Qualification-Mismatch and Long-Term Unemployment in a Growth-Matching Model



is influenced by several exogenous variables and it will change when the exogenous
environment changes. In the (θ^,
k) plane it has a positive concave shape.13

Furthermore, in the long-run labor market equilibrium the steady-state employ-
ment rate is given by14

e(θ) :=
L


p(θ)

V + p(θ} '


eg > 0.


(22)


Therefore, the employment probability depends positively on labor market tight-
ness
θ and on the matching-probability p(θ) and negatively on the separation rate
v. The higher the separation rate, the lower the steady-state employment rate.
Furthermore, the steady-state unemployment rate is determined as well as

1 = e(θ) + w(θ),

where the steady-state unemployment rate u(θ) is defined as u(θ) := U∕L.

Thus, the steady-state for the labor market is described by an efficient factor al-
location function that defines all equilibrium combinations of labor market tightness
and capital intensity.

Steady-State of the Goods Market

As common in neoclassical growth models, the long-run steady-state is charac-
terized by a constant capital intensity, i.e.

k = 0                                 (23)

The steady-state of the goods market can be described by a balanced capital accu-
mulation function
:15

ʌ

θβ = ʌ. k“ - (1 + c,s) ʌ k
c,∙<
Λv                 s

=: Φι(k)


(24)


This function shows all combinations of labor market tightness and capital intensity
characterizing the steady-state in the goods market.

Furthermore, in the (θ, k) plane the balanced accumulation function has - until
the maximum is reached - a positive slope, in the maximum a slope of zero and
behind the maximum a negative slope.16

13See appendix.

14See appendix.

10For a detailed derivation of the balanced accumulation fuction see the appendix.

16See appendix.

19



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