Trade and Employment From Myths to Facts - International Labour ...

Trade and Employment: From Myths to Facts
Box 3-6: Linear programming: Another approach to assess
the employment effects of trade
Linear programming models are an extension of input-output models that essentially
allow for multiple processes to produce the same good. Policy-makers lucky enough to
have detailed data on options that do not yet exist can add the technological coefficients
to the input-output matrix and ask a program such as LINDO (or even Excel if the
problem is small enough) for the “best” combination of sectors to maximize some
objective function.
Dorfman et al. (1958), the classic reference in the field, would use GDP as the welfare
function to be optimized. But it may occur to an enterprising policy-maker that she could
ask the program to maximize employment. She will be sorely disappointed, however,
since the program will almost certainly produce a nonsensical solution. It is obvious why:
employment was maximized when 100 per cent of the labour force was occupied in
agriculture or, for that matter, in hunter-gatherer activities.
Still, linear programming analysis can be highly useful for practical trade analysis in the
hands of skilled analysts and a relatively skilled data processing team. They must be
crafted for highly specific problems with well-defined constraints. The real value of the
approach comes not in solving the primal problem, the allocation of labour for example,
but in the duality theorem: the dual variable associated with a constraint that fails to
bind in the primal is always zero.
Consider an example in which a lengthy list of occupational categories is included in
the employment database. Calculate the primal solution that maximizes some agreedupon
objective function. The dual variable is known as the shadow value because it
measures the change in the objective function, if some small additional amount of the
binding resource could be found. If it turns out that the shadow value of the ith skill
category is zero, then there is no reason to design policy to increase its supply, at least
in the short run. This idea of complementary slackness, the relationship between the
primal constraint and the value of the associated dual variable, is one of the most
profound in economics. It explains why factors get the returns they do, their shadow
values, in an economy that obeys the laws of perfect competition. To the extent that the
economy differs from the competitive ideal, some additional constraints would have to
be built in.
Linear programming has an illustrious history since it was first used by the US Army in
its operations research. Its glory has faded somewhat as vastly more sophisticated programs
such as the General Algebraic Modelling System (GAMS) have become available.
This programming language, used extensively in CGE modelling, handles linear programming
as a special case and as a result has relegated the method to use in problems of
such extreme dimensions that the non-linear counterpart fails.
3.3.4 Social accounting matrices and computable general
equilibrium (CGE) models
3.3.4.1 An introduction into CGE modelling
As intimated above, CGE models are computer-based simulations capable of constructing
counterfactual scenarios that have been found to be very useful in policy
discussions. 31 A counterfactual is the state of the world in which current policies are
not in force but some others are. The plausibility of the counterfactual depends on:
31 See Ginsburgh and Keyzer (1997), Dervis et al. (1982) and Taylor (1990) for some general examples
of this literature. Of special interest on closure is Dewatripont and Michel (1987).
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