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World Economy Gravity Models 1
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gravity models
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Gravity models utilize the gravitational force concept as an analogy to explain the
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4
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volume of trade
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capital flows
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example
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gravity models establish a baseline for trade-flow volumes as determined by
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gross domestic product (GDP)
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population
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flows can then be assessed by adding the policy variables to the equation and estimating
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deviations from the baseline flows. In many instances
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gravity models have significant
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explanatory power
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leading Deardorff (1998) to refer to them as a “fact of life.”
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Alternative Specifications
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Gravity models begin with Newton’s Law for the gravitational force ( ) between two
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objects i and j. In equation form
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this is expressed as:
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GFij
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i j D
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M M
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GF
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ij
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i j
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ij ≠ = (1)
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In this equation
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the gravitational force is directly proportional to the masses of
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the objects ( Mi and M j ) and indirectly proportional to the distance between them ( Dij ).
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Gravity models are estimated in terms of natural logarithms
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denoted “ .” In this
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form
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what is multiplied in Equation 1 becomes added
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subtracted
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translating Equation 1 into a linear equation:
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ln
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i j GFij M i M j Dij ≠ ln = ln + ln − ln (2)
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Gravity models of international trade implement Equation 2 by using trade flows
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or exports from county i to country j ( ) in place of gravitational force
with arbitrarily
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small numbers sometimes being used in place of any zero values. Distance is often
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Eij
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World Economy Gravity Models 2
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measured using “great circle” calculations. The handling of mass in Equation 2 takes
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place via four alternatives. In the first alternative with the most solid theoretical
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foundations
mass in Equation 2 is associated with the gross domestic product (GDP) of
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the countries. In this case
Equation 2 becomes:
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ln Eij = α + β1 lnGDPi + β 2 lnGDPj + β 3 ln Dil (3)
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In general
the expected signs here are . However
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Equation 3 can lead to the interpretation of GDP as income
and when applied to
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agricultural goods
Engels’ Law allows for GDP in the destination country to have a
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negative influence on demand for imports. Hence it is also possible that .
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β1
β 2 > 0
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β 2 < 0
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In the second alternative
mass in Equation 2 is associated with both GDP and
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population (POP). In this case
Equation 2 becomes:
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(4) ln Eij = ϕ + γ 1 lnGDPi + γ 2 ln POPi + γ 3 lnGDPj + γ 4POPj + γ 5 ln Dij
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With regard to the expected signs on the population variables
these are typically
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interpreted in terms or market size and are therefore positive ( ). That said
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however
there is the possibility of import substitution effects as well as market size
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effects. If the import substitutions effects dominate
the expect sign is .
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γ 2
γ 4 > 0
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γ 4 < 0
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In the third and fourth alternatives
mass in Equation 2 is associated with GDP
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per capita and with both gross domestic product and GDP per capita
respectively. In
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these cases
Equation 2 becomes one of the following:
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ij
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j
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j
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i
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i
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ij D POP
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GDP
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POP
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GDP E ln ln ln ln 3 2 1 δ δ τ δ ⎟
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⎟ +
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⎠
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⎞
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⎜
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⎜
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⎝
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⎛ ⎟ +
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⎠
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⎞ ⎜
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⎝
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⎛ = + (5)
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World Economy Gravity Models 3
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ij
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j
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j
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j
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i
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i
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ij i
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D POP
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GDP
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GDP POP
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GDP E GDP
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ln
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ln ln ln ln
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37015
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37316
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ν ν
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ν µ ν ν
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⎟
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⎟ +
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⎠
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⎞
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⎜
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⎜
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⎝
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⎛
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+
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⎟ +
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⎠
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⎞ ⎜
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⎝
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⎛ = + +
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-6
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Since they involve the same variables
the parameters of Equations 4
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transformations on one another: ; ; ;
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and .
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γ 1 = δ 1 =ν 1 +ν 2 γ 2 = −δ 1 = −ν 2 γ 3 = δ 2 =ν 3 +ν 4
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γ 4 = −δ 4 = −ν 4
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Theoretical Considerations
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After being introduced by Tinbergen (1962)
the gravity model was considered to be a
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useful physical analogy with fortunate empirical validity. Subsequently
however
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connections have been made to key elements of trade theory. The standard assumption of
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the Heckscher-Ohlin model that prices of traded goods are the same in each country has
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proved to be faulty due to the presence of what trade economists call “border effects.”
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Properly accounting for these border effects requires prices of traded goods to differ
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among the countries of the world. Gravity models have been interpreted in these terms.
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Anderson (1979) was the first to do this
employing the product differentiation by
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country of origin assumption
commonly known as the “Armington assumption”
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(Armington
1969). By specifying demand in these terms
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presence of income variables in the gravity model
as well as their multiplicative (or log
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linear) form. This approach was also adopted by Bergstrand (1985) who more thoroughly
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specified the supply side of economies. The result was the insight that prices in the form
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of GDP deflators might be an important additional variable to include in the gravity
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equations described above. Price effects have also been captured using real exchange
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rates (e.g.
Brun et al.
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World Economy Gravity Models 4
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The monopolistic competition model of new trade theory has been another
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approach to providing theoretical foundations to the gravity model (Helpman
1987 and
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Bergstrand
1989). Here
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replaced by product differentiation among producing firms
and the empirical success of
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the gravity model is considered to be supportive of the monopolistic competition
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explanation of intra-industry trade. However
Deardorff (1998) and Feenstra (2004) have
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cast doubt on this interpretation
noting the compatibility of the gravity equation with
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some forms of the Heckscher-Ohlin model and
consequently
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evidence to distinguish among potential theoretical bases: product differentiation by
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country of origin; product differentiation by firm; and particular forms of HeckscherOhlin-based comparative advantage. In each of these cases
the common denominator is
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complete specialization by countries in a particular good. Without this feature
bilateral
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trade tends to become indeterminate.
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Alternatively
there are other approaches to gravity-based explanations of bilateral
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trade that do not depend on compete specialization. As emphasized by Haveman and
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Hummels (2004)
this involves accounting for trade frictions in the form of distancebased shipping costs or other trade costs
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costs can also be augmented to account for infrastructure
oil price
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as in Brun et al. (2005). The two approaches (complete vs. incomplete specialization) can
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be empirically distinguished by category of good
namely differentiated vs.
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homogeneous
as in Feenstra
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World Economy Gravity Models 5
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Assessment
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Due to its log-linear structure
the coefficients of the gravity model are in terms of
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elasticities or ratios of percentage changes. These “unitless” measures are comparable
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across countries and goods and give us direct measures of the responsiveness of trade
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flows to the trade potential variables of Equations 3-6. For GDP and distance
estimated
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elasticities tend to be close to 1.0 in value. For distance
comparison across groups of
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countries gives a measure of the degree of integration in the world economy. In addition
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to these standard variables
the coefficients of policy variables help us to understand the
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impacts of the represented policies on trade flows. It is also possible to obtain estimates
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of border effects independently of distance and other variables
as well as to investigate
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some issues in economic geography as in Redding and Venables (2004). Despite some
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ambiguity regarding its theoretical foundations
then
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empirical tool to help us understand trade and other economic flows in the world
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economy.
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See also: Applied General Equilibrium Models
Heckscher-Ohlin Model
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Trade
Monopolistic Competition Model
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Models
Revealed Comparative Advantage
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Further Reading
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Anderson
James E. 1979. A Theoretical Foundation for the Gravity Equation. American
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Economic Review 69(1): 106-116. A first attempt to provide theoretical
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foundations to the gravity model.
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World Economy Gravity Models 6
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Armington
Paul. 1969. A Theory of Demand for Products Distinguished by Place of
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Production. IMF Staff Papers 16(3): 159-176. The key contribution on product
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differentiation by country of origin.
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Bergstrand
Jeffrey H. 1985. The Gravity Equation in International Trade: Some
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Microeconomic Foundations and Empirical Evidence. Review of Economics and
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Statistics 67(3): 474-481. A second attempt to provide theoretical foundations to
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the gravity model.
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Bergstrand
Jeffrey H. 1989. The Generalized Gravity Equation
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Competition
and the Factor-Proportions Theory in International Trade. Review of
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Economics and Statistics 71(1): 143-153. An interpretation of the gravity model
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in terms of monopolistic competition.
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Brun
Jean-François
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Distance Died? Evidence from a Panel Gravity Model. World Bank Economic
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Review 19(1): 99-120. A useful exploration of distance in gravity models.
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Deardorff
Alan V. 1998. Determinants of Bilateral Trade: Does Gravity Work in a
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Neoclassical World? In Jeffrey A. Frankel
ed.
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Economy. Chicago: University of Chicago Press. A helpful review and assessment
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of the gravity model.
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Feenstra
Robert C. 2004. Advanced International Trade: Theory and Evidence.
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Princeton: Princeton University Press. Chapter 5 of this book reviews the gravity
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model in light of trade theory and also delves into a number of key estimation
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issues.
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World Economy Gravity Models 7
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Feenstra
Robert.C.
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Equation to Differentiate among Alternative Theories of Trade. Canadian Journal
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of Economics 34 (2): 430-447. Tests the gravity model over differentiated and
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homogenous goods
focusing on differences in estimated parameter values.
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Helpman
Elhanan. 1987. Imperfect Competition and International Trade: Evidence from
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Fourteen Industrial Countries. Journal of the Japanese and International
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Economies 1(1): 62-81. A claim for monopolistic competition models of intraindustry trade using gravity model evidence.
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Haveman
Jon and David Hummels. 2004. Alternative Hypotheses and the Volume of
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Trade: The Gravity Equation and the Extent of Specialization. Canadian Journal
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of Economics 37(1): 199-218. Explores gravity model explanations both in terms
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of complete specialization such as in monopolistic competition models and
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incomplete specialization with trade frictions.
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Redding
Stephen and Anthony J. Venables. 2004. Economic Geography and
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International Inequality. Journal of International Economics 62(1): 53-82. An
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application of the gravity framework to economic geography.
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Tinbergen
Jan. 1962. Shaping the World Economy: Suggestions for an International
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Economic Policy. New York: The Twentieth Century Fund. The first use of a
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gravity model to analyze international trade flows.
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Kenneth A. Reinert
School of Public Policy
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