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Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function

  • Jui-Chung Yang
  • Ke-Li Xu

The reaction coefficients of expected inflations and output gaps in the forecast-based monetary policy reaction function may be merely weakly  identified when the smoothing coefficient is close to unity and the nominal interest rates are highly persistent. In this paper we modify the method of Andrews and Cheng (2012, Econometrica)on inference under weak / semi-strong identification to accommodate the persistence issue. Our modification involves the employment of asymptotic theories for near unit root processes and novel drifting sequence approaches. Large sample properties with a desired smooth transition with respect to the true values of parameters are developed for the nonlinear least squares (NLS) estimator and its corresponding t / Wald statistics of a general class of models. Despite the not-consistent-estimability, the conservative confidence sets of weakly-identified parameters of interest can be obtained by inverting the t / Wald tests. We show that the null-imposed least-favorable confidence sets will have correct asymptotic sizes, and the projection-based method may lead to asymptotic over-coverage. Our empirical application suggests that the NLS estimates for the reaction coefficients in U.S.’s forecast-based monetary policy reaction function for 1987:3–2007:4 are not accurate sufficiently to rule out the possibility of indeterminacy.

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Paper provided by Job Market Papers in its series 2013 Papers with number pya307.

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Date of creation: 08 Dec 2013
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Handle: RePEc:jmp:jm2013:pya307
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  1. 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.
  2. Nikolsko-Rzhevskyy, Alex & Papell, David H., 2012. "Taylor rules and the Great Inflation," Journal of Macroeconomics, Elsevier, vol. 34(4), pages 903-918.
  3. Athanasios Orphanides, 2001. "Monetary policy rules, macroeconomic stability and inflation: a view from the trenches," Finance and Economics Discussion Series 2001-62, Board of Governors of the Federal Reserve System (U.S.).
  4. Tom Stark and Dean Croushore, 2001. "Forecasting with a Real-Time Data Set for Macroeconomists," Computing in Economics and Finance 2001 258, Society for Computational Economics.
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  10. Adam McCloskey, 2012. "Bonferroni-Based Size-Correction for Nonstandard Testing Problems," Working Papers 2012-16, Brown University, Department of Economics.
  11. van der Meer, Tjacco & Pap, Gyula & van Zuijlen, Martien C.A., 1999. "ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES," Econometric Theory, Cambridge University Press, vol. 15(02), pages 184-217, April.
  12. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(02), pages 287-333, April.
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  17. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  18. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
  19. Andrews, Donald W.K. & Cheng, Xu, 2013. "Maximum likelihood estimation and uniform inference with sporadic identification failure," Journal of Econometrics, Elsevier, vol. 173(1), pages 36-56.
  20. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
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  24. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.
  25. Jia Li, 2013. "Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local‐to‐Continuity Theory for the Pre‐Averaging Method," Econometrica, Econometric Society, vol. 81(4), pages 1673-1693, 07.
  26. Alex Nikolsko‐Rzhevskyy, 2011. "Monetary Policy Estimation in Real Time: Forward‐Looking Taylor Rules without Forward‐Looking Data," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(5), pages 871-897, 08.
  27. Anna Mikusheva, 2012. "One‐Dimensional Inference in Autoregressive Models With the Potential Presence of a Unit Root," Econometrica, Econometric Society, vol. 80(1), pages 173-212, 01.
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