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)


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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