Gravity Equation Seyed Ali Madanizadeh Sharif U. of Tech. April 2014 Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 1 / 16
Gravity equation: relates bilateral trade volumes X ni = κ X ny i τ ni Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 2 / 16
There is a strong tendency for bigger countries to import more. Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 3 / 16
Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 4 / 16
Yet imports clearly increase less than proportionally with market size. Larger countries are more likely to buy from their own domestic suppliers. The largest countries only import about 10 percent of their purchases. A simple cross-country regression shows that the elasticity of imports with respect to market size was 0.74 in the early 1970 s. This elasticity rose to 0.90 in the mid to late 1990 s. Thus, trade grew faster in big markets than in small markets. Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 5 / 16
To examine the role of exporter size we look at the extent to which countries that produce more also have greater penetration of their domestic and export markets. Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 6 / 16
In a benchmark world with no geographic barriers and complete specialization, all observations would lie along a 45 degree line (on a log scale): A country s market share in each destination would correspond to its share in world production, so that in each destination n country i would have a share Y i /Y W ; where Y W is world production, independent of n. A regression through the scatter of Figure 3 does in fact deliver a coeffi cient of one, but note the huge variation across destinations. Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 7 / 16
Define B in = (X in X ni ) / (X ii X nn ) = 1/ τ ni τ in Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 8 / 16
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Countries far apart trade much less with each other. Comparing Figures 4 and 5, between the early 1970 s and the mid to late 1990 s, we see that the index of bilateral trade increased by nearly an order of magnitude at all distances. While the scatter shifts up over time, the slope of this relationship remains fairly stable. Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 10 / 16
How are these patterns of trade between countries reflected in the export behavior of individual producers? Bernard and Jensen (1995) began to document facts about producer-level exporting based on total foreign shipments of individual U.S. manufacturing plants. The most striking fact emerging from these data is how little most producers participate in export markets. Less than 15 percent of U.S. manufacturing plants reported exporting in 1987 (this percentage rose to 21 by 1992), and of those that did export, most reported sending less than 10 percent of their shipments abroad. In these respects, French firms appear very similar to U.S. plants. Only 17% of these French manufacturing firms report exporting in 1986. We see not only that a small minority export, but among those that do, most sell in only a few export destinations. Only about 1000 firms sell in more than 30 export markets. Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 11 / 16
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Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 13 / 16
Back to Gravity General form: X ni = κ (Y n) α (Y i ) β (dist ni ) γ log X ni = log κ + α log (Y n ) + β log (Y i ) γ log (dist ni ) Typical empirical estimates give α, β, γ 1. Typical R 2 0.80 Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 14 / 16
McCallum (AER 1995) Trade between US States and Canadian provinces log X ni = log κ + α log (Y n ) + β log (Y i ) γ log (dist ni ) + δdummy ni where dummy ni = 1 if n, i in Canada. Incredible finding: e δ 22 Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 15 / 16
Anderson and van Wincoop (AER 2003) Tariff equivalent of US-Canada border about 50% (large but not implausible). Seyed Ali Madanizadeh (Sharif U. of Tech.) Gravity Equation April 2014 16 / 16