Learning Outcome:

At the end of this lesson, you will understand the Armington import aggregation function and how it determines the imported/domestic content of the commodities demanded by consumers. 

Domestic-Import Aggregation in the SAM

Commodities that are used as intermediate inputs and for final demand in an economy are "composites."  They are composed of a mix of the domestically-produced and imported varieties of the same product. The commodity columns of the SAM report how composites are assembled.  They show the sourcing of a commodity from domestic producers and from imports.

As an example, Figure 1 presents the commodity columns of the US333 SAM. The columns are torn out of the full SAM, so you can focus only on the commodity aggregation of domestic and imported varieties into a composite commodity. 

The supplies of the domestically-produced varieties are reported in the activity rows (cells shaded in orange). The domestic manufacturing activity, for example, supplies $6,657 billion worth of MFG goods. The supplies of imported varieties are reported in the ROW row (shaded in green). The total supply of the composite MFG commodity, for example, includes $1,878 billion worth of imported MFG. 

Table 1.  Import and Domestic Sourcing in the US333 SAM

Larger version of table available HERE.

The columns of Table 1 also report sales and trade taxes.  For example, in the MFG column, consumers pay $263 billion in sales taxes on purchases of MFG and $23 billion in import tariffs. Producers pay export taxes on MFG of $3 billion. The sum total of the MFG commodity column reports that the supply of the composite MFG commodity is worth $8,824 billion, valued in retail (tax-inclusive) prices. 

Armington Import Aggregation Function

How are the shares of the domestic and imported varieties in the total supply of a commodity determined? The Armington import aggregation function is widely used in CGE models, including the UNI-CGE model, to describe this decision. It is called an "aggregation" function because it describes how a commodity is assembled by aggregating domestic and imported varieties. The function is named after Paul Armington, an economist who developed the idea that consumers differentiate between the domestic and imported varieties of the same good, with preferences about whether the varieties are more or less substitutable as their relative prices change. 

As an example, let's imagine a decision made by consumers in Italy about the varieties of cheese that they will purchase. First, they decide on the quantity of the commodity "cheese" in their basket of goods (See the lesson on Basics of Household Demand to learn more about this first stage in the household's demand decision). Once they have decided on the cheese quantity, the second stage in their decision is to choose the quantity mix of domestic Italian cheese or imported cheese. Consumers are assumed to differentiate between the two cheeses and to find them imperfect substitutes. Perhaps Italian cheeses are best consumed on their own, and imported cheeses are best consumed as a cooking ingredient. The Armington function describes how the Italian consumers choose the least-cost mix of Italian and imported cheese in their basket, given the relative cheese prices, consumers' preferences about the varieties' substitutability, and the total quantity of cheese they can afford to buy. 

Two implications of the Armington assumption in a CGE model are:

(1) There can be two-way trade in the same commodity.  For example, Italy may export its cheese, and at the same time, import foreign cheese. This is possible because the two varieties of cheese are assumed to be differentiated in some way and Italian consumers want some of both types of cheese. The assumption of differentiated varieties of the same good, such as cheese, provides a realistic picture of world trade, in which the same commodity can be imported, exported and domestically produced by a country. 

(2) There may be different prices for different varieties of the same good. For example, the price for Italian cheese may increase relative to imported cheese due to factors such as Italian labor shortages or production taxes. Or, the relative price of imported cheese may increase due to foreign economic developments. The two cheeses can have different prices because they are not exactly the same product. The Armington function describes the consumer as comparing the two prices as they assemble the least-cost mix of cheese that is consistent with their preferences and budgets.

Armington Import Demand Elasticity

The Armington import aggregation function includes an elasticity, called the Armington import demand elasticity, for each commodity in the model. The elasticity describes consumers' willingness to substitute between the domestic and imported varieties of a given quantity of a commodity in their basket as their relative prices change. In the UNI-CGE model, this parameter is named ESUBQc (Elasticity of SUBstitution between domestic and imports for commodity c).

When the ESUBQ parameter value is low, consumers make minimal changes in the quantity ratio of domestic and imported varieties as prices price change, even if the relative price change is large.  An example of a commodity with a low Armington elasticity may be a good that commands strong loyalties, such as demand for domestic versus imported cars. 

A high Armington elasticity parameter value describes consumers who find the goods to be very substitutable and will readily shift between varieties if their relative prices change. An example of a commodity with a high Armington elasticity may be the demand for domestic versus imported dry milk powder, which is almost indistinguishable among sources.  

Because low values of the Armington parameter lead to relatively small changes in traded quantities when prices change, the general equilibrium effects on the rest of the economy are also small.  High values of the Armington elasticity lead to large quantity changes in the domestic-versus-import sourcing of a commodity, and can result in relatively large general equilibrium impacts on the rest of the economy.  For example, large changes in trade flows may lead to large changes in domestic production, import tariff revenues and the government budget. 

Graphical Depiction of the Armington Aggregation Function

Figure 1 depicts the decision about the composition of domestic versus imported varieties of a good in a given basket, using cheese as an example. In the figure, the import aggregation function is shown as isoquant Q₁. It shows all combinations of the imported (QM) and domestic (QD) quantities of cheese that yield the same quantity Q of the composite commodity, "cheese."  The further Q₁ lies from the origin, the greater the quantity of the composite cheese commodity.  As the consumer moves down the isoquant, the share of domestic cheese in quantity Q of cheese become larger relative to the imported variety.   

C₁ is an isocost line with a slope of -PD₁/PM₁, where PD₁ is the initial price of domestic cheese and PM₁ is the initial price of the imported variety.  C₁ represents the consumer's budget - it shows all combinations of imported and domestic cheese that cost the same amount. The further it lies from the origin, the higher is the consumer budget for cheese. The consumer gets the most cheese for the least cost by choosing the ratio at the tangency between their budget line and the highest achievable isoquant, at QM₁ of imports and QD₁ of domestic cheese.  

The Armington import demand elasticity, ESUBQ, describes the curvature of the isoquant, C1. The higher the parameter value, the more willing are consumers to substitute between the varieties as their relative prices change - and the flatter is the isoquant. 

In Figure 1, an increase in the price of domestic cheese relative to the price of the imported variety is shown as a change in the slope of the isocost curve from C₁ to C₂. Minimizing the cost of the composite good leads to a relatively large shift in the composition of the composite commodity "cheese."  The same basket of cheese, quantity Q₁, now contains a higher ratio of imported cheese. The consumer buys quantity QM₂ of imported cheese and QD₂ of the domestic variety, at the tangency of basket Q₁ and isocost C₂.

A low Armington elasticity parameter value describes consumers who find the varieties to be relatively poor substitutes and are reluctant to shift between varieties, even when price differences become large. In this case, the isoquant, Q₁, has more curvature, as depicted in Figure 2. The same change in relative prices seen in Figure 1, from C₁ to C₂, results in relatively small changes in the quantity shares of imported and domestic cheeses used in the composite quantity Q₁ of cheese. Because quantity shifts are smaller in this case, the economy-wide impacts are generally smaller compared to the case of a higher-valued Armington import demand elasticity.  

The sensitivity of economy-wide impacts to the assumed values of the Armington elasticity parameter is an important consideration for CGE modelers.  Modelers address the sensitivity of results to the ESUBQ parameter assumption by critically evaluating the source of the estimated parameter values and by testing for the robustness of results across a range of elasticity values.

In the equation, QQ_c is the quantity of composite commodity c, which is composed of quantities of the imported variety (QM_c) and the domestic variety (QD_c). Parameter alphaq_c is a shift parameter whose fixed value is calculated during the CGE model calibration. Parameter delta_c is a share parameter whose fixed value is also calculated during calibration. Delta measures the share of imports in the quantity of the composite commodity c, and 1-delta is the share of the domestic variety.  Parameter rhoq_c is an exponent term that is a transformation of the Armington import demand elasticity, ESUBQ.  Parameter  rhoq_c is calculated for each commodity c as:  

Copyright: Cornerstone CGE CC 4.0 BY-NC-SA 
Image:  Daniel Julia, CC BY-SA 2.0 <https://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons