Lecture 8 THE GRAVITY MODEL By Carlos Llano, References for the slides: Feenstra, Advanced International Economics. Ariel Economía, 2000. Francisco Requena.

Lecture 8

THE GRAVITY MODEL

By Carlos Llano,References for the slides:• Feenstra, Advanced International Economics. Ariel Economía, 2000.• Francisco Requena. Seminar given at the MEI-UAM in 2010.• Web de Tierry Mayer, http://team.univ-paris1.fr/teamperso/mayer/thierry.htm

1. Introduction

2. The gravity model

3. Applications4. Practice

Index

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• The gravity equation has been widely used to model all kind of interactions in space that can be explained from the interplay of the attraction and repulsion forces.

• There are many applications in the fields of trade, transport and immigration (Sen y Smith, 1995; Roy y Thill, 2004).

1. Introduction

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1. Physics:• The law of gravity states that the force of gravity

between two objects depends on the product of the masses of the two objects and the square of the distance between them (Baldwin y Taglioni, 2006):

1. Introduction

212

2112

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Dist

MMGFG

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• In economics the force of gravity (FG) is substituted by the intensity of the flow, and the masses M1 and M2 are replaced by variables that cover the size of both elements, and that will depend on the analyzed phenomenon.

• The bilateral trade flow intensity between two specific geographical areas (countries or regions), is directly proportional to the emission and absorption capacity of the points of origin and destination, and inversely proportional to the cost of interaction between the two points.– Emission/absorption capacity = production capacity and demand – The cost of interaction = distance or traveling time

1. Introduction

ij

jiij T

YYKX

1 2 3ln ln ln lnij i j ijE GDP GDP D

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Gravity with exogenous prices (Feenstra, 2004)

• DS Monopolistic Competition model between N countries and K products.

• Exogenous prices (no transport costs)• Preferences

– Identical and homotetic demand between countries– Therefore, the demand of products from i consumed in j is

proportional to the j’s GDP– The GDP in i:

– The GDP in the World:

K

k

ik

i YY1

N

i

iW YY1

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• J country's participation in global spending:• With the assumptions that all countries produce different

goods and have an identical and homothetic demand, exports of product k from i to j are:

• Adding to all products exported:

• Then calculate the volume of trade between i and j:

W

ij

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jijk YsX

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jiW

ijji YYY

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Gravity with exogenous prices (Feenstra, 2004)

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Example: Helpman, 1987The effect of the economic size of countries

• The relative volume of trade within a region (group of countries) depends on the relative size of the countries in that region.

• The smaller the disparity between the economic size of the countries within a region (the larger the similarity) the larger the ratio between trade/GDP in that region.

W

AA

Y

Ys

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ijji YYY

XXV

2

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iiA

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V 212

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• Let’s consider the situation where a country i have to decide how to import from a country j:

• The representative consumer in country j maximizes a CES utility function subject to a budget constraint

σ= elasticity of substitution(> 1); N = # of products from i)

• There are iceberg transportation costs, so prices differ between countries (cif vs fob prices):

• Exports from country i to country j are:

• The income of country i is equal to the sum of expenditures in products imported from country i:

• CES preferences imply that exports from i to j are:

ijq

1

1

1

max

N

iiji

ccN

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N

ijijiji YqpN

1

iijij pp

ijijiij qpNX

N

jiji XY

1

jj

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1

Gravity with endogenous prices (Feenstra, 2004)

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The relative price issue in the gravity model

• Do trade flows between i and j depend only on bilateral trade costs, regardless of the level of trade costs that prevails among other bilateral flows?

• If trade costs between i and j decrease, are affected trade flows between other countries?

• If the costs of bilateral trade in other flows decrease, how is affected the trade flows between the rest?

• The answer to these questions requires some economic theory:– Adding micro-foundations expect to get something like a gravity

equation, but in response to the problem of relative prices– Anderson and van Wincoop, (2004): model gravity with gravitas "

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The Gravity Model a la Anderson and van Winkoop, 2004

• The impact of trade costs on exports from i to j is complex because it depends on a first-order (or direct) and second-order effects (as reflected in the multilateral resistance terms)

C

i k

ki

ki

kijk

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k

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1

1

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1

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1

Inward multilateral resistance

Outward multilateral resistance

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1. McCallum (AER, 1995):1. On average, the exports of Canadian provinces to other Canadian

provinces are some 20 times larger than their exports than the equivalently situated U.S. states (same size and distance).

2. Engels and Rogers (AER, 1996):1. Evidence from urban price movements suggests that the border

imposes barriers to arbitrage comparable to 1.700 miles pf physical space.

3. Gil et al (World Economy, 2005):1. The Spanish CCAA trade between them is 20 times the trade with

the bordering CCAA. 1. Border effect?, physical differences, accessibility, cultural, legal

differences…?, specific effects of sector agglomeration (clusters)?

1. Introduction: Border Effect

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(Anderson and van Wincoop, 2004), Feenstra, 2004

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(Anderson and van Wincoop, 2004), Feenstra, 2004

http://www.uam.es/carlos.llano/master_ec_intern/Chapter_5.zip

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(Anderson and van Wincoop, 2004), Feenstra, 2004

http://www.uam.es/carlos.llano/master_ec_intern/Chapter_5.zip

http://www.uam.es/carlos.llano/master_ec_intern/Chapter_5_full.zip