IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v56y2015icp34-54.html
   My bibliography  Save this article

Identification of DSGE models—The effect of higher-order approximation and pruning

Author

Listed:
  • Mutschler, Willi

Abstract

This paper shows how to check rank criteria for a local identification of nonlinear DSGE models, given higher-order approximations and pruning. This approach imposes additional restrictions on (higher-order) moments and polyspectra, which can be used to identify parameters that are unidentified in a first-order approximation. The identification procedures are demonstrated by means of the Kim (2003) and the An and Schorfheide (2007) models. Both models are identifiable with a second-order approximation. Furthermore, analytical derivatives of unconditional moments, cumulants and corresponding polyspectra up to fourth order are derived for the pruned state-space.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:dyncon:v:56:y:2015:i:c:p:34-54
    DOI: 10.1016/j.jedc.2015.04.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188915000731
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2015.04.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stephanie Schmitt‐Grohé & Martín Uribe, 2012. "What's News in Business Cycles," Econometrica, Econometric Society, vol. 80(6), pages 2733-2764, November.
    2. Sergey Ivashchenko, 2014. "DSGE Model Estimation on the Basis of Second-Order Approximation," Computational Economics, Springer;Society for Computational Economics, vol. 43(1), pages 71-82, January.
    3. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    4. Iskrev, Nikolay, 2008. "Evaluating the information matrix in linearized DSGE models," Economics Letters, Elsevier, vol. 99(3), pages 607-610, June.
    5. Zhongjun Qu, 2014. "Inference in dynamic stochastic general equilibrium models with possible weak identification," Quantitative Economics, Econometric Society, vol. 5, pages 457-494, July.
    6. Bianchi, Francesco, 2016. "Methods for measuring expectations and uncertainty in Markov-switching models," Journal of Econometrics, Elsevier, vol. 190(1), pages 79-99.
    7. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models—Rejoinder," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 211-219.
    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. Robert Kollmann, 2013. "Tractable latent state filtering for non-linear DSGE models using a second-order Approximation," CAMA Working Papers 2013-29, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    11. Robert Kollmann, 2015. "Tractable Latent State Filtering for Non-Linear DSGE Models Using a Second-Order Approximation and Pruning," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 239-260, February.
    12. 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.
    13. Elena Rusticelli & Richard Ashley & Estela Bee Dagum & Douglas Patterson, 2009. "A New Bispectral Test for NonLinear Serial Dependence," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 279-293.
    14. Andreasen, Martin M., 2011. "Non-linear DSGE models and the optimized central difference particle filter," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1671-1695, October.
    15. Hannan, E J, 1976. "The Identification and Parameterization of ARMAX and State Space Forms," Econometrica, Econometric Society, vol. 44(4), pages 713-723, July.
    16. Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.
    17. Gary Koop & M. Hashem Pesaran & Ron P. Smith, 2013. "On Identification of Bayesian DSGE Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 300-314, July.
    18. Deistler, Manfred & Seifert, Hans-Gunther, 1978. "Identifiability and Consistent Estimability in Econometric Models," Econometrica, Econometric Society, vol. 46(4), pages 969-980, July.
    19. 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.
    20. Siddhartha Chib & Srikanth Ramamurthy, 2014. "DSGE Models with Student- t Errors," Econometric Reviews, Taylor & Francis Journals, vol. 33(1-4), pages 152-171, June.
    21. 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.
    22. Andrew Binning, 2013. "Third-order approximation of dynamic models without the use of tensors," Working Paper 2013/13, Norges Bank.
    23. Martin M. Andreasen, 2010. "Non-linear DSGE Models and The Central Difference Kalman Filter," CREATES Research Papers 2010-30, Department of Economics and Business Economics, Aarhus University.
    24. Ivana Komunjer & Serena Ng, 2011. "Dynamic Identification of Dynamic Stochastic General Equilibrium Models," Econometrica, Econometric Society, vol. 79(6), pages 1995-2032, November.
    25. Mutschler, Willi, 2018. "Higher-order statistics for DSGE models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 44-56.
    26. Stephen Pollock, 2011. "On Kronecker Products, Tensor Products And Matrix Differential Calculus," Discussion Papers in Economics 11/34, Division of Economics, School of Business, University of Leicester, revised Jul 2011.
    27. Michael K. Johnston & Robert G. King & Denny Lie, 2014. "Straightforward approximate stochastic equilibria for nonlinear rational expectations models," CAMA Working Papers 2014-59, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    28. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
    29. 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.
    30. 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.
    31. Fabio Milani, 2012. "The Modeling of Expectations in Empirical DSGE Models: A Survey," Advances in Econometrics, in: DSGE Models in Macroeconomics: Estimation, Evaluation, and New Developments, pages 3-38, Emerald Group Publishing Limited.
    32. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(3), pages 776-799, June.
    33. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    34. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Pruning in perturbation DSGE models: Guidance from nonlinear moving average approximations," SFB 649 Discussion Papers 2013-024, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    35. Martin M. Andreasen, 2013. "Non‐Linear Dsge Models And The Central Difference Kalman Filter," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 929-955, September.
    36. Edward Herbst & Frank Schorfheide, 2014. "Sequential Monte Carlo Sampling For Dsge Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1073-1098, November.
    37. Yong Bao, 2013. "On Sample Skewness and Kurtosis," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 415-448, December.
    38. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    39. 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.
    40. Magnus, Jan R., 2010. "On the concept of matrix derivative," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2200-2206, October.
    41. Deistler, Manfred, 1976. "The Identifiability of Linear Econometric Models with Autocorrelated Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 26-46, February.
    42. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, October.
    43. Kim, Jinill, 2003. "Functional equivalence between intertemporal and multisectoral investment adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 533-549, February.
    44. Hannan, E J, 1971. "The Identification Problem for Multiple Equation Systems with Moving Average Errors," Econometrica, Econometric Society, vol. 39(5), pages 751-765, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fabio Canova & Filippo Ferroni & Christian Matthes, 2015. "Approximating Time Varying Structural Models With Time Invariant Structures," Working Paper 15-10, Federal Reserve Bank of Richmond.
    2. Prosper Dovonon & Alastair Hall, 2018. "The Asymptotic Properties of GMM and Indirect Inference under Second-order Identi?cation," CIRANO Working Papers 2018s-37, CIRANO.
    3. Mutschler, Willi, 2018. "Higher-order statistics for DSGE models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 44-56.
    4. Adjemian, Stéphane & Bastani, Houtan & Juillard, Michel & Karamé, Fréderic & Mihoubi, Ferhat & Mutschler, Willi & Pfeifer, Johannes & Ratto, Marco & Rion, Normann & Villemot, Sébastien, 2022. "Dynare: Reference Manual Version 5," Dynare Working Papers 72, CEPREMAP, revised Mar 2023.
      • Stéphane Adjemian & Houtan Bastani & Michel Juillard & Frédéric Karamé & Ferhat Mihoubi & Willi Mutschler & Johannes Pfeifer & Marco Ratto & Sébastien Villemot & Normann Rion, 2023. "Dynare: Reference Manual Version 5," PSE Working Papers hal-04219920, HAL.
      • Stéphane Adjemian & Houtan Bastani & Michel Juillard & Frédéric Karamé & Ferhat Mihoubi & Willi Mutschler & Johannes Pfeifer & Marco Ratto & Sébastien Villemot & Normann Rion, 2023. "Dynare: Reference Manual Version 5," Working Papers hal-04219920, HAL.
    5. Prosper Dovonon & Alastair R. Hall, 2017. "The Asymptotic Properties of GMM and Indirect Inference Under Second-Order Identification," Economics Discussion Paper Series 1705, Economics, The University of Manchester.
    6. Adjemian, Stéphane & Juillard, Michel & Karamé, Fréderic & Mutschler, Willi & Pfeifer, Johannes & Ratto, Marco & Rion, Normann & Villemot, Sébastien, 2024. "Dynare: Reference Manual, Version 6," Dynare Working Papers 80, CEPREMAP, revised Sep 2024.
    7. Dovonon, Prosper & Hall, Alastair R., 2018. "The asymptotic properties of GMM and indirect inference under second-order identification," Journal of Econometrics, Elsevier, vol. 205(1), pages 76-111.
    8. Ivashchenko, Sergey & Mutschler, Willi, 2020. "The effect of observables, functional specifications, model features and shocks on identification in linearized DSGE models," Economic Modelling, Elsevier, vol. 88(C), pages 280-292.
    9. repec:bny:wpaper:0041 is not listed 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. 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.
    2. Mutschler, Willi, 2018. "Higher-order statistics for DSGE models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 44-56.
    3. Mutschler, Willi, 2014. "Identification of DSGE Models - A Comparison of Methods and the Effect of Second Order Approximation," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100598, Verein für Socialpolitik / German Economic Association.
    4. Ivashchenko, Sergey & Mutschler, Willi, 2020. "The effect of observables, functional specifications, model features and shocks on identification in linearized DSGE models," Economic Modelling, Elsevier, vol. 88(C), pages 280-292.
    5. Mutschler, Willi, 2015. "Note on Higher-Order Statistics for the Pruned-State-Space of nonlinear DSGE models," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113138, Verein für Socialpolitik / German Economic Association.
    6. Pedro Chaim & Márcio Poletti Laurini, 2022. "Data Cloning Estimation and Identification of a Medium-Scale DSGE Model," Stats, MDPI, vol. 6(1), pages 1-13, December.
    7. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    8. Zadrozny, Peter A., 2022. "Linear identification of linear rational-expectations models by exogenous variables reconciles Lucas and Sims," CFS Working Paper Series 682, Center for Financial Studies (CFS).
    9. Komunjer, Ivana & Zhu, Yinchu, 2020. "Likelihood ratio testing in linear state space models: An application to dynamic stochastic general equilibrium models," Journal of Econometrics, Elsevier, vol. 218(2), pages 561-586.
    10. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Modelling and Estimating Large Macroeconomic Shocks During the Pandemic," CREATES Research Papers 2021-08, Department of Economics and Business Economics, Aarhus University.
    11. Morris, Stephen D., 2017. "DSGE pileups," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 56-86.
    12. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Identifying Economic Shocks in a Rare Disaster Environment," CEIS Research Paper 517, Tor Vergata University, CEIS, revised 18 Jul 2024.
    13. Benchimol, Jonathan & Ivashchenko, Sergey, 2021. "Switching volatility in a nonlinear open economy," Journal of International Money and Finance, Elsevier, vol. 110(C).
    14. Chatelain, Jean-Bernard & Ralf, Kirsten, 2018. "Publish and Perish: Creative Destruction and Macroeconomic Theory," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 46(2), pages 65-101.
    15. 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.
    16. Zhongjun Qu, 2018. "A Composite Likelihood Framework for Analyzing Singular DSGE Models," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 916-932, December.
    17. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
    18. Paccagnini, Alessia, 2017. "Dealing with Misspecification in DSGE Models: A Survey," MPRA Paper 82914, University Library of Munich, Germany.
    19. Anna Mikusheva, 2014. "Estimation of dynamic stochastic general equilibrium models (in Russian)," Quantile, Quantile, issue 12, pages 1-21, February.
    20. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.

    More about this item

    Keywords

    Identification; Pruning; Higher-order moments; Cumulants; Polyspectra; Analytical derivatives;
    All these keywords.

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

    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:eee:dyncon:v:56:y:2015:i:c:p:34-54. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.