Lecture 2c THE GRAVITY MODEL By Carlos Llano, References for the topic: Head and Mayer, 2012: Gravity Equations: Workhorse, Toolkit, and Cookbook. Handbook of International Economics, Vol. 4, eds. Gopinath, Helpman, and Rogof, Forthcomming. Feenstra, Advanced International Economics, Chapter 5, Steven Brakman, Peter A.G. van Bergeijk. (2009?): The Gravity Model in International Trade: Advances and ApplicationsSteven BrakmanPeter A.G. van Bergeijk. 1

1.Introduction 2.The gravity model 3.Applications 4.Practice Index 2

Tema 5 -EE 3 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): 1. Introduction M2M2 M1M1 Dist 12

Tema 5 -EE 4 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 by Gross Output or GDP. –Yj = Absorption capacity of importing area: Proxy by Gross Output or GDP –Tij= The cost of interaction: proxy by the physical distance, traveling time… 1. Introduction The “gravity equation” suggests a metaphor with physics:

Tema 5 -EE 5 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. 1. Introduction

Tema 5 -EE 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”. Experts suggest some important milestones in the development of modern “gravity equation”: 1.Anderson (1979): “Theoretical Foundation for the Gravity Equation”, American Economic Review, 1979, 69, : Trefler and “the missing trade”; : Anderson and van Wincoop (2004): “Gravity with gravitas: a solution to the border puzzle”, AER, 93, : HMR (2008); Chaney (2008)… 1. Introduction 6

Tema 5 -EE 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 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:

Tema 5 -EE 8 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: Gravity with exogenous prices (Feenstra, 2004)

Tema 5 -EE 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.

Tema 5 -EE 10 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: Gravity with endogenous prices (Feenstra, 2004)

Tema 5 -EE 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 "

Tema 5 -EE 12 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) Inward multilateral resistance Outward multilateral resistance

Tema 5 -EE 13 Rose, 1994: 1.Gravity model (50 years, 175 countries). 2.Little evidence about countries joining or belonging to the GATT/WTO have a different trade patterns from outsiders. 3.Generalized System of Preference (GSP) seems to have a strong effect. Part I: Do we really Know that the WTO increase trade. Rose, 1994; 2004.

Tema 5 -EE 14 Rose, 1994: 1.Gravity model (50 years, 175 countries).

Tema 5 -EE 15 Rose, 1994: 1.Gravity model (50 years, 175 countries).

Tema 5 -EE  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 … Part II. The Border Effect. US-Canada 16

Tema 5 -EE  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: 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). Part II. The Border Effect. US-Canada 17

Tema 5 -EE How can we explain the puzzle? 1.External barriers to trade (tariffs and non-tariff barriers…). 2.Endogenous responses: agglomeration economies… 3.Information barriers (Rauch, 2001) 4.Social and Business Networks (Combes et al, 2005) 5.Elasticity of substitution + heterogeneity of firms (Evans, 2003; Chaney, 2008) 6.Misspecification of the model (Anderson & van Wincoop, 2003 …) 7.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) Part II. The Border Effect. US-Canada 18

Tema 5 -EE PapersSpatial units Sectors Period Ext. Border Region-to-Region McCallum Canada-United StateNo Helliwell Canada-United StateNo Hillbery Canada-United StateNo Helliwell Canada-United StateNo Head & Mayer United States (Wolf, 1997,2000)Yes Country-to-Country Wei OCDENo Helliwell OCDENo Nitsch EU-10No Head & Mayer EU-9Yes EU-12Yes Chen EU-7Yes19966 Region-to-country Anderson & Smith Canada-United StateNo Gil et al. Spain (17 regions), Rest of Spain and OECD-27No Minondo País Vasco, Rest of Spain, 201 countriesNo Helble France, EU-14; Germany, EU-14No20028; Requena &Llano Spain (17 regions) OECD-28Yes1995 & Ghemawat et al. Cataluña, Rest of Spain, OECDYes Llano et al. Spain (17 regions; 50 Provinces, OECD)No2000 & 0540 Part II. The Border Effect. US-Canada 19

Tema 5 -EE 20 (Anderson and van Wincoop, 2004), Feenstra, 2004

Tema 5 -EE 21 1.Gil et al (2005): 1.The Spanish CCAA trade between them is 20 times the trade with the bordering CCAA. 2.Llano-Verduras et al (2011): 1.The Spanish border effect decrease to a factor of 5 when using provinces instead of regions. 3.Garmendia et al (2012): Internal-border-provinces. Part III. The Border Effect. Spain

Tema 5 -EE Interregional trade of goods Largest Interregional commodity flows 2.8% 1.9% 2.2% 2.9% 1.7% 1.9% 2% 1.9% 22

Tema 5 -EE Computer Lab

Tema 5 -EE 24 (Anderson and van Wincoop, 2004), Feenstra, 2004