The optimal control methods we use are, firstly, standard linear-quadratic
techniques based on a liberalization of the model and the optimal control
applied to the full nonlinear model. This approach has been frequently used
in the literature of applying optimal control to nonlinear models. The second
approach is that of applying nonlinear optimization to the stacked over time
nonlinear model. This approach has also been used in the literature. The final
approach we use is that of model based predictive control. This approach has
recently been used with large complicated engineering models, but has not
been applied as frequently to economic models.
2 The Model
The labour market model we use is based on a standard matching model frame-
work. The model is developed and described in Herbert and Leeves (2003). A
summary description of variables in the model is given in Tables 1, 2 and 3.
The model consists of equations for wages, vacancies, job-matching, unemploy-
ment and the dynamics of stock movements. The model includes endogenous
job creation and job destruction (UEV , NEV , ENV , ENV , EUV) and ex-
ogenous flows of workers between states. The time-step for the model is one
month.
2.1 Wages
The wages equation is derived from the bargaining of employers and workers
following a Nash bargaining rule. The resulting equation is:
β (yt-1 + c - τ)ξ0,t + (1 - β) bξ 1 ,t
r + (1 - β )(ξ2 ,t + ξ3 ,t ) + βξ4 ,t
(1)
where
ξ0,t
ξ1,t
ξ2,t
ξ3,t
ξ4,t
FEU,t-1
r + ~β---
Et-1
FUE,t-1
Ut-1
r + ξ2,t + ξ3,t
πqnFEN,t-1 + πqu FEU,t-1
Et-1
FUEV,t-1 + FN EV,t-1
FUE,t-1
Ut-1
Vt-1
FEU,t-1
+ Et-1
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