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

θ^β =

(1 ^—^a^{) (1} — ^β (1 — ω) λ₀

^t⅛A (1+C∕)

k“-¹ + β(u — V) + v

— k".
λ

ʌ ʌ

Considering U = V =

—θ, the function can be rewritten as

β 1 + C₁

k^a~¹ —

⁽¹^—^a^{) (1}^—^β⁽¹^—^ω) ʌo

ʌ
θ)θʌ

k^aθ~^β+ v

λ θ. (25)

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

θ^β >

⁽¹^—^a^{) (1}^—^β⁽¹^— ш⁾ λ₀

Г -I k

ʌ ʌ

C_v0λ 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

k= , '

1 + CjS

k^a

ʌo

— (λ + e) k.

(26)

¹⁷See appendix.

¹⁸For a detailed derivation see appendix.