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Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments

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  • Kitamura, Yuichi
  • Phillips, Peter C. B.

Abstract

This paper develops a general theory of instrumental variables (IV) estimation that allows for both I(1) and I(0) regressors and instruments. The estimation techniques involve an extension of the fully modified (FM) regression procedure that was introduced in earlier work by Phillips-Hansen (1990). FM versions of the generalized instrumental variable estimation (GIVE) method and the generalized method of moments (GMM) estimator are developed. In models with both stationary and nonstationary components, the FM-GIVE and FM-GMM techniques provide efficiency gains over FM-IV in the estimation of the stationary components of a model that has both stationary and nonstationary regressors. The paper exploits a result of Phillips (1991a) that we can apply FM techniques in models with cointegrated regressors and even in stationary regression models without losing the method's good asymptotic properties. The present paper shows how to take advantage jointly of the good asymptotic properties of FM estimators with respect to the nonstationary elements of a model and the good asymptotic properties of the GIVE and GMM estimators with respect to the stationary components. The theory applies even when there is no prior knowledge of the number of unit roots in the system or the dimension or the location of the cointegration space. An FM extension of the Sargan (1958) test for the validity of the instruments is proposed.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 80 (1997)
Issue (Month): 1 (September)
Pages: 85-123

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Handle: RePEc:eee:econom:v:80:y:1997:i:1:p:85-123

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  2. Dean Corbea & Sam Ouliaris & Peter C.B. Phillips, 1991. "A Reexamination of the Consumption Function Using Frequency Domain Regressors," Cowles Foundation Discussion Papers 997, Cowles Foundation for Research in Economics, Yale University.
  3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  4. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  5. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  7. Peter C.B. Phillips & Mico Loretan, 1989. "Estimating Long Run Economic Equilibria," Cowles Foundation Discussion Papers 928, Cowles Foundation for Research in Economics, Yale University.
  8. 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.
  9. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September.
  10. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
  11. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824, November.
  12. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  13. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  14. Corbae, D. & Ouliaris, S. & Phillips, P.C.B., 1991. "A Rexamination of the Consumption Function Using Frequency Domain Regressions," Working Papers 91-25, University of Iowa, Department of Economics.
  15. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  16. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  17. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  18. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Estimation and Inference in Models of Cointegration: A Simulation Study," Cowles Foundation Discussion Papers 881, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. David De La Croix & Jean-Pierre Urbain, 1998. "Intertemporal substitution in import demand and habit formation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(6), pages 589-612.
  2. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
  3. Jae-Young Kim, 2000. "The Generalized Method of Moments in the Bayesian Framework and a Model of Moment Selection Criterion," Econometric Society World Congress 2000 Contributed Papers 1779, Econometric Society.
  4. Dietmar Bauer & Alex Maynard, 2010. "Persistence-robust Granger causality testing," Working Papers 1011, University of Guelph, Department of Economics and Finance.
  5. Bertille Antoine & Eric Renault, 2012. "Efficient Minimum Distance Estimation with Multiple Rates of Convergence," Discussion Papers dp12-03, Department of Economics, Simon Fraser University.
  6. Croix,David,de la & Urbain,Jean-Pierre, 1996. "Intertemporal substitution in import demand and habit formation ," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. Barnett, William A. & de Peretti, Philippe, 2009. "Admissible Clustering Of Aggregator Components: A Necessary And Sufficient Stochastic Seminonparametric Test For Weak Separability," Macroeconomic Dynamics, Cambridge University Press, vol. 13(S2), pages 317-334, September.
  8. Eiji Kurozumi & Kazuhiko Hayakawa, 2006. "Asymptotic Properties of the Efficient Estimators for Cointegrating Regression Models with Serially Dependent Errors," Hi-Stat Discussion Paper Series d06-197, Institute of Economic Research, Hitotsubashi University.
  9. P. M. Robinson & M. Gerolimetto, 2006. "Instrumental variables estimation of stationary and non-stationary cointegrating regressions," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 291-306, 07.
  10. Chan, Hing Lin & Lee, Shu Kam & Woo, Kai-Yin, 2003. "An empirical investigation of price and exchange rate bubbles during the interwar European hyperinflations," International Review of Economics & Finance, Elsevier, vol. 12(3), pages 327-344.
  11. Shin, Dong Wan & Oh, Man-Suk, 2004. "Fully modified semiparametric GLS estimation for regressions with nonstationary seasonal regressors," Journal of Econometrics, Elsevier, vol. 122(2), pages 247-280, October.
  12. Park, Suk K. & Ahn, Sung K. & Cho, Sinsup, 2011. "Generalized method of moments estimation for cointegrated vector autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2605-2618, September.
  13. CHEN, Chuanglian & CHEN, Guojin & YAO, Shujie, 2012. "Do imports crowd out domestic consumption? A comparative study of China, Japan and Korea," China Economic Review, Elsevier, vol. 23(4), pages 1036-1050.
  14. Dutkowsky, Donald H. & McCoskey, Suzanne K., 2001. "Near integration, bank reluctance, and discount window borrowing," Journal of Banking & Finance, Elsevier, vol. 25(6), pages 1013-1036, June.
  15. Bauer, Dietmar & Maynard, Alex, 2012. "Persistence-robust surplus-lag Granger causality testing," Journal of Econometrics, Elsevier, vol. 169(2), pages 293-300.
  16. Shin, Dong Wan & Joon Kim, Han & Jhee, Won-Chul, 2007. "Asymptotic efficiency of the ordinary least-squares estimator for sur models with integrated regressors," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 75-82, January.
  17. Mustapha Baghli, 2004. "Modelling the FF/MM rate by threshold cointegration analysis," Applied Economics, Taylor & Francis Journals, vol. 36(6), pages 533-548.

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