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Maximum likelihood inference in weakly identified dynamic stochastic general equilibrium models

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  • Isaiah Andrews
  • Anna Mikusheva

Abstract

This paper examines the issue of weak identification in maximum likelihood, motivated by problems with estimation and inference in a multidimensional dynamic stochastic general equilibrium model. We show that two forms of the classical score (Lagrange multiplier) test for a simple hypothesis concerning the full parameter vector are robust to weak identification. We also suggest a test for a composite hypothesis regarding a subvector of parameters. The suggested subset test is shown to be asymptotically exact when the nuisance parameter is strongly identified. We pay particular attention to the question of how to estimate Fisher information and we make extensive use of martingale theory.

Suggested Citation

  • Isaiah Andrews & Anna Mikusheva, 2015. "Maximum likelihood inference in weakly identified dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 6(1), pages 123-152, March.
    • Handle: RePEc:wly:quante:v:6:y:2015:i:1:p:123-152
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    1. Giovanni Angelini & Luca Fanelli, 2016. "Misspecification and Expectations Correction in New Keynesian DSGE Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(5), pages 623-649, October.
    2. Guerron-Quintana, Pablo & Inoue, Atsushi & Kilian, Lutz, 2017. "Impulse response matching estimators for DSGE models," Journal of Econometrics, Elsevier, vol. 196(1), pages 144-155.
    3. Khalaf, Lynda & Lin, Zhenjiang, 2021. "Projection-based inference with particle swarm optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    4. Adolfson, Malin & Laséen, Stefan & Lindé, Jesper & Ratto, Marco, 2019. "Identification versus misspecification in New Keynesian monetary policy models," European Economic Review, Elsevier, vol. 113(C), pages 225-246.
    5. Giesen, Sebastian & Scheufele, Rolf, 2016. "Effects of incorrect specification on the finite sample properties of full and limited information estimators in DSGE models," Journal of Macroeconomics, Elsevier, vol. 48(C), pages 1-18.
    6. Lynda Khalaf & Beatriz Peraza López, 2020. "Simultaneous Indirect Inference, Impulse Responses and ARMA Models," Econometrics, MDPI, vol. 8(2), pages 1-26, April.
    7. 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.
    8. Morrisy, Stephen D., 2017. "Efficient estimation of macroeconomic equations with unobservable states," Economic Modelling, Elsevier, vol. 60(C), pages 408-423.
    9. Lee, Adam & Mesters, Geert, 2024. "Locally robust inference for non-Gaussian linear simultaneous equations models," Journal of Econometrics, Elsevier, vol. 240(1).
    10. Morris, Stephen D., 2017. "DSGE pileups," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 56-86.
    11. 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.
    12. Adam Lee, 2024. "Locally Regular and Efficient Tests in Non-Regular Semiparametric Models," Papers 2403.05999, arXiv.org.
    13. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    14. Adam Lee & Geert Mesters, 2021. "Robust non-Gaussian inference for linear simultaneous equations models," Economics Working Papers 1792, Department of Economics and Business, Universitat Pompeu Fabra.
    15. Stefano Grassi & Marco Lorusso & Francesco Ravazzolo, 2021. "Adaptive Importance Sampling for DSGE Models," BEMPS - Bozen Economics & Management Paper Series BEMPS84, Faculty of Economics and Management at the Free University of Bozen.
    16. James H. Stock & Mark W. Watson, 2017. "Twenty Years of Time Series Econometrics in Ten Pictures," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 59-86, Spring.
    17. Andrews, Donald W.K. & Cheng, Xu & Guggenberger, Patrik, 2020. "Generic results for establishing the asymptotic size of confidence sets and tests," Journal of Econometrics, Elsevier, vol. 218(2), pages 496-531.
    18. Joan Alegre & Juan Carlos Escanciano, 2023. "Robust Minimum Distance Inference in Structural Models," Papers 2310.05761, arXiv.org.
    19. Joaquim Andrade & Pedro Cordeiro & Guilherme Lambais, 2019. "Estimating a Behavioral New Keynesian Model," Papers 1912.07601, arXiv.org.
    20. Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf & Abdallah Zalghout, 2020. "Identification-Robust Inequality Analysis," Cahiers de recherche 03-2020, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    21. 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.

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