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Estimation of Autoregressive Roots Near Unity Using Panel Data

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Abstract

Time series data are often well modelled by using the device of an autoregressive root that is local to unity. Unfortunately, the localizing parameter (c) is not consistently estimable using existing time series econometric techniques and the lack of a consistent estimator complicates inference. This paper develops procedures for the estimation of a common localizing parameter using panel data. Pooling information across individuals in a panel aids the identification and estimation of the localising parameter and leads to consistent estimation in simple panel models. However, in the important case of models with concomitant deterministic trends, it is shown that pooled panel estimators of the localising parameter are asymptotically biased. Some techniques are developed to overcome this difficulty and consistent estimators of c in the region c

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File URL: http://cowles.econ.yale.edu/P/cd/d12a/d1224.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1224.

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Length: 63 pages
Date of creation: Jun 1999
Date of revision:
Publication status: Published in Econometric Theory (2000), 16(6): 927-997
Handle: RePEc:cwl:cwldpp:1224

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Bias; local to unity; panel data; pooled regression; subgroup testing;

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References

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  1. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  3. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
  4. Phillips, Peter C.B. & Moon, Hyungsik Roger & Xiao, Zhijie, 2001. "How To Estimate Autoregressive Roots Near Unity," Econometric Theory, Cambridge University Press, vol. 17(01), pages 29-69, February.
  5. repec:fth:calaec:17-98r is not listed on IDEAS
  6. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation for Research in Economics, Yale University.
  7. James H. Stock, 1991. "Confidence Intervals for the Largest Autoresgressive Root in U.S. Macroeconomic Time Series," NBER Technical Working Papers 0105, National Bureau of Economic Research, Inc.
  8. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July.
  9. Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
  10. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
  11. Moon, Hyungsik R. & Phillips, Peter C.B., 1999. "Estimation of Autoregressive Roots near Unity using Panel Data," University of California at Santa Barbara, Economics Working Paper Series qt7fd8x80m, Department of Economics, UC Santa Barbara.
  12. Xiao, Zhijie & Phillips, Peter C.B., 1999. "Efficient Detrending In Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 15(04), pages 519-548, August.
  13. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
  14. repec:fth:calaec:1-99 is not listed on IDEAS
  15. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
  16. repec:fth:calaec:17-98 is not listed on IDEAS
  17. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(05), pages 1131-1147, October.
  18. Uhlig, Harald, 1994. "On Jeffreys Prior when Using the Exact Likelihood Function," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 633-644, August.
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