6 Quantitative analysis
The data shown in figure 1 suggest a correlation between the composition of public spending and
the skill premium. The model presented above provides one possible economic mechanism to explain
that correlation. In this section we try to measure the quantitative relevance of our mechanism by
calibrating a two-sector version of the model: sector 1 will be the low-tech sector and sector 2 the high-
tech one.19 Since the only available data on public spending composition concern investment, in the
calibration exercise we need to reinterpret the model in terms of intermediate goods. As is common in
the literature, an alternative interpretation of quality-ladder models is one where households consume
a homogeneous consumption good which is assembled from differentiated intermediate goods. The
static utility function in (1) can then be interpreted as a CRS production function in which superior
quality intermediate goods are more productive in manufacturing the final good.20
The exercise consists of choosing the 8 parameters of the model {D, Tr, ρ, γ, n, μ, λι, λ2} to match
salient long-run features of the US economy. Since we work with intermediate goods, we need to choose
our unit of time to be large enough to match their average life time. For this purpose we choose five
years as our unit of time.21 After calibrating the model we explore the effects of government policy
on the skill premium between two 5-years periods, 1976-80 and 1987-91.22 We compute the increase
in the skill premium produced by shocking the model with the change in the composition of public
spending showed in figure 1, and compare it with the actual increase observed in the data.
The calibration of some parameters is standard. Since in steady-state ρ is equal to the interest
rate r, we calibrated it to match a 7 percent average real return on the stock market estimated in
Mehra and Prescott (2003); in our five-year time unit this leads to setting ρ = 0.35.23 We also explore
the sensitivity of the results to calibrating the interest rate to a lower bound of 3 percent, close to the
return on riskless assets which is often used in calibrating business cycle models, leading to ρ = 0.15,
and to an upper bound of 10 percent, which is close to Mehra and Prescott estimates of return on
assets for some recent subperiods; this leads to ρ = 0.5.
We calibrate n to match a population growth rate of 1.14% (Bureau of labor Statistics,1999).
Since our time unit is 5 years, both ρ and n must be multiplied by five, as we do in table II below.
We choose the total working life time D = 40 as in Dinopoulos and Segerstrom (1999) and the total
schooling time Tr = 5 to match the average years of college in the US - both values must be adjusted
1 9 All the results obtained for the model with a continuum of sectors hold for this simplified version.
20 See Grossman and Helpman (1991) ch. 4.
2 1 Since there is no capital in the model we consider intermediate goods as fully depreciating every period. Average
full depreciation period of intermediate goods is 8-10 years. We choose the lenght of a period to be not greater than the
average training time, which we reasonably assume to be 5 years.
22We choose 1976-80 as the starting year because it corresponds to the moment when the composition of public
spending starts moving faster towards high-tech goods, and it is also very close to the turning point of the dynamics of
the skill premium. We limit the analysis to the period 1976-91 because these are the years where the bulk of the increase
in the U.S. skill premium took place (see figure 1).
2 3 Jones and Williams (2000) suggest that the interest rate in R&D-driven growth models is also the equilibrium rate
of return to R&D, and so it cannot be simply calibrated to the risk-free rate on treasury bills - which is around 1%. They
in fact calibrate their R&D-driven growth model with interest rates ranging from 0.04 to 0.14. A different argument
suggests that in the presence of efficient financial market the return on R&D firms stocks will be equalized at the margin
to that of risk-free assets, which is around 2 - 3 p erecent.
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