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Trade, Size, and Frictions: the Gravity Model

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Trade, Size, and Frictions: the Gravity Model Trade, Size, and Frictions: the Gravity Model James E. Anderson January 10, 2019 Contents 1 Size and Trade Patterns 3 2 Frictionless Gravity 6 3 Gravity with Frictions 8 4 Multilateral Resistance as Incidence 9 4.1 Comparative Statics . 12 4.2 Solving for Arbitrage Equilibrium . 15 5 Share Equation 16 6 Empirical Gravity 17 7 Measuring Globalization and Other Open Questions 21 7.1 Missing globalization . 21 7.2 What Are “Trade Costs"? . 22 7.3 Linking Gravity to Other Trade Models . 23 8 Note on Feenstra-Taylor’s Gravity Treatment 23 9 References 23 Why So Little Trade? Most economic activity is localized. Trade is tiny compared to its potential. Thomas Friedman’s “the world is flat" is hugely wrong — world trade < 10% of potential in a frictionless world. Big countries trade more (e.g. US and China) but small ones are relatively (size-adjusted) more open (e.g. Belgium). Distance and borders apparently kill of a lot of trade, given relative country size. The gravity model organizes these striking regularities in a model that is used to infer the size of barriers to trade. The model applies within countries and within regions (and even within institutions such as BC). The model is also very useful for describing migration and foreign direct investment. 1 A big achievement of the gravity model is to make sense of multi-country interac- tions. Intuitively, the more country A trades with country B, the less is left over for trade with country C. Frictions between B and C thus affect A’s trade with either B or C. Realistic models of hundreds of countries or regions appear likely to be hope- lessly complex. The gravity model reduces this complexity to describe each country’s relationship as effectively to a ‘world’ economy, as buyer and as seller. This insight is a useful link to the models in most of the rest of the course that explicitly describe a country’s interaction with the outside world in a two economy setup. Once the estimated relationships of the model are obtained, useful comparative static experiments may be conducted. For example, the effects of free trade agreements such as NAFTA can be measured (Anderson and Yotov, 2016). These effects include trade flow changes. They can also include wage and welfare effects when gravity is combined with supplemental data and the sort of models of the structure of production to be analyzed later in the course. These notes develop the model of how trade patterns are determined by size (of countries, regions and sectors) and trade frictions. The model is applied to data to make sense of the world. Some further implications are drawn. 2 1 Size and Trade Patterns 1 International Trade Map of World Trade FIGURE 1-1 World Trade in Goods, 2006 ($ billions) Trade in merchandise goods between selected countries and regions of the world. Chapter 1: Trade in theGlobal Economy Trade Chapter 1: Copyright © 2011 Worth Publishers· Essentials of International Economics· Feenstra/Taylor, 2/e. 6 of 41 Size is measured by national product instead of geographic area. Bring some notion of big economies to interpret the width of arrows in relation to economic size and the power of the relationship is obvious. 3 The size and trade relationship is much more obvious in this display of Japan’s trade with EU members. For clarity, each EU member’s GDP and trade with Japan are nor- malized (divided by) the GDP and trade of Greece respectively. Notice the good fit of the line (75% to 85% of variation of trade is explained by size alone) and the slope of the best-fit line is ≈ 1. 4 No- tice that the log of trade/GDP is powerfully decreasing in log of distance in the dia- grams. And the slope is less than −1 but fairly close to it. If we interpret a slope of −1, it means that doubling distance cuts trade in half, all else equal. The bottom panel suggests that other factors besides distance play into trade size, indicating that a richer set of factors need to be investigated. 5 1 International Trade Trade Compared with GDP TABLE 1-2 Trade/GDP Ratio in 2008 Countries with the highest ratios of trade to GDP tend to be small in economic size. Countries with the lowest ratios of trade to GDP tend to be very large in economic size. Chapter 1: Trade in theGlobal Economy Trade Chapter 1: Copyright © 2011 Worth Publishers· Essentials of International Economics· Feenstra/Taylor, 2/e. 12 of 41 Size and Trade Summary Observations • bilateral trade rises with the size of either trading partner • countries further apart trade less • borders appear to impede trade a lot The gravity model explains these patterns. 2 Frictionless Gravity Frictionless World Benchmark Size has a lot of explanatory power. Bigger incomes buy more from everywhere; bigger sales sell more to everywhere. Developing a model where size alone determines trade patterns is thus useful in abstracting from complex frictions. A particularly important use for such a model is to provide a benchmark for what a frictionless world would look like. 6 Frictionless Gravity Model Assume: • demand at each destination for goods from all origins • market clearance • perfect arbitrage with, for now, no trade costs Expenditure by j is Ej; sales of i is Yi; world sales is Y . In a completely smooth homogenized world, the exports flow from i to j, Xij is given by: Xij Yi YiEj = ) Xij = (1) Ej Y Y Equation (1) ) the share of j’s expenditure on goods from i is equal to the share of world expenditure (= sales) on goods from i. Figure 1 says (1) fits well, Xij propor- tional to Ej. Natural frictionless benchmark. Frictionless Gravity Equilibrium Market clearance (material balance) implies that X Xij = Yi: (2) j P P World budget constraint ) j Ej = i Yi = Y . Thus (1) is consistent with market clearance: check by summing right hand side of (1) over j and using the world P budget constraint to set j Ej=Y = 1. If we impose a no net trade budget constraint for each country then Ei = Yi, hence Xij = YiYj=Y , but the more general specification (1) is far more realistic. Implications of Frictionless Gravity Define si = Yi=Y , country i’s share of world sales, and bi = Ei=Y , country i’s share of world expenditure. Assume balanced trade for now, bi = si. Then: Xij = sisjY: Implications 1. Any country trades more with bigger partners. 2. Smaller countries are more naturally open: X Xij=Yj = 1 − sj i6=j which is decreasing in sj. 3. Faster growing country pairs have increasing share of world trade: Xij=Y = sisj is increasing in si; sj. For more implications when unbalanced trade is modeled, see Anderson (2011). 7 Aside on Growth Rate Accounting Point 3 on the previous slide uses a basic property of growth rate accounting. Let xb denote the growth rate of x. Then (the Hat Rule) x = y=z ) xb = yb − zb and x = yz ) xb = yb + z:b Thus the rate of growth of Xij=Y is equal to sbi + sbj. And sbi = Ybi − Yb. The Hat Rule follows from log differentiation: d ln y=z = d ln y − d ln z = yb− zb. 3 Gravity with Frictions Evidence of Frictions Trade is much smaller than indicated by (1). US has 25 percent of world GDP, exports should be 75 % of GDP vs. 10-15 % actual. (XUS;ROW =YUS = EROW =Y = 0:75) • Trade falls sharply with distance (with effect Dij reflecting distance between i and j): YiEj 1 Xij = : (3) Y Dij (3) gives a pretty good fit with actual trade data (viz. Figure 2). Implication: doubled distance ) halved trade. • Crossing borders further reduces trade a lot. i.e., Dij = dijBij where Bij > 1 = Bii for i 6= j in equation (3) is the effect of a border between i and j and dij is distance. Economic Theory of Gravity Equation (3) or its variants allowing for borders and other effects was inspired by 2 Newton’s Law of Gravity (where Dij = dij, the square of bilateral distance between i and j, Yi is mass at i and 1=Y is the gravitational constant). Thus it is called the gravity equation or model. It has no economic theory behind it. Economic theory leads to an expenditure share called structural gravity. (It is de- rived from one of three well justified foundations.) X Y D −θ ij = i ij ; (4) Ej Y SiPj where θ > 0. 8 Behind the Share Equation The intuitive meaning of (4) is that bilateral trade falls as the ‘economic distance’ between origin and destination rises. Equation (4) restricts the responsiveness to a constant elasticity −θ < 0. [For the derivation see Anderson (2011). ] Equation (4) is linear in logarithms — suggests fitting a straight line on data points relating log trade shares to log distance. The slope is −θ times the elasticity of eco- nomic distance (Dij, trade cost) with respect to geographic distance dij. Essentially this is the empirical procedure used. But complicated by needing mul- tivariate inference. Si and Pj act on the bilateral trade flow data as common exporter and importer country shifters (fixed effects to be inferred). Economic Theory of Gravity Repeating the share equation (4) X Y D −θ ij = i ij : Ej Y SiPj The right hand side of share equation is in two parts. Yi=Y is the frictionless expendi- −θ −θ −θ ture share prediction. (Dij=SiPj) is the effect of trade frictions. Si and Pj are not observable but can be inferred in an econometric version of the model along with 1−σ Dij .
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