IDEAS home Printed from https://ideas.repec.org/a/ksa/szemle/827.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.kszemle.hu/tartalom/letoltes.php?id=827
    Download Restriction: Registration and subscription. 3-month embargo period to non-subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    4. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Özer Karagedikli & Troy Matheson & Christie Smith & Shaun P. Vahey, 2010. "RBCs AND DSGEs: THE COMPUTATIONAL APPROACH TO BUSINESS CYCLE THEORY AND EVIDENCE," Journal of Economic Surveys, Wiley Blackwell, vol. 24(1), pages 113-136, February.
    2. Bennett T. McCallum, 2009. "Determinacy, Learnability, and Plausibility in Monetary Policy Analysis: Additional Results," Central Banking, Analysis, and Economic Policies Book Series, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.),Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 7, pages 203-225, Central Bank of Chile.
    3. Meyer-Gohde, Alexander, 2021. "On the accuracy of linear DSGE solution methods and the consequences for log-normal asset pricing," IMFS Working Paper Series 154, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    4. Castillo, Paul & Rojas, Youel, 2014. "Términos de intercambio y productividad total de factores: Evidencia empírica de los mercados emergentes de América latina," Revista Estudios Económicos, Banco Central de Reserva del Perú, issue 28, pages 27-46.
    5. Gomme, Paul & Klein, Paul, 2011. "Second-order approximation of dynamic models without the use of tensors," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 604-615, April.
    6. Carlo A. Favero, 2007. "Model Evaluation in Macroeconometrics: from early empirical macroeconomic models to DSGE models," Working Papers 327, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    7. Fang Yao, 2008. "Lumpy Labor Adjustment as a Propagation Mechanism of Business Cycles," SFB 649 Discussion Papers SFB649DP2008-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. repec:hal:spmain:info:hdl:2441/7l23tbn4rd9539sljmp8of2hcb is not listed on IDEAS
    9. Ajevskis Viktors, 2017. "Semi-global solutions to DSGE models: perturbation around a deterministic path," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(2), pages 1-28, April.
    10. Patrice Borda & Nlandu Mamingi, 2007. "On the persistence of unemployment in small open economies," Working Papers hal-04053066, HAL.
    11. Barbara Annicchiarico & Alessandra Pelloni, 2014. "Productivity growth and volatility: how important are wage and price rigidities?," Oxford Economic Papers, Oxford University Press, vol. 66(1), pages 306-324, January.
    12. Yue Ma & Guy Meredith & Matthew S. Yiu, 2002. "A Currency Board Model of Hong Kong," Working Papers 012002, Hong Kong Institute for Monetary Research.
    13. McCallum, Bennett T., 2004. "On the relationship between determinate and MSV solutions in linear RE models," Economics Letters, Elsevier, vol. 84(1), pages 55-60, July.
    14. Francisco A. Gallego & Klaus Schmidt-Hebbel & Luis Servén, 2004. "General Equilibrium Dynamics of External Shocks and Policy Changes in Chile," Working Papers Central Bank of Chile 271, Central Bank of Chile.
    15. Richard W. Evans & Kerk L. Phillips, 2018. "Advantages of an Ellipse when Modeling Leisure Utility," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 513-533, March.
    16. Adnan Haider & Musleh ud Din & Ejaz Ghani, 2012. "Monetary Policy, Informality and Business Cycle Fluctuations in a Developing Economy Vulnerable to External Shocks," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 51(4), pages 609-681.
    17. Juan Paez-Farrell, 2008. "Assessing sticky price models using the Burns and Mitchell approach," Applied Economics, Taylor & Francis Journals, vol. 40(11), pages 1387-1397.
    18. Benny Kleinman & Ernest Liu & Stephen J. Redding, 2023. "Dynamic Spatial General Equilibrium," Econometrica, Econometric Society, vol. 91(2), pages 385-424, March.
    19. Gary S. Anderson, 2018. "Reliably Computing Nonlinear Dynamic Stochastic Model Solutions: An Algorithm with Error Formulas," Finance and Economics Discussion Series 2018-070, Board of Governors of the Federal Reserve System (U.S.).
    20. Francesco Bianchi & Giovanni Nicolò, 2021. "A generalized approach to indeterminacy in linear rational expectations models," Quantitative Economics, Econometric Society, vol. 12(3), pages 843-868, July.
    21. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ksa:szemle:827. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Odon Sok (email available below). General contact details of provider: http://www.kszemle.hu .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.