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



Figure 4: Analysis of the Stability for the Steady-State.


dynamic factor allocation function17

θβ =


(1 a) (1 β (1 ω) λ0


t⅛A (1+C∕)


k“-1 + β(u — V) + v


— k".
λ


ʌ ʌ

Considering U = V =


ʌ

θ, the function can be rewritten as


β 1 + C1


ka~1


(1 a) (1 β (1 ω) ʌo


ʌ
θ)θʌ


kaθ~β+ v


λ θ. (25)


Equation (25) shows the transitional dynamics for θβ, i.e. labor market tightness
increases if

θβ >


(1 a) (1 β (1 ш) λ0

Г                                -I k

ʌ ʌ

Cv0λ v λ+ ɪkɑ-i

Thus, labor market tightness increases, if the realized level of labor market tightness
is greater than the equilibrium level and vice versa.

Furthermore, the following dynamic capital accumulation function can be derived

ЯЧ18

as

k= , '

1 + CjS


ka


ʌo


(λ + e) k.


(26)


17See appendix.

18For a detailed derivation see appendix.

21



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