Transcript General Equilibrium Models of Trade and Open Economies

General Equilibrium Models of
Trade and Open Economies
T.Huw Edwards
Department of Economics
Loughborough 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.
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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 fixedcoefficients 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
Nation 3’s
Type of
cars
Nation 2’s type of
cars
CES aggregation
Nation 1’s type
Of cars
Utility from clothes
Utility from food
CES aggregate Utility from cars
CES
Aggregate
Overall
Utility
In Nation
1
• 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 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.
• 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’.