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Global Identification in DSGE Models Allowing for Indeterminacy

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  • Zhongjun Qu

    (Boston University)

  • Denis Tkachenko

    (National University of Singapore)

Abstract

This paper presents a framework for analyzing global identification in log linearized DSGE models that encompasses both determinacy and indeterminacy. First, it considers a frequency domain expression for the Kullback-Leibler distance between two DSGE models, and shows that global identification fails if and only if the minimized distance equals zero. This result has three features. (1) It can be applied across DSGE models with different structures. (2) It permits checking whether a subset of frequencies can deliver identification. (3) It delivers parameter values that yield observational equivalence if there is identification failure. Next, the paper proposes a measure for the empirical closeness between two DSGE models for a further understanding of the strength of identification. The measure gauges the feasibility of distinguishing one model from another based on a finite number of observations generated by the two models. It is shown to be equal to the highest possible power in a Gaussian model under a local asymptotic framework. The above theory is illustrated using two small scale and one medium scale DSGE models. The results document that certain parameters can be identified under indeterminacy but not determinacy, that different monetary policy rules can be (nearly) observationally equivalent, and that identification properties can differ substantially between small and medium scale models. For implementation, two procedures are developed and made available, both of which can be used to obtain and thus to cross validate the findings reported in the empirical applications. Although the paper focuses on DSGE models, the results are also applicable to other vector linear processes with well defined spectra, such as the (factor augmented) vector autoregression.

Suggested Citation

  • Zhongjun Qu & Denis Tkachenko, 2015. "Global Identification in DSGE Models Allowing for Indeterminacy," Boston University - Department of Economics - Working Papers Series wp2015-001, Boston University - Department of Economics.
  • Handle: RePEc:bos:wpaper:wp2015-001
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    2. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    3. Peter A. Zadrozny, 2022. "Linear Identification of Linear Rational-Expectations Models by Exogenous Variables Reconciles Lucas and Sims," CESifo Working Paper Series 10078, CESifo.
    4. Paccagnini, Alessia, 2017. "Dealing with Misspecification in DSGE Models: A Survey," MPRA Paper 82914, University Library of Munich, Germany.
    5. Majid M. Al-Sadoon & Piotr Zwiernik, 2019. "The Identification Problem for Linear Rational Expectations Models," Working Papers 1114, Barcelona School of Economics.
    6. Sokbae Lee & Yuan Liao & Myung Hwan Seo & Youngki Shin, 2018. "Factor-Driven Two-Regime Regression," Papers 1810.11109, arXiv.org, revised Sep 2020.
    7. Fillat, José L. & Garetto, Stefania & Oldenski, Lindsay, 2015. "Diversification, cost structure, and the risk premium of multinational corporations," Journal of International Economics, Elsevier, vol. 96(1), pages 37-54.
    8. Zhongjun Qu & Denis Tkachenko, 2023. "Using arbitrary precision arithmetic to sharpen identification analysis for DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 644-667, June.
    9. Giovanni Angelini & Giuseppe Cavaliere & Luca Fanelli, 2022. "Bootstrap inference and diagnostics in state space models: With applications to dynamic macro models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 3-22, January.
    10. Josué Diwambuena & Raquel Fonseca & Stefan Schubert, 2021. "Italian Labour Frictions and Wage Rigidities in an Estimated DSGE," BEMPS - Bozen Economics & Management Paper Series BEMPS88, Faculty of Economics and Management at the Free University of Bozen.
    11. Giovanni Nicolo, 2020. "Monetary Policy, Self-Fulfilling Expectations and the U.S. Business Cycle," Finance and Economics Discussion Series 2020-035, Board of Governors of the Federal Reserve System (U.S.).
    12. Majid M. Al-Sadoon, 2020. "Regularized Solutions to Linear Rational Expectations Models," Papers 2009.05875, arXiv.org, revised Oct 2020.
    13. Timothy Uy, 2015. "Zeros and the Gains from Openness," 2015 Meeting Papers 1158, Society for Economic Dynamics.
    14. Juan Carlos Parra‐Alvarez & Olaf Posch & Mu‐Chun Wang, 2023. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(2), pages 304-330, April.
    15. Alessandria, George & Choi, Horag & Kaboski, Joseph P. & Midrigan, Virgiliu, 2015. "Microeconomic uncertainty, international trade, and aggregate fluctuations," Journal of Monetary Economics, Elsevier, vol. 69(C), pages 20-38.
    16. 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).
    17. 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.
    18. Majid M. Al-Sadoon, 2020. "The Spectral Approach to Linear Rational Expectations Models," Papers 2007.13804, arXiv.org, revised Jun 2023.

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    More about this item

    Keywords

    Dynamic stochastic general equilibrium models; frequency domain; global identification; multiple equilibria; spectral density;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles

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