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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. 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. 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.
  3. 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.
  4. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  5. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
  6. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  7. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  8. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  9. Corbae, Dean & Ouliaris, Sam & Phillips, Peter C B, 1994. "A Reexamination of the Consumption Function Using Frequency Domain Regressions," Empirical Economics, Springer, vol. 19(4), pages 595-609.
  10. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  11. Phillips, Peter C B & Loretan, Mico, 1991. "Estimating Long-run Economic Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 407-36, May.
  12. 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.
  13. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  14. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  15. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  16. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824.
  17. 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.
  18. 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.
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