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Estimation of Autoregressive Roots Near Unity Using Panel Data

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Author Info
Hyungsik R. Moon (Dept. Economics, UCLA, Santa Barbara)
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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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 < 0 are developed for panel models with deterministic and stochastic trends. A limit distribution theory is also established and test statistics are constructed for exploring interesting hypotheses, like the equivalence of local to unity parameters across subgroups of the population. The methods are applied to the empirically important problem of the efficient extraction of deterministic trends. They are also shown to deliver consistent estimates of distancing parameters in nonstationary panel models where the initial conditions are in the distant past.

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Publisher Info
Paper provided by Cowles Foundation, 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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Related research
Keywords: Bias; local to unity; panel data; pooled regression; subgroup testing;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  2. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December. [Downloadable!] (restricted)
    Other versions:
  3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
    Other versions:
  4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  5. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Nonstationary Panel Data Analysis: An Overview of Some Recent Developments," Cowles Foundation Discussion Papers 1221, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  6. Peter C.B. Phillips & Hyungsik R. Moon & Zhijie Xiao, 1998. "How to Estimate Autoregressive Roots Near Unity," Cowles Foundation Discussion Papers 1191, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  7. Hyungsik Moon & Peter Phillips, 1999. "Estimation of Autoregressive Roots near Unity using Panel Data," University of California at Santa Barbara, Economics Working Paper Series wp1-99, Department of Economics, UC Santa Barbara. [Downloadable!]
    Other versions:
  8. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers 1222, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  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. [Downloadable!] (restricted)
  10. Christopher L. Cavanagh & Graham Elliott & James Stock, 1995. "Inference in Models with Nearly Integrated Regressors," University of California at San Diego, Economics Working Paper Series 95-29, Department of Economics, UC San Diego.
    Other versions:
  11. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers 1134, Cowles Foundation, Yale University. [Downloadable!]
  12. 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. [Downloadable!]
  13. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  14. repec:cup:etheor:v:11:y:1995:i:5:p:1131-47 is not listed on IDEAS
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Erik Hjalmarsson, 2006. "Predictive regressions with panel data," International Finance Discussion Papers 869, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  2. Jushan Bai & Chihwa Kao & Serena Ng, 2007. "Panel Cointegration with Global Stochastic Trends," Center for Policy Research Working Papers 90, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
    Other versions:
  3. Erik Hjalmarsson, 2008. "Predicting global stock returns," International Finance Discussion Papers 933, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  4. Hyungsik Roger Moon, 2000. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometric Society World Congress 2000 Contributed Papers 0913, Econometric Society. [Downloadable!]
    Other versions:
  5. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Estimation of Autoregressive Roots Near Unity Using Panel Data," Cowles Foundation Discussion Papers 1224, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  6. Chihwa Kao & Long Liu, 2007. "Consistent Estimation with Weak Instruments in Panel Data," Center for Policy Research Working Papers 95, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
  7. Moon, H.R. & Perron, B., 2002. "Testing for a Unit Root in Panels with Dynamic Factors," Cahiers de recherche 18-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ. [Downloadable!]
    Other versions:
  8. Hjalmarsson, Erik, 2005. "Predictive regressions with panel data," Working Papers in Economics 160, Göteborg University, Department of Economics. [Downloadable!]
  9. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Maximum Likelihood Estimation in Panels with Incidental Trends," Cowles Foundation Discussion Papers 1246, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  10. J. Breitung, . "The Local Power of Some Unit Root Tests for Panel Data," Sonderforschungsbereich 373 1999-69, Humboldt Universitaet Berlin.
  11. Jamie Emerson & Chihwa Kao, 2000. "Testing for Structural Change of a Time Trend Regression in Panel Data," Center for Policy Research Working Papers 15, Center for Policy Research, Maxwell School, Syracuse University. [Downloadable!]
  12. Erik Hjalmarsson, 2007. "The Stambaugh bias in panel predictive regressions," International Finance Discussion Papers 914, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  13. Peter C.B. Phillips & Hyungsik R. Moon & Zhijie Xiao, 1998. "How to Estimate Autoregressive Roots Near Unity," Cowles Foundation Discussion Papers 1191, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  14. Peter C.B. Phillips & Donggyu Sul, 2003. "Bias in Dynamic Panel Estimation with Fixed Effects, Incidental Trends and Cross Section Dependence," Cowles Foundation Discussion Papers 1438, Cowles Foundation, Yale University, revised Jun 2004. [Downloadable!]
    Other versions:
  15. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Nonstationary Panel Data Analysis: An Overview of Some Recent Developments," Cowles Foundation Discussion Papers 1221, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  16. Ai Deng, 2005. "Understanding Spurious Regression in Financial Economics," Boston University - Department of Economics - Working Papers Series WP2005-048, Boston University - Department of Economics. [Downloadable!]
  17. Erik Hjalmarsson, 2005. "Estimation of average local-to-unity roots in heterogenous panels," International Finance Discussion Papers 852, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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