Master Thesis - Humboldt-Universität zu Berlin

The effective returns on domestic and foreign bonds are affected by a risk
premium on bold holdings represented by AR(1) shock ɛ b t = ρ b ɛ b t−1 + ηt, b with
ηt b an i.i.d. - Normal error term. Foreign interest rate is in addition affected
by a risk premium on foreign bond holdings shock, ɛ t following a similar
AR(1) process to ɛ S t .
Current income and financial wealth can be used for consumption and investment
in physical capital. Real consumption Ct τ corresponds to a real
expenditure of (1 + τt c )Ct τ , whereby τt c , an exogeneous variable is designated
as a tax based on consumption, with τt
c = ɛ c t = τ c + ρ c ɛ c t−1 + ηt c , with ηt c an
i.i.d. - Normal error term. Capital formation is described by equation (6),
where we assume the adjustment cost function of changes in investment to
have the following features: S(1) = 0, S ′ (1) = 0, and S ′′ (1) = 1/ϕ represents
the adjustment costs.
4.1.2 Labor market:
K t = K t−1 (1 − δ) + (1 − S
( ) ɛ
I
t I t
)I t (6)
I t−1
The labour supply and wage-setting processes are modelled as in Smets and
Wouters (2003). The elasticity of demand for individual labor supply is assumed
to be constant.
Households are wage-setters in the labour market
and, following Calvo (1983), they can set their wage optimaly with probability
1 − ξ w . With the complementary probability, their wage is indexed to
both past inflation in the consumption price and trend inflation with respective
shares γ w and 1 − γ w . Thus, households choose nominal wage in order to
maximise their intertemporal objective function subject to the intertemporal
budget constraint and to the following labour demand:
l τ t =
( W
τ
t
W t
) −(1+λw)/λ w
L t (7)
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