htm
Index
1.
2.
3.
4.
Introduction
The gravity model
Applications
Practice
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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 (Sen y Smith, 1995;
Roy y Thill, 2004).
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1. Introduction
1. Physics:
• The law of gravity states that the force of gravity
between two objects depends on the product of the
masses of the two objects and the square of the
distance between them (Baldwin y Taglioni, 2006):
M1 * M 2
FG12  G
Dist 122
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•
1. Introduction
In economics the force of gravity (FG) is substituted by the intensity of the
flow, and the masses M1 and M2 are replaced by variables that cover the
size of both elements, and that will depend on the analyzed phenomenon.
X ij  K
•
Yi Y j
Tij
The bilateral trade flow intensity between two specific geographical areas
(countries or regions), is directly proportional to the emission and absorption
capacity of the points of origin and destination, and inversely proportional to
the cost of interaction between the two points.
–
–
Emission/absorption capacity = production capacity and demand
The cost of interaction = distance or traveling time
ln Eij    1 ln GDPi   2 ln GDPj  3 ln Dij
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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 homotetic 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:
• CES preferences imply that exports from i to j are:
N p q
i 1
i
ij ij




 Yj
pij   ij pi
X ij  N i pij qij
N
Yi   X ij
j 1
1
  ij pi 

X ij  N i 
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 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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1. Introduction: Border Effect
1. McCallum (AER, 1995):
1. On average, the exports of Canadian provinces to other Canadian
provinces are some 20 times larger than their exports than the
equivalently situated U.S. states (same size and distance).
2. Engels and Rogers (AER, 1996):
1. Evidence from urban price movements suggests that the border
imposes barriers to arbitrage comparable to 1.700 miles pf physical
space.
3. Gil et al (World Economy, 2005):
1. The Spanish CCAA trade between them is 20 times the trade with
the bordering CCAA.
1. Border effect?, physical differences, accessibility, cultural, legal
differences…?, specific effects of sector agglomeration (clusters)?
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(Anderson and van Wincoop, 2004), Feenstra, 2004
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(Anderson and van Wincoop, 2004), Feenstra, 2004
http://www.uam.es/carlos.llano/master_ec_intern/Chapter_5.zip
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(Anderson and van Wincoop, 2004), Feenstra, 2004
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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