3.4 The role of the elasticity of substitution and external economies
of scale
This section performs robustness checks with respect to the elasticity of substitution σ
between varieties of inputs and with respect to the degree of external economies of scale ν.
This exercise confirms the overall validity of Results 1 and 2 discussed ab ove and further
allows insights into the details of the model mechanisms.
First, we focus on an increase in the elasticity of substitution σ. This parameter has
crucial implications for the role of the competitiveness and income effects discussed in
Result 1c.
The implications of changing σ are illustrated in Figure 4 which makes similar assump-
tions as Figure 3. Instead of relative country size, the y-axis now varies the elasticity of
substitution between 3.8 and 10, and the x-axis varies values of trade costs (equal between
all countries) as in Figure 2.24 The following result summarizes.
Result 3 [The elasticity of substitution and spill-overs]
The higher the elasticity of substitution, the smaller is the increase in unemployment rates
in all countries following a rise of country 1’s unemployment benefits.
A higher σ more strongly insulates firms from foreign competition as exports are
proportional to τ 1-σ.25 For given levels of trade costs, this term becomes smaller with
increases in σ and thus bilateral trade flows become lower. As a consequence, countries
depend less on global demand and more on domestic demand. This has two implications.
On the one hand, the country where the labor market shock occurs is hit harder as it
can not spill-over part of the negative shock to other countries, on the other hand trading
partners are less affected due to lower trade volumes. Hence, in country 1, the income
effect is stronger with higher σ , while it is weaker in the rest of the world.
Note further that, when ν < 1, the monopolistic competition model exhibits a monopoly
distortion that leads to excess entry. The strength of this distortion, however, depends
on σ (big if σ is small). So, as we increase σ, we reduce the distortion, which has positive
effects on the level of aggregate productivity and hence labor market outcomes. This ex-
plains why the increase in unemployment is smaller in country 1 for higher σ's. Overall,
the smaller changes in unemployment of country 1 as well as the lower trade volumes for
higher values of σ imply that adverse spill-overs from country 1 to the rest of the world
should decrease with rising σ. In a world with increased product differentiation (σ falls),
cross-country interdependencies become more pronounced.
Up to now we have analyzed our model for the case of ν = 0, which implies that
absolute size effects do not influence the level of unemployment. Hence, whenever we
would increase the population in all countries, the rate of unemployment would not change.
However, new trade theory (see for example, Helpman and Krugman, 1985) and the new
economic geography (see for example, Fujita, Krugman, and Venables, 1999; or Baldwin,
24 Note that σ is bounded from below by the condition σ 1 > bi for given bi and βi.
σ-βi i
25This can be seen from rearranging equation (3).
24