Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments
It is well known that standard asymptotic theory is not applicable or is very unreliable in models with identification problems or weak instruments. One possible way out consists of using a variant of the Anderson-Rubin ((1949), AR) procedure. The latter allows one to build exact tests and confidence sets only for the full vector of the coefficients of the endogenous explanatory variables in a structural equation, but not for individual coefficients. This problem may in principle be overcome by using projection methods (Dufour (1997), Dufour and Jasiak (2001)). At first sight, however, this technique requires the application of costly numerical algorithms. In this paper, we give a general necessary and sufficient condition that allows one to check whether an AR-type confidence set is bounded. Furthermore, we provide an analytic solution to the problem of building projection-based confidence sets from AR-type confidence sets. The latter involves the geometric properties of "quadrics" and can be viewed as an extension of usual confidence intervals and ellipsoids. Only least squares techniques are needed to build the confidence intervals. Copyright The Econometric Society 2005.
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Volume (Year): 73 (2005)
Issue (Month): 4 (07)
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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.:
- James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
- Ann Harrison, 1995.
"Openness and Growth: A Time-Series, Cross-Country Analysis for Developing Countries,"
NBER Working Papers
5221, National Bureau of Economic Research, Inc.
- Harrison, Ann, 1996. "Openness and growth: A time-series, cross-country analysis for developing countries," Journal of Development Economics, Elsevier, vol. 48(2), pages 419-447, March.
- Harrison, Ann, 1991. "Openness and growth : a time series, cross-country analysis for developing countries," Policy Research Working Paper Series 809, The World Bank.
- Alastair R. Hall & Glenn D. Rudebusch & David W. Wilcox, 1994.
"Judging instrument relevance in instrumental variables estimation,"
Finance and Economics Discussion Series
94-3, Board of Governors of the Federal Reserve System (U.S.).
- Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-98, May.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, December.
- Donald, Stephen G. & Whitney Newey, 1999.
"Choosing the Number of Instruments,"
99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
- N. Gregory Mankiw & David Romer & David N. Weil, 1990.
"A Contribution to the Empirics of Economic Growth,"
NBER Working Papers
3541, National Bureau of Economic Research, Inc.
- Dufour, J.M. & Kiviet, J.F., 1995.
"Exact Inference Methods for First-Order Autoregressive Distributed Lag Models,"
Cahiers de recherche
9547, Universite de Montreal, Departement de sciences economiques.
- Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
- Dufour, J.M. & Kiviet, J.F., 1995. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Cahiers de recherche 9547, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Douglas A. Irwin & Marko Tervio, 2000.
"Does Trade Raise Income? Evidence from the Twentieth Century,"
NBER Working Papers
7745, National Bureau of Economic Research, Inc.
- Irwin, Douglas A. & Tervio, Marko, 2002. "Does trade raise income?: Evidence from the twentieth century," Journal of International Economics, Elsevier, vol. 58(1), pages 1-18, October.
- Alastair Hall & Fernanda P. M. Peixe, 2000.
"A Consistent Method for the Selection of Relevant Instruments,"
Econometric Society World Congress 2000 Contributed Papers
0790, Econometric Society.
- Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
- Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
- Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(02), pages 222-240, April.
- Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-83, January.
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