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No such thing like perfect hammer: comparing different objective function specifications for optimal control

Author

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  • Dmitri Blueschke

    () (Klagenfurt University, Austria)

  • Ivan Savin

    () (Friedrich Schiller University Jena)

Abstract

The linear-quadratic (LQ) optimization is a close to standard technique in the optimal control framework. LQ is very well researched and there are many extensions for more sophisticated scenarios like nonlinear models. Usually, the quadratic objective function is taken as a prerequisite for calculating derivative-based solutions of optimal control problems. However, it is not clear whether this framework is so universal as it is considered. In particular, we address the question on whether the objective function specification and the corresponding penalties applied, are well suited in case of a large exogenous shock an economy can experience because of, e.g., the European debt crisis. While one can still efficiently minimize quadratic deviations in state and control variables around policy targets, the economy itself has to go through a period of turbulence with economic indicators, such as unemployment, inflation or public debt, changing considerably over time. In this study we test four alternative designs of the objective function: a least median of squares based approach, absolute deviations, cubic and quartic objective functions. The analysis is performed based on a small-scale model of the Austrian economy and finds that there is a certain trade-off between quickly finding optimal solution using the LQ technique (reaching defined policy targets) and accounting for alternative objectives, such as limiting volatility in the economic performance.

Suggested Citation

  • Dmitri Blueschke & Ivan Savin, 2015. "No such thing like perfect hammer: comparing different objective function specifications for optimal control," Jena Economic Research Papers 2015-005, Friedrich-Schiller-University Jena.
  • Handle: RePEc:jrp:jrpwrp:2015-005
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    References listed on IDEAS

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    1. Blueschke-Nikolaeva, V. & Blueschke, D. & Neck, R., 2012. "Optimal control of nonlinear dynamic econometric models: An algorithm and an application," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3230-3240.
    2. Blueschke, D. & Blueschke-Nikolaeva, V. & Savin, I., 2013. "New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 821-837.
    3. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    4. Peter Winker & Marianna Lyra & Chris Sharpe, 2011. "Least median of squares estimation by optimization heuristics with an application to the CAPM and a multi-factor model," Computational Management Science, Springer, vol. 8(1), pages 103-123, April.
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    Cited by:

    1. Dimitri Blueschke & Viktoria Blüschke-Nikolaeva & Ivan Savin, 2015. "Slow and steady wins the race: approximating Nash equilibria in nonlinear quadratic tracking games," Jena Economic Research Papers 2015-011, Friedrich-Schiller-University Jena.

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    More about this item

    Keywords

    Differential evolution; nonlinear optimization; optimal control; least median of squares; cubic optimization; quartic optimization;

    JEL classification:

    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination
    • E63 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Comparative or Joint Analysis of Fiscal and Monetary Policy; Stabilization; Treasury Policy

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