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

Listed author(s):
  • D. Blueschke

    ()

    (Alpen-Adria-Universität Klagenfurt)

  • I. Savin

    (Karlsruhe Institute of Technology
    Université de Strasbourg
    Friedrich Schiller University of Jena
    Ural Federal University)

Abstract Linear-quadratic (LQ) optimization is a fairly standard technique in the optimal control framework. LQ is very well researched, and there are many extensions for more sophisticated scenarios like nonlinear models. Conventionally, 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 as universal as it is considered to be. In particular, we address the question 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 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. 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 illustrates a certain trade-off between quickly finding an optimal solution using the LQ technique (reaching defined policy targets) and accounting for alternative objectives, such as limiting volatility in economic performance. As an implication, we argue in favor of the considerably more flexible optimization technique based on heuristic methods (such as Differential Evolution), which allows one to minimize various loss function specifications, but also takes additional constraints into account.

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File URL: http://link.springer.com/10.1007/s10100-016-0446-7
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Article provided by Springer & Slovak Society for Operations Research & Hungarian Operational Research Society & Czech Society for Operations Research & Österr. Gesellschaft für Operations Research (ÖGOR) & Slovenian Society Informatika - Section for Operational Research & Croatian Operational Research Society in its journal Central European Journal of Operations Research.

Volume (Year): 25 (2017)
Issue (Month): 2 (June)
Pages: 377-392

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Handle: RePEc:spr:cejnor:v:25:y:2017:i:2:d:10.1007_s10100-016-0446-7
DOI: 10.1007/s10100-016-0446-7
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  1. Alex Cukierman, 2002. "Are contemporary central banks transparent about economic models and objectives and what difference does it make?," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 15-36.
  2. Lyra, M. & Paha, J. & Paterlini, S. & Winker, P., 2010. "Optimization heuristics for determining internal rating grading scales," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2693-2706, November.
  3. 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.
  4. Abiodun Egbetokun & Ivan Savin, 2014. "Absorptive capacity and innovation: when is it better to cooperate?," Journal of Evolutionary Economics, Springer, vol. 24(2), pages 399-420, April.
  5. 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.
  6. Ivan Savin & Dmitri Blueschke, 2016. "Lost in Translation: Explicitly Solving Nonlinear Stochastic Optimal Control Problems Using the Median Objective Value," Computational Economics, Springer;Society for Computational Economics, vol. 48(2), pages 317-338, August.
  7. 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.
  8. Antonio Fatás & Ilian Mihov, 2003. "The Case for Restricting Fiscal Policy Discretion," The Quarterly Journal of Economics, Oxford University Press, vol. 118(4), pages 1419-1447.
  9. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
  10. 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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