agents knew at the beginning of the period, 1976, the paradigm shift that would gradually have brought
the government expenditure composition up to its 1991 level. This assumption is most natural within
the fully rational expectations approach we are adopting. Specifically, let us - as before - call βt (ω)
the time t value of government expenditure in sector ω ∈ [0, 1] as a fraction of private consumption.
Let us assume that these fractions change according to the following differential equations:
•
βt(ω)=(1-ψ)(G(ω)-βt(ω)),ω∈[0,1] (24)
where G(ω), ω ∈ [0, 1] are the long-run (steady-state) government expenditure shares and ψ < 1.
Equations (24) are globally stable, and the lower ψ the quicker the government expenditure speed of
adjustment toward the new steady state. The paradigm shift occurred after 1976 can be interpreted
as a sudden permanent change in G(ω): the new values of the G(ω), ω ∈ [0, 1] implies that the old
steady state is left forever and the economy sluggishly starts heading to the new one, according to
eq.s (24). Under rational expectations all the relevant effects of the new eq.s (24) are assumed to
be correctly anticipated by the agents. Of course, such transitional dynamics behavior of the policy
variables entails a transitional dynamics behavior of all the endogenous variables. More importantly,
the expectation of a transition in the government expenditure composition during the relevant period
affects the individual education and consumption decisions, wages, as well as firm production and
R&D employment decisions.
When incorporating a permanent change in vector G(ω), ω ∈ [0, 1] of eq.s (24) in a fully dynamic
version of our model, there is a number of technical issues to consider, as the forward-looking aspect
of the educational choice renders time t’s schooling choice dependent on the whole future trajectory
of the skill premium and of the interest rates, which are necessarily off their steady state values.32
Moreover, the values of the stock variables - human capital and technological difficulty indexes - after
the shift would still reflect for long time the results of the past education and R&D employment choices.
This renders the formal derivation of the dynamics very challenging, because in some of the differential
equations state variables values are forwarded or lagged in time. However, a discretized version of these
equations can be solved and their stability properties analyzed. We solve the transitional dynamics
numerically, and report the results in figure 3 below. All our simulations satisfy Blanchard-Kahn
conditions and hence the equilibrium trajectories obtained are unique. Moreover, we do not restrict
the analysis to a local approximation, but simulate the whole non-linear saddle paths. Consistently
with our previous steady-state analysis, we have coarsely partitioned the set of industries into "low
tech" industries and "high tech" industries, assuming an equal weight33 . All parameters have been
calibrated from their steady-state values, as shown in the previous section. In what follows, we
show the numerical simulations of the whole transitional paths of the relevant endogenous variable
in response to the change in the government expenditure expected (future) steady-state levels. The
only simplifying assumption that we adopt in the simulation of the transition paths is that of keeping
the interest rate at its steady-state value, calibrated at 7 percent. This is motivated by the fact that
in the data the average return on assets do not vary much in the period considered (see Mehra and
32 The equilibrium dynamic systems of equations is derived in appendix II.
33This could be easily generalized.
19