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Inference and Speci?cation Testing in DSGE Models with Possible Weak Identification

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Author Info

  • Zhongjun Qu

    ()
    (Department of Economics, Boston University)

Abstract

This paper considers inference and model diagnostics for log-linearized DSGE models allow- ing an unknown subset of parameters to be weakly (including un-) identified. The framework allows for latent state variables, measurement errors and also permits analysis using only part of the spectrum, say at the business cycle frequencies. The latter is important because DSGE mod- els are often designed to explain business cycle movements, not very long-run or very short-run ?uctuations. For inference, we first characterize weak identi?cation from a frequency domain perspective and propose a score test for the structural parameters based on the frequency domain maximum likelihood. The construction heavily exploits the structures of the DSGE solution, the score function and the information matrix. In particular, we show that the test statistic can be represented as the explained sum of squares from a complex-valued multivariate linear regression, where weak identification surfaces as (imperfectly) multicollinear regressors. Then, we prove that asymptotically valid inference can be carried out by inverting this test statistic and using Chi-square critical values. Next, we suggest procedures to construct uniform confidence bands for the impulse response function, the time path of the variance decomposition, the individual spectrum and the absolute coherency. For model diagnostics, we propose a family of frequency domain misspecification tests that are robust to weak identification. They can be used to test for misspecification in the mean, in the spectrum as well as misspecification within a band of frequencies. A simulation experiment using a calibrated model suggests that the tests have adequate size even in relatively small samples. It also suggests that it is possible to have informative confidence sets in DSGE models with unidentified parameters, particularly regard- ing the impulse responses functions. Although the paper focuses on DSGE models, the methods developed are potentially applicable to other dynamic models with well defined spectra, such as the stationary (factor-augmented) structural vector autoregression.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2011-058.

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Length: 66 pages
Date of creation: Jan 2011
Date of revision:
Handle: RePEc:bos:wpaper:wp2011-058

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Related research

Keywords: Business cycle; frequency domain; impulse response; inference; model diagnostics; rational expectations models; weak identification;

References

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  1. Altug, Sumru, 1989. "Time-to-Build and Aggregate Fluctuations: Some New Evidence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 889-920, November.
  2. Iskrev, Nikolay, 2010. "Local identification in DSGE models," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 189-202, March.
  3. Lawrence J. Christiano & Robert J. Vigfusson, 2001. "Maximum likelihood in the frequency domain: the importance of time-to-plan," Working Paper 0106, Federal Reserve Bank of Cleveland.
  4. David N. DeJong & Chetan Dave, 2007. "Introduction to Structural Macroeconometrics
    [Structural Macroeconometrics]
    ," Introductory Chapters, Princeton University Press.
  5. Donald W.K. Andrews & Xu Cheng, 2010. "Estimation and Inference with Weak, Semi-strong, and Strong Identification," Cowles Foundation Discussion Papers 1773R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2011.
  6. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
  7. Jean-Marie Dufour & Lynda Khalaf & Maral Kichian, 2009. "Structural Multi-Equation Macroeconomic Models: Identification-Robust Estimation and Fit," Working Papers 09-19, Bank of Canada.
  8. Thomas J. Sargent & Paolo Surico, 2011. "Two Illustrations of the Quantity Theory of Money: Breakdowns and Revivals," American Economic Review, American Economic Association, vol. 101(1), pages 109-28, February.
  9. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2007. "Assessing Structural VARs," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 1-106 National Bureau of Economic Research, Inc.
  10. Zhongjun Qu & Denis Tkachenko, 2010. "Identification and Frequency Domain QML Estimation of Linearized DSGE Models," Boston University - Department of Economics - Working Papers Series WP2010-053, Boston University - Department of Economics.
  11. Hansen, Lars Peter & Sargent, Thomas J., 1993. "Seasonality and approximation errors in rational expectations models," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 21-55.
  12. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
  13. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, September.
  14. Kleibergen, Frank & Mavroeidis, Sophocles, 2009. "Weak Instrument Robust Tests in GMM and the New Keynesian Phillips Curve," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 293-311.
  15. Guerron-Quintana, Pablo A. & Inoue, Atsushi & Kilian, Lutz, 2009. "Frequentist Inference in Weakly Identified DSGE Models," CEPR Discussion Papers 7447, C.E.P.R. Discussion Papers.
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Citations

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Cited by:
  1. Donald W. K. Andrews & Xu Cheng, 2011. "Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure," Cowles Foundation Discussion Papers 1824, Cowles Foundation for Research in Economics, Yale University.
  2. Donald W.K. Andrews & Xu Cheng, 2011. "GMM Estimation and Uniform Subvector Inference with Possible Identification Failure," Cowles Foundation Discussion Papers 1828, Cowles Foundation for Research in Economics, Yale University.

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