Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments
It is well known that standard asymptotic theory is not valid or is extremely unreliable in models with identification problems or weak instruments [Dufour (1997, Econometrica), Staiger and Stock (1997, Econometrica), Wang and Zivot (1998, Econometrica), Stock and Wright (2000, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. One possible way out consists here in using a variant of the Anderson-Rubin (1949, Ann. Math. Stat.) procedure. The latter, however, 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, which in general does not allow for individual coefficients. This problem may in principle be overcome by using projection techniques [Dufour (1997, Econometrica), Dufour and Jasiak (2001, International Economic Review)]. AR-types are emphasized because they are robust to both weak instruments and instrument exclusion. However, these techniques can be implemented only by using costly numerical techniques. In this paper, we provide a complete analytic solution to the problem of building projection-based confidence sets from Anderson-Rubin-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 required for building the confidence intervals. We also study by simulation how “conservative” projection-based confidence sets are. Finally, we illustrate the methods proposed by applying them to three different examples: the relationship between trade and growth in a cross-section of countries, returns to education, and a study of production functions in the U.S. economy.
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- Jean-Marie Dufour & Jan F. Kiviet, 1998.
"Exact Inference Methods for First-Order Autoregressive Distributed Lag Models,"
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, Universite de Montreal, Departement de sciences economiques.
- 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.
- 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.
- 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, 1991. "Openness and growth : a time series, cross-country analysis for developing countries," Policy Research Working Paper Series 809, The World Bank.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
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