A DISCUSSION ON ARMINGTON TRADE SUBSTITUTION

ELASTICITIES

No. 2002-01-A

OFFICE OF ECONOMICS WORKING PAPER

U.S. International Trade Commission

Christine A. McDaniel

Edward J. Balistreri

Office of Economics

U.S. International Trade Commission

January 2002

The authors are with the Office of Economics of the U.S. International Trade Commission. Office

of Economics working papers are the result of the ongoing professional research of USITC

Staff and are solely meant to represent the opinions and professional research of individual

authors. These papers are not meant to represent in any way the views of the U.S. International

Trade Commission or any of its individual Commissioners. Working papers are circulated to

promote the active exchange of ideas between USITC Staff and recognized experts outside the

USITC, and to promote professional development of Office staff by encouraging outside

professional critique of staff research. 

address correspondence to:

Office of Economics

U.S. International Trade Commission

Washington, DC 20436 USA
A Discussion on Armington Trade Substitution Elasticities

Christine A. McDaniel*

 Edward J. Balistreri*

December 2001

Abstract:

Applied partial and general equilibrium models used to examine trade policy are almost

universally sensitive to trade elasticities. Indeed, the Armington elasticity, the degree of

substitution between domestic and imported goods, is a key behavioral parameter that drives the

quantitative, and sometimes the qualitative, results that policymakers use. While standard

transparent approaches to econometric estimation of these elasticities have been offered for the

last 30 years, the estimates are viewed as too small by many trade economists. A few robust

findings emerge from the econometric literature: (1) more disaggregate analyses find higher

elasticities, (2) long-run estimates are higher than short-run estimates, and (3) time series

analyses generally find lower elasticities relative to cross-sectional studies. We offer simulation

results to illustrate the sensitivity of general equilibrium models to Armington elasticites. We

conclude with remarks on the current challenges that remain in determining these important

parameters.

______________________________________

*Prepared for the conference “Impact of Trade Liberalization Agreements on Latin America and

the Caribbean” organized by the Centre d’Etudes Prospectives et d’Informations Internationales

(CEPII) and the Inter-American Development Bank (IDB). The authors are with the Research

Division, Economics Office, U.S. International Trade Commission, 500 E Street, SW,

Washington, D.C. 20436. Views expressed herein are those of the authors and do not necessarily

represent the views of the U.S. International Trade Commission or any of its Commissioners.
1

I. Introduction

Using economic models to evaluate changes in trade policy generally requires the

conversion of policy changes into price effects. Model analyses use these price shifts to

determine how policy is expected to affect output, employment, trade flows, economic welfare,

and other variables of interest. The direction and magnitude of a trade policy change on

individual variables depends on the size of the shock as well as the behavioral relationships

present in the economy. When evaluating policy shifts within an economic model, these

behavioral relationships largely take the form of elasticities reflecting the responsiveness of one

set of variables to a change in a second set. For example, trade policy changes the effective price

of traded goods relative to domestically produced goods. As a result, a key relationship for

model analysis is the degree of substitution between imported and domestic goods. This key

relationship is commonly identified as the Armington elasticity. 1

In general, knowledge of elasticities is important for policy considerations. Changes in

tariffs and taxes will affect a country’s trade opportunities, level of income, and employment.

The size of these impacts will largely depend on the magnitude of elasticities. The Armington

elasticity is an essential component of trade policy analysis. Partial and general equilibrium

models that rely on the Armington structure are universally sensitive to these elasticities. Indeed,

a modeler’s central Armington choice will drive key quantitative, and sometimes qualitative,

results that policymakers use.

In the following section we review literature estimates of Armington elasticities. We

point out some of the key differences and robust findings in these studies. In section III we

 

1

The constant elasticity of substitution (CES) specification for the trade substitution elasticity is derived from

Armington (1969).
2

exemplify the importance of the elasticity estimates by offering results from a stylized policy

analysis. We make concluding remarks in section IV.

.

II. Econometric Estimates

Comprehensive industry-level estimates of Armington elasticities have appeared

intermittently over the last few decades. The five main studies available for U.S. imports include

Stern, Francis, and Schumacher (1976), Shiells, Stern, and Deardorff (1986), Reinert and

Roland-Holst (1992), and Shiells and Reinert (1993), and most recently, Gallaway, McDaniel

and Rivera (2000). These studies employ standard, transparent approaches to Armington

estimation. Many trade economists, however, view these elasticity estimates with skepticism

and believe that domestic and imported goods are much more substitutable than the estimates

suggest. We highlight specification and identification issues with these single equation

techniques.

One of the first systematic studies to provide import-demand elasticities for the U.S. was

carried out by Stern, Francis, and Schumacher (1976). This study offers “best estimates” of U.S.

import-demand elasticities for 28 industries at the 3-digit ISIC level. Interestingly, rubber

products, wearing apparel, metal products excluding machinery and transport equipment were

among the sectors found to be “extremely import sensitive,” while food, beverages, textiles,

tobacco, machinery including electrical machinery, and iron and steel were classified as

“moderately import sensitive.” The wood and paper products industries were considered “import

inelastic.”

Shiells, Stern, and Deardorff (1986) estimated trade substitution elasticities using a

simple stock-adjustment model with annual data from 1962-1978 for 163 disaggregated
3

industries. The authors obtained statistically significant Armington elasticities for 122 of 163

sectors estimated. Their estimates compared adequately with previous estimates from Stern et al.

(1976).

Reinert and Shiells (1993) disaggregated U.S. imports into those from the NAFTA

members and those from the rest of the world (ROW). Using quarterly data over 1980-1988,

they obtained estimates for 128 mining and manufacturing sectors. Elasticities were estimated

using three specifications: (i) generalized least squares estimation technique, based on a CobbDouglas price aggregator; (ii) maximum likelihood estimation using a CES price aggregator;

and, (iii) a simultaneous equation estimator that uses a Cobb Douglas price aggregator and

employs a distributed lag model. Reinert and Shiells found the estimates to be relatively

insensitive across the three alternative estimation procedures.

Reinert and Roland-Holst (1992) estimated Armington elasticities for 163 U.S. mining

and manufacturing sectors. They obtained significant estimates for approximately two-thirds of

the 3-digit SIC industries estimated using quarterly data from 1980-1988. Their statistically

significant estimates range from 0.14 to 3.49

Gallaway, McDaniel and Rivera (2000) offer the most comprehensive, disaggregated,

and up-to-date set of Armington elasticity estimates. The authors consider explicitly the longrun aspect that is applicable to applied partial and general equilibrium modeling. They provide

estimates for 311 industries at the 4-digit SIC level over the period 1989 to 1995. Significant

long-run estimates range from 0.53 to 4.83. Long-run estimates are up to five times as large as

short-run estimates, and on average twice as large as the short-run estimates. This is important

since long-run estimates are more appropriate for most trade policy analysis than short-run

estimates. A comparison of the Gallaway, McDaniel and Rivera 4-digit estimates to Reinert’s
4

and Roland-Holst’s 3-digit provides further insight to the well-known aggregation bias: the more

detailed commodity level, the greater the ease of substitutability.

Hummels (1999) departs from the above literature. Using a multi-sector model of trade

to isolate channels through which trade cost or resistance affects trade volume across countries or

regions he is able to solve for the implied substitution elasticity. Assuming that all distance

related trade resistance is a freight charge he computes a range for the substitution elasticity of 2

to 5.3. More compelling are Hummels’ direct substitution elasticity estimates in a framework

that includes a more general interpretation of trade resistance. His average estimates are 4.8, 5.6,

and 6.9 for aggregation at the 1-digit, 2-digit, and 3-digit levels respectively.

The cross-sectional estimates presented by Hummels are much higher than the central

values obtained in the time-series studies of U.S. data. The average of 6.9 reported by Hummels

at the 3-digit level is well above the average long-run estimate of 1.6 reported by Gallaway,

McDaniel and Rivera at the 4-digit level. The large divergence in these estimates indicates

misspecification.

Although Riedel (1988) and Riedel and Athukorala (1994) do not directly estimate

Armington elasticities, their estimations of Hong Kong’s export demand elasticity have been

cited as evidence that Armington elasticities are likely higher than the estimates reviewed

above.2 Riedel (1988) and Riedel and Athukorala (1994) argue that direct estimation of export

demand for a small economy perform poorly because observed quantities are determined by

price and supply conditions (export demand is perfectly elastic). They identified the system by

inverting the demand function and considering the export supply function. Under this

 

2

 Specifically Harrison, Rutherford and Tarr (2001) make this argument. In their “low elasticities” case an

Armington of 4 and a lower-level elasticity of substitution between imports from different regions of 8 is assumed.

Although high this assumption is generally consistent the direct econometric estimates. In their central case,
5

specification they present compelling evidence that Hong Kong is a price-taker.3 The indication

is that the world market does not distinguish between Hong Kong goods and those of other

countries and that the Armington elasticity is very high. This is important evidence that

researchers need to consider when disaggregating small economies, because the optimal tariff is

inversely related to the Armington elasticity.

One of the most useful aspects of econometric estimates is that they offer guidance on

relative ease of substitutability across sectors. For example, in reviewing the econometric

estimates reported in the papers mentioned above, plastic materials and resins, photographic

equipment, paperboard boxes and malt beverages are sectors with some of the highest Armington

estimates. On the other side, military weapons (ordnance), games and toys, nonrubber footwear,

gray iron foundries, and cereal breakfast foods are sectors with some of the lowest Armington

estimates (Gallaway, McDaniel, and Rivera, 2000).

What explains the wide variation in these substitution elasticities across sectors? In an

attempt to explain such variation, Blonigen and Wilson (1999) find that increased multinational

presence in the downstream industries increases the elasticity of substitution unless importing

behavior in the downstream industries is unusually high as well. This finding suggests an import

bias by foreign transplant firms. Their results also offer some evidence that home bias variables,

such as, entry barriers and union presence, may lower the Armington elasticity.

The reviewed papers that offer econometric estimates are useful to modelers in that they

provide a starting point for specifying key behavioral parameters. However, the lack of

consensus on point estimates reflects the sensitivity of the estimation results to the technique

 

however, they assume an Armington of 15 and a lower-level elasticity of 30. They contend that these higher

elasticities are similar to the point estimates obtained by Riedel (1988).
6

employed. There are, however, a few robust findings. First, long-run estimates are much higher

than short-run. Researchers using short-run estimates should be concerned about understating

trade response. Second, the level of aggregation is important; the more disaggregate the sample

the higher the estimated substitution elasticity. In light of this, it is important to question

common practices in flexible aggregation models. These include: applying aggregate estimates

to individual sectors that are the focus of study, and applying the average elasticity from

disaggregate estimates to an aggregated commodity. We feel that it is important for modelers to

consider these known biases and not to adopt econometric point estimates indiscriminately.

Finally, model misspecification is particularly problematic when estimated parameters

are exogenous inputs to an entirely independent structural trade model. The specifications of

Stern, Francis, and Schumacher (1976), Shiells, Stern, and Deardorff (1986), Reinert and

Roland-Holst (1992), and Shiells and Reinert (1993), and Gallaway, McDaniel and Rivera

(2000) all suffer from the general critique that they are structurally inconsistent with the general

equilibrium because they do not consider the supply side of the market. The negative estimates

commonly found in these studies may, at least in part, be attributed to model misspecification.

Even the work by Hummels (1999), which is consistent with a general equilibrium, is not

necessarily consistent with the structure of most applied computational models.4 In sum,

sensitivity to estimation technique and misspecification are reasons that prudence is in order

when adopting estimates from the literature.

 

3

 Riedel and Athukorala (1993) use similar methodology and show that Korea is a price-taker in the market for

machinery.

4

 Large scale applied models often assume constant returns and perfect competition. Hummels (1999) motivates his

empirical trade model with a richer general equilibrium theory that includes monopolistic competition.
7

III. The Sensitivity of Policy Analysis to Armington Estimates

To illustrate the importance of the Armington elasticity in applied general equilibrium

models we compute examples in which the quantitative and qualitative results vary across

assumed elasticities, which are within the range of the cited literature. The model is a direct

extension of the widely available GTAPinGAMS system.5 The multi-region social accounts are

based on an aggregation of GTAP version 4, which uses 1997 as a base year. The accounts are

projected onto a steady-state expansion from 1997 to 2050. The dynamic structure is one of neoclassical capital accumulation driven by exogenous population growth. Agents are assumed to

be forward looking and accumulate capital to maximize intertemporal utility. 6

For these illustrative experiments we simply use the steady-state equilibrium as the

baseline.7 The model is also greatly simplified by aggregating up to include only three goods

(agricultural products, manufactured products, and services), and four regions (Columbia,

NAFTA members, other Latin American countries, and the rest of the world).

We focus on Columbia to illustrate an important implication of the Armington trade

structure. It is typical to find applied models with a regional aggregation that explicitly breaks

out focus countries of interest but most of the rest of the world is captured in residual aggregates.

An implication of this is that relatively small countries (Columbia in our example) are assigned a

unique variety in the demand system of their trade partners. The Armington structure results in a

great deal of market power, and relatively high optimal tariffs, even for small countries (each

country is a monopoly suppliers of its variety).

 

5

The GTAPinGAMS system is maintained by Tom Rutherford, University of Colorado. Documentation is available

in Rutherford and Paltsev (2000).

6

 We consider the dynamic equilibrium because we are interested in exploring the dependency of trade responses on

capital flows. In the central case we assume perfect international intertemporal capital markets over the computed

horizon (2005 to 2050). Lau, Pahlke,and Rutherford (1997) present a practical method for representing the neoclassical dynamic equilibrium for computation.
8

Using the simulation model we compute welfare for the representative Columbian agent

under various levels of protection holding the response of the other regions constant. Figure 1

presents these results for a range of Armington elasticities. With low Armington elasticities, 1 or

3, (which are roughly consistent with the long-run time-series econometric estimates of

Gallaway, McDaniel, and Rivera, 2000) unilateral liberalization from the benchmark rate of

protection is harmful to Columbia. Adopting a higher estimate, 5, (roughly consistent with

Hummels, 1999) indicates that marginal liberalization is beneficial to Columbia. Only when we

adopt an elasticity of 8 is total liberalization superior to the benchmark, and even then the

optimal for Columbia is at a rate of protection that is about 40% of the current level. In this

example, both the qualitative and quantitative effects of liberalization are sensitive to our choice

of elasticity.

 

7

 In actual policy analysis a more credible baseline might be considered that includes, at least, medium-run

differential growth rates across countries.
9

Figure 1.

Figure 1 illustrates that the Armington parameter not only determines the sign and

magnitude of liberalization, but that it also might be used to mitigate some of the undesirable

features of the Armington structure. If we believe that Columbia, the country of focus, is

generally a price taker on world markets, but the Armington structure is chosen for its

tractability, then assuming a high elasticity compensates for the implicit market power granted

when Columbia produces a unique variety. Obviously, a more satisfying solution would be to

get rigorous proof that Columbia is truly a price taker (estimate the trade elasticities in an

econometric model that includes the Columbian variety). Unfortunately, compromises and

simplifying assumptions must be made in applied work. Given the infeasibility of a full

structural estimation of the applied computational model, a researcher might identify the

Unilateral Columbian Trade Policy:

 Welfare Sensitivity to Armington Specification

0.985

0.99

0.995

1

1.005

0 20 40 60 80 100 120 140

Level of Protection Relative to the Benchmark (%)

Welfare Index

Armington=1

Armington=3

Armington=5

Armington=8
10

sensitivity and offer an argument for the chosen elasticities. The professional audience can then

make an informed judgment about the validity of the results.

 Another important point to recognize is that, although many simulation models adopt

the Armington structure, other structural assumptions play an important roll in determining the

trade response independent of the chosen elasticity value. For example, an important structural

assumption in dynamic models is the extent that international capital markets are available. In

general, changes in trade policy will generate incentives for countries to adjust their capital

position to take advantage of the best rates of return.

To illustrate the impact of structural assumptions about capital flows on trade response,

we again simulate liberalization by Columbia. The Armington elasticity is held fixed at 5 across

scenarios, and we model a complete liberalization of tariffs. In the central case we make an

assumption that within the model horizon there can be no change in net indebtedness. Within

horizon international capital flows are unrestricted, but any net accumulations of debt have to be

paid back before the terminal period (2050). In the most restrictive scenario we make an

assumption that there is no change in Columbia’s capital flows (period by period balance of

payments). In the least restrictive case we approximate the infinite horizon solution with perfect

capital markets. In this case net accumulated debt need only be serviced, but never retired.

Figure 2 presents the effect of these alternative assumptions on the change in Columbian

imports.
11

Figure 2.

When the model is simply closed by maintaining no change in net indebtedness the trade

response is very similar to the perfect capital markets case. In the period-by-period balance of

payments case, however, the initial response is significantly less. This is because, when capital

markets are available, Columbia can borrow against future exports and take advantage of lower

import prices in the short-run. All of the models converge to approximately the same response in

the long run. So, although the Armington elasticity largely determines the ultimate response, the

structure of international capital markets interacts with the Armington to determine the

adjustment dynamics. We highlight this because dynamic models are gaining influence in policy

arenas, and adjustment dynamics are often of central importance.

Unilateral Columbian Liberalization: Import response under a 

given Armington elasticity but alternative structural assumptions about capital markets

15.0%

15.5%

16.0%

16.5%

17.0%

17.5%

18.0%

18.5%

2005 2010 2015 2020 2025 2030

Year

Change in the Value of Columbian Imports

Perfect Intertemporal Capital Markets

Within Horizon Capital Flows

Period by Period Balance of Payments
12

IV. Concluding Remarks

There is no question that measurement of Armington elasticities is of fundamental

importance in determining the response of trade models to policy experiments. There is equally

little doubt that measurement of these elasticities is very difficult. The estimates from the

literature provide little guidance on the correct point estimate to apply to a given commodity in a

given model for a given aggregation. Most of the controversy surrounding Armington

elasticities reduces to a general structural inconsistency between the econometric models used to

measure the response and the simulation models used to evaluate policy.

Three robust findings emerge from the econometric literature. First, long-run estimates

of Armington elasticities greatly exceed short-run estimates. Second, aggregation matters and

interacts with the Armington specification. Finally, single equation time-series approaches

identify smaller responses relative to cross-sectional estimation that includes a consideration of

supply conditions.

Given the sensitivity of econometric estimates many modelers turn to sensitivity analysis

of simulation results, which is quite useful to economists but has had limited impact in policy

arenas. Quantitative impacts from simulation models are often used in a way that is at odds with

the notion of comparative welfare analysis that acknowledges simplifying assumptions and

uncertainty over key parameter values. Policymakers often utilize single figures to support

policy positions. Unfortunately, acknowledging the existence of second moments in policy

forums may weaken the same argument that it strengthens in academic review.

The consumers of simulation results, thus, demand a definitive literature point estimate of

key parameters to further their cause. However, all estimated parameters are conditional upon

the structure under which they were estimated. Structurally different simulation models need to
13

maintain the flexibility to adjust and reject estimated parameters that produce unrealistic

responses. The responsibility, of course, falls on the researcher to define and identify a range of

responses. Once sensitivity analysis reveals the problem, adjustments away from econometric

estimates are warranted. Ironically, when dealing with models that do not maintain the same

structure, rejection of econometric estimates might be necessary to produce simulation responses

consistent with the data used to estimate the econometric model.

Structural inconsistency across simulation models is also important to consider when

adopting a given set of elasticities. Obviously, the same parameter set will produce different

responses across different models, and even across different aggregations of the same model.

Thus, the adoption of parameter sets used in previous studies or standard models does not

abdicate the researcher’s responsibility to think carefully about and defend the estimates.

Structurally consistent estimation/calibration of computational models is an area of

promising research. Following the lead of the real business cycle literature and a philosophical

acceptance of calibration as a method of estimation (Dawkins, Srinivasan, and Whalley (2001)),

there is a new direction in the literature that combines aspects of stochastic estimation in

structural general equilibrium models (Liu, Arndt, and Hertel (2001), and Francois (2001)).

These ideas are in their infancy, but appear encouraging in their useful approach to solve a very

difficult measurement problem.
14

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