Economía Y Gravedad

Gravity for Beginners∗
Keith Head† February 5, 2003

Contents
1 The 1.1 1.2 1.3 Basic Gravity Equation Origins: Newton’s Apple . . . . . . . . . . . . . . . . . . . . . . . . . . . Economists Discover Gravity . . . . . . . . . . . . . . . . . . . . . . . . . Economic Explanations for Gravity . . . . . . . . . . . . . . . . . . . . . 2 2 2 3 4 4 5 8 9 9 9 9 10

2 Estimation of the GravityEquation 2.1 Economic Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Remoteness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 “Augmenting” the Gravity Equation 3.1 Income per Capita . . . . . . . . . . . 3.2 Adjacency . . . . . . . . . . . . . . . . 3.3 CommonLanguage and Colonial Links 3.4 Border Effects . . . . . . . . . . . . . .

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4 Evaluating Trade-Creating Policies 11 4.1 Free Trade Agreements . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11 4.2 Monetary Agreements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Original Version: October, 2000. This version prepared for UBC Econ 590a students, January 2003. This is a work in progress and I welcome comments and suggestions. The most up-to-date version is available at economics.ca/keith/gravity.pdf † Faculty of Commerce, University of British Columbia, 2053 Main Mall,Vancouver, BC, V6T1Z2, Canada. Tel: (604)822-8492, Fax: (604)822-8477, Email:keith.head@ubc.ca

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1

The Basic Gravity Equation

The gravity equation is a popular formulation for statistical analyses of bilateral flows between different geographical entities. In this paper, I provide an overview of the development and use of this equation. I also include some practical tips forresearchers who want to use the equation in their own work.

1.1

Origins: Newton’s Apple

In 1687, Newton proposed the “Law of Universal Gravitation.” It held that the attractive force between two objects i and j is given by Fij = G where notation is defined as follows • Fij is the attractive force. • Mi and Mj are the masses. • Dij is the distance between the two objects. • G is a gravitationalconstant depending on the units of measurement for mass and force. Mi Mj , 2 Dij (1)

1.2

Economists Discover Gravity

In 1962 Jan Tinbergen proposed that roughly the same functional form could be applied to international trade flows. However, it has since been applied to a whole range of what we might call “social interactions” including migration, tourism, and foreign direct investment. Thisgeneral gravity law for social interaction may be expressed in roughly the same notation: Miα Mjβ Fij = G , (2) θ Dij where notation is defined as follows ˜ • Fij is the“flow” from origin i to destination j. Alternatively, let Fij represents total volume of interactions between i and j (i.e. the sum of the flows in both ˜ directions: Fij = Fij + Fji ). • Mi and Mj are the relevant economic sizes of thetwo locations. – If F is measured as a monetary flow (e.g. export values), then M is usually the gross domestic product (GDP) or gross national income (GNI, formerly GNP) of each location. – For flows of people, it is more natural to measure M with the populations. • Dij is the distance between the locations (usually measured center to center). Note that we return to Newton’s Law (equation 1) if α= β = 1 and θ = 2. 2

1.3

Economic Explanations for Gravity

The gravity equation can be thought of as a kind of short-hand representation of supply and demand forces. If country i is the origin, then Mi represents the total amount it is willing to supply to all customers. Meanwhile Mj represents the total amount destination j demands. Distance acts as a sort of tax “wedge,” imposing...