Comparison of Optimal Control Solutions in a Labor Market Model



has to be solved by numeric methods. We use purely numeric optimization
approaches including quasi-Newton and direct simplex searches.

4 Results

4.1 Policy Strategy

The results from the linear-quadratic control method are given in Figure 2.
The lack of the constraint on the control can be clearly seen as the suggested
changes in ALMPs commencements fall outside the range of a plausible policy
strategy, with the maximum value of
λ of over 1000 being nonsensical.

The results from the MBPC control method are given in Figure 3. When com-
pared to Figure 2, we see that (a) the values of
λ are realistic (b) better results
are obtained for the unemployment rate and long term unemployment with-
out any detriment to short term unemployment and (c) there is less oscillatory
transient dynamics.

The results for the nonlinear optimization method are given in Figure 4. The
first point to note is that these results are for a shorter time horizon than
the previous methods. This is due to the fact that for the longer time horizon
none of the optimization algorithms was successful in reducing the objective
function. When compared to the linear-quadratic and MBPC methods we see
that (a) no steady-state value for
λ is achieved and (b) the results for the
unemployment rate and long-term unemployment are not as good as with the
previous methods.

4.2 Computational Effort

The programming effort and the computational effort of the program for solv-
ing the linear-quadratic method is not extensive. Basically it is using linear al-
gebra and the solving of matrix Ricatti equations for a time step. The optimal
control is then applied to the full nonlinear model. This procedure continues
for each time-step in the time horizon.

The MBPC method requires more effort. At each time step the full nonlin-
ear model is predicted for a predetermined time window and the from the
output a predictive model is developed. From the predictive model the op-
timal control is generated and it is applied to the current time-step of the
full nonlinear model. The optimal control generation requires the solution of

10



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