GMM Estimation of Autoregressive Roots Near Unity with Panel Data

Author Info

Listed author(s):
• Hyungsik Roger Moon
• Peter C. B. Phillips

Abstract

This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data and incidental deterministic trends. Such models arise in empirical econometric studies of firm size and in dynamic panel data modeling with weak instruments. The two moment conditions in the GMM approach are obtained by constructing bias corrections to the score functions under OLS and GLS detrending, respectively. It is shown that the moment condition under GLS detrending corresponds to taking the projected score on the Bhattacharya basis, linking the approach to recent work on projected score methods for models with infinite numbers of nuisance parameters (Waterman and Lindsay (1998)). Assuming that the localizing parameter takes a nonpositive value, we establish consistency of the GMM estimator and find its limiting distribution. A notable new finding is that the GMM estimator has convergence rate $n^{1/6}$ n 1 / 6 , slower than $\sqrt{n}$ n , when the true localizing parameter is zero (i.e., when there is a panel unit root) and the deterministic trends in the panel are linear. These results, which rely on boundary point asymptotics, point to the continued difficulty of distinguishing unit roots from local alternatives, even when there is an infinity of additional data. Copyright The Econometric Society 2004.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00498.x
File Function: link to full text

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 72 (2004)
Issue (Month): 2 (March)
Pages: 467-522

as
in new window

 Handle: RePEc:ecm:emetrp:v:72:y:2004:i:2:p:467-522 Contact details of provider: Phone: 1 212 998 3820Fax: 1 212 995 4487Web page: http://www.econometricsociety.org/Email: More information through EDIRC Order Information: Web: https://www.econometricsociety.org/publications/econometrica/access/ordering-back-issues Email:

References

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.:

as
in new window

1. repec:cdl:ucsbec:6-99 is not listed on IDEAS
2. Peter C.B. Phillips, 1992. "Hyper-Consistent Estimation of a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 1040, Cowles Foundation for Research in Economics, Yale University.
3. Quah, Danny, 1994. "Exploiting cross-section variation for unit root inference in dynamic data," Economics Letters, Elsevier, vol. 44(1-2), pages 9-19.
4. Breitung, Jörg & Pesaran, Mohammad Hashem, 2005. "Unit roots and cointegration in panels," Discussion Paper Series 1: Economic Studies 2005,42, Deutsche Bundesbank, Research Centre.
5. Bernard, Andrew B & Jones, Charles I, 1996. "Productivity across Industries and Countries: Time Series Theory and Evidence," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 135-146, February.
6. Moon, Hyungsik R. & Phillips, Peter C.B., 2000. "Estimation Of Autoregressive Roots Near Unity Using Panel Data," Econometric Theory, Cambridge University Press, vol. 16(06), pages 927-997, December.
7. Coakley, Jerry & Kulasi, Farida & Smith, Ron, 1996. "Current Account Solvency and the Feldstein-Horioka Puzzle," Economic Journal, Royal Economic Society, vol. 106(436), pages 620-627, May.
8. 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.
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. Hyungsik Roger Moon & Peter C. B. Phillips, 2004. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometrica, Econometric Society, vol. 72(2), pages 467-522, 03.
11. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
12. Wu, Yangru, 1996. "Are Real Exchange Rates Nonstationary? Evidence from a Panel-Data Test," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(1), pages 54-63, February.
13. Schmalensee, Richard, 1989. "Inter-industry studies of structure and performance," Handbook of Industrial Organization,in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 2, chapter 16, pages 951-1009 Elsevier.
14. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
15. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
16. Moon, Hyungsik R & Phillips, Peter C B, 1999. " Maximum Likelihood Estimation in Panels with Incidental Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 711-747, Special I.
17. Pesaran, M. Hashem & Smith, Ron, 1995. "Estimating long-run relationships from dynamic heterogeneous panels," Journal of Econometrics, Elsevier, vol. 68(1), pages 79-113, July.
18. Evans, David S, 1987. "Tests of Alternative Theories of Firm Growth," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 657-674, August.
19. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, January.
20. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
21. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
22. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2005. "Bias Corrected Instrumental Variables Estimation for Dynamic Panel Models with Fixed E¤ects," Boston University - Department of Economics - Working Papers Series WP2005-024, Boston University - Department of Economics.
23. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
24. MacDonald, Ronald, 1996. "Panel unit root tests and real exchange rates," Economics Letters, Elsevier, vol. 50(1), pages 7-11, January.
25. Bronwyn H. Hall & Jacques Mairesse, 2000. "Univariate Panel Data Models and GMM Estimators: An Exploration Using Real and Simulated Data," Econometric Society World Congress 2000 Contributed Papers 1114, Econometric Society.
26. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
27. Arellano, Manuel & Honore, Bo, 2001. "Panel data models: some recent developments," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 53, pages 3229-3296 Elsevier.
28. Oh, Keun-Yeob, 1996. "Purchasing power parity and unit root tests using panel data," Journal of International Money and Finance, Elsevier, vol. 15(3), pages 405-418, June.
29. Peter C.B. Phillips, 1986. "Towards a Unified Asymptotic Theory for Autoregression," Cowles Foundation Discussion Papers 782R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1986.
30. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
31. 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.
32. Hugo Kruiniger, 2000. "GMM Estimation of Dynamic Panel Data Models with Persistent Data," Working Papers 428, Queen Mary University of London, School of Economics and Finance.
33. repec:cdl:ucsbec:1-99 is not listed on IDEAS
34. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
35. Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2003. "Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 115(1), pages 53-74, July.
36. McCloughan, Patrick, 1995. "Simulation of Concentration Development from Modified Gibrat Growth-Entry-Exit Processes," Journal of Industrial Economics, Wiley Blackwell, vol. 43(4), pages 405-433, December.
37. Pedroni, Peter, 1999. " Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 653-670, Special I.
38. Maddala, G S & Wu, Shaowen, 1999. " A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 631-652, Special I.
Full references (including those not matched with items on IDEAS)

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Corrections

When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:72:y:2004:i:2:p:467-522. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)

or (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.