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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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  • Kitamura, Yuichi & Phillips, Peter C. B., 1997. "Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments," Journal of Econometrics, Elsevier, vol. 80(1), pages 85-123, September.
  • Handle: RePEc:eee:econom:v:80:y:1997:i:1:p:85-123
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    3. 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.
    4. 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.
    5. Hassan B. Ghassan & Hassan R. Alhajhoj, 2016. "Long-Run Dynamic Relationship between FDI and Domestic Investment in GCC Countries," Journal of Economics and Econometrics, Economics and Econometrics Society, pages 16-43.
    6. Bauer, Dietmar & Maynard, Alex, 2012. "Persistence-robust surplus-lag Granger causality testing," Journal of Econometrics, Elsevier, vol. 169(2), pages 293-300.
    7. Ghassan, Hassan B. & Alhajhoj, Hassan R., 2012. "Long Run Relationship between IFDI and Domestic Investment in GCC Countries," MPRA Paper 62544, University Library of Munich, Germany, revised Jul 2013.
    8. 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.
    9. Antoine, Bertille & Renault, Eric, 2012. "Efficient minimum distance estimation with multiple rates of convergence," Journal of Econometrics, Elsevier, pages 350-367.
    10. 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.
    11. 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, July.
    12. Xu Cheng, 2014. "Uniform Inference in Nonlinear Models with Mixed Identification Strength," PIER Working Paper Archive 14-018, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. Kurozumi, Eiji & Hayakawa, Kazuhiko, 2009. "Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors," Journal of Econometrics, Elsevier, vol. 149(2), pages 118-135, April.
    14. Dietmar Bauer & Alex Maynard, 2010. "Persistence-robust Granger causality testing," Working Papers 1011, University of Guelph, Department of Economics and Finance.
    15. David De La Croix & Jean-Pierre Urbain, 1998. "Intertemporal substitution in import demand and habit formation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 589-612.
    16. 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.
    17. Mustapha Baghli, 2004. "Modelling the FF/MM rate by threshold cointegration analysis," Applied Economics, Taylor & Francis Journals, vol. 36(6), pages 533-548.
    18. Palm, Franz C. & Pfann, Gerard A., 1998. "Sources of asymmetry in production factor dynamics," Journal of Econometrics, Elsevier, vol. 82(2), pages 361-392, February.
    19. Cheng, Xu, 2015. "Robust inference in nonlinear models with mixed identification strength," Journal of Econometrics, Elsevier, vol. 189(1), pages 207-228.
    20. 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.
    21. 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.
    22. 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.

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