IDEAS home Printed from https://ideas.repec.org/p/cqe/wpaper/4315.html
   My bibliography  Save this paper

Higher-order statistics for DSGE models

Author

Listed:
  • Willi Mutschler

Abstract

This note derives closed-form expressions for unconditional moments, cumulants and polyspectra of order higher than two for linear and nonlinear (pruned) DSGE models. The procedures are demonstrated by means of the Smets and Wouters (2007) model (first-order approximation), the An and Schorfheide (2007) model (second-order approximation) and the canonical neoclassical growth model (third-order approximation). Both the Gaussian as well as Student's t-distribution are considered as the underlying stochastic process. Useful Matrix tools and computational aspects are also discussed.

Suggested Citation

  • Willi Mutschler, 2015. "Higher-order statistics for DSGE models," CQE Working Papers 4315, Center for Quantitative Economics (CQE), University of Muenster.
  • Handle: RePEc:cqe:wpaper:4315
    as

    Download full text from publisher

    File URL: https://www.wiwi.uni-muenster.de/cqe/sites/cqe/files/CQE_Paper/CQE_WP_43_2015.pdf
    File Function: Version of November 2015
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. van Binsbergen, Jules H. & Fernández-Villaverde, Jesús & Koijen, Ralph S.J. & Rubio-Ramírez, Juan, 2012. "The term structure of interest rates in a DSGE model with recursive preferences," Journal of Monetary Economics, Elsevier, vol. 59(7), pages 634-648.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
    4. Martin Andreasen, 2010. "How to Maximize the Likelihood Function for a DSGE Model," Computational Economics, Springer;Society for Computational Economics, vol. 35(2), pages 127-154, February.
    5. Lilia Maliar & Serguei Maliar & Sébastien Villemot, 2013. "Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions," Computational Economics, Springer;Society for Computational Economics, vol. 42(3), pages 307-325, October.
    6. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 639-669.
    7. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August.
    8. Vasco Cúrdia & Marco Del Negro & Daniel L. Greenwald, 2014. "Rare Shocks, Great Recessions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1031-1052, November.
    9. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
    10. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.),Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    11. Zhongjun Qu & Denis Tkachenko, 2012. "Identification and frequency domain quasi‐maximum likelihood estimation of linearized dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 3(1), pages 95-132, March.
    12. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    13. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    14. Francois Gourio, 2012. "Disaster Risk and Business Cycles," American Economic Review, American Economic Association, vol. 102(6), pages 2734-2766, October.
    15. Kim, Jinill & Ruge-Murcia, Francisco J., 2011. "Monetary policy when wages are downwardly rigid: Friedman meets Tobin," Journal of Economic Dynamics and Control, Elsevier, vol. 35(12), pages 2064-2077.
    16. Siddhartha Chib & Srikanth Ramamurthy, 2014. "DSGE Models with Student- t Errors," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 152-171, June.
    17. Gary Anderson, 2008. "Solving Linear Rational Expectations Models: A Horse Race," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 95-113, March.
    18. Del Negro, Marco & Schorfheide, Frank, 2008. "Forming priors for DSGE models (and how it affects the assessment of nominal rigidities)," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1191-1208, October.
    19. Thomas A. Lubik & Frank Schorfheide, 2004. "Testing for Indeterminacy: An Application to U.S. Monetary Policy," American Economic Review, American Economic Association, vol. 94(1), pages 190-217, March.
    20. Hong Lan & Alexander Meyer-Gohde, 2013. "Decomposing Risk in Dynamic Stochastic General Equilibrium," SFB 649 Discussion Papers SFB649DP2013-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    21. Martin M Andreasen & Jesús Fernández-Villaverde & Juan F Rubio-Ramírez, 2018. "The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications," Review of Economic Studies, Oxford University Press, vol. 85(1), pages 1-49.
    22. Ivana Komunjer & Serena Ng, 2011. "Dynamic Identification of Dynamic Stochastic General Equilibrium Models," Econometrica, Econometric Society, vol. 79(6), pages 1995-2032, November.
    23. Guerrieri, Luca & Iacoviello, Matteo, 2015. "OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily," Journal of Monetary Economics, Elsevier, vol. 70(C), pages 22-38.
    24. Ascari, Guido & Fagiolo, Giorgio & Roventini, Andrea, 2015. "Fat-Tail Distributions And Business-Cycle Models," Macroeconomic Dynamics, Cambridge University Press, vol. 19(2), pages 465-476, March.
    25. Mutschler, Willi, 2015. "Identification of DSGE models—The effect of higher-order approximation and pruning," Journal of Economic Dynamics and Control, Elsevier, vol. 56(C), pages 34-54.
    26. Lilia Maliar & Serguei Maliar, 2015. "Merging simulation and projection approaches to solve high‐dimensional problems with an application to a new Keynesian model," Quantitative Economics, Econometric Society, vol. 6(1), pages 1-47, March.
    27. Luca Sala, 2015. "Dsge Models in the Frequency Domains," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 219-240, March.
    28. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    29. Giovanni Lombardo & Harald Uhlig, 2018. "A Theory Of Pruning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 1825-1836, November.
    30. Ruge-Murcia, Francisco J., 2007. "Methods to estimate dynamic stochastic general equilibrium models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2599-2636, August.
    31. Jushan Bai & Serena Ng, 2005. "Tests for Skewness, Kurtosis, and Normality for Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 49-60, January.
    32. Grüne, Lars & Semmler, Willi & Stieler, Marleen, 2015. "Using nonlinear model predictive control for dynamic decision problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 112-133.
    33. Xavier Gabaix, 2012. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 645-700.
    34. Mavroeidis, Sophocles, 2005. "Identification Issues in Forward-Looking Models Estimated by GMM, with an Application to the Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 421-448, June.
    35. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    36. Hong Lan & Alexander Meyer-Gohde, 2013. "Pruning in Perturbation DSGE Models - Guidance from Nonlinear Moving Average Approximations," SFB 649 Discussion Papers SFB649DP2013-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    37. Junior Maih, 2014. "Efficient Perturbation Methods for Solving Regime-Switching DSGE Models," Working Papers No 10/2014, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    38. Yong Bao, 2013. "On Sample Skewness and Kurtosis," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 415-448, December.
    39. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    40. 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.
    41. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," Review of Economic Studies, Oxford University Press, vol. 37(4), pages 537-542.
    42. Martin Andreasen, 2012. "On the Effects of Rare Disasters and Uncertainty Shocks for Risk Premia in Non-Linear DSGE Models," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(3), pages 295-316, July.
    43. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    44. Stephanie Schmitt-Grohé & Martin Uribe, 2013. "Downward Nominal Wage Rigidity and the Case for Temporary Inflation in the Eurozone," Journal of Economic Perspectives, American Economic Association, vol. 27(3), pages 193-212, Summer.
    45. Francisco J. Ruge-Murcia, 2013. "Generalized Method of Moments estimation of DSGE models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.),Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 20, pages 464-485, Edward Elgar Publishing.
    46. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.),Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729, Elsevier.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    higher-order moments; cumulants; polyspectra; nonlinear SDGE; pruning;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cqe:wpaper:4315. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Susanne Deckwitz). General contact details of provider: http://edirc.repec.org/data/cqmuede.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.