Transportation Cost Heterogeneity and the Patterns of ...ost/papers/heterogeneity.pdf · lem. Fox...
Transcript of Transportation Cost Heterogeneity and the Patterns of ...ost/papers/heterogeneity.pdf · lem. Fox...
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: [email protected]. 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
References
[1] Anania, G. (2001a), “Modeling the GATT Agreement on Agriculture,” in T. Heckeleiet al., eds., Agricultural Sector Modelling and Policy Information Systems, Kiel: VaukVerlag.
[2] Anania, G. (2001b), “Modeling Agricultural Trade Liberalization and Its Implicationsfor the European Union,” Osservatorio sulle politiche agricole dell’UE, Working Paper12.
[3] Anderson, J. E., and E. van Wincoop (2004), “Trade Costs,” Journal of EconomicLiterature, 42, 691–751.
[4] Armington, P. S. (1969), “A Theory of Demand for Products Distinguished by Placeof Production,” IMF Staff Papers, 16, 159–178.
[5] Baughman, L. (2004), “Shrimp Antidumping Petition Would Jack Up Prices toShrimp-Consuming Industries,” Trade Partnership report, accessed on 09/08/2004 athttp://www.citac.info/shrimp/new_releases/ShrimpPrices_6_10_04.pdf.
[6] Bowen, H. P., A. Hollander, and J.-M. Viaene (1998), Applied International TradeAnalysis, London: MacMillan.
[7] Brainard, W., and H. Scarf (2000), “How to Compute Equilibrium Prices in 1891,”Cowles Foundation Discussion Paper 1272.
[8] Buongiorno, J., S. Zhu, D. Zhang, J. Turner, and D. Tomberlin (2003), The GlobalForest Products Model: Structure, Estimation, and Applications, Academic Press.
[9] Cox, T. L., J. R. Coleman, J.-P. Chavas, and Y. Zhu (1999), “An Economic Analysisof the Effects on the World Dairy Sector of Extending Uruguay Round Agreement to2005,” Canadian Journal of Agricultural Economics, 47, 169–184.
[10] Enke, S. (1951), “Equilibrium among Spatially Separated Markets: Solution by Elec-trical Analogue,” Econometrica, 19, 40–47.
[11] Feenstra, R. C. (2000), World Trade Flows, 1980–1997, Center for International Data,University of California, Davis.
[12] Fox, K. A. (1953), “A Spatial Equilibrium Model of the Livestock-Feed Economy inthe United States,” Econometrica, 21, 547–566.
[13] Francois, J., and L. Baughman (2001), “Estimated Economic Effects of Proposed Im-port Relief Remedies for Steel,” Trade Partnership Worldwide report, accessed athttp://www.tradepartnership.com/pdf_files/Steel_Remedy.pdf on 09/08/2004.
[14] Francois, J., and K. Reinert (1997), Applied Methods for Trade Policy Analysis, Cam-bridge, U.K.: Cambridge University Press.
18
[15] Francois, J., and C. Shiells, eds., (1994) Modeling Trade Policy: Applied General Equi-librium Assessments of North American Free Trade, Cambridge, U.K.: CambridgeUniversity Press.
[16] Ginsburgh, V., and M. Keyzer (1997), The Structure of Applied General EquilibriumModels, Cambridge, MA: MIT Press.
[17] Halpern, L., and M. Koren (2004), “Pricing to Firm: An Analysis of Firm- andProduct-Level Import Prices,” CEPR Discussion Paper 4568.
[18] Hausman, J. (2002), “Critique of CITAC Study,” accessed on 09/08/2004 athttp://www.steel.org/news/pr/2002/images/MIT_CITAC.pdf.
[19] Henderson, J. M. (1955), “A Short-Run Model of the Coal Industry,” Review of Eco-nomics and Statistics, 37, 336–346.
[20] Henderson, J. M. (1956), “Efficiency and Pricing in the Coal Industry,” Review ofEconomics and Statistics, 38, 50–60.
[21] Hertel, T., ed. (1997), Global Trade Analysis, Cambridge, U.K.: Cambridge UniversityPress.
[22] Hertel, T. (1999), “Applied General Equilibrium: Analysis of Agricultural and Re-source Policies,” Purdue University, Department of Agricultural Economics, Staff Pa-per 99-2.
[23] Hummels, D. (1999), “Have International Transportation Costs Declined?” PurdueUniversity working paper.
[24] IISI (2001), Steel Statistical Yearbook, International Iron and Steel Institute, Brussels.
[25] IISI (2002), World Steel in Figures, International Iron and Steel Institute, Brussels.
[26] Judge, G. G., and T. Takayama, eds. (1973), Studies in Economic Planning Over Spaceand Time, Amsterdam: North-Holland.
[27] Lee, H., B. McCarl, U. Schneider and C. Chen (2004), “Leakage and Comparative Ad-vantage Implications of Agricultural Participation in Greenhouse Gas Emission Mit-igation,” University of Western Ontario, Department of Economics Research Report2004–1.
[28] Mæstad, O. (2003), “Environmental Policy in the Steel Industry: Using EconomicInstruments,” Report, Environment Directorate, OECD, Paris.
[29] McDaniel, C., and E. Balistreri (2002), “A Discussion on Armington Trade SubstitutionElasticities,” USITC Office of Economics Working Paper No. 2002-01-A.
[30] McFadden, D. (1989), “A Method of Simulated Moments for Estimation of DiscreteResponse Models without Numerical Integration”, Econometrica, 57, 995–1026.
19
[31] Ostrovsky, M. (2005), “Stability in Supply Chain Networks,” Harvard University work-ing paper.
[32] Pakes, A., and D. Pollard (1989), “Simulation and the Asymptotics of OptimizationEstimators,” Econometrica, 57, 1027–1057.
[33] Radelet, S., and J. Sachs (1998), “Shipping Costs, Manufactured Exports, and Eco-nomic Growth,” Harvard Institute for International Development working paper.
[34] Ruijs, A., C. Schweigman, C. Lutz, and S. Sirpe (2000), “Modelling Cereal Trade inBurkina Faso,” in C. Lutz, ed., Food Markets in Burkina Faso, CDS Research Report,Groningen.
[35] Samuelson, P. A. (1952), “Spatial Price Equilibrium and Linear Programming,” Amer-ican Economic Review, 42, 283–303.
[36] Scarf, H. E. (1967), “On the Computation of Equilibrium Prices,” in W. Fellner et al.,eds., Ten Economic Studies in the Tradition of Irving Fisher, New York: Wiley.
[37] Scarf, H. E., and J. B. Shoven, eds. (1984), Applied General Equilibrium Analysis,Cambridge, U.K.: Cambridge University Press.
[38] Shoven, J. B., and J. Whalley (1992), Applying General Equilibrium, Cambridge, U.K.:Cambridge University Press.
[39] Srinivasan, T. N., and J. Whalley, eds. (2002), General Equilibrium Trade Policy Mod-eling, Cambridge, MA: MIT Press.
[40] Takayama, T., and G. G. Judge (1971), Spatial and Temporal Price Allocation Models,Amsterdam: North Holland.
[41] UNCTAD (2000), PC-TAS: Trade Analysis System on Personal Computer, 1996–2000,International Trade Centre UNCTAD/GATT, Geneva.
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
TA
BLE
1: W
INE
AN
D C
HEE
SE IN
TER
NA
TIO
NA
L TR
AD
E FL
OW
S, 1
997
Pane
l A: W
ine
Impo
rter
Expo
rter
UK
Ger
man
yU
SAB
elgi
um
Japa
n N
ethe
rl.
Switz
erl.
Fran
ce
Den
mar
k C
anad
aFr
ance
10
02.2
825.
183
1.0
556.
031
9.8
331.
533
0.7
—21
6.2
157.
6Ita
ly
356.
069
5.3
441.
641
.688
.345
.113
2.4
156.
857
.969
.0Sp
ain
243.
422
2.6
97.3
31.0
21.6
64.6
59.1
101.
575
.012
.5A
ustra
lia23
9.5
11.4
116.
13.
110
.27.
010
.02.
05.
424
.4Po
rtuga
l96
.723
.543
.354
.84.
942
.29.
313
3.4
19.9
12.0
Ger
man
y16
1.0
—36
.019
.558
.740
.79.
617
.415
.111
.7U
SA12
4.3
24.8
—4.
840
.3
19.2
22.9
9.4
10.7
78.6
Chi
le71
.717
.413
9.1
3.7
20.7
13.5
4.9
8.9
19.3
37.9
UK
—18
.535
.710
.5
13.8
6.
62.
259
.52.
51.
8S.
Afr
ica
78.2
18.0
7.8
7.2
7.3
19.8
5.7
3.3
5.5
9.0
Pane
l B: C
hees
e
Im
porte
rEx
porte
r
Ger
man
yIta
lyU
KB
elgi
umFr
ance
U
SAFm
. USS
RJa
pan
Net
herl.
Spai
nFr
ance
67
4.7
209.
618
9.4
258.
4—
61.7
17.1
30.1
98.8
105.
9N
ethe
rland
s
808.
990
.049
.823
7.6
192.
545
.610
.324
.1—
98.6
Ger
man
y—
534.
512
9.5
118.
913
4.1
20.3
295.
018
.810
7.4
51.7
Den
mar
k
357.
127
.167
.817
.829
.245
.524
.347
.630
.941
.0Ita
ly18
8.2
—74
.442
.512
8.5
138.
20.
412
.522
.511
.7N
. Zea
land
13.5
0.0
51.9
12.8
1.6
47.6
44.6
121.
617
.10.
1B
elgi
um49
.911
2.3
93.0
—48
.33.
30.
50.
970
.315
.6A
ustra
lia2.
20.
019
.70.
92.
916
.02.
416
7.1
5.4
0.3
Switz
erla
nd
84.6
119.
012
.424
.457
.327
.91.
32.
54.
38.
9Ir
elan
d4.
85.
725
9.8
7.3
9.7
8.9
0.4
2.0
8.1
1.8
Not
es: I
nter
natio
nal t
rade
flow
s of w
ine
and
chee
se in
199
7 fo
r the
10
larg
est e
xpor
ters
and
impo
rters
of e
ach
good
. All
num
bers
are
in m
illio
ns
of d
olla
rs. D
ata
sour
ce: “
Wor
ld T
rade
Flo
ws,
1980
-199
7” (F
eens
tra, 2
000)
. SIT
C c
odes
112
1 (W
ine
of fr
esh
grap
es) a
nd 0
240
(Che
ese
and
curd
).
22
TA
BLE
2: S
OY
BEA
NS,
LIV
E C
OW
S, A
NTH
RA
CIT
E, N
ATU
RA
L G
AS
AN
D IR
ON
OR
E IN
TER
NA
TIO
NA
L TR
AD
E FL
OW
S, 1
997
Pane
l A: S
oybe
ans
Impo
rter
Expo
rter
Net
herla
nds
Japa
nM
exic
oG
erm
any
Spai
n Ta
iwan
Chi
naS.
Kor
ea
Bel
gium
B
razi
l U
SA
725.
0 12
96.3
10
15.5
495.
247
0.0
690.
160
1.7
395.
720
0.0
194.
0B
razi
l
647.
414
5.4
19.8
362.
425
4.1
61.4
96
.310
.815
2.5
—Pa
ragu
ay21
8.9
13.5
8.7
0.3
168.
6C
anad
a6.
724
.40.
00.
910
.80.
05.
21.
16.
0N
ethe
rland
s—
97.0
0.1
25.6
Arg
entin
a11
.48.
10.
022
.87.
72.
0C
hina
65.9
—B
oliv
ia0.
4G
erm
any
20.9
—0.
10.
2B
elgi
um4.
05.
8—
Pane
l B: L
ive
cow
s
Im
porte
rEx
porte
r
USA
Italy
Spai
n N
ethe
rland
s In
done
sia
Mex
ico
Fran
ce
Leba
non
Phili
ppin
es
Bel
gium
Fran
ce
906.
6 29
0.4
29.7
—
46.1
60
.1C
anad
a
988.
90.
00.
122
.70.
10.
0A
ustra
lia0.
016
1.7
3.6
91.4
Ger
man
y0.
137
.619
.0
128.
824
.451
.214
.1B
elgi
um21
.42.
311
4.9
71.7
—M
exic
o20
7.8
—U
SA—
0.0
137.
4 1.
50.
1Sp
ain
43.3
—
1.7
2.3
21.1
0.2
Pola
nd55
.7
2.1
1.0
0.0
3.6
0.1
Net
herla
nds
4.2
6.2
—5.
90.
88.
2
23
TA
BLE
2 (C
ON
TIN
UED
)
Pane
l C: H
igh-
grad
e co
al (a
nthr
acite
)
Im
porte
rEx
porte
r
Ja
pan
S. K
orea
Ta
iwan
UK
Ger
man
y N
ethe
rl.Ita
lyFr
ance
Bra
zil
Bel
gium
Aus
tralia
30
48.9
734.
756
9.8
223.
547
.870
.312
1.1
148.
916
1.1
136.
6U
SA
336.
5
163.
487
.530
7.0
44.0
209.
334
4.6
173.
237
0.2
205.
3C
anad
a10
92.5
331.
5 51
.789
.422
.021
.768
.627
.560
.431
.6S.
Afr
ica
241.
112
8.5
307.
517
0.6
114.
510
2.8
93.0
162.
1In
done
sia
456.
410
5.7
295.
34.
24.
696
.5Po
land
41.6
157.
2
50.7
9.9
43.9
9.7
14.0
Chi
na50
7.0
313.
116
5.9
6.0
0.5
18.7
25.2
7.5
Fm. U
SSR
217.
133
.510
.44.
15.
11.
213
.46.
119
.3C
olom
bia
7.7
3.0
110.
814
8.6
142.
057
.155
.52.
19.
9C
zech
oslo
v.44
.5Pa
nel D
: Nat
ural
gas
Im
porte
rEx
porte
r
Ja
pan
USA
Ger
man
y F.
USS
R
Fran
ce
Italy
B
elgi
umS.
Kor
eaC
zech
.A
reas
NES
Fm. U
SSR
27
75.2
—11
16.2
2.5
1646
.9
C
anad
a
8233
.4A
lger
ia35
0.5
1.9
1022
.2
2010
.2
520.
7In
done
sia
3426
.3 11
46.3
Nor
way
33.7
1669
.10.
011
71.2
2.4
546.
662
.3N
ethe
rland
s12
.027
10.2
0.0
523.
549
3.7
653.
40.
4S.
Ara
bia
1681
.6
20.8
62
.0
93.9
1.
1
Mal
aysi
a16
25.3
2.7
647.
4U
AE
1955
.56.
61.
9G
erm
any
0.1
6.8
—0.
016
.26.
013
0.7
63.0
1251
.2
24
TA
BLE
2 (C
ON
TIN
UED
)
Pane
l E: I
ron
ore
Impo
rter
Expo
rter
Ja
pan
Chi
naG
erm
any
S. K
orea
Fr
ance
U
KIta
lyB
elgi
umTa
iwan
Pola
ndA
ustra
lia
12
02.1
628.
397
.832
1.7
80.5
103.
218
.37.
616
7.5
B
razi
l
468.
214
2.4
292.
411
5.7
129.
445
.493
.912
6.7
47.8
14.9
Indi
a39
9.0
144.
21.
05.
314
.17.
5So
uth
Afr
ica
149.
8 14
1.8
15.8
9.1
79.6
16
.5
0.3
17
.0
Mau
ritan
ia25
.478
.124
.879
.544
.2C
anad
a26
.26.
089
.917
.737
.352
.21.
2Fm
. USS
R12
9.9
Swed
en1.
420
.610
.85.
10.
025
.10.
017
.1C
hile
27.5
11.0
Peru
9.7
9.6
1.0
Not
es:
Inte
rnat
iona
l tra
de f
low
s of
soy
bean
s, liv
e co
ws,
high
-gra
de c
oal,
natu
ral
gas,
and
iron
ore
in 1
997
for
the
10 l
arge
st e
xpor
ters
and
im
porte
rs o
f ea
ch g
ood.
All
num
bers
are
in m
illio
ns o
f do
llars
. Dat
a so
urce
: “W
orld
Tra
de F
low
s, 19
80-1
997”
(Fe
enst
ra, 2
000)
. SIT
C R
ev. 2
co
des
2222
(So
ya b
eans
), 00
11 (
Ani
mal
s of
the
bov
ine
spec
ies,
incl
. bu
ffal
oes,
live)
, 32
21 (
Ant
hrac
ite,
whe
ther
/not
pul
veriz
ed,
not
aggl
omer
ated
), 34
1A (G
as, n
atur
al a
nd m
anuf
actu
red)
, and
281
5 (I
ron
ore
and
conc
entra
tes,
not a
gglo
mer
ated
). A
reas
NES
sta
nds
for a
reas
not
id
entif
ied
in th
e da
ta.
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.
28
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.
29
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.
30
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.
31
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.
32