Comparison of Optimal Control Solutions in a Labor Market Model



Table 3

Flows that Contain Endogenous and Exogenous Components.

Description

Variable

Flow from employment to unemployment; job destruction

FEUV

Total flow from unemployment to employment

FUE

Total outflow from unemployment

UO

Total outflow from employment

EO

Total inflow to unemployment

UI

Total inflow to employment

EI

Table 4

Numerical values for baseline model (*=Number of persons/jobs x 1000, annual
averages).

Variable

Value

Variable

Value

U*

750

Feu *

600

FENV *

300

Fuev *

200

FNEV *

400

Feuv *

300

E*

8,600

UO *

4,600

V*

75

r

0.03

θ

0.9

c

0.9

α

0.5

EO *

4,200

V I*

600

τ

0.08

VOU*

200

У

1

VOEX*

400

b

0.3wss

rate to 5% and has no participants in ALMPs. This unemployment target is
a substantial reduction from the baseline rate of nearly 8%, and is a target
that will be difficult for any method to achieve.

The input to the model (or control) is the proportion of the long-term un-
employed on ALMPs (
λ). The control target is zero. There is no constraint
within the model on this proportion so the control method should incorporate
a realistic constraint. We use the constraint of 0
λ 0.5 so that a maxi-
mum of 50% of the long-term unemployed can participate in ALMPs in any
one month.

We follow the convention of using a quadratic objective function where the
optimization aims to reduce the sum of squared deviations from the output
(unemployment) and control (
λ) targets. The deviations are weighted and we



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