2.2 Vacancies
Vacancies are also derived from the employer-worker bargaining and result in:
( FuEV,t-1 + FNEV,t-1)( yt-1 — Wt-1 — τ )
c (r + ξ 2 ,t-1)
(2)
2.3 Job Matching Function
The job matching function uses Cobb-Douglas technologies to match the un-
employed to vacancies. It differentiates between the short-term unemployed
(US), the long-term unemployed who have participated in ALMPs (LP ) and
the long-term unemployed who have not participated in the ALMPs (LNP ).
The matching function is:
(3)
FuEV,t = cm Vt1--1α (US,t-1 + θ (ULNP,t-1 + σULP,t-1)α
The policy choice (or control) is λ, where λ = ULP/(ULNP + ULP ).
2.4 Unemployment
Short-term unemployment is divided into 12 one-month duration classes, with
U1,t = UIt (4)
and
Uk,t = (1 — πS,t)Uk-1,t-1 (5)
Total short-term unemployment is the summation of all duration classes:
12
US,t = Uk,t (6)
k=1
Long-term unemployment is given by:
UL,t = Ut — US,t — λt-1UL,t-1 + λt-6UL,t-6 (7)
There is an escape probability from short-term unemployment (πS) and long-
term unemployment (πL). They are represented respectively by:
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