General Equilibrium Models of Trade and Open Economies

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General Equilibrium Models of Trade and Open
Economies

• T.Huw Edwards
• Department of Economics
• Loughborough University.
• February, 2006.

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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.

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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.

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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).

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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
  PgPWgtg, where PWg is the World traded price
  (inclusive of transport to the countrys 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.

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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.

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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 (ww1wn).
• PgPWgtga1gw1a2gw2angwn. Note that a1g is
  the input-output coefficient for use of factor 1
  in producing good g.

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• 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.
• Efaf1Y1af2Y2afnYn.
• 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.

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• 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.

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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.

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Specialisation
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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.

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• 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.

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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 gt x is fixed in the
  long-run).

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• 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.

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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.

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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.

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A typical Armington Structure

• Factors of prodn

Nation 3s Type of cars
Nation 2s type of cars
CES aggregation
Nation 1s type Of cars
CES aggregate Utility from cars
CES Aggregate Overall Utility In Nation 1
Utility from clothes
Utility from food
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• 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.

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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.

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• 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.

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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.

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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.

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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.

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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!

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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.

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• 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 openness?more
  competition?lower profit markups (and less
  deadweight loss). This is more true the smaller
  and the less open the economy is to start with.

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• 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.

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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.

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• 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.