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Gravity With Gravitas (guest)

The article presented in this post is titled "Gravity With Gravitas", published by Anderson and Van Wincoop in the American Economic Review, there is a reference in research on determinants of international trade (GDP, distance, border). It is summarized by François Beauchamp and Clement Dupêcher.
F. C

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Being part of the 6 "puzzle" highlighted by Obstfeld and Rogoff, border effects
were initially demonstrated by McCallum in 1995. Empirically, it has used trade data on bilateral trade in 1988 between Canadian provinces and U.S. states, two countries with similarities. His empirical study included data from 10 Canadian provinces and 30 U.S. states and a simple way (by linear regression) he wanted to determine whether border effects existed between the two countries. With this formula,

McCallum came to the conclusion that at equal distance and GDP with similar provinces traded 22 times more with another province with a state. Mathematically, this means that the dummy "border" is equal to 3.09, which exp (3.09) = 22. The figure 22 demonstrates that despite a complete disappearance of borders between Canada and the United States, there is a marked preference for intra-provincial.

Anderson and van Wincoop are for their party's postulate: there seems to be indeed a real border effect. But it happens to a similar result if one starts with the theoretical bases? First, we need to know quickly that they are limits to the model of McCallum (1) that its findings are based on an empirical model (no theoretical basis) and (2) by its lack of static comparisons ( robustness test). In other words, the omission of variables does not allow him to have accurate results and prevents its equation of reasoning in a general equilibrium framework. Moreover, the equation of McCallum does not take into account the multilateral resistance variable which is to take into consideration the fact that a country on a bilateral exchange with a main partner but also with several other countries. Thus, it is clear that the results of McCallum are overstated. Finally, Anderson and Van Wincoop take into account in their model the effect of "great nation" that helps explain the independence of a small country with its main partner when protectionist barriers are slowing the flow of trade.

Model developed by Anderson in 1979, which is based on theories of CES function (Arrow, Solow et al, 1961) on preferences will be the starting point in building their general equilibrium model. The CES function is, in consumer theory, a constant elasticity of substitution, that is to say that for every pair of baskets of goods, a decrease of 1% of the quantity of good A can be compensated by the c% increase in the quantity of good B, where c is a constant independent of the pair of baskets. In addition, the model is also based on regional specialization and finally, the internal distances measured by the proxy WEI (1996) which evaluates as a quarter of the distance between the regional capital and the nearest border.

They then develop a method that estimates a theoretical gravity equation and then they use the gravity model in general equilibrium to generate static comparisons from which we can directly calculate and compare the effects borders. Consider the equation they developed:

With:

• Yw is world GDP,
• Yi and Yj, GDP of country i and j
• Tij corresponding to the cost of transport to go from i to j,
• Pi and Pj are the indices of consumer prices of i and j,
• Sigma is the elasticity Alternative

The results obtained with this new equation are different from those obtained by McCallum: Anderson and van Wincoop find a border effect equal to 10.5. This difference with the factor of 22 from McCallum is that they use data from 1993 instead of 1988. Only by the entry into force of NAFTA (North American Free Trade Agreement, 1989) and the decrease barriers to trade, the coefficient based on McCallum's equation reduces to 16.4 for Canadian provinces and with existing data for U.S. states, they arrive at a factor of 1.5.
For best results, they also looked at McCallum's equation with the addition of the variable Remotness "appeared after the paper McCallum to see if this variable friction can play a significant role.
Equation:

Calculation of "Remotness"

It can see that the new equation takes into account this variable, but it gives mixed results and especially with no connection with reality. The results remain substantially the same as the results of McCallum (1993).

To incorporate a variable taking into account multilateral resistance (plays the same role as the variable Remotness) just explain trade with other countries of the lead partner. The authors focused on the effect that great country we know can play a role in trade flows.
It follows three implications:

• reduce barriers higher level of trade between large countries and between small countries
• barriers further increase the internal trade of small countries that trade within large countries,
• barriers increase over the ratio of internal trade of the country 1 that trade between country 1 and country 2 (1 with the country which is a small country and country 2 which is a large country)

Therefore, the border effect is lower in the U.S. and Canada because it is a great country. Indeed, trade between U.S. states is large and specialized, which allows them to better withstand a rate hike or a border effect.

After showing the effect of "great country", the authors model the transport cost Tij. They will adopt the hypothesis developed by other economists that Tij is the product of the distance Dij (distance between region i and region j) and Bij variable taking the value 1 if regions i and j are in the same country and the value 1 plus a tariff at the border if the regions i and j are in different countries. The authors do not want to add new variables to stay as close as possible to McCallum's equation and to focus on the multilateral resistance indexes, missing the analysis of McCallum. Now they can compare the theoretical gravity equation with that estimated in empirical studies.

For further analysis, the authors decided to make 2 different models: a model with 2 countries (U.S., Canada) and a model with several countries (USA, Canada and other developed countries, called for ROW ROW).

The barrier between the U.S. and Canada is lower between 20 countries around the world. The only barrier higher than the others is that between Canada and countries around the world. This approach, although with limitations is really robust, error terms are very close to 0, with the exception of bilateral trade between Canada and the United States. Border effects are greater in the case of trade between two major countries: trade decreases more between the U.S. and the world between Canada and the rest of the world by the fact that Canada is a small country.
The border effect for Canada is due to the combination of its small economic size, the omission of certain variables and endogeneity property (The dummy takes the value 0 for the intra-provincial trade and 1 for state-province while the multilateral resistance is correlated with the distance and the dummy). The model shows that multi-country borders have a greater effect on trade between Canadian provinces than on interstate commerce. Trade between Canadian provinces is 10 times greater between states and provinces. The impact is less for the states. Finally, they believe that borders reduce bilateral trade between the U.S. and Canada by 44%, 29% of trade between the countries of the world.
This paper shows that the gravity equations had no theoretical basis. Anderson and Van Wincoop then estimated a gravity equation based on a CES of 1979 by Anderson himself.
Three results emerge from the study:

• McCallum omitted variables lead to overestimation of the border effect,
• Intra-national replaces heavily on international trade,
• The border effect is greater for smaller countries than larger countries.

But their model has some limitations, however. They assume that each region specializes in the production of a single well. But in reality, there is certainly an international specialization, but it is not nearly as advanced (these are Haveman and Hummels which showed that the imported goods do not generally come as some exporting countries, two countries for majority of imported goods). Barriers to trade can also affect the structure of production (intermediate goods), which has not been considered by Anderson and McCallum. Finally, a parameter plays heavily on the border effect, according to Helliwell: the results of border effects are very sensitive to the distance in-country. However, Anderson and van Wincoop have chosen an arbitrary measure of internal distance.
Many extensions have been made. For example, Hillberry and Hummels discuss border effect on the location of intermediate goods producers (Kei-Mu theory Yi analyzing the effect of tariffs on trade in the case of vertical specialization). Such integration would change the results of the border effect, which is an interesting extension.
we said, despite its limitations, this paper represents a major advance in economic analysis and for considering the border effect as a stylized fact. The puzzle is Obstfeld and Rogoff (partly) solved by finding a theoretical basis for the purely empirical equation McCallum and adding the multilateral resistance variables.


François Beauchamp

Clement Dupêcher