Gravity force in physics (the analogy)
F(ij) = G x M(i) x M(j) / d(ij)^2
Quote it to set up the analogy, and to make the point that the trade version does not square its denominator.
- F(ij)
- Force between objects i and j
- G
- Gravitational constant
- M(i), M(j)
- Masses of the two objects
- d(ij)
- Distance between them, squared in the denominator
Intuitive gravity model of trade
X(ij) = C x Y(i) x Y(j) / t(ij)
The main equation of this chapter. Use it whenever a question gives two GDPs and a measure of trade costs or distance, or asks what happens to trade when one of those changes.
- X(ij)
- Exports or trade from country i to country j
- C
- Constant, estimated from data; carries the units
- Y
- Economic mass, in practice GDP
- t(ij)
- Bilateral trade costs: distance, adjacency and policy factors
Gravity model, textbook form
T = C x Y(1) x Y(2) / D
The textbook's version, with distance in place of trade costs. Identical logic; use it when the question gives kilometres rather than a cost index.
- T
- Value of trade between countries 1 and 2
- D
- Distance between them, first power
Estimating the constant
C = T x D / (Y(1) x Y(2))
When one country pair's trade is observed and you must predict another pair. Fit C first, keep four or five significant figures, then substitute the second pair.
- T
- Observed trade for the benchmark pair
- D
- Distance for the benchmark pair, in the same units you will reuse