Transportation Cost Heterogeneity and the

Patterns of Commodity Trade Flows

Michael Ostrovsky∗

Harvard University

April 7, 2005

Preliminary and incomplete

Abstract

Conventional approaches to modeling international commodity trade flows

assume either perfect substitutability of goods from different countries, which

results in unrealistically sharp predictions, or product differentiation by the

country of origin, which is plausible for some goods, but is hard to justify for

many fungible commodities. This paper introduces an alternative model, which

relies on heterogeneity in bilateral transportation costs between the agents who

compose countries or regions. The model is applied to data on international

trade flows in the global steel supply chain, which includes iron ore suppli-

ers, iron and steel scrap suppliers, steel producers, and steel consumers. The

heterogeneity-based approach is shown to fit the data better than commonly

used Spatial Price Equilibrium and Applied Partial Equilibrium models.

∗Email address: mostrovsky@hbs.edu. I thank Drew Fudenberg, Elhanan Helpman, Bengt Holm-strom, Miklos Koren, Marc Melitz, Ariel Pakes, Parag Pathak, Al Roth, and Michael Schwarz forhelpful comments and suggestions.

1

1 Introduction

This paper introduces a new model of international commodity trade flows, based

on the heterogeneity of bilateral transportation costs. Many recent policy debates

involve economic analysis based on various models of multi-regional trade flows. The

list of all such studies is extremely long, so I will mention just a few typical examples.

Francois and Baughman (2001) use a computable general equilibrium model to predict

the effect of proposed steel tariffs in the U.S. (see also Hausman, 2002, for a critique

of their analysis). Baughman (2004) uses a partial equilibrium model to estimate the

effect of shrimp tariffs. Anania (2001a), Lee, McCarl, Schneider and Chen (2004),

and Ruijs, Schweigman, Lutz, and Sirpe (2000) use spatial equilibrium models to

assess the implications of the 1994 GATT “Agreement on agriculture” on wheat

consumption, production, and trade in the EU; to examine the effects of the efforts

to reduce greenhouse gas emissions on food production and trade; and to study the

impact of transportation costs on cereal trade in Burkina Faso, respectively. See

also Hertel (1997, 1999) and Anania (2001b) for surveys of parts of the vast applied

literature.

The early empirical papers studying multi-regional trade flows were based on the

Enke-Samuelson Spatial Price Equilibrium model (SPE) or its analogues (Enke, 1951;

Samuelson, 1952; Fox, 1953; Henderson, 1955, 1956). SPE-based models assume that

commodities produced in different regions are perfect substitutes for one another,

that each region has classical demand and supply curves for the commodities, and

that there are bilateral transportation costs between pairs of regions. Spatial Price

Equilibrium is a set of region-specific prices and quantities produced, consumed, and

traded, such that all markets clear and there is no arbitrage. This approach, while

relatively easy to implement, has an important shortcoming. The model makes very

2

sharp predictions about trade flows: many importers buy the goods from only one

country—the one for which the sum of production and transportation costs is the

lowest—and similarly, many exporters sell the goods to only one country (more pre-

cisely, with one traded commodity, the total number of positive trade flows in a matrix

with n exporters and n importers is less than 2n). The actual trade flows for most

goods do not exhibit such sharp patterns. As a result, many subsequent papers (in

particular, those in the Applied General or Partial Equilibrium tradition) introduce

imperfect substitutability by making the assumption that goods are differentiated by

the region of origin and that the elasticity of substitution between the goods from any

two regions is constant (Armington, 1969). This assumption makes intuitive sense for

some goods, e.g., wine and cheese, but not for fungible commodities, such as coal and

oil. Empirical evidence supports this intuition: for reasonable values of the elasticity

of substitution parameter, Armington-based models predict substantial positive trade

flows in a given commodity for any pair of regions, while trade matrices for fungible

goods contain many empty cells.

After reviewing the standard approaches to modeling trade flows, and present-

ing some empirical evidence that they cannot adequately explain trade flow data for

various commodities, I propose an alternative way of introducing imperfect substi-

tutability, based on the following intuition. Consider a particular commodity. Each

country consists of small agents who can supply one unit of this commodity at var-

ious reservation prices and of small agents who want to purchase one unit of this

commodity, also at various reservation prices. Aggregate demand and supply curves

for the countries approximate classical demand and supply curves; the smaller the

unit of discretization (i.e., the amount of good supplied or demanded by each agent),

the closer the approximation. There is also an average bilateral transportation cost

associated with each pair of countries. The actual transportation cost between a pair

3

of agents is equal to the average transportation cost between their countries plus

a pair-specific random shock—this shock can represent a variety of different things,

from a common language or history of previous cooperation to idiosyncratic demand

preferences. The prediction of the model is a chain stable network (Ostrovsky, 2005).

When there are several chain stable networks, the model gives a range of predictions,

bounded by upstream- and downstream-optimal chain stable networks.

I apply this theory to data on international trade flows in the global steel supply

chain, which includes iron ore suppliers, iron and steel scrap suppliers, steel producers,

and steel consumers. The theory fits the data better than models based on either

Spatial Price Equilibrium (SPE) or Applied Partial Equilibrium with the Armington

assumption (APE). The SPE model predicts too few positive trade flows. The APE

model makes completely unrealistic predictions even for a very high value of the

elasticity of substitution, σ = 25: most of the trade flows that are equal to zero in

the actual data are predicted to be positive and large. Even for an endogenously

calibrated value of σ (σ = 365, chosen to minimize the sum of squared differences

between the actual and predicted trade flows), the fit of the APE model is worse than

the fit of the heterogeneity-based model with an endogenously calibrated standard

deviation of bilateral transportation costs. Moreover, unlike σ = 365, the estimate

of the standard deviation makes intuitive sense: κ = .123, i.e., 12.3% of the average

transportation cost.

The rest of this paper is organized as follows. Section 2 reviews the existing

approaches to modeling commodity trade flows, discusses their shortcomings, and

introduces a new approach, based on the heterogeneity of bilateral transportation

costs. Section 3 illustrates the approaches using data on trade flows in the global

steel supply chain and shows that the heterogeneity-based model fits the data best.

Section 4 concludes.

4

2 Commodity Trade Flows: Modeling Approaches

There are two major traditions in the empirical literature on commodity trade flows.

The first one goes back to papers by Enke (1951) and Samuelson (1952) on Spa-

tial Price Equilibrium (SPE). In the original specification, world trade in a single

commodity is considered. The primitives of the model are demand and supply curves

for the commodity in each country and bilateral transportation costs between coun-

tries. Spatial Price Equilibrium is a set of bilateral trade flows, quantities produced

and consumed in each country, and country-specific prices, such that markets clear

and a “no arbitrage” condition holds: for any pair of countries that trade, the dif-

ference between the price in the importing country and the price in the exporting

country is equal to the transportation cost, and for any pair of countries that do

not trade, that difference is at most as high as the transportation cost. Enke (1951)

describes an analog electric circuit that determines equilibrium prices and quantities

in this setting. Samuelson (1952) provides a computational algorithm for finding an

equilibrium by showing that it is equivalent to solving a certain maximization prob-

lem. Fox (1953) presents the first empirical application of this approach, estimating

an SPE model of the livestock-feed industry in the United States. Takayama and

Judge (1971) provide a textbook treatment of the approach and describe numerous

extensions and generalizations, while Judge and Takayama (1973) present a number

of empirical applications. More recently, economists have developed several global

spatial price equilibrium models, such as the World Dairy Markets Model (Cox et al.,

1999) and the Global Forest Products Model (Buongiorno et al., 2003).

A major shortcoming of the SPE model is that, due to the assumption of perfect

substitutability, it makes extremely sharp predictions about trade flows, and these

predictions are not supported by the data. More precisely, spatial equilibrium condi-

5

tions imply that once total consumption and production quantities in each country

are determined, trade flows are such that the total cost of transportation is min-

imized. This, in turn, implies that, generically, if country A exports the good to

countries C and D, country B cannot also export the good to both C and D. If all

four of these flows were positive, there would exist a reallocation of trade flows such

that the total transportation cost would decrease while countries’ total import and

export quantities would remain unchanged. Similarly, if country A exports a good

to country C, then C cannot also export the good to A. More generally, the total

number of positive trade flows between n exporters and n importers has to be less

than 2n (Samuelson, 1952). Tables 1 and 2 present data on trade flows for a variety

of goods, using the 4-digit Standard International Trade Classification (SITC): wine,

cheese, soybeans, live cows, anthracite, natural gas, and iron ore. It is clear that the

data do not support these predictions even for fungible commodities. For each com-

modity, there are many pairs of countries exporting a certain good to each other, and

many pairs of exporters selling substantial amounts to several common importers:

e.g., Mexico and the United States sell more than $100 million worth of live cows to

each other (Table 2, Panel B); both Australia and Indonesia sell hundreds of millions

of dollars worth of anthracite to Japan, South Korea, and Taiwan (Table 2, Panel

C); both Norway and the Netherlands sell large volumes of natural gas to Germany,

France, and Belgium (Table 2, Panel D); and so on.

Because of this shortcoming of the SPE model, much of the literature on interna-

tional and inter-regional trade flows uses an alternative specification, introduced by

Armington (1969). In this specification, goods are differentiated by the country of

origin, and consumers have Constant Elasticity of Substitution utility functions (or

utility functions with similar properties) over those goods. The model is solved by

finding a set of prices such that excess demand for all goods is equal to zero. The

6

methodology for finding equilibrium prices goes back to Scarf’s (1967) work on the

computation of general equilibrium prices and even further to Irving Fisher’s me-

chanical and hydraulic devices designed for the same purpose (Scarf, 1967; Brainard

and Scarf, 2000), although in various special cases equilibrium prices may be found

by simpler methods. Papers on trade flows that follow this approach are a part of

the broader Applied Partial and General Equilibrium tradition, which is covered in

numerous textbooks and surveys, including Scarf and Shoven (1984), Shoven and

Whalley (1992), Francois and Shiells (1994), Francois and Reinert (1997), Ginsburgh

and Keyzer (1997), Bowen, Hollander, and Viaene (1998), and Srinivasan and Whal-

ley (2002).

The Armington assumption of differentiation by the country of origin is plausible

for goods such as wine and cheese, but is hard to justify for fungible commodities

such as coal or natural gas. The assumption also implies that, unless the elasticity

of substitution is much higher than what is usually considered in the literature, there

will be a positive trade flow between every exporting country and every importing

country, which also seems much less plausible for fungible commodities than for goods

that are truly differentiated. The data support this intuition. Table 1 shows trade

flows between ten largest exporters and ten largest importers of wine and cheese in

1997. Every single cell in these matrices contains a positive number (except for the

ones corresponding to flows from a country to itself, which are not reported in the

international trade data, but are of course positive). This evidence is consistent with

the intuition that wine and cheese may be differentiated by the country of origin.

Table 2 shows contrasting evidence for five commodities: soybeans, live cows, high-

grade coal (anthracite), natural gas, and iron ore. Over 40% of the cells are empty,

and the patterns of trade suggest that their main determinants are not as much

the countries of origin as the distances between trading partners (of course, there

7

may also be other considerations, e.g., seasonality in the market for soybeans). For

example, in the market for live cows, virtually all imports to the U.S. come from

Mexico and Canada, virtually all imports to European countries come from other

European countries, and virtually all imports to Indonesia and the Philippines come

from Australia.1 It is possible to match these qualitative features of the empirical

trade flows in an Armington-based model, as I will show below; however, it requires an

extremely high value of the elasticity of substitution, which becomes hard to interpret

or estimate. It may also be possible to use a different functional form for the utility

function, so that marginal utilities are bounded; however, there are no papers that

actually use such functional forms, and such models would still make a qualitative

prediction that seems counterintuitive for fungible goods—the prediction that the

buyer’s relative value for a marginal unit of commodity X from country A vs. his

value for a marginal unit of the same commodity from country B depends in a very

particular way on what fraction of good X that the buyer already owns came from

country A and what fraction came from country B.

Even though the SPE- and Armington-based models have trouble explaining them,

the numbers in Table 2 are not particularly surprising. For example, the fact that

both Norway and the Netherlands ship substantial amounts of natural gas to both

Germany and France can be explained by the following simple intuition. The aver-

age cost of shipping gas from the Netherlands to France is close to the average cost

of shipping gas from the Netherlands to Germany. Similarly, shipping costs from

Norway to Germany and from Norway to France are close to each other. However,

individual exporters and importers may be located in different parts of the countries,

or some of them may speak a common language with each other, or have better con-

1Note that this also makes the data inconsistent with another approach to modeling trade flows:country-specific (rather than country-pair specific) trade costs.

8

tacts in a particular country, etc.—there can be plenty of reasons why transportation

cost between a particular firm in the Netherlands and a particular firm in France

may be somewhat different from the average transportation cost between firms in

these countries.2 However, these differences are not large enough to justify shipping

natural gas from either country to Japan, which gets its imports from closer sources:

Indonesia, Malaysia, Saudi Arabia, and the United Arab Emirates. Similar intuition

explains cross-hauling of live cows between Mexico and the US: the border between

the countries is long, and for some Mexican consumers who live close to it, it is easier

to get cows from a nearby source in the US, while for some American consumers who

live close to a different part of the border, it is easier to get cows from Mexico.

The theory of matching in two-sided markets and vertical networks makes it pos-

sible to formalize this intuition, as follows. In the model, each country consists of a

large number of small agents, each interested in maximizing its own welfare. There are

constant per-unit shipping costs between pairs of countries. For each pair of agents,

the actual trading cost is equal to the shipping cost between their countries plus an

independent random shock ε ∼ N(0, κ2), where κ is an exogenous parameter. In gen-

eral, κ can be different for different pairs of agents or countries, the distributions can

have different shapes, and shocks can be correlated for some pairs of agents.3 After

setting up such a market and drawing random shocks, the T -algorithm of Ostrovsky

(2005) is used to find the upstream- and downstream-optimal chain stable networks,

which provide the bounds for the possible outcomes in this market, i.e., chain stable

networks.

2Halpern and Koren (2004) discuss various sources of such shocks and present direct evidencethat their magnitudes can be large.

3In particular, if κ is distributed according to a type I extreme value distribution, shocks are“buying agent–selling country”- rather than “buying agent–selling agent”-specific, and demand andsupply functions are linear or exponential, then in the limit, as the units of discretization of pricesand quantities go to zero, the model converges to an analytically tractable problem.

9

3 Modeling the Global Steel Supply Chain

In this section, I illustrate the above modeling approaches using data on the global

steel supply chain. Figure 1 presents a schematic description of the chain. There are

four types of agents: consumers of steel, producers of steel, suppliers of iron ore, and

suppliers of scrap. Scrap and iron ore are substitutable inputs used by steel producers

to make primary steel goods (bars, rods, sheets, plates, etc.), which are then shipped

to steel consumers, to be used in construction or production of final goods, such as

cars and appliances. The world is divided into 10 regions, following the classification

of the International Iron and Steel Institute (IISI, 2002): the European Union (15),

Other Europe, former USSR, NAFTA, Central and South America, Africa and the

Middle East, China, Other Asia, and Oceania. All regions have all four types of

agents, except for Japan, which does not have any suppliers of iron ore.

Table 3 presents data on the flows of iron ore (Panel A), scrap (Panel B), and

steel (Panel C) in year 2000, in millions of tons. The data is from the reports of

the International Iron and Steel Institute (IISI, 2001, 2002) and the PC-TAS version

of the UN Comtrade database (UNCTAD, 2000). For all three goods, much of the

volume is purchased in the same region as it was produced, but inter-regional trade

flows are very large as well. Mæstad (2003) estimates that “the steel industry is

responsible for about 20% of world seaborne trade and close to 40% of the dry bulk

market.”

I will now evaluate the alternative models of trade flows based on how well their

predictions fit Table 3. I start with the SPE model, describe the Armington-based

approach next, and conclude with the model based on transportation cost hetero-

geneity.

10

3.1 Spatial Price Equilibrium

The basic ingredients required to set up an SPE model are demand and supply func-

tions for the commodities in all regions and bilateral transportation costs. I estimate

them as follows.

Demand for steel in each region i is equal to Qconsi = Kcons

i (P steeli )σcons

, where P steeli

is the lowest price of steel available to consumers in region i, σcons is the elasticity of

demand, assumed to be the same for all regions, and Kconsi is a scale parameter.

Supply of iron ore in each region i is equal to Qorei = Kore

i (P orei )σore

, where P orei

is the highest price of iron ore available to producers in region i, σore is the elasticity

of supply, assumed to be the same for all regions, and Korei is a scale parameter. The

supply of scrap is parameterized analogously.

The structure of steel production is somewhat more complicated. To make steel,

a producer needs to use one of two primary inputs: iron ore or scrap. Scrap quality

varies substantially. Home and prompt industrial scrap, generated through edge

trimming and rejects by steel mills and manufacturers, is virtually 100% iron. In

contrast, obsolete scrap, obtained from iron-bearing items such as old cars, appliances,

demolished buildings, etc., contains various impurities, even though to some extent,

shredded steel can be separated from other materials by magnets.4 Unfortunately, it

is virtually impossible to find data on the variation of scrap quality across countries,

and so I assume that for all scrap, its iron content is 95%, meaning that one ton of

scrap can be converted into 0.95 tons of steel. The data on the iron content of ore is

more readily available: it is close to 60% for all regions except China, where the iron

content of ore is 28% (IISI, 2002). Producing steel from scrap is much cheaper than

producing it from iron ore, and I assume that the difference is constant, i.e., for any

4See, e.g., entries for “Scrap” and “Shredded Scrap” in the American Iron and Steel Institute’sSteel Glossary at http://www.steel.org/learning/glossary/s.htm.

11

producer, for any quantity q, if the marginal cost of converting scrap into one ton of

steel is equal to x, then the marginal cost of converting iron ore into one ton of steel is

equal to x+ scrap premium. I estimate scrap premium as the average world import

price of one unit of scrap (i.e., 1/.95 tons of scrap) minus the average import price

of one unit of iron ore (i.e., 1/.6 or 1/.28 tons of iron ore), which is equal to $119.56

per unit.5 Each region’s cost of converting inputs into steel has a constant elasticity,

i.e., Qprodi = Kprod

i (P steeli − P input

i )σprod, where σprod is the elasticity of production,

assumed to be the same for all regions, P steeli is the highest steel price available to

producers in region i, P inputi is the lowest per-unit input price6 available to producers

in region i, and Kprodi is a scale parameter.

I take elasticities of supply, demand, and production from Mæstad (2003): σore =

1, σscrap = 0.5, σprod = 0.9, and σcons = −0.3. For each region i, scale parameters

Ki are estimated by plugging in the actual quantities produced or consumed in this

region, the elasticities, and the average import and export prices for that region7 into

the demand and supply curves specified above, and then solving for Ki.

The final ingredient required to set up the model is the matrix of bilateral trade

costs. Direct measures of these costs are notoriously hard to get, and so I use the

following standard approach to estimating them (Radelet and Sachs, 1998; Hummels,

1999; Anderson and van Wincoop, 2004). Each trade flow is recorded twice in the

UN Comtrade database: once from the point of view of the exporter, and once from

the point of view of the importer. Exporters report the values of the goods they sell

on free-on-board (f.o.b.) basis, while importers report them on cost-insurance-freight

(c.i.f.) basis. The difference can be viewed as the cost of trade.

5The price data is from the UN Comtrade database for the year 2000.6That is, P scrap

i /.95 or P orei /(conversion factor)+ scrap premium, where conversion factor is

equal to .28 for Chinese iron ore and .6 for all other iron ore.7Prices and quantities are for the year 2000, based on the data from the UN Comtrade database

and the International Iron and Steel Institute reports.

12

For many pairs of regions, reported trade flows are zero, and so I need to take an

additional step to construct the matrix of trade costs. For each of three commodities,

I take the available differences between c.i.f. and f.o.b. prices, and regress them on

great circle distances between the capitals of the largest steel-producing countries in

the corresponding regions.8 I then plug bilateral distances back into the estimated

regressions, to get the costs of transportation for each commodity and each pair of

regions.

Next, I find equilibrium trade flows, reported in Table 4. The flows are qualita-

tively reasonable, but, as expected, there are too few positive trade flows compared

to the actual data in Table 3.

3.2 Applied Partial Equilibrium with Armington Substitutes

The Armington-based model is very similar to the SPE-based model, with one excep-

tion. Consumers’ and producers’ elasticities of substitution in the Armington-based

model are finite. This change is incorporated as follows. Consider the SPE demand

function Q = KP σcons. The corresponding utility function is given (up to a constant)

by

U ′(Q) =

(Q

K

) 1σcons

,

where Q =∑n

j=1 Qj, and Qj is the amount imported from region j. Now, to incor-

porate finite elasticities of substitution, the composite good Q is defined as

Q =

(n∑

j=1

Qσ−1

σj

) σσ−1

,

8Prices are from the UN Comtrade database, year 2000. I discard observations in which quantitiesreported by exporters and importers do not match (i.e., differ by more than 10%) or are very small(i.e., less than 10 thousand tons). Regressions are weighted by the shipped quantities.

13

where σ is the elasticity of substitution. Utility over Q is defined exactly as before.

It is easy to verify that the elasticity of substitution is constant, i.e., for any set

of prices, optimally chosen quantities satisfyQj

Qk=

P σk

P σj. The intermediate composite

good, turned by a producer into steel, is defined analogously. Note that as σ goes to

infinity, this model converges to the SPE model.

The elasticity of substitution, σ, is a free parameter in this model. In empirical

applications, it is usually assumed to be less than 10, and is virtually always less than

20 (McDaniel and Balistreri, 2002). However, the model cannot match the actual

trade flows in the steel industry even remotely for such values of σ. Table 5 gives the

results for σ = 25, and it is clear that the predictions are very far from the actual

flows. The elasticity of substitution can be estimated endogenously, and I do that

next. The metric that I minimize is the sum of squared differences between the actual

and the predicted trade flows, measured in the units of steel (that is, scrap flows are

multiplied by 0.9, iron ore flows are multiplied by 0.6, and iron ore flows from China

are multiplied by 0.28). The value that minimizes this metric is σ = 365, and the

flows are reported in Table 6. While the predictions are reasonable, the elasticity of

substitution required to get them is extremely high, and is hard to interpret.

3.3 Matching Model with Heterogeneous Transportation Costs

Let me now describe the setup of the model of trade flows based on the heterogeneity

of bilateral transportation costs. First, I take demand and supply curves, as well

as bilateral transportation costs, from the SPE setup. Next, I pick the units of

discretization: the unit of quantity is 1,000,000 tons of steel and the unit of price is

$1 per ton. Each region is a set of small agents of four types: iron ore (and scrap)

suppliers, who can supply one unit of iron ore (scrap), each at a certain reservation

14

price; steel consumers, who demand one unit of steel, also at a certain reservation

price, and steel producers, who can convert one unit of input into one unit of steel at a

certain cost. The costs and reservation prices are chosen in such a way that aggregate

demand and supply curves approximate those in the SPE setup. For example, for a

particular region, the reservation price of the first consumer of steel is equal to the

marginal benefit from an extra ton of steel after one million tons; the reservation

price of the second consumer of steel is equal to the marginal benefit from an extra

ton of steel after two million tons, and so on.

I then pick the amount of heterogeneity in bilateral transportation costs, i.e.,

the standard deviation of random shocks, κ, and generate the matrix of bilateral

transportation costs between the agents. The cost of transporting a unit of good

G from agent A to agent B is equal to the average cost of transporting good G

from A’s region to B’s region (estimated in the SPE setup), plus ε · tG, where ε is a

random draw from the normal distribution N(0, κ2) and tG is the average bilateral

transportation cost of good G. Without loss of generality, I assume that sellers

pay transportation costs. Thus, the payoff of a supplier of iron ore or scrap, S,

who sells one unit to a steel producer, B, at price p (i.e., forms a contract c =

(S, B, l ≡ 1, p); serial number l is redundant in this setting, since the capacity of

each agent is equal to one unit) is equal to (price received from the producer) −

(reservation price) − (shipping cost); the payoff of a consumer of steel is equal to

(reservation price) − (price paid to the producer); and the payoff of a producer of

steel is equal to (price received from the customer)− (price paid to the supplier)−

(cost of production) − (cost of shipping to the customer). Cost of production

takes into account whether the input is iron ore or steel. The payoff from forming

a downstream contract without forming an upstream contract is set to −∞. For all

types of agents, outside options are normalized to zero. This defines a supply chain

15

matching market. Hence, I can find the upstream- and downstream-optimal chain

stable networks by applying the T -algorithm, and thus get bounds on the model’s

predictions.

The only remaining question is how to pick parameter κ. I determine it using,

in essence, the Method of Simulated Moments (McFadden, 1989; Pakes and Pollard,

1989): generate random shocks, and then vary parameter κ to find the value that fits

the actual data best. I use the same measure of fit as in Section 5.2.2: the sum of

squared differences between predicted and actual trade flows, measured in units of

steel. The only difference from the standard MSM approach is that my model provides

boundaries rather than point predictions. For that reason, I find κ that minimizes

the average of the measure of fit of the upstream-optimal chain stable network and

the measure of fit of the downstream-optimal chain stable network. The estimated

value is κ = .123, i.e., 12.3% of the average transportation cost. The flows in the

extreme chain stable networks are reported in Tables 7 and 8.

Table 9 shows the measures of fit for all of the models described in this section.

The fit of both extreme chain stable networks is better than the fit of any other model,

including the Armington-based model with an endogenously calibrated elasticity of

substitution. Combined with the more realistic underlying assumptions, as well as

more reasonable estimates of the endogenously determined parameter, this suggests

that the heterogeneity-based model is a better way to model commodity trade flows

than the standard approaches currently used in the literature.

4 Conclusion

The standard approaches to modeling multi-regional commodity trade flows assume

either perfect substitutability of goods from different countries, which results in un-

16

realistically sharp predictions, or product differentiation by the country of origin,

which is plausible for some goods, but is hard to justify, both theoretically and em-

pirically, for many commodities. This paper introduces an alternative model, which

incorporates heterogeneity in bilateral transportation costs between the agents who

compose countries or regions. This model fits the data better than the standard mod-

els do, while relying on more natural assumptions and using more realistic parameter

values. The theory of matching provides a theoretically and computationally con-

venient framework for incorporating such heterogeneity, but it is possible that other

approaches can also accommodate it. Finding alternative ways of accommodating

heterogeneity in bilateral transportation costs and determining relative strengths and

weaknesses of different approaches are important areas for future research.

17

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18

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20

SteelConsumers(all regions)

SteelProducers

(all regions)

Scrap Suppliers(Japan)

Iron ore andScrap Suppliers

(EU15, Other Europe,Fmr. USSR, NAFTA,

C. & S. America,Africa & Middle East,

China, Other Asia, Oceania)steel

scrap

scrap

iron ore

FIGURE 1: STEEL SUPPLY CHAIN

21

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TER

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25

TABLE 3: IRON ORE, SCRAP, AND STEEL INTERNATIONAL TRADE FLOWS, 2000

Panel A: Iron ore Customer

Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union (15) 17.3 1.0 0.2 3.6 0.3 Other Europe 0.5 5.3 Former USSR 4.2 22.8 130.3 0.2 NAFTA 14.7 0.3 98.9 0.7 0.8 1.1 0.7 C. & S. America 65.8 7.2 10.3 66.3 12.0 17.3 32.6 18.8 0.3 Africa & Middle East 17.5 1.4 0.2 13.7 7.3 5.7 1.0 China 224.0 Japan Other Asia 1.1 0.6 1.3 11.0 20.8 39.4 1.5 Oceania 20.7 1.7 0.9 0.1 0.2 33.3 71.6 31.2 11.0 Panel B: Scrap

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union (15) 79.0 2.4 1.1 0.2 2.2 Other Europe 3.6 23.2 0.4 Former USSR 2.3 2.7 42.5 0.1 0.1 2.6 1.5 NAFTA 0.2 73.3 0.9 0.1 2.0 C. & S. America 12.5 Africa & Middle East 0.3 1.6 0.7 China 23.6 0.1 Japan 0.1 0.9 43.5 1.4 Other Asia 0.5 0.1 38.1 Oceania 0.1 0.1 0.4 2.4 Panel C: Steel

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union (15) 135.9 8.7 0.8 8.2 0.8 4.1 0.6 0.1 2.5 0.2 Other Europe 12.9 29.7 0.1 2.4 0.5 2.6 0.2 1.3 Former USSR 6.8 8.0 63.1 4.9 1.8 10.2 9.4 0.1 12.1 NAFTA 0.6 132.1 0.4 0.3 C. & S. America 2.3 0.2 4.9 40.6 0.3 0.2 2.6 Africa & Middle East 1.8 0.9 0.2 14.4 0.4 2.2 0.1 China 0.6 0.2 1.7 0.1 0.2 119.6 0.4 7.5 Japan 0.5 0.2 0.1 3.4 0.5 1.5 4.0 89.8 17.9 0.4 Other Asia 2.0 5.4 0.3 0.8 5.8 4.3 78.1 0.5 Oceania 0.2 0.6 0.1 0.2 0.1 1.0 8.1

Notes: Trade flows of iron ore, scrap, and primary steel products in 2000 among 10 world regions. All numbers are in millions of metric tons. Data sources: International Iron and Steel Institute (IISI 2001, 2002), UN Comtrade (UNCTAD, 2000).

26

TABLE 4: SPATIAL PRICE EQUILIBRIUM—PREDICTED TRADE FLOWS

Panel A: Iron ore Customer

Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 18.2 Other Europe 8.0 Former USSR 0.2 33.9 127.1 45.6 NAFTA 73.3 C. & S. America 74.9 38.0 70.5 Africa & M. East 5.1 30.8 China 185.7 Japan Other Asia 81.0 Oceania 48.4 110.6 15.6 9.5 Panel B: Scrap

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 76.3 Other Europe 27.8 Former USSR 65.5 NAFTA 64.3 C. & S. America 9.2 Africa & M. East 3.8 China 20.9 Japan 38.7 Other Asia 29.7 Oceania 2.4 Panel C: Steel

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 128.4 Other Europe 43.8 10.8 Former USSR 29.9 61.8 13.3 10.5 22.9 NAFTA 127.8 C. & S. America 8.2 42.8 Africa & M. East 22.1 China 127.3 Japan 89.7 11.2 2.1 Other Asia 86.2 Oceania 8.0

Notes: Trade flows of iron ore, scrap, and steel predicted by the Spatial Price Equilibrium model. All numbers are in millions of metric tons.

27

TABLE 5: APPLIED PARTIAL EQUILIBRIUM, σ = 25—PREDICTED TRADE FLOWS

Panel A: Iron ore Customer

Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 4.4 1.9 4.1 2.2 0.9 0.6 3.0 2.0 1.8 0.1 Other Europe 1.8 1.2 2.0 0.9 0.4 0.3 1.6 1.1 1.0 Former USSR 28.0 14.8 37.8 14.2 5.5 3.9 25.9 17.2 15.4 0.6 NAFTA 8.7 3.7 8.4 20.5 5.2 1.4 8.0 6.7 5.2 0.3 C. & S. America 19.3 9.5 17.7 29.1 38.5 8.2 12.4 9.3 7.6 1.1 Africa & M. East 5.2 3.3 5.5 3.4 3.5 5.0 5.7 3.8 3.4 0.4 China 6.2 3.8 10.1 2.7 0.4 0.8 59.4 28.3 30.5 0.4 Japan Other Asia 5.3 3.0 7.0 4.0 1.1 1.1 18.9 15.0 13.8 0.5 Oceania 8.8 5.7 11.7 9.5 6.8 5.6 31.1 28.7 21.9 5.7 Panel B: Scrap

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 50.0 5.6 15.7 0.4 0.4 0.1 0.2 Other Europe 5.4 13.7 7.2 0.1 0.1 0.3 0.1 0.1 Former USSR 11.4 5.4 44.2 0.2 0.9 0.2 0.3 NAFTA 0.4 0.1 0.2 60.2 0.2 C. & S. America 0.1 9.1 Africa & M. East 3.7 China 0.1 0.2 13.5 2.4 4.4 Japan 0.1 6.0 23.3 7.8 Other Asia 0.1 0.1 9.4 6.6 12.6 Oceania 0.1 0.1 0.1 2.1 Panel C: Steel

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 43.4 9.2 12.6 19.2 4.8 4.6 12.7 7.1 10.1 0.7 Other Europe 15.2 6.1 5.9 7.0 2.2 2.9 6.8 3.6 5.4 0.4 Former USSR 36.9 10.6 18.1 17.8 4.2 4.9 17.8 9.7 14.1 0.9 NAFTA 16.1 3.5 5.1 60.3 8.0 2.6 7.7 5.6 6.9 0.7 C. & S. America 6.9 1.8 2.0 13.5 15.4 3.8 2.2 1.4 1.8 0.6 Africa & M. East 3.4 1.3 1.2 2.4 2.0 5.5 2.1 1.2 1.7 0.5 China 12.3 3.9 5.9 8.9 1.5 2.7 36.9 18.7 28.4 1.7 Japan 8.5 2.6 4.0 8.1 1.2 1.8 23.0 22.8 24.1 1.8 Other Asia 7.6 2.4 3.6 6.2 1.0 1.7 21.5 14.8 22.5 1.3 Oceania 0.6 0.2 0.3 0.8 0.4 0.5 1.4 1.2 1.4 1.0

Notes: Trade flows of iron ore, scrap, and steel predicted by the Applied Partial Equilibrium model with constant elasticity of substitution, σ = 25. All numbers are in millions of metric tons.

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TABLE 6: APPLIED PARTIAL EQUILIBRIUM, σ = 365—PREDICTED TRADE FLOWS

Panel A: Iron ore Customer

Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 17.1 0.6 0.4 0.1 Other Europe 0.2 7.7 0.1 0.1 Former USSR 21.9 19.3 125.4 34.8 1.0 3.8 NAFTA 0.1 71.4 0.1 0.1 0.1 C. & S. America 53.3 16.8 1.3 38.2 70.5 0.4 0.1 0.1 Africa & M. East 0.2 2.8 30.6 2.9 0.1 0.3 China 180.4 0.1 2.5 Japan Other Asia 22.9 8.2 49.7 Oceania 33.7 100.4 40.2 9.4 Panel B: Scrap

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 76.1 Other Europe 27.8 Former USSR 65.5 NAFTA 64.1 C. & S. America 9.3 Africa & M. East 3.9 China 21.0 Japan 38.7 Other Asia 29.8 Oceania 2.4 Panel C: Steel

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 120.0 0.2 0.2 7.8 0.1 0.1 Other Europe 3.6 40.9 0.3 0.3 8.9 0.7 0.2 Former USSR 34.5 2.7 61.4 6.9 0.7 24.9 0.5 7.1 0.1 NAFTA 127.1 C. & S. America 7.3 42.8 1.1 Africa & M. East 22.1 China 105.1 0.9 22.0 0.2 Japan 1.2 85.5 14.9 1.5 Other Asia 5.7 2.9 76.9 0.3 Oceania 7.9

Notes: Trade flows of iron ore, scrap, and steel predicted by the Applied Partial Equilibrium model with constant elasticity of substitution, σ = 365. All numbers are in millions of metric tons.

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TABLE 7: UPSTREAM-OPTIMAL CHAIN STABLE NETWORK—PREDICTED TRADE FLOWS

Panel A: Iron ore Customer

Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 18.3 3.3 Other Europe 8.3 Former USSR 13.3 1.7 103.3 31.7 6.7 6.7 NAFTA 90.0 C. & S. America 81.7 31.7 3.3 26.7 76.7 5.0 6.7 1.7 Africa & M. East 26.7 15.0 3.3 China 203.6 21.4 Japan Other Asia 11.7 31.7 38.3 Oceania 26.7 86.7 53.3 10.0 Panel B: Scrap

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 82.1 1.1 Other Europe 29.5 Former USSR 55.8 NAFTA 70.5 C. & S. America 9.5 Africa & M. East 4.2 China 22.1 Japan 42.1 Other Asia 1.1 30.5 Oceania 2.1 Panel C: Steel

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 137.0 9.0 Other Europe 3.0 41.0 9.0 Former USSR 27.0 5.0 65.0 3.0 17.0 3.0 NAFTA 137.0 C. & S. America 8.0 45.0 2.0 Africa & M. East 23.0 China 110.0 2.0 22.0 Japan 2.0 92.0 22.0 Other Asia 15.0 81.0 Oceania 8.0

Notes: Trade flows of iron ore, scrap, and steel in the upstream-optimal chain stable network in the heterogeneity-based model. All numbers are in millions of metric tons.

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TABLE 8: DOWNSTREAM-OPTIMAL CHAIN STABLE NETWORK—PREDICTED TRADE FLOWS

Panel A: Iron ore Customer

Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 18.3 3.3 Other Europe 8.3 Former USSR 13.3 1.7 103.3 31.7 6.7 6.7 NAFTA 90.0 C. & S. America 81.7 31.7 3.3 26.7 76.7 5.0 6.7 1.7 Africa & M. East 26.7 15.0 3.3 China 200.0 25.0 Japan Other Asia 11.7 31.7 38.3 Oceania 28.3 86.7 51.7 10.0 Panel B: Scrap

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 82.1 1.1 Other Europe 29.5 Former USSR 55.8 NAFTA 70.5 C. & S. America 9.5 Africa & M. East 4.2 China 22.1 Japan 42.1 Other Asia 1.1 30.5 Oceania 2.1 Panel C: Steel

Customer Supplier EU OE USSR NA C&SA A&ME CHN JP OA OC European Union 137.0 9.0 Other Europe 2.0 41.0 1.0 9.0 Former USSR 28.0 5.0 64.0 3.0 18.0 2.0 NAFTA 137.0 C. & S. America 8.0 45.0 2.0 Africa & M. East 23.0 China 112.0 3.0 19.0 Japan 1.0 90.0 25.0 Other Asia 13.0 1.0 82.0 Oceania 8.0

Notes: Trade flows of iron ore, scrap, and steel in the downstream-optimal chain stable network in the heterogeneity-based model. All numbers are in millions of metric tons.

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TABLE 9: SUMMARY—FIT OF ALTERNATIVE MODELS

Model Fit Spatial Price Equilibrium (Table 4) 6,940 Applied Partial Equilibrium, σ = 25 (Table 5) 49,933 Applied Partial Equilibrium, σ = 365 (Table 6) 6,110 Upstream-optimal Chain Stable Network (Table 7) 4,714 Downstream-optimal Chain Stable Network (Table 8) 4,695

Notes: This table presents a quantitative measure of goodness-of-fit of alternative models mentioned in the paper. The measure is the sum of squared differences between actual and predicted trade flows for all pairs of regions and all goods, where flows are measured in units. One unit corresponds to one million tons of steel and to the quantities of inputs (iron ore, scrap) required to produce one million tons of steel.

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