No such thing as a perfect hammer: comparing different objective function specifications for optimal control.

Area of Science:

• Economics
• Econometrics
• Computational Economics

Background:

• Linear-quadratic (LQ) optimization is a standard optimal control technique.
• The quadratic objective function is conventionally required for derivative-based solutions.
• The universality of LQ optimization, especially during large economic shocks, is questioned.

Purpose of the Study:

• To assess the suitability of LQ optimization objective functions during significant exogenous economic shocks.
• To investigate alternative objective functions beyond the standard quadratic form.
• To compare LQ optimization with heuristic methods for economic policy.

Main Methods:

• Testing four alternative objective functions: least median of squares, absolute deviations, cubic, and quartic.
• Analysis using a small-scale model of the Austrian economy.
• Comparison of LQ optimization with heuristic optimization methods (e.g., Differential Evolution).

Main Results:

• LQ optimization efficiently minimizes deviations but may not adequately address economic turbulence during shocks.
• Alternative objective functions reveal a trade-off between solution speed and accounting for economic volatility.
• Heuristic methods demonstrate greater flexibility in handling diverse loss functions and constraints.

Conclusions:

• The standard LQ optimization framework may be insufficient for economies experiencing large exogenous shocks.
• Flexible optimization techniques, such as heuristic methods, are preferable for economic policy due to their adaptability.
• Consideration of alternative objective functions and constraints is crucial for robust economic policy.