Comparison of Optimal Control Solutions in a Labor Market Model

a quadratic programming problem. The MBPC method thence requires more
programming and computational effort than the linear-quadratic approach.

The nonlinear optimization requires the most effort. For the results presented
in Figure 4 the Nelder-Mead direct simplex search algorithm was used. The
algorithm required over 20,000 evaluations of the stacked nonlinear model
to produce these results. Using a quasi-Newton optimization approach the
algorithm failed to reduce the objective function after 100,000 evaluations of
the stacked model.

5 Conclusion

This paper compared three methods of deriving optimal control for the same
nonlinear labor market model. The methods were the standard linear-quadratic
control with a derived linear model and control applied to the nonlinear model;
model based predictive control; and a fully nonlinear optimization with the
model stacked over time. The paper found that for this model the MBPC
produced the best results.

References

Herbert, R. D., 1998. Observers and Macroeconomic Systems. Kluwer Aca-
demic Press, Boston, U.S.A.

Herbert, R. D., Bell, R. D., 2004. Constrained macroeconomic policy devel-
opment with a separate predictive model. Mathematics and Computers in
Simulation 64 (3-4), 467-476.

Herbert, R. D., Leeves, G. D., 2003. Labour market policies and long-term
unemployment in a flow model of the Australian labour market. Australian
Economic Papers 42 (2), 197-213.

Rossiter, J. A., 2003. Model Based Predictive Control: A Practical Approach.
CRC Press, New York, U.S.A.

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