1. Lecture 2c THE GRAVITY MODEL By Carlos Llano,
References for the topic:
UNCTAD:
Head, K. and Mayer, T., (2014). Gravity Equations: Workhorse, Toolkit, and Cookbook. Chapter 3 in Gopinath, G, E. Helpman and K. Rogoff (eds), vol. 4 of the Handbook of International Economics, Elsevier: 131–-195.
Feenstra, Advanced International Economics, Chapter 5, 2004.
Steven Brakman, Peter A.G. van Bergeijk. (2009?): The Gravity Model in International Trade: Advances and Applications

2. Index
Introduction
The gravity model
Applications
Practice

3. 1. Introduction
The law of gravity states that the force of gravity between two objects depends on the product of their masses and the square of the distance between them (Baldwin y Taglioni, 2006):
Dist12 M1 M2

4. 1. Introduction The “gravity equation” is a metaphor with physics:
The bilateral trade flow intensity between two specific geographical areas (i-j, countries / regions), is positively correlated with the emission and absorption capacity of the points of origin and destination, and inversely proportional to the cost of interaction between the two points.
Yi = Emission capacity of exporting area. Proxy: Gross Output or GDP.
Yj = Absorption capacity of importing area: Proxy: Gross Output or GDP.
Tij= The cost of interaction. Proxy: physical distance, traveling time…

5. 1. Introduction
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.
The use of “the gravity equation” is dated in the 50’ in the field of regional science, geography and urban planning: Wilson, Cesario, Isard…;
In economics, Timbergen (1962) is usually reported as the first author using it.

6. 1. Introduction
The gravity model has been described as: “the backbone of empirical international trade analysis”.
It has shown a great list of achievements in applied work, but it has been criticized for many years for its “lack of theoretical base”.
Milestones in the development of modern “gravity equation”:
Anderson (1979): “Theoretical Foundation for the Gravity Equation”, American Economic Review, 1979, 69,
1995: Trefler and “the missing trade”;
2004: Anderson and van Wincoop (2004): “Gravity with gravitas: a solution to the border puzzle”, AER, 93,
2008: HMR (2008); Chaney (2008)…
Recent Reviews:
UNCTAD:
Head, K. and Mayer, T., (2014). Gravity Equations: Workhorse, Toolkit, and Cookbook. Chapter 3 in Gopinath, G, E. Helpman and K. Rogoff (eds), vol. 4 of the Handbook of International Economics, Elsevier: 131–-195.

7. Gravity with exogenous prices (Feenstra, 2004)
DS Monopolistic Competition model between N countries and K products.
Exogenous prices (no transport costs)
Preferences
Identical and homothetic 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:

8. Gravity with exogenous prices (Feenstra, 2004)
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:

9. Example: Helpman, 1987 The 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.

10. Gravity with endogenous prices (Feenstra, 2004)
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:
La participación de un país en la demanda mundial (s) depende de los precios 10

11. 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"

12. The Gravity Model a la Anderson and van Winkoop, 2004
Outward multilateral resistance
Inward multilateral resistance
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)

13. Part I: Do we really Know that the WTO increase trade. Rose, 1994; 2004.
Gravity model (50 years, 175 countries).
Little evidence about countries joining or belonging to the GATT/WTO have a different trade patterns from outsiders.
Generalized System of Preference (GSP) seems to have a strong effect. 13

14. Rose, 1994:
Gravity model (50 years, 175 countries). 14

15. Rose, 1994:
Gravity model (50 years, 175 countries). 15

16. Part II. The Border Effect. US-Canada
Border effect is considered as one of the main puzzles of international macroeconomics (Obstfeld & Rogoff, 2000).
McCallum(1995) found that a Canadian province trades 22 times more with another Canadian province than with any State from US, controlling by size and distance.
Then, a number of authors have tried to estimate similar effects in other countries…
…Using alternative specifications, and looking for different explanations…

17. Part II. The Border Effect. US-Canada
External border effect: how many times a region trades more with another region of the same country than with any other (non-adjacent) region from another country.
Helliwell (1996, 1998), Anderson and van Wincoop (2003),…
Internal border effect (home bias): how many times a region trades more with itself than with another (non-adjacent) region of the same country.
Canada: Helliwell (1997);
US: Wolf (2000), Hillberry and Hummels (2003; 2008), Millimet and Osang (2006), …
Others: Combes et al. (2005, France), Djankow & Freund (2000, USSR), Poncet (2003, China); Daumal & Zignago (2005, Brazil);
Spain: Requena & Llano (2009), Garmendia et al (2012).

18. Part II. The Border Effect. US-Canada How can we explain the puzzle?
External barriers to trade (tariffs and non-tariff barriers…).
Endogenous responses: agglomeration economies…
Information barriers (Rauch, 2001)
Social and Business Networks (Combes et al, 2005)
Elasticity of substitution + heterogeneity of firms (Evans, 2003; Chaney, 2008)
Misspecification of the model (Anderson & van Wincoop, 2003 …)
Spatial aggregation artefact & mismeasurement of distance:
Imputed intra-national trade/distance (Head&Mayer, 2000; 2002)
Non-linear relationship between distance and trade (Hillberry and Hummels, 2008; Llano-Verduras et al, 2011)

19. Part II. The Border Effect. US-Canada
Papers
Spatial units
Sectors
Period
Ext. Border
Region-to-Region
1995. McCallum
Canada-United State No
1988 22
1996. Helliwell
1998. Hillbery
1993 20
2001 Helliwell
15-10
2002 Head & Mayer
United States (Wolf, 1997,2000)
Yes
1997 11
Country-to-Country
1996. Wei
OCDE
10-2.6
1997 Helliwell
1996 13
2000 Nitsch
EU-10
7-10
2000 Head & Mayer
EU-9
30-11
EU-12
2004. Chen
EU-7 6
Region-to-country
1999. Anderson & Smith 12
2005. Gil et al.
Spain (17 regions), Rest of Spain and OECD-27 21
2003. Minondo
País Vasco, Rest of Spain, 201 countries
20-26
2007. Helble
France, EU-14; Germany, EU-14
2002
8; 3
2010.Requena &Llano
Spain (17 regions) OECD-28
1995 & 00
13 
2010. Ghemawat et al.
Cataluña, Rest of Spain, OECD 55
2011. Llano et al.
Spain (17 regions; 50 Provinces, OECD)
2000 & 05 40

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

21. Part III. The Border Effect. Spain
Gil et al (2005):
The Spanish CCAA trade between them is 20 times the trade with the bordering CCAA.
Llano-Verduras et al (2011):
The Spanish border effect decrease to a factor of 5 when using provinces instead of regions.
Garmendia et al (2012): Internal-border-provinces. 21

22. Interregional trade of goods. 2005
Interregional trade of goods Largest Interregional commodity flows
MADRID
P.VASCO
ASTURIAS
COM. VALENCIANA
ANDALUCIA
CASTILLA-LA MANCHA
GALICIA
EXTREMADURA
MURCIA
BALEARES
ARAGON
CASTILLA-LEÓN
RIOJA
CANTABRIA
NAVARRA
CATALUÑA
SPAIN 19
9,5
1,9
POPULATION %
% REGIONAL GVA
/ NATIONAL GVA 13 ,6 a ,1
(2) 5 ,8
(3) 3 ,4
(4) 1
(5) ,2
1.9%
2.8%
2.2%
2.9%
1.9%
1.9% 2%
1.7%

23. Computer Lab

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