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

Author

Listed:
  • 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. 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.
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    More about this item

    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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