The Gravity Model of Trade
Introduction:
The gravity equation is one of the most significant models used in economics for relating the bilateral trade flows to the Gross Domestic Product (GDP). The impact of the distance and other trade barriers are also identified in the model.
The model has been used widely for inferring the impact of various factors like exchange rate mechanism, ethnic ties, custom unions etc on the trade flows. In the theoretically derived gravity model of Anderson and van Wincoop, it is suggested that the empirically based gravity model lacks the theoretical foundation. The theory was first developed by Anderson.
According to the theory, there is a decrease in the trade between two regions after controlling their size in terms of their bilateral trade barrier relative to the average trade barrier of the two regions. It has been suggested that a region is more inclined in having a bilateral trade relation with the given bilateral partner if the country is more resistant to trade with all other regions.
This can be referred as a multilateral resistance. Anderson and van Wincoop stated that the empirical model of Gravity did not include the concept of multilateral resistance or the ‘remoteness’ variable related with the bilateral partner’s distances.
It is important to consider the distance as one of the trade barriers in case of bilateral trade. Thus there were various limitations of the empirical trade model(Anderson, 2010). The main aim of the paper is to contrast between the Gravity model proposed by Anderson and van Wincoop and the empirical gravity model and address why the model is superior to the empirically based gravity model.
The Gravity Model of Trade:
The Gravity model of trade is one of the significant theories of economics that explains the bilateral trade flows between the two countries based on the size of the economies (by using GDP measures) and the distance between the two units(Anderson, 2010). The basic model that was first proposed by Tinbergen in 1962 took the form of,
Here i and j are two countries, M is the economic mass of each country, G is a constant, F is the trade flow and D is the distance. The model can also be used to test the effectiveness of the alliances and the treaties on trade.
The theory has gained empirical success over the years as it accurately predicted the flow of trade between various countries. The pattern of international trade was estimated in the gravity model and the basic form of the model consisted spatial and geographical factors.
It has been stated that the empirical Gravity model lacks the theoretical justification and thus more theoretical integration is required.
Theoretical framework:
The Heckscher-Ohlin model of international trade is one of the theoretical frameworks that have been used in the Gravity model. According to the Heckscher-Ohlin model, a country will produce and export the specific factor intensive commodity if the country is abundant in that factor.
That means a capital abundant country will produce and export a capital –intensive commodity and a labour-abundant country will produce and export a labour-intensive commodity(Burger, Van Oort and Linders, 2009). The model is one of the main contributors of the bilateral trade theory and thus it is also used in the Gravity model.
But it has also been stated that real life scenarios are more complicated and thus the comparative advantage theories do not match the real life situations. In that regards the Liontief paradox can be mentioned for identifying the discrepancy between the empirical findings and the economic theory(Bergeijk and Brakman, 2010).
Staffan Linder proposed an alternative theory that predicted the patterns of trade can be determined by the aggregate preference of goods within countries. According to the model the preference of goods will determine the demand and thus production of different goods and that will also affect the trade. This is referred as the Linder Hypotheses(McPherson, Redfearn and Tieslau, 2000).
James Anderson and Jeffrey Bergstrand later developed econometric models bridging the gaps between the economic theories and the empirical tests(Baier and Bergstrand, 2009). In this model the theories of differentiated goods measuring the gains from trade and the magnitude of various barriers of trade has been used for developing the theory.
The concept of reciprocal dumping has been used in the model as well for identifying the problems in terms of the intra-industry trade(Bergeijk and Brakman, 2010).
Gravity with Gravitas:
The Gravity model was established by the economists James E. Anderson and Eric van Wincoop. According to the authors there is a lack of theoretical foundation in the empirical gravity equation. There are basically two implications of the model that are important.
First, some of the variables are omitted in the analysis and thus the estimation results are biased to a certain degree. Second, the comparative static exercise cannot be conducted by using the empirical model and thus it is a large drawback as comparative statics exercise is very important for evaluating the bilateral trade practices.
The authors thus tried to improve the model and they developed the gravity model by identifying the issues of the empirical model. In their paper the “Gravity with Gravitas”, the authors tried to develop a method that effectively and consistently can estimate the theoretical equation of gravity(Anderson and Van Wincoop, 2001).
They also used the estimated general equilibrium gravity model for identifying the impact of trade barriers on the trade flows by conducting the comparative statics exercise. They also resolved the “border puzzle” by applying the theoretical gravity model. They applied various theories in order to measure and understand the trade border effects(Baier and Bergstrand, 2009). So these are the main improvements over the empirical gravity model.
The Gravity Model:
In the gravity model various theories have been used for evaluating the gravity model and presenting more useful interpretation. The constant elasticity of substitution has been the main basis of the theoretical foundation for the gravity model. Anderson and van Wincoop have manipulated the CES expenditure system in order to derive the model in a simple form.
On such basis the authors have derived the three intuitive components of the trade resistance by decomposition. They are the bilateral trade barriers between the two countries, the resistance of the first country to trade with other regions and the resistance of the second country to trade with other regions(Carrere, 2006).
They assumed that all the goods are differentiated by place of origin in the first building block. They assumed that the supply of each good is fixed and each region has specialised in the production of only one good.
The identical homothetic preference was used in the second building block and CES utility function is used in the model. The gravity equation proposed by the authors is,
The above equation is the simplified gravity model. The authors simultaneously tried to obtain the equilibrium price by using the market clearing constraints. This can make the gravity equation more operational. The price indices depend on the bilateral resistance tij and thus it has been identified as the multilateral resistance variable.
The gravity equation also states that the bilateral trade depends on the bilateral trade barrier between the two countries after controlling for size, relative to the product of their multilateral resistance indices (Caruso, 2003). The price of the goods from one country can be significantly affected by the trade resistance of the country with other regions and that can affect the bilateral trade between the two countries.
The Gravity model states that bilateral trade is homogenous of degree zero in the costs of trade. The main implication of the model is that the relative trade barriers between the regions determine the trade flow between the countries(Dan, 2008).
When there is a bilateral trade between two regions, the average bilateral trade between the two countries determine the trade flow compared to the trade barrier that they face with other regions. There are various implications that are presented here(Fang-ming, 2005).
The first implication is that, the size-adjusted trade between the large countries are reduced by the trade barriers between large countries more than between small countries. The second implication is that, the size-adjusted trade are increased by the trade barriers within small countries more than the large countries(Feenstra, Markusen and Rose, 2001).
The third implication is that the size-adjusted trade ratio is increased by the trade barriers within country 1 relative to the same for country 1 and 2 where country 1 is smaller and country 2 is larger(Guang-hua, 2008).
Gravity model improvement:
It is evident that the empirical gravity model had some of the drawbacks. The model lacked the theoretical implications and it also failed to include some of the important factors that are related with or that can affect the bilateral trade.
Some of the variables are exchange rate and price level variables. The exchange rate and price level can be stated as the variables that can significantly affect the bilateral trade and the gravity model but such factors have not been included in the empirical gravity model(Langdana and Murphy, 2014).
Thus the significant variance caused by these factors in the gravity model has not been explained. According to the empirical results on price level, the variance in the impact of the price level depends upon the relationship that is being examined. Anderson and van Wincoop used a non-linear system of equations to account for the endogenous changes due to the price terms changes from the liberalisations of trade.
Anderson and van Wincoop first proposed their theory by using only two countries U.S and Canada. They also extended their theory to a multi-country model which is more realistic(NANDASIRI, 2008).
One small difference that can be identified in the between the empirical model and the model of Anderson and van Wincoop is that they imposed the unitary income elasticity in the theoretical gravity equation. In the empirical model, non-unitary income elasticities have been taken into consideration.
The non-unitary income elasticity affected the border estimates of McCallum and thus the implication of unitary income elasticity was an improvement over the empirical model. They also extended the model and assumed non-unitary elasticity for the sensitivity analysis(Peng, 2008).
In the two-country model, they added an error term to the logarithmic form of the gravity equation. The error term represent the errors measured in trade. In this gravity model, two multilateral resistance terms have been added and they are not observables.
They used the income shares, borders and distances as the observables of the model. They tried to minimise the errors and the bias of the model explaining the bilateral trade. They used the fixed effects estimator in the sensitivity analysis(Porojan, 2001).
One of the drawbacks of the existing theory is that they assumed that all countries import from all countries all varieties of goods which are not possible. Thus in the new theory they suggested that the assumption of fixed cost, difference in preference, and homogenous goods should be considered.
The literature used in this model also estimates the impact of borders for the trade relations between wide ranges of OECD countries. A sensitivity analysis has been conducted as well. So it can be said that the gravity model proposed by Anderson and van Wincoop is the improved version of the empirical gravity model.
The empirical model lacked the theoretical foundation. The model proposed a biased estimation. It also lacked the understanding of the main source that was driving the results and it used incorrect comparative statics analysis. The authors have developed a method that can efficiently and consistently estimate the theoretical gravity equation(Silva and Tenreyro, 2006).
They have also proposed methods that can resolve the border puzzle. They found that by a plausible and substantial magnitude, the borders can reduce the bilateral national trade levels.
Conclusion:
In conclusion it can be said that the gravity model that was proposed by Anderson and van Wincoop was an improved version of the gravity model. They based their model on the existing gravity theory but they implied various theories and implications in order to minimise the errors of the empirical model.
They used various assumptions and presented suggestions that can direct fruitfully for the future research. Thus it can be said the model is an extension and an improvement over the empirical gravity model.
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