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

Chapter 3: Assessing the impact of trade on employment: Methods of analysis
can include both skilled and unskilled labour or, indeed, as many labour categories
as one wishes. 21
If fixed coefficients is an excessively pessimistic foundation on which to analyse
the effect of trade on employment, perhaps the Cobb-Douglas is at the other extreme.
While fixed coefficient analyses implicitly assume an elasticity of substitution equal
to zero, Cobb-Douglas production functions assume that factors can easily substitute
one another. Ideally, one would want to pin down the “true” elasticity of substitution
by collecting a sufficient quantity of relevant data and estimate either of the more
sophisticated production functions mentioned above. An alternative to this relatively
costly and time-consuming procedure would be to assume that the “truth” lies somewhere
in the middle. This would correspond to running the simulation once under
the assumption of fixed coefficients and once under the assumption of a Cobb-
Douglas function. The generated employment effects would then arguably provide
upper- and lower-bound estimates for the employment effects of trade.
A second point is time: like winter snows, the frozen elasticity of substitution
in the fixed coefficients case will tend to melt away with time. Thus, a reasonable
strategy might be to use the fixed coefficient model for small changes around the
initial equilibrium, reserving the more sophisticated approaches for longer time
frames and larger departures from the base data. 22 It has also been argued that the
fixed coefficient case could provide estimates for economies characterized by low
labour mobility. 23
There is some evidence that for longer-term estimates in economies with sufficient
labour mobility, Cobb-Douglas functions may actually represent good proxies
for the actual elasticity of substitution. An early study of trade and employment in
development was undertaken by Krueger and her associates for the NBER and published
in a three-volume work (Krueger, 1983). Behrman (1983) in one chapter
estimates a CES production for 70 countries for the period 1967-73. The total number
of observations is increased by using data on 26 sectors per country, with a total η
= 1,723. The author finds, for this data set, that the Cobb-Douglas does indeed
apply since the estimated CES elasticities of substitution are close to one. Behrman
concludes that trade analysis based on fixed coefficients will be off the mark, as
firms do actively substitute capital for labour as supplies of the latter dry up.
21 − ρ − ρ − 1 / ρ
For the CES function of the form Q = Α[αΚ + (1 – α ) L ] , where Q is output, Α is
scaling parameter, the elasticity of substitution is σ = 1/(1 + ρ) and α is the share of the return to
capital in output. As ρ goes to zero, the CES approaches the Cobb-Douglas. The translog function
takes the form: ln Q = ln γ 0 + α1 ln K + α2 ln L + β1 (ln K) 2 + β2 (ln L) 2 + γ1 (ln K)(ln L), where the
elasticity of substitution is σ = − [(Α + Β) / Q,](Α + Β − 2α2 Α / Β − 2 β2Β / Α− 2γ 1)
where Α = β1 +2β2 ln L + γ 1 ln K and Β = α1 + 2 α2 ln K + γ 1 ln L.
22 A subtle, but highly relevant, implication of the unitary elasticity of the Cobb-Douglas production
function is the property that the total remuneration to a factor of production is constant with respect
to changes in factor proportions. Thus, if the wage rate falls by ε per cent, then employment
increases by ε per cent, and the wage bill remains fixed
23 The issue of labour mobility is extensively discussed by Davidson and Matusz (2004; 2010).
Labour mobility significantly affects the adjustment process following trade reform, as discussed
in detail in Chapter 6 of this volume.
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