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Identification of DSGE Models - the Effect of Higher-Order Approximation and Pruning

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  • Willi Mutschler

Abstract

Several formal methods have been proposed to check local identification in linearized DSGE models using rank criteria. Recently there has been huge progress in the estimation of non-linear DSGE models, yet formal identification criteria are missing. The contribution of the paper is threefold: First, we extend the existent methods to higher-order approximations and establish rank criteria for local identification given the pruned state-space representation. It is shown that this may improve overall identification of a DSGE model via imposing additional restrictions on the moments and spectrum. Second, we derive analytical derivatives of the reduced-form matrices, unconditional moments and spectral density for the pruned state-space system. Third, using a second-order approximation, we are able to identify previously non-identifiable parameters: namely the parameters governing the investment adjustment costs in the Kim (2003) model and all parameters in the An and Schorfheide (2007) model, including the coeffcients of the Taylor-rule.

Suggested Citation

  • Willi Mutschler, 2014. "Identification of DSGE Models - the Effect of Higher-Order Approximation and Pruning," CQE Working Papers 3314, Center for Quantitative Economics (CQE), University of Muenster.
    • Handle: RePEc:cqe:wpaper:3314
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    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 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," Working Papers ECARES ECARES 2013-24, ULB -- Universite Libre de Bruxelles.
    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. 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.
    26. 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.
    27. 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.
    28. 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.
    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. Fabio Milani, 2012. "The Modeling of Expectations in Empirical DSGE Models: a Survey," Working Papers 121301, University of California-Irvine, Department of Economics.
    31. 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.
    32. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    33. 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.
    34. 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.
    35. 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.
    36. Yong Bao, 2013. "On Sample Skewness and Kurtosis," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 415-448, December.
    37. Sungbae An & Frank Schorfheide, 2007. "Bayesian Analysis of DSGE Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 113-172.
    38. 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.
    39. Magnus, Jan R., 2010. "On the concept of matrix derivative," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2200-2206, October.
    40. 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.
    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. 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.
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    Citations

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    Cited by:

    1. Sergey Ivashchenko & Willi Mutschler, 2019. "The effect of observables, functional specifications, model features and shocks on identification in linearized DSGE models," CQE Working Papers 8319, Center for Quantitative Economics (CQE), University of Muenster.
    2. 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, revised 23 Oct 2015.
    3. Prosper Dovonon & Alastair Hall, 2018. "The Asymptotic Properties of GMM and Indirect Inference under Second-order Identification," CIRANO Working Papers 2018s-37, CIRANO.
    4. Prosper Donovon & Alastair R. Hall, 2017. "The Asymptotic Properties of GMM and Indirect Inference under Second Inference," The School of Economics Discussion Paper Series 1705, Economics, The University of Manchester.
    5. repec:eee:econom:v:205:y:2018:i:1:p:76-111 is not listed on IDEAS
    6. Mutschler, Willi, 2018. "Higher-order statistics for DSGE models," Econometrics and Statistics, Elsevier, vol. 6(C), pages 44-56.

    More about this item

    Keywords

    non-linear DSGE; rank condition; analytical derivatives; pruned state-space;

    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

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