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:

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:

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 proportional 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 economic 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 .

Si,Pj are indexes of all outward and inward bilateral trade costs Dij, respectively, called outward and inward multilateral resistance. Si is the appropriate ‘average’ portion of trade costs borne by seller i to all destinations. Pj is the appropriate average portion of trade costs borne by buyer j from all sources. Behind the scenes, all 3rd party effects are incorporated into multilateral resistance.

4 Multilateral Resistance as Incidence

Si and Pj are also interpreted as sellers’ and buyers’ general equilibrium incidence of trade costs. The incidence interpretation is developed by first reviewing the partial equilibrium incidence analysis of trade cost in a single market, as in the first course in economics. Then the logic is extended to incidence in multiple markets connected by the force of spatial arbitrage. The analysis begins with arbitrage. Supply and demand schedules constrain the forces leading to equilibrium in any market. Spatial arbitrage across separated markets redistributes goods to equalize prices net of trade costs in each market, shifting supplies to each particular market in the path to arbitrage equilibrium. Gravity describes arbitrage equilibrium sales in any bilateral (country pair) market. Autos are an example, produced by many countries and purchased from many countries. Economic agents allocate autos across destination markets to maximize profits. If the price paid for BMWs net of trade costs differs across destination countries there

9 are arbitrage gains to be made by shifting autos from low net price to high net price destinations. Arbitrageurs are the agents who reallocate planned goods sales across markets until no profit is to be made from further reallocation. In arbitrage equilibrium, sellers from i receive net price pi = pij/tij from any destination j, hence pij = pitij for any pair i and j. Arbitrage permits a single supply and demand diagram to portray the connection of multiple markets, and in particular how changes in one bilateral trade cost tij affect all bilateral markets, including bilateral pairs not involving either i or j. The working of arbitrage is illustrated in Figure 1. Total supply yi from origin i is allocated to two destination markets, j and l. The vertical axis records net seller prices, s s buyer prices deflated by trade cost factors pij = pij/tij and pil = pil/til. Demand in j slopes downward because buyers substitute against increasingly expensive goods. Supply slopes upward because the same force is at work on the demand in l that is deducted from supply to form residual supply. Thus supply to j taken from l comes A at increasing opportunity cost. The initial allocation at xij allows arbitrage profits: s s pij − pil > 0 is the profit from shifting one unit from market l to market j. Arbitrage e 1 equilibrium at xij drives arbitrage profits to zero. Gravity models of trade assume that spatial arbitrage is perfectly efficient. The focus is on the determinants of bilateral trade in a spatial arbitrage equilibrium. Focus on any single bilateral market with a supply and demand analysis thus has in the back- ground the relationship of the focus market to all other markets in a world equilibrium system. The supply and demand diagram is next used to model economic incidence – the decomposition of trade costs into the portions borne by sellers (sellers’ incidence) and buyers (buyers’ incidence). Perfect spatial arbitrage is assumed here and henceforth. Introductory economics derives the incidence analysis for a tax in a single isolated market, reviewed below. Incidence in the gravity model extends in Section ?? from a single bilateral market to overall incidence with the world for countries as buyers and sellers. Figure 2 below is the familiar (to Economics 101 students) supply and demand diagram describing equilibrium in a particular bilateral trade market for a particular type of good such as autos. A bilateral import demand schedule intersects with an export supply schedule representing the residual of total supply minus the aggregate of all other bilateral demands. Now origin i serves many destinations, including (importantly) its own domestic market. The left vertical axis in Figure 2 measures possible bilateral buyers’ prices for goods from origin i sold in destination j, pij. The right vertical axis is the aggregate supply of goods from seller i, assumed invariant to price. The horizontal axis measures possible bilateral trade volume on goods from i in j. Demand is decreasing

1The transition path from the initial disequilibrium to the arbitrage equilibrium is the subject of a literature on spatial price arbitrage that uses gravity structure with data on prices at points in time that are close together. The gravity model of trade, in contrast, assumes arbitrage equilibrium and uses gravity structure for trade flows over an interval of time (usually a year) taken to reflect long run equilibrium. Trade policy analysis is appropriately focused on long run considerations because trade policy is usually set with long term commitments. Empirical gravity models interpret the inevitable arbitrage imperfections in observed annual trade flows as unsystematic, hence unrelated to the model’s determinants of trade.

10 Figure 1: Spatial Equilibrium and Arbitrage

11 D in price, demand schedule xij slopes downward (as is conﬁrmed by international trade RS empirical work). Supply schedule xij is a residual supply: total quantity yi minus the quantity sold from i to all destinations (including the domestic one xii) except j. Residual supply slopes upward (is increasing in the cost of serving j) because shifting more sales to j means taking sales away from other markets at increasing opportunity cost of the foregone sales to other markets. Opportunity cost rises because less sales in other markets raises their willingness to pay for the remaining goods, as reduced allocations drive them up their demand schedules. (In an alternative visual presentation, RS xij is also the aggregate demand for goods from i by all destinations other than j, plotted with its origin at yi and its quantity rising moving to the left from yi.) For now, D RS treat xij , xij as generic demand and supply schedules in partial equilibrium. The ﬁgure depicts an equilibrium with a trade friction tij > 1 driving a wedge between the price paid by the buyer pitij and the net price pi received by the seller. The hypothetical frictionless equilibrium is at point F. The trade friction shifts up the D residual supply curve by the proportion tij so that it intersects the demand curve xij at pitij. The vertical line projected down from the intersection strikes residual supply RS schedule xij at seller price net of trade costs pi. The incidence of trade cost is read off the left hand vertical axis of the diagram. F pitij/Pj is equal to the frictionless equilibrium price pij. The friction (usually a tax in Economics 101) pushes the price the seller receives down from its friction- F less level pij = pitij/Pj to pi. The buyers incidence of the trade cost is Pj. Si = (pitij/Pj)/pi = tij/Pj is the sellers’ incidence of the trade cost. Then SiPi = tij, the actual friction is equivalent to the product of the sellers’ incidence Si and the buyers’ incidence Pi. The decomposition is based on the frictionless equilibrium price labeled F pij = pitij/Pj. More usefully for present purposes, consider reducing tij by actually dividing it by SiPj. The new buyers’ and sellers’ incidences are reduced to 1 and the F equilibrium quantity is raised to xij.

4.1 Comparative Statics Now turn to consider incidence across multiple markets when a trade cost changes. As an illustration, calculate the effect of NAFTA from a base year around its inception, hence controlling for other effects on trade that happened after NAFTA’s inception. Alternatively, calculate the effect of NAFTA changes from the current base. Figure 3 illustrates the partial equilibrium comparative statics of a rise in tij. The 0 rise in tij at constant pi implies that sellers would be making a loss on sales of xij. Ar- bitrage shifts sales to other markets, raising the price paid in j and lowering the prices paid in markets l other than j. Eventually equilibrium is reached with equilibrium 1 1 1 1 1 1 1 1 quantity xij and buyers’ price pij = pi tij. Sellers receive pi tij/Pj Si . It would be an accident if the new partial equilibrium values for pi, Si and Pj on Figure 3 were magically consistent with equilibrium in markets l 6= j. Quantity sold in 0 1 market ij falls by xij − xij. Thus residual supply to markets l other than j rises by this RS 0 1 amount: xil shifts to the right by xij − xij. Residual supply to markets other than j is also affected by the change in seller i’s price pi and by seller and buyer incidences Si and Pj. Moreover, any shifts in equilibrium prices in other markets lj would feed

12 Figure 2: Demand and Supply Diagram

13 Figure 3: Comparative Statics of Trade Cost Change

RS back to shift residual supply to market ij, xij . The left vertical axis of Figure 3 could 1 be taken to record the magically consistent effects on market ij, but the values for pi , 1 1 Si and Pj on the axis cannot be solved by a single shift in the tax-inclusive residual supply schedule moving along an invariant demand schedule. The ‘magic’ requires finding new values for pi, Si and Pj consistent with equilibrium in all markets simultaneously. (See technical Section 4.2 for details.) Further small shifts in demand and residual supply schedules in all markets are required for this. Nevertheless, the initial impacts of the tax change are appropriately illustrated in Figure 3, as are valid ideas of what more shifting of supplies in spatial arbitrage must occur to find the new equilibrium. In this hypothetical equilibrium, it is as if all sellers pay a cost factor Si to get their goods to a hypothetical world market (or for each unit shipped only 1/Si units arrive on the world market) while all buyers pay a cost factor Pj (or for each unit purchased only 1/Pj units arrive at destination). For each country in the aggregate the incidence breakdown is just as in the figure above: sellers bear S of the total trade cost to get their goods to the world market, while buyers bear P to bring their bundle of

14 goods (one from each origin country) home from the world market. Each country i’s relationship to the world is captured in the pair of sufﬁcient statistics Si,Pi.

4.2 Solving for Arbitrage Equilibrium This section is technical but should be read to provide understanding about various comparative static studies of projected trade agreements or their dissolution, and of the projected effects of trade wars. Equation (4) multiplied by total expenditure Ej explains expenditure on good i by D RS j, pijxij = Xij. (This is an inessential difference from xij and xij in Figure 2 for present purposes.) Consider Sis and Pjs that are arbitrary, such as Si = 1 and Pj = 1 for all i and j. (Early uses of gravity in fact ignored the incidence terms, effectively setting them equal to 1.) A simple requirement of economic logic is that the model of distribution of goods being represented satisﬁes two adding up properties:

P e 1. the sum of bilateral sales adds up to total sales, j Xij = Yi for each country i; and

P e 2. the sum of bilateral purchases adds up to the total expenditure, i Xij = Ej for each country j. Gravity equation (4) does not satisfy the adding up requirements for arbitrary trade frictions tij and arbitrary Si,Pj – it would be fortuitous if the adding up restrictions were met. The diagrammatic analysis in Figure 2 (and subsequent discussion of comparative statics of changes in trade frictions in Section 3) suggest that residual supply and bilateral demand functions shift to adjust toward a solution (equilibrium) where the allocations add up properly.2 The adding up requirements (with N countries there are 2N of them) give the requirements of this solution in an equation system form. Under suitable restrictions on demand and supply structure this leads to the gravity equation form (4) and equations (7) and (8) below. This form also reveals the interpretation of the solution = equilibrium values Si and Pj as sellers’ and buyers’ overall incidence of trade costs. Hoping that the fog of algebra to follow is sufﬁciently penetrated, this section concludes with drawing out the interpretation. P e To see the implications of adding up for sales for i, ﬁrst divide j Xij = Yi e through by Yi. Use equation (4) to form Xij in the resulting expression. The result is

X Ej 1 = (t /S P )−θ, ∀i. (5) Y ij i j j

The implications of adding up for budgets follow exactly analogous steps to yield:

X Yi 1 = (t /S P )−θ, ∀j. (6) Y ij i j i

2The implication is that equation (4) is plausible as a description of spatial arbitrage equilibrium. The impact of the set of bilateral trade frictions gets aggregated into an overall average, and the impact of the bilateral friction on equilibrium trade involves bilateral relative to multilateral (overall) friction. For that reason, Si and Pj are called multilateral resistances.

15 The equations describe the incidence interpretation previously assigned to Si and −θ −θ Pj. Multiply both sides of (5) by Si and similarly multiply both sides of (6) by Pj . The results are −θ X Ej tij S−θ = (7) i Y P j j and −θ X Yi tij P −θ = . (8) j Y S i i The right hand side of equation (7) is a weighted average of the −θ power transforms −θ of bilateral sellers incidences (tij/Pj) . Thus Si is interpreted as sellers’ incidence facing i overall for the world market. Similarly equation (8) implies that the −θ power transform of buyers’ overall incidence is a weighted average of the −θ power transforms of bilateral buyers’ incidences. Comparative statics of trade cost changes are calculated by solving numerically for the set of new Sis and Pjs implied by the system of equations (7)-(8). Numerical solvers in computers do this easily. Essentially they guess at solutions and update to come closer to satisfying the system of equations, and iterate to the solution. Then the e solution values for the new Xijs are calculated. In full general equilibrium comparative statics, the gravity module of distribution is nested inside a larger equilibrium system solved iteratively. This is the method used in (legitimate) studies that quantify the projected effects of NAFTA 2.0 and Brexit.

5 Share Equation

Behind the Share Equation, 2 While share equation (4) is certainly quite special, it is more general than it at ﬁrst appears.

The three theoretical justiﬁcations for (4) are: 1. consumers (producers) gain from variety of goods consumed (used in production)

2. consumers (producers) differ in their ideal varieties, characterized by a probability distribution, and equation (4) gives the proportion of buyers who prefer the variety of region i. 3. consumers want only one variety of any good but there are many goods and producers differ in their productivities, characterized by a probability distribution. The shares in equation (4) refer to proportions of all goods produced by i and sold to j. With fairly plausible restrictions on the way gains from variety work in item 1 and on the probability distributions in items 2 and 3, equation (4) results. In the gains from variety case the paramter σ is the elasticity of substitution between varieties. In the

16 probability distribution cases 2 and 3 the parameter −θ is a dispersion parameter (like the variance parameter of the normal distribution) of the probability distribution. For relatively homogeneous types of products, variant 3 is the natural interpretation while for differentiated products variants 1 or 2 are the natural interpretation.

Gravity, Migration and Investment The gravity model can also be applied to migration of labor and to foreign direct investment. The same structure yields similarly good ﬁt with data. The theoretical underpinnings change a bit in details that do not matter for many purposes.

Gravity also tends to explain portfolio investment (cross country ownership of stocks and bonds) but here the theory base is lacking.

2 Migration and Foreign Direct Investment Map of Migration FIGURE 1-3

Foreign-Born Migrants, 2005 (millions) This figure shows the number of foreign-born migrants living in selected countries and regions of the world for 2005 in millions of people. Chapter 1: Trade in theGlobal Economy Trade Chapter 1:

6 Empirical Gravity

Empirical Gravity

Example: econometric inference of coefﬁcients δ, b in assumed function:

δ bij Dij = dijb (9) where dij is the distance between i and j, bij = 1 if there is a border between i and j and bij = 0 if there is no border (inter- or intra-regional trade). b > 0 is the border

17 resistance. It can be identiﬁed when shipments data includes internal as well as external trade.

Speciﬁcation (9) makes the border resistance the same for all countries, but this can be relaxed to allow variation by country and also by direction of trade.

More elaborate versions of (9) allow for language differences, contiguity, former colonial ties, etc.

Inference Infer best ﬁtting coefﬁcients δ, b along with Si and Pj from

−θ δ bij ! Xij dijb = ij (10) YiEj/Y SiPj where ij is the random error term representing the forces not explained by the model.

Estimated equations like (10) usually “explain" 90% of the variation in trade. Co- efﬁcients are precisely estimated.

Coefﬁcient −θ can be inferred if some trade cost is directly observed. Otherwise, distance elasticity −δθ is inferred, for example. θ itself is not needed for many purposes.

−δθ et al. coefﬁcients are inferred. Distance elasticities −δθ ≈ −1 typically. Border effects −3 ≤ −θ ln b ≤ −1 typically.

−θ can be inferred if some trade cost element of Dij is directly observed. Typically 10 > θ > 2. Gravity fits well with either aggregate or disaggregated trade flow data. But esti- mates on aggregated data (i) bias downward the average effect of trade costs and (ii) mask large variation across sectors in the effect of distance, for example, on trade flows. Gravity fits well to explain services trade flows. See for example Anderson, Milot and Yotov (2013). Empirical Puzzles • If we use cross-border fixed effects to pick up all possible frictions, the friction is (much) larger than distance, contiguity, common language, etc. • Border frictions within countries are substantial. • Suggests Ònon-tariffÓ barriers Ñ regulation, hidden favoritism to local firms, maybe hidden subsidies. • Suggests frictions in building networks Ñ necessary for any trade. Investment in Òmarketing capitalÓ vulnerable to business confidence, etc. • Importance: when is trade ÒunfairÓ?

18 Structural Gravity Implications Use the estimated coefﬁcients to form the ratio of predicted (indicated by a tilde) to predicted frictionless trade:

!−θ Xeij Deij = (11) YiEj/Y Πe iPej A particularly interesting instance of (11) is for internal trade, i = j. This is Con- structed Home Bias, the predicted excess (relative to frictionless) amount of local trade.

!−θ Deii CHBi = (12) Πe iPei

Home Bias Most all countries’ international trade is far less than predicted by frictionless benchmark. For example, US has 25% of world GDP, frictionless export share should be 75% vs. actual share ≈ 10%.

Openness to trade is associated with gains from trade. CHB is a measure of foregone potential gains. CHB relates directly to a welfare measure as emphasized in Arkolakis, Costinot & Rodriguez-Clare (AER, 2012) for a broad class of gravity-type models. They show that the share of expenditure falling on domestic goods Xii/Ei is inversely related to gains from trade. Speciﬁcally, assuming balanced trade Yi = Ei, real income relative to autarky (where the share is equal to 1) is given by:

X −1/θ ii . Ei The gains measure requires an estimate of trade elasticity −θ. To illustrate, US imports in 2000 relative to domestic gross expenditure (not GDP, a value-added concept) were 7%, implying the domestic expenditure share is 93%. For θ = 4, the gain from trade relative to autarky is 1.8%. For θ = 1, the gain is 7.5%. For θ = 0.5 the gain is 16%. The simplicity of this measure has stimulated a recent surge in measuring gains from trade. Since the measure is very sensitive to the trade elasticity used, the literature focuses on estimating credible elasticities.

CHB in Manufacturing Using manufacturing trade and production data for 76 countries from 1990-2002, Anderson and Yotov (2011) estimate CHBs.

The results below add another major implication about the relationship of size and trade: While bigger producers trade less in the frictionless benchmark, they tend to trade more (a lot more) relative to the frictionless benchmark.

19 • CHB is very large • CHB is (much) lower for bigger producers • the lower CHB is due almost entirely to lower Π, interpretable as sellers’ incidence of trade costs.

• falling (rising) CHB over time is due to falling (rising) Π, associated with increasing (decreasing) sales shares Yi/Y . • lower Π is equivalent to productivity improvement Intuitively, lower Π for larger producers is naturally associated with their larger home market in the absence of frictions. This is a tendency, not a tight proposition.

Table 1: Constructed Home Bias Indexes by Country Countries with Lowest CHB Countries with Highest CHB ISO 1996 %∆CHB ISO 1996 %∆CHB USA 3 -11 MUS 658 -37 JPN 5 41 LVA 679 -43 DEU 8 0 CRI 694 -33 FRA 11 2 EST 704 -54 CHN 12 -51 AZE 737 154 ITA 13 -14 BOL 778 -5 GBR 14 15 JOR 866 -28 CAN 19 0 PAN 872 -15 HKG 20 -22 OMN 948 -49 KOR 20 -28 SLV 1186 -54 ESP 25 -2 MDA 1224 24 BRA 32 56 TZA 1254 -28 MYS 36 -52 MNG 1328 139 BLX 37 30 SEN 1336 -5 NLD 39 24 TTO 1577 -58 RUS 39 33 ARM 2423 -39 AUT 41 13 KGZ 2554 276 IND 44 -13 MOZ 2630 -44

Another way to look at size-incidence effect is that smaller producers tend to be (greatly) disadvantaged by the global incidence of resistance to trade. It is important to note that this disadvantage operates independently of any economies of scale, though indeed economies of scale may add further to the disadvantage. Another implication is that inferences of disadvantage due to economies of scale may falsely be drawn from observing the effects of what is actually differential incidence of resistance to trade.

Size and Trade Again Summarizing the key insights from the gravity literature:

20 1. Any country naturally trades more with bigger partners. 2. Smaller countries are more naturally open. 3. Faster growing country pairs have increasing share of world trade 4. Given natural openness, bigger countries tend to trade much more because they tend to have much lower Constructed Home Bias. 5. Bigger countries lower CHB due mostly to lower outward multilateral resistance = sellers’ incidence.

Projections A valuable use of the empirical gravity model is to project missing data. • Use estimated gravity coefﬁcients (estimated using other data and (11)) to calculate −θ δ bij ! YiEj dijb = Xeij. Y SiPj

• Can be used to check or replace bad or suspicious data (e.g. smuggling) • Used to forecast effects of big changes — e.g., fall of Iron Curtain on E. Euro- pean countries. • Can be used to forecast effects of building a canal, bridge, etc.

7 Measuring Globalization and Other Open Questions 7.1 Missing globalization Estimation of gravity coefficients on various datasets yields no recent evidence of decreasing coefficients on distance (or other frictions such as borders). This appears puz- zling — the Mystery of the Missing Globalization. One answer to the puzzle is that if all trade costs (distance) shrink(s) uniformly, all relative trade costs (distances) tij/tkl (dij/dkl) remain the same and so would all relative trade Xij/Xkl. Thus no decrease in the distance coefficient would be found in estimated gravity equations across time, even though the world was ‘getting smaller’. (This point can be formally demonstrated by analyzing the effect of a uniform proportional change in all Ds on the system of equations (??)-(??). Multiply all Ds by factor τ and all initial P s and Πs by τ 1/2. All equations continue to hold.) The uniformity explanation does seem roughly plausible: better shipping and com- munications stimulate short distance trade within countries as well as long distance trade between countries. Recent data on changes over time in trade costs: • sea freight rates have risen (container rates) but quality is much better (container- ization). See M. Levinson The Box.

21 • Some freight has shifted from surface to air; much more expensive but presum- ably time saved is worth the expense. • Observed willingness-to-pay difference is lower bound estimate of quality improvement. Hard to sort out further effects of quality change, but may be large.

• Tariffs fell most among big countries in the 50s through 70s, so not too much action there. • end of Multi-Fibre Arrangement is much more signiﬁcant for textiles and ap- parel. • some regulatory agreements have fostered trade, especially in services.

• Free Trade Agreements seem to foster trade much more than the implied tariff cuts. The inference is that the FTA fosters investment by firms in foreign marketing and commercial networks, etc. World trade T is rising (except for the 2008 sharp recession) relative to value of world shipments Y , good by good and overall. What is the explanation, if gravity coefficients are constant? • measurement of constant gravity coefficients may be wrong. • production/expenditure patterns shifting may induce trade-increasing changes. Specialization may explain the changing location of production.

Work is proceeding on both points. On the ﬁrst bullet point, better methods may turn up movement of coefﬁcients. On the second bullet point, a starting point is the following decomposition: X X T/Y = Xeij/Y = 1 − Xeii/Y i,j;i6=j i

Xeii = CHBiEiYi/Y using the deﬁnition (12), so X T/Y = 1 − CHBisibi. i

Here bi = Ei/Y , the expenditure share of country i. (i) if CHB falls for big (in sales and purchases) countries, then T/Y falls, even if CHB rises for small countries. (ii) si and bi tend to track closely across countries. Globalization means they tend to be 3 less closely associated. If si and bi diverge more across countries, their correlation is P lower and this raises 1 − i CHBisibi, tending to raise T/Y all else equal.

3 For aggregate trade, bi − si > 0 implies international borrowing. For sectoral goods trade bi − si 6= 0 implies net trade, associated with bigger international trade.

22 7.2 What Are “Trade Costs"? The measured trade costs inferred from gravity have a number of potential explana- tions: • information costs • non-monetary barriers — regulation, licensing,... • taste differences • extortion, insecure contracts See Anderson & van Wincoop (2004) for a survey that attempts to quantify some of these components and relate them to the costs inferred from gravity.

7.3 Linking Gravity to Other Trade Models Gravity can be nested inside the large family of general equilibrium trade models under assumptions that preserve modular structure. It is understood as a model describing the distribution of goods (or service, or people or foreign investment) within a sector for given total sales and total expenditure at each location. The assumptions permitting modularity are technical, but prominently include a simple restriction on the resource use in distribution itself: resources are used in the same proportion in both production and distribution. This is called the iceberg melting assumption: when goods leave the factory, it is as if some melts away en route to the buyer: of y units shipped, only y/t arrive at the destination. Since the resources lost in distribution must be paid for, the seller receives pty from the buyer, of which py pays for the cost of production (p is the “sellers’ price") and p(t − 1)y pays the distribution cost. We can equivalently think that the buyer pays the seller py to obtain at destination the number y/t = x of goods to consume due to iceberg melting. His full price per unit consumed is π = pt where the buyers’ full price is solved from the following logic: py = πx = πy/t ⇒ π = pt. The iceberg melting metaphor is extremely useful for understanding and the simpliﬁcation brings tremendous economy of thought to describing economic interaction. It is possible to relax slightly the iceberg melting assumption and still preserve modularity. But more general (and realistic) distribution cost models require sacriﬁcing modularity: all the allocation between sectors must be analyzed simultaneously with the distribution of goods and services within sectors. How misleading the modular structure is, particularly the iceberg melting assumption, is an important open question.

8 Note on Feenstra-Taylor’s Gravity Treatment

Feenstra and Taylor treat gravity as a manifestation of monopolistic competition only in Chapter 6. Instead, it should be understood as nesting inside many possible models (such as the Ricardian, Speciﬁc Factors and Heckscher-Ohlin models of Chapters 2- 4) that describe the allocation of resources across sectors and of the determination of

23 “who produces what" within sectors. Gravity at the empirical level is really about measuring “trade costs" where the quotation marks emphasize that the measures may include differences in tastes or technology that effectively impede trade relative to a homogeneous smooth world. Gravity is also about the general equilibrium problem of allocating goods (from sellers’ perspective) or purchases (from buyers’ perspective) across markets, taking the levels of total sales and total expenditure in each location as given.

9 References

Anderson, James E. (2011), “The Gravity Model", Annual Review of Economics, 3: 133-60. Anderson, James E. and Yoto V.Yotov (2011), “Specialization: Pro- and Anti-globalizing, 1990-2002", NBER Working Paper No. 16301, revised. Anderson, James E. and Yoto V. Yotov (2010), “The Changing Incidence of Geogra- phy", American Economic Review, 100: 2157-2186. Anderson, James E. and Yoto V. Yotov (2016), “Terms of Trade and Global Efﬁciency Effects of Free Trade Agreements, 1990-2002", Journal of International Economics, forthcoming. Anderson, James E., Catherine A. Milot and Yoto V. Yotov (2013), “How Much Does Geography Deﬂect Services Trade? Canadian Answers", International Economic Re- view, (2014), 55 (3), 791-818. Anderson, James E. and Eric van Wincoop (2004), “Trade Costs", Journal of Economic Literature, 42, 691-751.