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Nemlineáris, sztochasztikus differenciaegyenletek megoldása Uhlig-algoritmussal
[Solving non-linear, stochastic differential equations with Uhlig algorithms]

Author

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  • Horváth, Áron

Abstract

A modern közgazdasági elemzések során gyakran alkalmaznak sztochasztikus, dinamikus modelleket. A mikroökonómiai alapokra épülő makroökonómiai modellekben például az általános egyensúlyi modellek megoldásaként adódó feltételek nemlineáris, sztochasztikus differenciaegyenlet-rendszerrel írhatók le. Receptszerű írásomban megmutatom, hogy az egyszerűbb rendszerek - a számítástechnika fejlődésének köszönhetően - már graduális szintű közgazdasági tudással megoldhatóvá és elemezhetővé váltak. A Blanchard-Kahn [1980] tanulmányhoz fűződő algoritmus egy mátrix-egyenletrendszer megoldásaként mutatja be a modellek rekurzív formáját. Harald Uhlig német közgazdász ezt alakította át számítógépes alkalmazás céljából (Uhlig [1999]), így a felhasználók körében gyakran rá hivatkoznak. A módszer alkalmazhatóságának két fontos megszorító kritériuma van: a modelleknek létezzen állandósult állapotuk, és legyenek lineárisan közelíthetők. Két példával illusztráljuk, hogy a megoldáshoz szükséges eszköztár nem haladja meg a bonyolultabb multiplikátorelemzések szintjét. A reál üzleti ciklusok (RBC) modelljén részletesen sorra vesszük a lépéseket, majd röviden egy rövid távú alkalmazkodást megjelenítő, ragadós áras modellt is bemutatunk. Journal of Economic Literature (JEL) kód: A23, C63.

Suggested Citation

  • Horváth, Áron, 2006. "Nemlineáris, sztochasztikus differenciaegyenletek megoldása Uhlig-algoritmussal [Solving non-linear, stochastic differential equations with Uhlig algorithms]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(3), pages 235-252.
    • Handle: RePEc:ksa:szemle:827
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    References listed on IDEAS

    as
    1. Carl E. Walsh, 2003. "Monetary Theory and Policy, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232316, December.
    2. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    3. King, Robert G. & Rebelo, Sergio T., 1999. "Resuscitating real business cycles," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 14, pages 927-1007, Elsevier.
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    JEL classification:

    • A23 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - Graduate
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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