Comparison of Optimal Control Solutions in a Labor Market Model

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)

2.3 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
(U_S), 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:

FuEV,t ⁼ cm Vt¹-^-1^α (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 ^{— π}S,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 (π_S) and long-
term unemployment (πL). They are represented respectively by:

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