Equilibrium Growth, Inflation, and Bond Yields - Duke University's ...

Intermediate Goods The intermediate goods sector will be characterized by a continuum of monopo-
listic firms. Each intermediate goods firm produces Xi,t with physical capital Ki,t, R&D capital Ni,t, and
labor Li,t inputs using the following technology, similar to Peretto (1999),
where total factor productivity (TFP) is
Xi,t = K α i,t (Zi,tLi,t) 1−α
Zi,t ≡ AtN η 1−η
i,tNt where At represents a stationary aggregate productivity shock, Nt ≡ � 1
0 Njdj is the aggregate stock of R&D
and the parameter η ∈ [0, 1] captures the degree of technological appropriability. Thus, firm-level TFP
is comprised of two aggregate components, At and Nt, and a firm-specific component Ni,t. In contrast
to the neoclassical production function with labor augmenting technology, TFP contains an endogenous
component determined by firm decisions. In particular, the firm can upgrade its technology directly by
investing in R&D. Furthermore, there are spillover effects from innovating; namely, firm-level investments
in R&D will also improve aggregate technology. These spillover effects are crucial for generating sustained
growth in the economy and a standard feature in modern endogenous growth models. 11
The law of motion for At, in logs, is
at = (1 − ρ)a ⋆ + ρat−1 + σɛt
where at ≡ log(At), ɛt ∼ N(0, 1) is i.i.d., and a ⋆ > 0 is the unconditional mean of at.
The law of motion for Ki,t is
�
Ii,t
Ki,t+1 = (1 − δk)Ki,t + Φk Ki,t
Ki,t
� �
� � 1 1− ζ
Ii,t
Ii,t
k
Φk =
+ α2,k
Ki,t
Ki,t
α1,k
1 − 1
ζk
where Ii,t is capital investment (using the final goods) and the function Φk(·) captures capital adjustment
costs. The parameter ζk represents the elasticity of new capital investments relative to the existing stock
of capital. The parameters α1,k and α2,k are set to values so that there are no adjustment costs in the
11 See, for example, Romer (1990), Grossman and Helpman (1991), and Aghion and Howitt (1994).
8
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