General Equilibrium Models of Trade and Open Economies

T.Huw EdwardsDepartment of EconomicsLoughborough University.

February, 2006.

The way trade is modelled matters!

• This is true for all kinds of models of the economy, not just for specific models of trade.

• In some formulations of trade, most final goods prices (in the absence of tariff or non-tariff barriers) in an open economy are set on World markets. This affects all kinds of economic policy: one economist argues that effectively ‘your wages are being set in Beijing’.

The Heckscher-Ohlin Formulation

• See Krugman and Obstfeld, International Economics (Addison Wesley).

• The Heckscher-Ohlin (H-O) formulation is the standard neoclassical model of international trade, and closely linked to the associated Stolper-Samuelson Theorem.

Assumptions• WEAK CASE ASSUMPTIONS• Goods are produced with constant returns to scale and

diminishing returns to substitution.• Goods are homogenous, regardless of their supplier.• Factors are completely mobile between sectors, but

immobile between countries. Countries differ in factor endowments.

• There is perfect competition.

• STRONG CASE ASSUMPTIONS• Technology is the same across all countries• There are no transport costs• There is the same number of factors as produced goods• All countries produce all goods (no specialisation).

Modelling a H-O economy: 1. The single country model

• We are assuming the country is a small, open economy.

• Because the country is a price-taker on World markets, the domestic price of every good is Pg=PWg+tg, where PWg is the World traded price (inclusive of transport to the country’s borders) and tg is the tariff.

• This assumption has a great simplifying effect for GE modellers. It means that the production and consumption sides of the economy are effectively SEPARABLE: they can usually be modelled apart.

Two cases

• The country has n factors of production.• The country will never produce more goods than

it has factors of production. There are therefore two situations:– 1. The ‘Heckscher-Ohlin-Samuelson’ situation. The

country produces the same number of goods (n) as it has factors.

– 2. The specialisation situation. The country produces less than n goods.

– Most of the neoclassical trade literature focuses on case 1.

The HOS model with no specialisation

• Because we are assuming perfect competition, we can write down a Zero Profit Condition for each industry, relating the price of each of n goods to the wages of each of the n factors (w=w1…wn).

• Pg=PWg+tg=a1gw1+a2gw2+…+angwn. Note that a1g is the input-output coefficient for use of factor 1 in producing good g.

• There are also n equations (one for each factor) relating use of the factor in each industry to the total endowment, Ef. The latter is taken as being exogenous.

• Ef=af1Y1+af2Y2+…+afnYn.

• In this case, Yg is the output of industry g.• Finally, there are also n2 equations for

each of the n x n input-output coefficients.• The number of unknowns equals the

number of equations, so the model should solve exactly.

• Key properties of the H-O-S model are that factor prices are determined solely by final market prices (which depend on World traded prices and tariffs) and technology. Changes in factor endowments result in a change in the relative production of different goods, but NOT in changes in relative factor prices, UNLESS there is specialisation.

• Input-output ratios are constant unless there is specialisation.

2. The multi-country model

• The above model can be extended to a multi-country framework, so long as the number of goods equals the number of factors, and each country produces each good.

Specialisation

A specialised economy

• The relative change in prices at which a 2 x 2 economy will become specialised depends upon the initial levels of production of the two industries, the relative factor intensities of the two industries and the elasticity of substitution between the two factors.

• An economy can become specialised for small changes in goods prices (due to World price change or changes in protection) if it is already nearly specialised, or if the elasticity of substitution between the factors is high.

• By contrast, if technology is of the Leontief fixed-coefficients variety (Rybczynski) then the economy will never become completely specialised.

• If the economy is specialised, so it produces fewer goods than the number of factors, then it is still possible to determine the relative factor wages.

• These will now vary according to factor endowments.

• However, the general equilibrium model structure is different. Effectively, factor wages vary to change the input-output coefficients within the one industry to equate factor use with factor endowments.

• It is not easy to incorporate both the HOS and the specialised economy model within a single code.

A fixed factor: the Ricardo-Viner model

• One way to make the H-O model more ‘conservative’ (and realistic) is to introduce a fixed factor.

• This may be a totally sector-specific factor (land).

• Alternatively, a factor may not be mobile between sectors. Or a proportion of a factor is assumed to be immobile (for example, many models assume x% of the capital stock in each industry is fixed in the short-run, and y% > x% is fixed in the long-run).

• Introducing a fixed factor reduces the rate at which the economy tends towards complete specialisation.

• It also reduces the effect of traded prices on all factor wages (an effect derived in two papers by Mussa and Mayer, both JPE, 1974).

• Factor wages are sensitive to endowments.

• See Edwards and Whalley, NBER paper 9265, Oct 2002.

The Armington Formulation• The Armington model is the most popular general

equilibrium formulation.• It is seen as less extreme in its predictions than the HOS

model. • It is also more easily reconciled with the observable

behaviour of economies.• It does not suffer from the problem of complete

specialisation (or at least, rarely).• The downside of the Armington formulation is that it is

seen as relatively ‘ad hoc’ by theorists.• Armington models require the production and

consumption sides of the economy to be modelled simultaneously.

Armington: key assumptions

• Goods are produced subject to diminishing returns to substitution and constant returns to scale.

• There are also diminishing returns to substitution in consumption.

• WITHIN each country there is perfect competition.

• HOWEVER, goods within an industry produced by different countries are assumed to be QUALITATIVELY different, and are imperfect substitutes.

A typical Armington Structure

• Factors of prodn

CES aggregation

Nation 1’s typeOf cars

Nation 2’s type of cars

Nation 3’s Type of cars

CES aggregate Utility from cars

Utility from clothes

Utility from food

CES AggregateOverallUtility In Nation1

• Note how this structure involves 3 levels of nested CES functions:

• Factors are aggregated to produce goods

• Goods from different source nations are aggregated together

• Finally different classes of goods are aggregated together to produce overall utility.

Typical elasticities of substitution

• Aggregation of factors:– Often between 0.5 and 1 (factors are complements). If 1, a

Cobb-Douglas production structure is used (which is simpler).– Materials inputs often use fixed (Leontief) coefficients.

• Aggregation of national varieties:– Elasticities are usually higher. Say 1.25 in the short run or 2-4 in

the longer term. Sometimes depends on the commodity.• Top level choice between goods:

– Elasticities are often close to unity. A Cobb-Douglas function, or even a Stone-Geary linear expenditure system (which takes more account of the income elasticities of luxury goods versus necessities) are popular here.

– IT IS USUAL TO CARRY OUT SENSITIVITIES WITH DIFFERENT SUBSTITUTION ELASTICITIES.

• Where the elasticities of substitution between nations are high, the properties of the model are similar to a Heckscher-Ohlin model. Often, in these cases, we will introduce sectorally-fixed factors (a la Ricardo-Viner) for reasons of greater realism.

• When elasticities of substitution are lower, properties are quite different. In particular there are:– Strong optimal subsidy effects of tariffs (use of

monopoly power on World markets). A country can change its terms of trade.

– Tax export effects for other taxes.

Single- or Multi-Country Armington Models

• Armington Models with a number of different countries are often used to examine regional trade agreements (trade creation versus trade diversion effects). Usually, the selection of countries is chosen with particular relevance to the regional agreement in question. Other countries are lumped together as ‘Rest of the World’.

• Where the model is more concerned with internal tax policies, then a single-country Armington structure is appropriate. Import demand is modelled as above (taking the Rest of the World prices as given, but the exchange rate as variable). Export demand is assumed to have a single, downward sloping demand curve for each commodity.

Trade Closure• In GENERAL EQUILIBRIUM models, trade is usually

assumed to balance. • The price of one good (or factor) in one region is set as

the denominator for the model, and normalised at unity. • Modellers often assume the trade balance remains at its

level in the base year. Alternatively, adjustments may be made for changes in international aid etc. Or all countries may be assumed to move to complete balance in trade.

• Remember, the balances of consumers, government and the external sector must sum to zero.

• In PARTIAL EQUILIBRIUM models, the exchange rate is assumed to be fixed and trade balance is ignored.

CAPITAL MOBILITY

• Some models allow for capital to be mobile between countries.

• Often the way this is done is to assume a fixed capital stock Worldwide, but allow it to move between countries to equate interest rates across all countries.

• If capital flows into a country, we need to remember that interest, profits and dividend will be paid to foreigners. These should therefore be deducted from exports in the trade balance.

Dynamic CGE models• Dynamic CGE models are closer in spirit to macro models

(particularly if they also have ‘sticky’ prices and money).• They take account of savings, investment and exchange rate

overshooting effects. This sort of effect implies an Armington trade structure, or something similar.

• They usually have forward-looking expectations. In practice this is often treated as meaning perfect certainty, so the model is solved forwards to an end-point. The tricky bit is getting plausible ‘terminal conditions’.

• These models tend to be hard to solve, and are often very sensitive to choice of terminal conditions.

• Multi-country models are usually too large to solve as anything other than static models.

• Broadly speaking, people need to choose between a multi-country model of trade, with regional and sectoral effects modelled in detail, or a dynamic model with more macroeconomic adjustments but less regional and sectoral detail. HORSES FOR COURSES!

Other formulations: Dixit-Stiglitz

• A separate note on Dixit-Stiglitz models is available on the resources site.

• Dixit-Stiglitz models are much harder to program and solve, compared to Armington, but generally suggest that trade has much deeper effects on the whole economy.

• These models assume that all firms produce differentiated products, and that there are economies of scale at the firm level.

• Consumers have a ‘love of variety’. This is modelled by aggregating together all firms’ output with a CES aggregation, with an elasticity of substitution greater than unity.

• The CES aggregation of produce of an industry is therefore across all firms, not just across countries.

• In the short run, the number of firms in each country is fixed. In many ways, this model is similar to Armington, except that changing openness to trade may lead to changes in profit markups. In general, greater opennessmore competitionlower profit markups (and less deadweight loss). This is more true the smaller and the less open the economy is to start with.

• In the long-run the number of firms in an industry varies to ensure monopolistic profits just cover the fixed cost of entry. – In this case, opening up to trade produces a

further gain, insofar as some firms close, leading to scale economies.

– Individual countries may lose.– Where firms produce inputs, and there are

‘love of variety effects’ in intermediates, the model may well have multiple equilibria.

Heterogeneous Firms Models• These are probably the latest development

in GE models. They assume that not all firms are equally efficient.

• Critically, firms only find out how efficient they are after they have entered the industry and produced at a minimum economic scale for a fixed period of time.

• After that time, firms below a reservation level of efficiency close, while the more efficient remain open.

• Trade shocks can produce batting-order effects, raising efficiency among the surviving firms in declining industries (see Edwards, International Review of Applied Economics, forthcoming April? 2006). Greater trade openness generally leads to rising efficiency for this reason.

• If there are costs to entering foreign markets, then only efficient firms will export. The opening up of export markets may provide a selection mechanism in favour of the most efficient firms (recent work by Ghironi and Melitz and by Bernard, Schott and Redding confirms this).

THIS TYPE OF MODEL IS MUCH MORE COMPLICATED, BUT RICHER IN ITS EFFECTS ACROSS THE WHOLE ECONOMY. HETEROGENEOUS FIRM MODELS SHOULD NOT YET BE CONSIDERED ‘TRIED AND TESTED’.