Objectives
1
2
3
Understanding the impact of distance and
economy size on trade using the gravity
model
Apply the gravity model for the cases of FDI,
and migration
See how people use the gravity model to
evaluate economic policy issues
The Origin of
the Gravity Equation
 Newton’s “Law of Universal Gravitation” (1687):
The attractive force (Fij) between i and j
Fij  G
M iM j
Dij
2
 Mi, Mj are the masses
 D is distance between two objects
 G is gravitational constant
Mi
F
D
Mj
Economists and Gravity
 Model many social interactions (migration,
tourism, trade, FDI)

Fij  G
Mi M j
Dij


 Fij is the flow from i to j
 M’s are measure of economic mass
 D is the distance
Estimation of the Gravity Equation
 Take logs:
ln Fij  R   ln M i   ln M j   ln Dij   ij
Overall explanatory power
 R2 between 0.65 and 0.95
 Suggests using gravity as a benchmark for
volume of trade.
 Can then use gravity based benchmark to
evaluate economic policy
The role of economic mass
 Usually measured using GDP
 Most theoretical explanations predict coefficient
equal to one
 Estimates often not significantly different from 1,
but range is from 0.7 to 1.1
The role of distance
 Distance usually measured using great circle
distance based on latitude and longitude
 Head (2000) averages results from 62
regressions in eight papers, for sample years
ranging from 1928 to 1995
 Average distance effect is 1.01
 Doubling distance halves trade
Distance and trade costs
 Trade costs:
 Direct (transport)
 Indirect (government policy; language)
 Is distance just capturing the effect of trade costs
(acting as a proxy) or does it play an additional
role?
Data on trade costs
 IMF bilateral data of total exports from A (free on
board) to imports of B (cost-insurance-freight)
 Composition of trade depends on t.c.
 National customs data for a few countries
 Direct industry/shipping company info
 Ocean shipping prices/air freight from trade
journals (Hummels)
 Quotes from shipping standard container from
Baltimore (Venables)
Magnitude
 Wide dispersion of trade costs
 US 3.8% value of imports (1994)
 Brazil 7.3%
 Paraguay 13.3%
 Unweighted (get rid of composition effect)
 Median cif/fob ratio 1.28 (28% t.c.)
 2 to 3 times higher than weighted
Empirical Results
Shipping 40’
container ($000)
Shipping 40’
container ($000)
Land locked dummy
3.45
(4.75)
2.17
(2.94)
Distance
(000km)
0.38
(2.60)
Dist. Sea
0.19
(2.12)
Dist. Land
1.38
(4.66)
R2
0.32
0.47
Effect of distance on t.c.




Mean cost if not landlocked $4,620
Landlocked increases cost by $3,450
Overland 7 times more expensive than sea
For cif/fob ratios
 Elasticity w.r.t distance 0.2 to 0.3
 Common border reduces substantially
 R2 = 0.45
Distance and gravity
 Distance explains around 45% variation in
transport costs
 Regressions of trade flows on both distance and
t.c. still gives significant coefficient on distance
(although magnitude lower)
 Distance must be a proxy for both t.c. and other
information costs.
Using gravity to test for border effects.
 Home bias: preference towards home products;
 Comparison between intranational trade and
international trade;
 The borderless world – “National borders have
effectively disappeared”
 Use gravity to test:
ln X ij  a  b ln Mi  c ln M j  d (ln Dij )  eDUMMY
 McCallum (1995) using data on trade flows between
US and Canadian provinces (dummy=1 if in the same
country)
Using gravity to test for border effects.
 McCallum: Data referring to 1988 (before FTA
Canada-USA was signed): Intra-national data flows
only referred to Canada (exports from a province to
other Canada provinces: DumCA=1); International:
Exports from Canada provinces to USA states
(DumCA=0)
 Developments: addiction of data referring to 1993:
intra-national data for both CA and USA. Another
indicator=DumUSA=1 for trade between two USA
states;
 Dij is the distance between any two provinces or
states;
 Results
Empirical results
lnyi
lnyj
lndistij
DUMMY
R2
1.21
(0.03)
1.06
(0.03)
-1.42
(0.06)
3.09
(0.13)
0.811
Using gravity to test for border effects.
 Data referring to 1988 (before FTA Canada-USA was
signed): Intra-national data flows only referred to
Canada (exports from a province to other Canada
provinces: Dummy=1); International: Exports from
Canada provinces to USA states (Dummy=0)
 Data referring to 1993: intra-national data for both CA
and USA
 Dij is the distance between any two provinces or
states;
 Results
The importance of borders
 1988 or 1993: Coefficient on cross-provincial trade is
quite high (3.09 to 2.75). Exp(3.09)=22; Exp(2.75)=15.7
 1988: Canada-Canada province trade approx. 22 times
Canada-US state trade; 1993: reduced to 15,7
 Border effects (all impediments to trade across borders)
 Ontario’s shipments to British Columbia should be 0.6 times
shipments to Washington (US) [Washington is richer]
 BC receives 12.6 times more goods from Ontario than
Washington
 Border effect = 12.6/0.6 = 21
 Fallen to 12 since FTA implemented
The importance of borders
 Anderson and Wincoop (2003): border effects have an
asymmetric effect on countries of different size. More
precisely have a larger effect on small economies.
 Example:
 US is 10 times bigger than Canada (economic size)
 Without frictions to trade, Canada exports 90% of its GDP to US and
sells 10% internally; US exports 10% of GDP
 Suppose border effects reduce trade of a factor of ½
 => Canada exports 45% to US and sells internally 55%
 Its internal trade has increased of a factor 5.5, cross-border has
decreased by 0.5 => 5.5/0.5=11: internal trade has increased 11 times
more than cross-border trade
 =>US exports now 5% and sells internally 95%. Cross-state trade has
increased only slightly more than 2 times cross-border trade
Alternative approach: taking into account
of different prices in different countries

Anderson and Wincoop (2003):
ln X ij  ln Mi  ln M j  a  d (ln Dij )  eDUMMY  (1   ) ln(Pi )  (1   ) ln(Pj )


Imposes restrictions on the parameters of M;
Inverse indicator: DUMMY=1 for international (cross-border) trade 0
for internal trade; No distinction between Canadian or US crossborder trade (under a following assumption);
 Introduces 2 new variables: price terms of the two countries (whose
difference has a meaning). The two variables can be:
1. Constructed from Price Indexes data;
2. Estimated as a function of trade costs, where trade costs are a
function of distance and other factors (intercept). (N.B. If trade costs
are symmetric, then there cannot be a distinction between Canadian
and US trade) => this methodology is quite complicated, because it
involves the estimation of a recursive model of multiple equations.
Alternative approach: taking into account
of different prices in different countries

Anderson and Wincoop (2003):
ln X ij  ln Mi  ln M j  a  d (ln Dij )  eDUMMY  (1   ) ln(Pi )  (1   ) ln(Pj )
3. Introduce fixed-effects: two dummies one for the origin
country and another one for the destination country:
Di=1 if i is the exporter, 0 otherwise;
Dj=1 if j is the importer, 0 otherwise;
The two dummies are both equal to 1 only for cross-border
trade observations.
This implies: Di=(1-)lnPi and Dj=(1-)lnPj
Conclusions
 Distance matters for trade
 Consistent with both new trade theory and old
trade theory
 Theory has helped refine the gravity relationship
 Gravity can be used to test other hypotheses
even if we don’t know what drives gravity