RTT

 

cloth and wine. In case 1, the one assumed in Ricardo’s example, outputs can be immediately solved for from labor endowments, with prices then determined by demand. In the second two, relative prices are given by the relative labor requirements in the incompletely specialized country, with demand then determining outputs. At the intro level, the lesson from his sort of example is that gains from trade are possible, although we can only put bounds on what the gains are. At a more advanced level, students are told to solve for the equilibrium outcome by assuming one case and then checking that it satisfifies the requirement that prices don’t exceed costs or that labor is fully employed. Already the model has to confront a clumsy taxonomy.

International trade is a fifield rich in data. United Nations COMTRADE, currently the major source of statistics on merchandise trade, reports the annual value of bilateral trade between over 242 countries (making for 242 × 241 = 58,322 bilateral pairs) in 776 product categories going back to 1990. Given that even the two-country, two-good example is awkward to work out, what hope does the Ricardian model have of sorting out data of this complexity?

In fact, a handful of developments have recently culminated in a formulation of the Ricardian model that is highly amenable to exploiting exactly such data. This formulation has spawned a surge of studies to address various policy questions quantitatively. We chart this evolution and show where it has led.

Ricardian Trade Theory: From Textbook Example to Practical Tool

To begin, let’s reformulate Ricardo’s example in terms of England’s wage ω relative to Portugal’s, setting the Portuguese wage to 1. Making a unit of cloth in England will then cost 100ω, while making it in Portugal will cost 90. Making a unit of wine in England will cost 120ω, while making it in Portugal will cost 80. With free trade and perfect competition, the prices of cloth and of wine are the same in each location and constitute the lowest-cost way of producing each good. Say that ω is bigger than 90/100, the ratio of Portuguese to English workers required to make cloth. Then, since

90 > 80 __

100 120 (cloth) (wine)

Jonathan Eaton and Samuel Kortum 67

68 Journal of Economic Perspectives

both cloth and wine will be produced more cheaply in Portugal, leaving English labor out of work. Hence an English wage that is more than 90 percent of the Portuguese wage is not compatible with employment in England. At the other extreme, if ω is smaller than 80/120, then both cloth and wine will be cheaper if made in England, putting Portuguese labor out of work. Hence we need ω to be somewhere in between 2/3 and 9/10. (Because Ricardo granted Portugal an absolute advantage in both goods, he doomed English workers to a lower wage in order to be employed.) The idea that a Ricardian equilibrium involves identifying the source that can supply a good at minimum cost is at the heart of taking the model to more goods and countries.

Any hope of applying this example to actual world trade requires adding more goods and countries. How can we do that? Let’s proceed step by step.

More Goods

Let’s add another good, linen, while sticking with just our two countries. Say England needs 100 workers to make a unit of linen, and Portugal needs 100 workers as well. These numbers grant England an even stronger comparative advantage in linen than in cloth. We can extend the previous inequality to:

100 > 90 > 80. ___

100 100 120 (linen) (cloth) (wine)

This ordering of goods in terms of England’s relative productivity is called a chain of comparative advantage. Under free trade, the English relative wage ω breaks this chain between goods for which England’s relative productivity is above or below its relative wage. The goods to the left of the break are produced more cheaply in England and those to the right of the break are produced more cheaply in Portugal. For example, an ω of .95 breaks the chain between linen (produced more cheaply in England) and cloth and wine (cheaper from Portugal). An ω of .9 breaks it at cloth (costing the same from either country, with linen cheaper from England and wine cheaper from Portugal).

What determines the relative wage ω that breaks the chain? In general, fifinding it can be quite complicated but, if the two countries spend their income the same way (specififically, if tastes are identical and homothetic), the problem simplififies. We can then use the chain of comparative advantage to construct the demand curve for English labor relative to world labor (on the x-axis) as it varies with the English wage ω (on the y-axis).

If ω > 1, then English labor has priced itself out of all goods. Hence, the demand curve is just a vertical line at zero for ω above England’s relative productivity for good 1. At a wage ω = 1, England is competitive in linen, and buyers are indifferent between England and Portugal as a source. The demand curve for English labor is then flflat (perfectly elastic) between zero and the point at which the demand for linen is saturated at the price of 100. A decline in ω from this point renders England the sole producer of linen. Since the price of linen is 100ω, a drop in ω lowers the price

Figure 1

Wage Determination in the Many Good Model

1

9

10

ω

2

3

1 2

Putting Ricardo to Work 69

L1 L+L*

English share of world labor

Source: Authors.
Note: The solid downward-sloping line is the relative demand curve for English labor, and the solid vertical line is the relative supply curve for English labor.

of linen, increasing demand for it and hence for English labor. At the point ω = .9, England becomes competitive in cloth as well as linen. The demand curve for English labor thus hits another flflat zone as world buyers are indifferent between England and Portugal as sources of cloth (continuing to buy all their linen from England and wine from Portugal). Proceeding along the chain, the demand curve for English labor is a downward stairway with treads along which England and Portugal share produc- tion of a good connected by risers along which England and Portugal specialize in producing distinct sets of goods. The treads are horizontal, as with a standard staircase, but the risers are vertical only in an extreme case. Otherwise they slope downward to the next tread. The equilibrium can be found by imposing the vertical supply curve for English labor as a share of the world’s, which could cut the demand curve along a tread (corresponding to a good for which England and Portugal share production) or through a riser (with no shared goods).

We count fifive possible types of outcomes, going from linen, cloth, and wine made in England and wine elsewhere, to linen, cloth, and wine made in Portugal and linen elsewhere. Of course, more goods can be added by inserting them into the chain, raising the number of types of outcomes.

Figure 1 illustrates the case for four goods, adding one product to the example above—say, anchovies—for which England requires twice as many workers as

England’s relative wage

70 Journal of Economic Perspectives

Figure 2

Wage Determination with a Continuum of Goods

ω′

ω

A '( j ) A(j)

jL*
(1 – j)L

0jj'1 Goods produced in England Goods produced in Portugal

Source: Authors.
Notes: On the x-axis is a continuum of goods from 0 to 1 with England having the strongest comparative

_

advantage in goods nearer 0 and Portugal in goods nearer 1. England produces the goods from 0 to j. _

Portugal produces the goods from j through 1. The figure illustrates how a shift up in the productivity curve A( j ), meaning that England gets relatively more productive at making every good, raises England’s relative wage ω and expands the share of goods it produces. A partial derivation for the equation describing the upward-sloping curve is provided in footnote 2.

Portugal to produce a unit. Changing the English labor supply involves sliding the English relative labor supply curve L/(L + L*) along the x-axis where L is English labor and L* Portugal’s.

Trade economists now speak frequently of the extensive and intensive margins of trade. A country’s exports can increase on the intensive margin, exporting more of a given set of goods, or on the extensive margin, exporting a wider range of goods. The stairway shows how the two operate in a Ricardian framework. Along a riser, a drop in ω raises demand for English exports only at the intensive margin, by lowering the price of the given set of goods that England produces. When ω hits a tread, however, expansion is also at the extensive margin as England expands the set of goods it produces and exports.

An implication of the framework is that, given technologies around the world, having a larger share of the world labor force may require a country to have a lower wage. In order to employ more labor with its given set of technologies, a country needs to sell more of the goods it currently produces (going down a riser) or to take over goods from other countries (reaching a lower step). The result holds

England’s relative wage

even though technologies are constant returns to scale, because larger size reduces the gains from trade. This basic implication of the Ricardian model will survive its modern reincarnation.

While the construct is intuitive, stairways are trouble not only for wheeled vehicles but for comparative statics. Solving for the equilibrium is tedious.

More Goods than You Can Count

A classic paper by Dornbusch, Fischer, and Samuelson (1977) made life much simpler by replacing the stairway with a ramp. These authors had the insight that inserting more and more goods into the chain of comparative advantage would render the gaps between the ratios of the labor requirements miniscule, in which case the three types of equilibria around any good in the original model collapse to the same outcome. They assumed that the set of goods correspond to all the points on an interval between 0 and 1, and sorted the goods to form a chain of compara- tive advantage, with England having the strongest comparative advantage in goods closest to zero and Portugal in goods closest to one. They defifined a function A( j ) as the ratio of Portugal’s labor requirements to England’s labor requirements for good j, hence England’s relative productivity, for each j between 0 and 1. They went on to assume that A(j) was smooth and strictly decreasing. The downward sloping curve in Figure 2 illustrates such a function.

For any English wage ω between A(0) and A(1) there is some good, let’s call it _ _ _

j, satisfying A( j ) = ω. This good j costs the same whether it is produced in England _ _

or Portugal. England produces goods j ≤ j , Portugal goods j ≥ j . Who produces _

good j is irrelevant to anything else, because this good is only an infifinitesimal frac- _

tion of the total. Because j goes from 0 to 1, j is also the share of goods produced in England, for consumption in either England or Portugal. Because A(j) is decreasing, a change that increases England’s relative wage ω, given the function A( j ), must reduce the share of goods produced in England.

To fifigure out what ω will break the chain, we need to look at the demand side. _

A higher j means that England is producing a larger share of goods, increasing demand for its labor and hence its wage ω. Figure 2 depicts this positive relationship

_
between ω and j . Where it intersects the downward sloping A( j ) curve determines

the equilibrium.2

2 To get an exact expression for this upward-sloping relationship requires us to say something about

tastes. The simplest assumption is that individuals in either country spread their spending evenly across

the goods (as with symmetric Cobb–Douglas preferences). In this case the share of goods produced in

England becomes the share of spending devoted to goods produced in England. Labor market equilib-

rium requires full employment of workers in England and in Portugal at a relative wage ω, with English _

workers paid a fraction j of world income, which is just the wage income in each country added together: _

ωL = j(ωL + L*).

A lower English wage ω increases demand for English labor in two ways: At the intensive margin, a lower ω lowers the price of all goods England makes, so increases demand for them and thus for English workers. At the extensive margin, a lower ω increases the range of goods that England exports.

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72 Journal of Economic Perspectives

Figure 2 illustrates how a shift up in the productivity curve A( j ), meaning that England gets relatively more productive at making every good, raises England’s rela- tive wage ω and expands the share of goods it produces.

In all of the examples so far, if England and Portugal spend their incomes the same way (again, meaning identical, homothetic preferences) there is no reason for English and Portuguese to consume goods in different proportions. But a robust feature of data on trade and production is that countries tend to buy more goods from themselves. We could explain this fact in terms of the basic Ricardian model by assuming that Portuguese like wine more than the English. But it would be coin- cidental if tastes always happened to align with comparative advantage, and there is little evidence that they do.

A more plausible explanation is that moving goods between countries is costly. Another useful contribution of Dornbusch, Fischer, and Samuelson (1977) is to introduce trade costs into their Ricardian model. Specififically, they make Samuelson’s classic iceberg assumption that delivering one unit of any good from one country to the other requires shipping d units, where d ≥ 1. The specifification is consistent with a fraction of the goods getting lost, rotten, or broken in shipment, but admits many other interpretations as well.

Because of iceberg trade barriers, goods no longer cost the same in each loca- tion. Consider the case of cloth in Ricardo’s example. If the wage in England is .8, then cloth costs 80 if made in England and 90 if made in Portugal. But say that one-third of the cloth shipped from England to Portugal is ruined by saltwater in transport. Then 1.5 units of cloth need to be shipped to deliver 1 usable unit to Portugal, raising the cost of English cloth in Portugal to 120. It no longer pays for Portugal to import cloth from England rather than make it at home.

What happens to the Dornbusch, Fischer, and Samuelson (1977) model if we introduce a trade cost d to all goods? The trade cost creates a range of goods that are not traded as each country makes them more cheaply for itself. As long as d is not too big, there is still a range of goods (with j near zero) that England makes for everyone and another range (with j near one) that Portugal makes for everyone.

An important implication of the trade cost, which we exploit in our applications below, is that it introduces a relationship between any trade defificit that England runs with Portugal and its relative wage. A transfer from England to Portugal diverts spending away from the nontraded goods that England was producing for itself toward the production of those same goods in Portugal. As a consequence, the English wage falls, leading to an expansion of the range of goods that England exports and a contraction of the range that Portugal exports.

The work of Dornbusch, Fischer, and Samuelson (1977) moved the Ricardian framework far forward from being a toy example to becoming a tool that can address a variety of questions. For example, Matsuyama (2008) uses variants of the model to examine the consequences of country size, technological change, and technology transfer on the gains from trade and the distribution of income. But a limitation remains. There are still only two countries.

More Countries

It’s just as straightforward to add more countries to Ricardo’s example as more goods. Let’s add a third country, France, with labor requirements 120 in cloth and 60 in wine. Begin by rewriting Ricardo’s earlier inequality as

120 > 80 __

100 90 (England) (Portugal)

and then insert France into the chain to get:
120 > 80 > 60 .

100 90 120 (England) (Portugal) (France)

England, at one end of the chain, will produce cloth and France, at the other end, will produce wine. As before, tastes and the sizes of the labor forces in each country will determine where the chain is broken. As above, we count five types of possible outcomes. We are back to a stairway. More countries can be added, but the number of cases expands. As with two countries and many goods, finding the solution is relatively straightforward but tedious.

The Challenge: Many Goods with Many Countries

What about more goods and more countries? In this setting, chains no longer work. Jones (1961) provides an example with the following labor requirements for three countries in three goods:

America Britain Europe

Corn 10 10 10 Linen 5 7 3. Cloth 4 3 2

Two assignments—(America, Linen; Britain, Corn; Europe, Cloth) and (America, Corn; Britain, Cloth; Europe, Linen)—each satisfy Ricardo’s inequality for any two countries and any two goods looked at in isolation from the third.3 But only the

3 Graham (1948) solved for competitive equilibria in numerical examples of the Ricardian model with many countries and many goods. His generalizations from these examples were not always correct. McKenzie (1954) formalized Graham’s model and used it in his demonstration of the existence and uniqueness of a competitive equilibrium. In this journal, Weintraub (2011) provides a detailed account of McKenzie’s relatively unheralded contribution. McKenzie (1953) established the equivalence between an efficient solution and a competitive equilibrium in Graham’s model, and pointed to the inadequacy of bilateral comparisons in determining efficient specialization. The contribution of Jones (1961) is to obtain a simple characterization of efficient specialization in this model.

___

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74 Journal of Economic Perspectives

second is a possible competitive equilibrium. To see why, cross multiply Ricardo’s earlier inequality so that it appears a third way as:

120×90 > 100×80 . (incorrect ) ( correct )

assignment assignment

Note that England producing cloth and Portugal wine, the equilibrium assignment in Ricardo’s example, minimizes the product of the labor requirements for the tech- nologies used. Generalizing this result, Jones can rule out the first assignment in his example since it involves a higher value for the product of the labor requirements used (5 × 10 × 2 = 100 versus 10 × 3 × 3 = 90).4

Fun as this example is, it doesn’t provide much guidance into how to solve for the equilibrium in high-dimensional cases. For one thing, we’re still left with the problem of fifiguring out if the solution is on a tread or a riser. But now we have stair- ways running in multiple directions in ways that only M. C. Escher could diagram.

A Solution: Distributions of Worker Requirements

Again, we need a ramp. To construct one, let’s return to the Dornbusch, Fischer, and Samuelson (1977) formulation with a continuum of goods, but now allow for an arbitrary (integer) number I of countries. We must deal with unit labor require- ments for each good (one for each point on the unit interval) in each country (of which there are I ), vastly more numbers than Ricardo’s four.

To tackle the problem, let’s fifirst give up on actual numbers and, following Dornbusch, Samuelson, and Fisher (1977), label the labor requirement for good j in country i by ai( j ). With I > 2 countries and lots of goods, it doesn’t help to think about ratios of the a’s, so chains are out of the question. Instead, we will think about the a’s as the realizations of random variables drawn from a particular family of probability

4 This idea generalizes to the I-good, I-country case. To see why this rule works it helps to go back to prices and to think about finding the minimum cost source. Let’s index countries by i = 1,. . .,I and goods by j = 1,. . .,I and denote the amount of labor needed to make good j in country i as ai(j). Let wi be the wage in country i and p( j ) the world price of good j (as there are no transport costs). Let’s also number countries and goods so good j is produced by country i = j in an efficient outcome (so that we can label by j the country producing good j under the correct assignment). Perfect competition then means that p(j) = aj(j)wj (zero profits where good j is produced) and p(j) ≤ ai(j)wi for all other countries i (no profit opportunities anywhere else). Multiplying the equalities together for the correct assignment gives:

III ∏p(j) = ∏aj(j)∏wj.

j=1 j=1 j=1
Multiplying together the inequalities for any other one-to-one assignment i(j) of country i to good j gives:

Since the terms ∏ I j=1

can be true is if

j=1

p(j) and ∏ I w j=1 i(j)

j=1 j=1 j=1
= ∏ I w are the same in each, the only way both expressions

IIII
∏ p(j) ≤ ∏ [ai(j)(j)wi(j)] = ∏ ai( j )(j) ∏ wi(j) .

j=1 j II

∏ aj(j) ≤ ∏ ai(j)(j). j=1 j=1

distributions. This way of thinking about technology (the labor requirements to produce different goods in different locations) has two advantages: First, the distribu- tions themselves can be smooth, giving us our ramp. Second, we don’t have to keep track of all the individual ai( j )’s, of which there are many, but only the parameters of the distributions from which they are drawn, which can be small in number.

Before getting into the details, it’s useful to step back and articulate some principles that guide the choice of a family of distributions. First, we want to stay within the family when we move from the distribution of labor requirements to the distribution of the costs of producing goods. Second, we want to stay within the family when we consider the distribution of the price of a good in a country, which is the minimum of the cost of acquiring it across all potential source countries. Finally, we want a simple expression for the probability that a particular country is the low-cost source.

These considerations led us, in Eaton and Kortum (2002), to a family of what are called extreme-value distributions. The well-known central limit theorem states that if a large sample is taken from a well-behaved distribution, then the mean of the sample has an approximate normal distribution. Less well-known is that the highest or lowest observations in such a sample also can approach a particular distribution, called an extreme-value distribution. For example, consider the winning (fastest) times in a series of races. If each runner’s time is drawn from a particular distribu- tion, such as the lognormal, then the fastest time across a large number of races has an extreme value distribution, which, if the times are lognormal, turns out to be the type-III extreme value, or Weibull distribution.

What’s the connection between winning a race and the number of workers needed to make a product? As derived in Kortum (1997) and Eaton and Kortum (1999), if technologies for making a good are the results of inventions that occur over time, and if the output per worker delivered by an invention is drawn from the Pareto distribution, then output per worker using the most effificient (that is, winning) technology discovered to date have a type-II or Fréchet distribution.

The Ricardian language describes a technology by its worker requirement rather than by its reciprocal, output per worker. Translating our results on the Fréchet distribution above into Ricardian, the probability that the labor require- ment for producing any particular good j in country i is less than any positive number x forms a Weibull distribution, specififically:

Pr[ai(j) ≤ x] = 1 – e–(Aix)θ.

Its two parameters relate to absolute and comparative advantage. The parameter Ai captures country i’s absolute advantage: A higher value means that the labor requirement is likely to be lower for any good. Having absolute advantage vary across countries allows us to capture the fact that some countries are much more productive than others across a wide range of activities: for example, in the way Portugal is more productive than England across both goods in Ricardo’s example. A country that has accumulated more technology will have a higher Ai.

Jonathan Eaton and Samuel Kortum 75

76 Journal of Economic Perspectives

The parameter θ captures (inversely) how variable the labor requirement is, with a higher value meaning that a country’s labor requirement is typically close to its mean, weakening the force of comparative advantage. In Ricardo’s example above, suppose Portugal could make cloth with 67 workers rather than with 90. While Portugal would still be better at both goods than England, it’s no longer differentially much better at wine. As Ricardo’s inequality gets closer to equality, the scope for gains from trade decreases. Similarly, a high value of θ in our model reduces the gains from trade. Imposing a common θ across countries makes it easy for us to see how technologies around the world interact through trade.

The extreme value distribution is convenient, but how well does it reflflect reality? As described above, a way of generating this distribution is to draw worker effificien- cies repeatedly from a Pareto distribution, taking the largest. The upper tail of the distribution, representing the most effificient fifirms, itself resembles a Pareto distribu- tion. Wilfredo Pareto invented what we now call the Pareto distribution to describe how income was distributed. It turns out that the Pareto distribution, sometimes called a “power law,” describes the upper tail of a large number of magnitudes, such as city population and fifirm sales and employment. Hence the extreme value distribu- tion fifits the data quite well.

Since we now have I countries, iceberg trade costs can now vary with the pair of countries in question, so that delivering a unit of a good to country n requires shipping dni ≥ 1 units from country i (with dii = 1). These trade costs can capture a well-known regularity in data on trade, which is that the amount of trade between two countries tends to fall as the distance between them rises. This feature is known as “gravity,” and gravity models of trade build on this insight. The multi- country framework developed here will display gravity if iceberg costs between any two countries rise systematically with the distance between them. Here, although we incorporate iceberg costs, we steer away from giving them too specifific an interpreta- tion. The issue of how well iceberg costs capture reality remains subject to debate: see Anderson and van Wincoop (2004) for further discussion.

Putting all these ingredients together, the cost of producing a good j in country i and delivering it to country n is cni(j) = ai(j)wi dni, the product of the labor requirement in country i, the wage in i, and the iceberg cost of moving goods from i to n. As in Dornbusch, Fischer, and Samuelson (1977), wages and trade costs are the same for all goods produced in a country, and so cni( j ) has the same distribution as ai( j ), only with the absolute advantage parameter Ai replaced by Ani = Ai /(wi dni ). The positive effect of raw effificiency in country i (through a higher Ai) on the cost distribution in n is offset by a higher wage and a higher cost of shipping to country n.

Just as in the basic Ricardian model, perfect competition guarantees that the price pn( j ) of good j in country n is the lowest cost cni( j ) looking across all potential sources i. Unlike the simple Ricardian model with no trade costs, in the more general set-up here, which country I provides the good at lowest cost may differ across desti- nations n. We already saw such an outcome in the two-country Dornbusch, Fischer, and Samuelson (1977) model with trade costs: Each country produced a range of

goods for itself while other goods, for which differences in productivity were more extreme, were produced in only one country. While the multicountry formulation here is more complicated, the distribution of the price of a good j in country n is straightforward. It inherits the extreme value distribution from the costs cni(j) of which pn(j) is the minimum across all potential sources I, with its distribution remaining in the Weibull family.5

Aside from telling us about prices, the model can also tell us about trade between any two countries via the probability πni that a particular country i is the lowest cost source of a good in country n. This probability is lower the higher dni, the trade barrier in shipping from i to n, and the higher the wage in the source country, adjusted for absolute advantage. Since there are a continuum of goods, the probability πni is also the share of goods in country n supplied by country i. Furthermore, with symmetric Cobb–Douglas preferences, the πni’s also correspond to the fraction of country n’s spending devoted to goods bought from country i. These purchases are imports if i and n are different, but are domestic sales when i and n are the same.6 Because data on the value of trade and production are readily available to calculate trade shares, the πni’s provide a crucial link between the model and data.

Anything that lowers a country’s cost of serving a market (such as a lower tariff) means more purchases are shifted there; how much depends on θ. Remember that a larger θ means that technologies are more similar across goods from any given country. Hence a given change in costs implies a bigger shift in trade shares when θ is high, since relative costs don’t vary that much across countries.

Trade economists have long sought to measure the elasticity of trade with respect to relative costs, which are affected by such things as changes in tariffs or exchange rates. In our analysis, θ determines that elasticity. It plays an important role in all that follows. In our numerical analysis below, we use a value of θ = 4 suggested in a recent paper by Simonovska and Waugh (2011). Their recommended value is based on a careful analysis of the prices of 62 manufactured goods across 123 countries, and the estimate is in line with several earlier studies based on other evidence.

How does trade translate into welfare in this framework? The model delivers a handy expression for the real wage in country I, which is proportional to A π –1/θ.

5 In particular, the distribution of prices pn(j) emerges just by replacing Ai in the distribution of labor _

requirements with a term An, that aggregates the Ani’s from each source i: _θ I θ

_

The expression for An shows how higher efficiency, lower wages, and greater proximity of country n’s

trading partners translates into lower prices.
6 The trade share turns out to be country i’s contribution to the term An given in the previous footnote:

πni = (Ani/ An)θ. With Cobb–Douglas preferences, the ideal price index pn in country n is the geometric _

mean of the price distribution, which is simply γ/An. The constant γ is given as equation (5) in the online appendix available with this paper at ⟨http://e-jep.org⟩. We could be much more general in our specifi- cation of preferences, but for our analysis here nothing would be gained. For example, with Dixit–Stiglitz preferences, the only change is in the formula for γ, which then depends on the elasticity of substitution.

_

(An) = ∑(Ani) . i=1

Putting Ricardo to Work 77

_

i ii

78 Journal of Economic Perspectives

The absolute advantage parameter Ai captures labor productivity in the country. In

a closed economy, with πii = 1, productivity by itself determines the real wage. The

second term π –1/θ captures the gains from trade.7 A country i with a small home ii

share πii makes use (via imports) of technologies from elsewhere for a large range of goods. Without trade, of course, it would be using its own technologies to make these goods. How much a given drop in the home share in moving from autarky to trade raises welfare depends on how different the technologies embodied in imports are from the domestic technologies they replace. The smaller is θ, the bigger the differ- ence, on average, and hence the larger the gains. Hence a country without many advanced technologies itself may nevertheless have a high living standard because it specializes in the technologies in which it is most advanced and purchases the rest from abroad. Using our value of θ = 4, we can infer that a country importing 25 percent of what it consumes from abroad, hence purchasing 75 percent locally, gains about 7.5 percent in real income.

While it’s very useful to infer the gains from trade by knowing just the home share in expenditure and the parameter θ, the home share itself depends on wages around the world, which are determined by the labor market equilibrium in each country. In order to solve for wages, we need to know not only the trade costs but the labor endowment Li in each country and the trade defificit Di each country runs with the rest of the world.

In general, we can’t solve the system of labor market equilibrium conditions for wages analytically, although a computer can spit out the answers rapidly, even with several hundred countries. But with costless trade (that is, no iceberg costs), we can obtain an analytic solution. In this special case, the relative wage between two coun- tries is increasing in the ratio of their productivities (their Ai’s), with an elasticity of θ/(1 + θ). That this elasticity is below one reflflects the fact that in an open economy a country passes on some of the benefifits of its own higher productivity to others through lower export prices. In this way, even without international technology diffusion, international trade allows countries to benefifit from having trading part- ners with a high level of technology. The relative wage is decreasing in the ratio of labor endowments (the Li’s), with an elasticity of –1/(1 + θ). This elasticity is nega- tive, just as in the basic Ricardian model. A country with more workers, in order to employ them, produces more of an existing set of goods (the intensive margin), lowering their relative price. Here, in addition, the country diversififies into addi- tional goods (expanding at the extensive margin) in which its relative productivity is lower. Without trade barriers, the relative wage is independent of trade defificits, just as defificits don’t matter for wages in Dornbusch, Fischer, and Samuelson (1977) when there are no trade costs.

In a world of costless trade, we can see how countries’ endowments of labor and technology interact to determine their relative welfare. Recognizing that distance matters introduces location as a third major determinant of a country’s relative

7 Arkolakis, Costinot, and Rodríguez-Clare (2012) show how, with θ suitably reinterpreted, this result on the gains from trade generalizes to a wide class of models.

income and welfare. Proximity to large markets and to inexpensive sources of goods then becomes another important feature of a country in determining its welfare.

To get some sense of the magnitude of geography’s role in a country’s well-being let’s perform a numerical exercise with just two countries. Say that one country is large, with 99 percent of the world’s labor, and the other small, with 1 percent of the world’s labor. Let’s start by assuming free trade and labor effificiencies such that with no trade barriers the two countries have the same wage (and hence the same real wage since prices are the same). In a frictionless world with no trade barriers, the small country would spend only 1 percent of its income on goods from itself.

Now imagine introducing a trade barrier between the two countries, so that the iceberg costs are d = 2 for sending goods in either direction. In the resulting equilibrium, the small country spends just under half of its income on goods from itself (a typical amount for an actual small country). While the large country is virtu- ally unaffected by the change, the real wage in the small country falls to 38 percent of that in the large country. This decline is the result of two effects. First, to be competitive in the large country, the small country’s wage has to fall to 65 percent of the large country’s wage. Second, because goods from the large country are expen- sive to import, the price index is 70 percent higher.

With these trade barriers in place, how much of a productivity boost would we have to give the small country to bring its real wage back up to the level in the rich one? The answer is so much that under costless trade its wage would be more than double the large country’s. An implication of this example is that, by inflfluencing trade costs, geography can play as important a role in determining income differ- ences as technology.

Applying the Tool

Having shown how the Ricardian model can accommodate a complex world of many goods and many countries separated by trade barriers, we now connect it to data. We can then use it to ask many questions both about the world as it is and what it would look like under different circumstances. In this section, we investi- gate four particular questions: 1) How much do countries gain from trade, and how have these gains evolved over the last two decades? 2) How much will these gains grow if falling trade costs lead to further increases in world trade? 3) To what extent do countries benefifit from the technological improvements of their trading partners? 4) What are the costs to defificit countries of moving to balanced trade?

We fifit the model to data on 32 countries (31 actual countries and a “rest of the world” which combines all the others) as listed later in Table 3. The limit on the number of countries arises from the availability of data; adding countries adds little to computational complexity.

While any model is a simplifification, we can bring the model we have been discussing here much closer to reality with three embellishments: First, the model applies quite naturally to manufactures, the dominant component of trade for most

Jonathan Eaton and Samuel Kortum 79

80 Journal of Economic Perspectives

high-income countries. Indeed, manufactures make up 64 percent of trade in goods and services among our 31 actual countries. It is less clear how well this model applies to services or to products in which natural resources play a major role. To focus on trade in manufactures, we follow Alvarez and Lucas (2007) and divide the economy into two sectors, which we call manufacturing and services, with labor mobile between them. Among our set of countries, manufactures represent only a share α of about 0.2 of fifinal spending.

Second, while manufactures are not a large share of fifinal spending, a great deal of manufacturing output goes into the production of manufactures. Among our coun- tries, the share β of labor in manufacturing production is only about 0.3 with most of the rest manufactured intermediates. As pointed out, for example, by Krugman and Venables (1995), recognizing the importance of manufactures as inputs makes loca- tion as well as geography an important determinant of manufacturing costs. In Dekle, Eaton, and Kortum (2007), we describe in more detail how we set α and β.

Third, the textbook Ricardian model typically assumes that trade is balanced. However, we design our model to accommodate defificits both in manufacturing and in everything else. In fact, one of our exercises is to examine the consequence of shifting these defificits in order to balance each country’s current account. To fifinish putting numbers on the model we go to the OECD STAN (STructural ANalysis) Database for data on bilateral trade and production of manufactures and to the Economist Intelligence Unit for data on unilateral trade in goods and services, GDP, and the current account. Along with our values for the three parameters θ = 4, α = 0.2, and β = 0.3, these data tell us all that we need to know about the rest of parameters in order to answer our four questions. We can answer our fifirst question, about the magnitude of gains from trade, directly from data by using a relationship discussed in the previous section. The other three questions force us to consider all of the shifts in wages and prices around the world that would result from a change in trade costs, technology, or trade defificits.

We calculate counterfactuals in the following way: We shock the model by changing the relevant parameters. We denote the new level of a variable or parameter x as x ′ and

ˆ
the proportional change in it as xˆ = x ′/x. In particular, we consider changes dni in trade

ˆ
costs (keeping them at one when i = n), changes Ai in technology, or counterfactual

defificits D′ (and DM′ for manufactures). We then calculate the changes in wages wˆ and ni i

ˆ
prices pi needed to re-equilibrate the world economy. Our baseline is the world as it was

in 2009, the last year for which data are available for all of our countries.

Gains from Trade

As discussed above, we can measure the gains from trade using data on only the home share, πii. For this exercise we employ a direct measure of the home share: gross manufacturing production less gross exports, divided by gross manufacturing production less net exports.8 This statistic deserves some consideration on its own.

8 In our counterfactual simulations, we use a different measure, as in Dekle, Eaton, and Kortum (2007).

Table 2

The Home Share of Spending on Manufactures and Gains from Trade

Putting Ricardo to Work 81

Home share of spending

Implied gains from trade

Country

World GDP share (%) in 2006

Level in 2006 (%)

31.4 49.1 42.6 25.6

2.5 58.2 56.9 53.7 52.7 26.0 27.9 39.6 68.9 84.9 77.2 58.3 53.6 51.9 53.4 50.8 27.2 62.8 49.2 35.3 73.5

Change since 1996 (percentage points)

–16.2 –1.5 –14.7 –18.1 –19.6 –7.3 –10.3 –16.4 –11.6 –34.5 –10.0 9.9 –7.1 –5.6 –0.7 –7.9 –8.2 –2.5 –15.8 –10.2 –15.5 –10.2 –10.0 –20.0

Level in 2006 (%)

21.3 12.6 15.3 25.5 85.4

9.4

Change since 1996 (percentage points)

8.1 0.6 5.5

10.7 56.7 2.1 3.0 4.8 3.6 16.4 6.2 –5.7 1.7 1.1 0.1 2.3 2.6 0.9 4.7 3.4 9.0 2.7 3.4 8.6 1.9

Austria
Canada
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Mexico
New Zealand
Norway
Poland
Portugal
Slovenia
Spain
Sweden
Switzerland
United States
All others 33.62

0.66 2.60 0.29 0.56 0.03 0.42 4.60 5.94 0.54 0.23 0.03 0.46 3.80 8.88 1.94 1.94 0.22 0.68 0.69 0.41 0.08 2.51 0.81 0.80

9.9 10.9 11.3 25.1 23.7 16.7 6.4 2.8 4.4 9.4 11.0 11.6 11.0 12.0 24.3 8.1 12.5 18.9 –8.3 5.3

27.26

Source: Authors’ calculations from the OECD STAN (STructural ANalysis) Database, the Economist Intelligence Unit, and a model described in the text.
Notes: The home share is the share a country spends on domestic manufactures out of total country spending on manufactures. The last two columns calculate the implications of the level of the home share, and its changes over time, for countries’ gains from trade and how those gains have evolved. We look at the gains from trade only in manufactures.

Table 2 reports the home share in 2006 for the 25 countries with data on gross manufacturing production. The mean value of the home share is just under 50 percent. In a world of frictionless trade (all dni = 1), there is no reason for a country to spend a larger share of its income on its own goods than any other country. A country’s home share, in that case, would correspond to its share in world output. As Table 2 makes clear, for each of these countries the home share is many times larger than the country’s share in world GDP: three times higher for the United States, ten times for Germany, 50 times for Denmark, and 100 times for Greece. Such multiples illustrate the extent to which trade barriers continue to chop up world markets. Even though countries buy much more of their manufactures

82 Journal of Economic Perspectives

from home than a world of costless trade would predict, in line with theory large countries tend to buy much more from themselves than small countries: The overall correlation between home share and share in GDP is close to 0.5 in 2006.

The third column of Table 2 shows that the home share declined substantially between 1996 and 2006, reflflecting globalization of manufactures production over the period. (Only Ireland bucked this trend.) The last two columns calculate the implications of the level of the home share, and its changes over time, for countries’ gains from trade and how those gains have evolved. In making these calculations, our fifirst two embellishments to the model require two modififications. Since we look at the gains from trade only in manufactures, the fact that manufactures are only 20 percent of fifinal spending limits the benefifit. But since manufactures are a major input into the production of manufactures, there are large indirect benefifits of trade in lowering input costs. Putting the two together, the elasticity that trans- lates a smaller home share into larger gains from trade is no longer 1/θ but rather α/(βθ) = 1/6 . Thus, we calculate the gains from trade for country i at date t as

Gt = 100[(πt )–1/6 – 1] i ii

where πt is country i’s home share at date t. ii

Clearly, gains from trade are substantial, particularly for small countries: for example over 25 percent of income for Denmark, Estonia, and Hungary. For the largest countries, Japan and the United States, gains from trade amounted to 2–3 percent of GDP 20 years ago. But those gains are now over 50 percent higher.

Benefits of Further Globalization

Our measure of the gains from trade compares where we are now with no trade.

We can also consider the gains that would accrue in the future if globalization, driven

by lower trade costs, continues. Our counterfactual experiment considers a uniform ˆ

proportional 25 percent drop in the costs of trade, (dni = 0.75 for all foreign-country pairs), a magnitude chosen so that world trade in manufactures approximately doubles relative to world GDP. As a point of reference, world trade in goods and services did double relative to world GDP over the past 30 years.

Figure 3 plots the results against each countries’ share of world GDP. The gains, measured by the increase in the real wage, are substantial, with a median gain of about 10 percent. The gains are also very heterogeneous, with small coun- tries typically gaining proportionately much more than large countries. Given their size, isolated countries, such as Iceland, New Zealand, and Greece, gain much less than countries proximate to many others, such as Belgium–Luxembourg, the Netherlands, and Germany.

Benefits of Technological Improvements

As the basic Ricardian model illustrates, trade provides a conduit through which foreign countries benefifit from an improvement in a country’s ability to produce a good. We can measure the strength of this mechanism by considering the effects

Figure 3

Real Wage Response to a Decrease in Trade Barriers

Jonathan Eaton and Samuel Kortum 83

25

20

15

10

5

0

Estonia

I c eland

Austria Poland

Slovenia

Slovak Republic Hungary

Czech Republic

Belgium-Luxembourg

Net herlands

S wit z er land Mexico

Port ugal
DenmSwaerdken Korea Canada

New Zealand Norway

I rFei lna lna dn d Greece

T u r k e y
Aust ralia

Germany F r a n c e

ROW

United States

.5

.001 .01 Share of world GDP

China Japan

.1

Source: Authors’ calculations using data from the OECD STAN (STructural Analysis) Database and the Economist Intelligence Unit and a model described in the text.
Notes: We consider a uniform proportional 25 percent drop in the costs of trade, a magnitude chosen so that world trade in manufactures approximately doubles relative to world GDP. The figure plots the counterfactual change in real wage against each countries’ share of world GDP.

on welfare around the world from a shift in the distribution of technologies in a particular country i (as reflflected in the parameter Ai). Our particular experiment

ˆ
makes the United States 10 percent more productive, so that AUS = 1.1.

The world economy responds in two important ways: First, the U.S. wage rises by about 30 percent relative to other countries’ wages. Second, the U.S. real wage (in terms of goods and services) rises by about 6 percent, while real wages in other countries increase by only a small amount, if at all.

The effects of geography are apparent as the greatest foreign benefificiaries are Canada and Mexico, which experience a real wage gain one-tenth that in the United States. A few countries, if they are initially running a trade surplus in manufactures, experience a small real wage decline. (If we fifirst eliminate all trade imbalances and then increase U.S. technology, all foreign countries experience a real wage gain.)

Overall, the increase in U.S. technology raises the GDP-weighted real wage around the world by 1.6 percent, with 8 percent of this gain experienced outside the United States. Foreign countries gain both due to the lower prices of fifinal goods

Spain

I t aly

Counterfactual change (%) in real wage

84 Journal of Economic Perspectives

and of intermediate inputs relative to wages. Performing the same experiment, but with China in place of the United States, yields similar results. Better technology in China raises the world’s average real wage by 0.6 percent, with 10 percent of this gain experienced outside China. These results reflflect the fact that the improvement in technology in China adds to a smaller base, yet China’s greater export orienta- tion means the overall benefifits are spread somewhat more to foreign destinations.9

Consequences of Eliminating Current Account Imbalances

Our model, like Dornbusch, Fischer, and Samuelson (1977) with trade costs, implies that transfers between countries have implications for relative wages. Our fifinal counterfactual, following Dekle, Eaton, and Kortum (2007), considers exoge- nous shifts in manufacturing trade defificits that would simultaneously balance every country’s current account, holding fifixed any defificits outside of manufacturing. We also hold trade costs and technologies fifixed. Table 3 shows the results. To undo the huge 2009 U.S. defificit, the wage in most countries rises relative to the U.S. wage by over 13 percent in China and 14 percent in Germany since the large surpluses of these two must decline. The small European defificit countries of Greece and Portugal are the dramatic exceptions, declining 21 and 12 percent relative to the United States.

Figure 4 shows that initial current account balances (as a share of GDP), determining the required adjustment of trade imbalances, go a long way toward explaining the direction (positive) and magnitude of wage adjustment. A question is why Iceland, Portugal, and Greece experience very different wage responses even though their current account defificit to GDP ratios were similar in 2009. It turns out that another important factor in explaining the magnitude of the change in wages is the initial size of the manufacturing sector in a country’s GDP. This share is lowest in Greece, worsening the wage decline necessary to bring about current account balance via an increase in net exports of manufactures.

The consequences for the real wage are much more muted than those for the relative wage. Even Greece, the most negatively affected, suffers less than a 4 percent decline. The United States, with its large current account defificit, would see its real wage decline by only half of 1 percent. The reason is a combination of large home shares in manufacturing spending and small shares of manufactures in overall fifinal demand. For goods and services produced at home, prices move in line with wages. The change in the relative wage acts only through import prices.

More dramatic are the changes in the share of manufacturing in GDP required to rebalance current accounts. This share rises by over 10 percentage points in Iceland and by nearly as much in Greece and Portugal. It falls by over 4 percentage

9 Our results on the benefits of foreign technology are much smaller than some of the results in Eaton and Kortum (2002). The main reason is in that paper the mobile-labor case held wages fixed so that foreign countries did not suffer a decline in their terms of trade. Our results here, in that respect, are more in line with the immobile-labor case of Eaton and Kortum (2002). See Fieler (2011) and Hsieh and Ossa (2011) for a related analysis of the benefits to foreign countries of China’s technology gains. Hsieh and Ossa’s analysis is retrospective rather than counterfactual.

Table 3

Consequences of Eliminating Current Account Imbalances

Data

Current account balance (% GDP)

–5.0 2.4 0.6 –3.4 4.7 –3.7 3.1 4.2 2.0 –2.0 5.2 –11.5 –0.1 –12.2 –3.4 –2.5 2.4 3.5 –1.2 4.4 –3.6 11.6 –4.4 –11.4 –3.7 –1.7 –5.6 6.7 7.5 –2.7 –3.2 0.9

Counterfactuals Change in

Change in mfg share (percentage points)

3.5 –1.9 –0.5 2.6 –4.1 3.3 –2.4 –2.6 –1.7 1.6 –4.4 8.7 0.0 11.4 3.2 2.1 –2.0 –3.3 0.9 –3.7 2.9 –4.8 3.8 9.7 3.3 1.4 4.7 –5.2 –5.7 2.2 2.6 –0.6

GDP

(US$ Country billions)

Australia 973.7 Austria 382.0 Belgium-Luxembourg 525.2

Manufactures trade balance (% GDP)

–8.1 1.2 7.4 –4.7 10.6 6.4 1.3 –3.9 5.6 –1.2 8.6 –12.3 7.7 3.2 27.9 2.9 3.4 16.1 –2.9 7.5 –2.2 –6.0 0.1 –7.6 6.5 –1.4 –2.4 4.8 4.6 –2.7 –2.6 –5.4

Relative wage (%)

–4.6 11.4 8.3 –1.0 13.4 3.1 13.3 17.5 11.0 4.3 14.4 –20.7 7.4 –6.1 4.8 4.1 12.7 11.3 2.7 13.6 1.1 41.9 1.7 –11.9 3.3 5.0 –2.0 18.6 18.9 2.9 0.0 9.4

Real wage (%)

–1.4 0.3 0.0 –0.7 0.3 –0.9 0.4 1.5 0.1 –0.4 0.7 –3.7 –0.3 –2.1 –0.2 –0.4 0.2 0.2 –0.4 0.7 –0.6 3.9 –1.0 –2.6 –0.9 –0.5 –1.0 1.0 1.3 –0.6 –0.5 0.2

Putting Ricardo to Work 85

Canada
China
Czech Republic
Denmark
Estonia
Finland
France
Germany
Greece
Hungary
Iceland
Ireland
Italy
Japan
Korea
Mexico
Netherlands
New Zealand
Norway
Poland
Portugal
Slovak Republic
Slovenia
Spain
Sweden 403.5 Switzerland 492.3 Turkey 613.8 United States 13939.0 ROW 13961.0

1337.6 5050.5 190.2 308.9 19.3 241.3 2632.7 3308.3 326.4 128.8 12.1 223.8 2116.7 5031.6 834.1 879.2 796.2 116.2 370.7 430.5 234.9 87.8 49.2 1468.4

Source: Authors’ calculations from the OECD STAN (STructural ANalysis) Database, the Economist Intelligence Unit, and a model described in the text.
Notes: We consider the effects of exogenous shifts in manufacturing trade deficits that would simultaneously balance every country’s current account, holding fixed any deficits outside of manufacturing. Data are for 2009. “Relative wage” is the wage relative to the United States. “ROW” is “rest of world.”

points in the large, surplus countries (China and Germany) and by 5 percentage points in the smaller ones (Norway, Sweden, and Switzerland). These extreme predictions about the impact on the size of the manufacturing sector follow from our Ricardian assumption that labor can flflow seamlessly between manufacturing

86 Journal of Economic Perspectives

Figure 4

Wage Response to Eliminating Current Account Imbalances

40

20

0

–20

–40

Source: Authors’ calculations using data from the OECD STAN (STructural Analysis) Database and the Economist Intelligence Unit and a model described in the text.
Notes: We consider the effects of exogenous shifts in manufacturing trade deficits that would simultaneously balance every country’s current account, holding fixed any deficits outside of manufacturing, as in Table 3. The figure plots the counterfactual change in wage relative to the United States against the initial current account balance as a share of GDP. “ROW” is “rest of world.”

and other activities. In Dekle, Eaton, and Kortum (2008), we introduce rigidities and examine their effect.

Extending and Improving the Tool

Much recent work has extended this new old Ricardian trade theory in various ways, sometimes combining elements of it with other theories to address new ques- tions. Here we brieflfly discuss a few of these contributions.

The fifield of international trade has traditionally used industry as its unit of analysis, a natural choice given the heterogeneity of industries and the fact that most trade policy is implemented at the industry level. In moving from a small number of goods, with labor requirements specifified in a table, to a continuum of goods, with labor requirements only described probabilistically, we lose track of this industry dimension. A number of papers have brought industries back into the analysis,

Iceland Portugal

Greece

Spain Canada Australia

IrelanFdSrlaonvceenia Italy

CSlzoevcTahkuRrRkepMyubebxlliico Poland

New Zealand United States

ROW Belgium-Luxembourg

Hungary

Estonia SweSdweitnzerland

Germany DenmNaCerhtkhineralands

Japan FiAnulasntKrdioarea

Norway

–15 –10 –5 0 5 10 15 Current account (as % of GDP)

Counterfactual change (%) in wage (realtive to U.S. wage)

including Chor (2010) and Shikher (2011). The idea is that each industry k consists of a continuum of differentiated goods and each country i has an absolute advantage parameter Aik in each industry. Costinot, Donaldson, and Komunjer (forthcoming) use this approach to revisit the connection between trade and industry-level produc- tivity implied by Ricardian theory, avoiding ambiguities that plagued the early analysis of MacDougall (1951, 1952). Incorporating input-output linkages between industries, Caliendo and Parro (2010) use the model to explore the welfare gains from tariff reductions under the North American Free Trade Agreement (NAFTA).

While the basic Ricardian trade model treats labor as the only primary factor, many applications require incorporating other factors of production. In his monu- mental study measuring the gains from rail transport in nineteenth-century India, Donaldson (2010) applies this Ricardian model, replacing labor with land as the primary factor, with land rents appearing in place of wages. Incorporating several factors, and multiple industries, leads to a hybrid Ricardian–Heckscher-Ohlin model, as in Shikher (2011), used by Parro (2012) to account for the rise of the skill premium in developing and developed countries. Burstein and Vogel (2010) interweave these two theories at a deeper level, introducing a correlation between labor requirements and skill intensity at the level of the individual goods on the continuum.

Our applications above were limited to trade in manufactures among OECD countries. Extending the analysis more broadly, the theory has to confront the fact that low-income countries trade less than high-income ones, even taking into account their economic size and location. Waugh (2010) proposes a model in which barriers to exporting are the culprit, consistent with evidence on prices. Fieler (2011) pursues another explanation, introducing different classes of goods with different income elasticities of demand and with different degrees of technological hetero- geneity (in the notation in the model we have presented here, different θ’s). She fifinds that poor countries have a comparative advantage in goods that are both more income inelastic and more technologically homogeneous (that is, with a higher θ). Tombe (2011) fifinds that barriers to food trade are higher than for manufactures, particularly in poor countries. He also departs from the standard Ricardian tradition by introducing barriers to domestic labor mobility between rural areas (where food is produced) and cities (which produce manufactures and services).

In keeping with Ricardo’s original analysis, the models discussed so far mostly assume perfect competition. Breaking with that tradition, in Bernard, Eaton, Jensen, and Kortum (2003), we incorporate Bertrand competition, allowing the theory to make contact with data on individual producers. This extension also opens up the possibility of addressing pricing puzzles in international economics, as explored in Atkeson and Burstein (2008). While the basic model with Bertrand competition yields a distribution of price markups that is invariant to trade, de Blas and Russ (2010) develop a variant of the model that breaks that result. Holmes, Hsu, and Lee (2012) investigate a related model that yields new results on the gains from trade.

Having introduced imperfect competition, in Eaton and Kortum (2001) we show that innovation and growth fifit seamlessly into the theory. Incorporating technology diffusion and multinational production has turned out to be more challenging. The

Jonathan Eaton and Samuel Kortum 87

88 Journal of Economic Perspectives

problem is that the theory can easily deliver myriad treads and risers again when groups of countries have access to the same technologies for producing some goods. Recent work by Ramondo and Rodríguez-Clare (2009) has begun to map a way through these diffificulties. Another promising approach, representing a greater departure from the basic theory, is pursued by Alvarez, Buera, and Lucas (2011).

In short, the framework we present in this paper is tractable, versatile, and amenable to empirical analysis. It is keeping Ricardo busy.

■ We would like to thank Daisuke Fuji, Brodie Olsen, and Sebastian Sotelo for excellent research assistance.