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Estimators for Persistent and Possibly Non-Stationary Data with Classical Properties

  • Yuriy Gorodnichenko
  • Anna Mikusheva
  • Serena Ng

This paper considers a moments based non-linear estimator that is root-T consistent and uniformly asymptotically normal irrespective of the degree of persistence of the forcing process. These properties hold for linear autoregressive models, linear predictive regressions, as well as certain non-linear dynamic models. Asymptotic normality is obtained because the moments are chosen so that the objective function is uniformly bounded in probability and that a central limit theorem can be applied. Critical values from the normal distribution can be used irrespective of the treatment of the deterministic terms. Simulations show that the estimates are precise, and the t-test has good size in the parameter region where the least squares estimates usually yield distorted inference.

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File URL: http://www.nber.org/papers/w17424.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 17424.

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Date of creation: Sep 2011
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Publication status: published as Gorodnichenko, Yuriy & Mikusheva, Anna & Ng, Serena, 2012. "Estimators For Persistent And Possibly Nonstationary Data With Classical Properties," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1003-1036, October.
Handle: RePEc:nbr:nberwo:17424
Note: AP EFG IFM ME TWP
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  1. Laroque, Guy & Salanie, Bernard, 1997. "Normal estimators for cointegrating relationships," Economics Letters, Elsevier, vol. 55(2), pages 185-189, August.
  2. Artem Prokhorov & Peter Schmidt, 2008. "GMM Redundancy Results for General Missing Data Problems," Working Papers 08003, Concordia University, Department of Economics.
  3. Rossi, Barbara & Pesavento, Elena, 2003. "Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons," Working Papers 03-19, Duke University, Department of Economics.
  4. Eugene Canjels & Mark W. Watson, 1994. "Estimating deterministic trends in the presence of serially correlated errors," Working Paper Series, Macroeconomic Issues 94-19, Federal Reserve Bank of Chicago.
  5. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  6. So, Beong Soo & Shin, Dong Wan, 1999. "Cauchy Estimators For Autoregressive Processes With Applications To Unit Root Tests And Confidence Intervals," Econometric Theory, Cambridge University Press, vol. 15(02), pages 165-176, April.
  7. Phillips, Peter C.B. & Han, Chirok, 2008. "Gaussian Inference In Ar(1) Time Series With Or Without A Unit Root," Econometric Theory, Cambridge University Press, vol. 24(03), pages 631-650, June.
  8. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, 05.
  9. Olivier Coibion & Yuriy Gorodnichenko, 2010. "Strategic Interaction among Heterogeneous Price-Setters in an Estimated DSGE Model," Working Papers 93, Department of Economics, College of William and Mary.
  10. Han, Chirok & Phillips, Peter C. B. & Sul, Donggyu, 2011. "Uniform Asymptotic Normality In Stationary And Unit Root Autoregression," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1117-1151, December.
  11. Abowd, John M & Card, David, 1989. "On the Covariance Structure of Earnings and Hours Changes," Econometrica, Econometric Society, vol. 57(2), pages 411-45, March.
  12. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
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