Government spending composition, technical change and wage inequality

TABLE II

SIMULATION RESULTS

The robustness analysis shows that this result is sensitive to the ‘technology gap’ between the two
groups of industries, that is the distance between the quality jump in low and high-tech sectors, λ1 and
λ2. At the minimum distance, obtained at a low-tech markup of 22 percent and a high-tech markup
of 30 percent (λ1, λ2 = 2.1, 2.45), the model predicts a very small increase in inequality, consequently
a negligible share of inequality is explained by our mechanism (only 3.6 percent). On the other hand,
under the maximum technology gap, that is a 5 percent low-tech markup and a 110 percent high-tech
markup (λ1, λ2 = 1.25, 3.7), the policy shock explains 24 percent of the observed increase in inequality.
A second robustness check shows that the results are not too sensitive to changes in the intertemporal
preference parameter ρ. Calibrating ρ to match a 3 percent interest rate, thus reducing the discount
rate to ρ = 0.15, produces a small increase in the quantitative relevance of the policy mechanism
under the benchmark technology gap: the share of inequality attributable to the shock rises from 12
percent to 15 percent. The effect is stronger under the high technology gap, the share of inequality
attributable to the policy shock rises from 24 to 33 percent. The opposite result is obtained calibrating
ρ to match a 10 percent interest rate.

While the benchmark technology gap should be considered as the most plausible value (we have
no arguments for preferring the other values explored above), the upper bound for ρ, corresponding
to a 10 percent interest rate, can be considered implausible. In fact, most of the growth and business
cycle literature calibrates the discount factor to match interest rates in the range (0.3, 0.7). It follows
that our model can plausibly generate between 12 and 15 percent of the observed change in the skill
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premium.³⁰

Quantitatively our mechanism explains a relatively small but not negligible part of the observed
increase in the skill premium. We do not consider this a shortcoming of the paper for the following

³⁰ It is worth noticing that the measure of inequality that we use, wH/wL, could overstate the increase in the skill
premium when we bring the model to the data. This happens because the average wage of skilled workers in the model
is Jθ1 (θ — γ)wHdF (θ) = (θ₀ + 1 — 2γ) wH, the skilled wage times the average quality (efficiency) of skilled workers,
which is smaller than wH . We do not use this measure in the calibration because there is a semplification in the model
that counterbalances the overstatement of the skill premium generated by using wH as average skilled wages. In fact
we assumed that unskilled workers do not accumulate human capital, and so their average wage is simply wL. In the
data average wages of both skilled and unskilled are computed taking into account the ‘abilities’, or human capital, of
heterogeneous workers in the two groups. Hence, using wL in the model for the average unskilled wage understates the
real measure of the skill premium. Our take is to leave human capital accumulation out of the measure of inequality
in the calibration to avoid distortions in both directions. Nevertheless, we have run our simulation for the average skill
premium in the model, and as expected the quantitative effects of the policy shock is smaller but not substantially:
with the benchmark calibration the model explains 9 instead of 12 percent of the observed increase in inequality. The
reduction in the quatitative effects is due to the fact that when the relatice supply of skills increases the average quality
of skilled workers declines, while by construction the model cannot account for the reduction in the average quality of
unskilled workers, since the unskilled wage is fixed to 1.

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