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OPTIMAL INVARIANT INFERENCE WHEN THE NUMBEROF INSTRUMENTS IS LARGE

Published online by Cambridge University Press:  01 June 2009

Laura Chioda  and
Michael Jansson
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Abstract

This paper studies the asymptotic behavior of aGaussian linear instrumental variables model inwhich the number of instruments diverges with thesample size. Asymptotic efficiency bounds areobtained for rotation invariant inference proceduresand are shown to be attainable by procedures basedon the limited information maximum likelihoodestimator. The bounds are obtained by characterizingthe limiting experiment associated with the modelinduced by the rotation invariance restriction.

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Type
Research Article
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 793 - 805
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

The authors thank Whitney Newey, Jim Powell, aco-editor, and a referee for helpful comments.

References

REFERENCES

Anderson, T.W., Kunitomo, N., & Matsushita, Y. (2006) A New Light from Old Wisdoms: Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments. Working paper, University of Tokyo.Google Scholar
Anderson, T.W. & Rubin, H. (1949) Estimation of the parameters of a single equation in a complete set of stochastic equations. Annals of Mathematical Statistics 20, 46–63.10.1214/aoms/1177730090Google Scholar
Andrews, D.W.K., Moreira, M.J., & Stock, J.H. (2006) Optimal two-sided invariant similar tests for instrumental variables regression. Econometrica 74, 715–752.10.1111/j.1468-0262.2006.00680.xGoogle Scholar
Andrews, D.W.K. & Stock, J.H. (2007) Inference with weak instruments. In Blundell, R., Newey, W.K., & Persson, T. (eds.) Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress, vol. III, pp. 122–173. Cambridge University Press.Google Scholar
Bekker, P.A. (1994) Alternative approximations to the distributions of instrumental variables estimators. Econometrica 62, 657–681.10.2307/2951662CrossRefGoogle Scholar
Chamberlain, G. & Imbens, G. (2004) Random effects estimators with many instrumental variables. Econometrica 72, 295–306.10.1111/j.1468-0262.2004.00485.xGoogle Scholar
Chao, J.C. & Swanson, N.R. (2005) Consistent estimation with a large number of weak instruments. Econometrica 73, 1673–1692.10.1111/j.1468-0262.2005.00632.xGoogle Scholar
Chioda, L. & Jansson, M. (2005) Optimal Conditional Inference for Instrumental Variables Regression. Working paper, Princeton University.Google Scholar
Choi, S., Hall, W.J., & Schick, A. (1996) Asymptotically uniformly most powerful tests in parametric and semiparametric models. Annals of Statistics 24, 841–861.10.1214/aos/1032894469CrossRefGoogle Scholar
Donald, S.G. & Newey, W.K. (2001) Choosing the number of instruments. Econometrica 69, 1161–1191.10.1111/1468-0262.00238Google Scholar
Dufour, J.-M. (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 1365–1387.10.2307/2171740Google Scholar
Dufour, J.-M. (2003) Identification, weak instruments, and statistical inference in econometrics. Canadian Journal of Economics 36, 767–808.10.1111/1540-5982.t01-3-00001Google Scholar
Efron, B. (1975) Defining the curvature of a statistical problem (with applications to second order efficiency). Annals of Statistics 3, 1189–1242.10.1214/aos/1176343282Google Scholar
Fuller, W.A. (1977) Some properties of a modification of the limited information estimator. Econometrica 45, 939–953.10.2307/1912683CrossRefGoogle Scholar
Hahn, J. (2002) Optimal inference with many instruments. Econometric Theory 18, 140–168.10.1017/S0266466602181084Google Scholar
Hahn, J. & Hausman, J. (2003) Weak instruments: Diagnosis and cures in empirical econometrics. American Economic Review 93, 118–125.10.1257/000282803321946912CrossRefGoogle Scholar
Hansen, C., Hausman, J., & Newey, W. (2005) Estimation with Many Instrumental Variables. Working paper, University of Chicago Graduate School of Business.10.1920/wp.cem.2006.1906Google Scholar
Kleibergen, F. (2002) Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 1781–1803.10.1111/1468-0262.00353Google Scholar
Kunitomo, N. (1980) Asymptotic expansions of the distributions of estimators in a linear functional relationship and simultaneous equations. Journal of the American Statistical Association 75, 693–700.10.1080/01621459.1980.10477535Google Scholar
Moreira, M.J. (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048.10.1111/1468-0262.00438Google Scholar
Morimune, K. (1983) Approximate distributions of k-class estimators when the degree of overidentifiability is large compared with the sample size. Econometrica 53, 821–841.10.2307/1912160CrossRefGoogle Scholar
Muirhead, R.J. (1982) Aspects of Multivariate Statistical Theory. Wiley.10.1002/9780470316559CrossRefGoogle Scholar
Nagar, A.L. (1959) The bias and moment matrix of general k-class estimators of the parameters in simultaneous equations. Econometrica 27, 575–595.10.2307/1909352Google Scholar
Rothenberg, T.J. (1984) Approximating the distributions of econometric estimators and test statistics. In Griliches, Z. & Intriligator, M.D. (eds.), Handbook of Econometrics, vol. II. pp. 881–935 North-Holland.10.1016/S1573-4412(84)02007-9CrossRefGoogle Scholar
Rudin, W. (1976) Principles of Mathematical Analysis, 3rd ed. McGraw-Hill.Google Scholar
Staiger, D. & Stock, J.H. (1997) Instrumental variables estimation with weak instruments. Econometrica 65, 557–586.10.2307/2171753Google Scholar
Stock, J.H., Wright, J.H., & Yogo, M. (2002) A survey of weak instruments and weak identification in generalized method of moments. Journal of Business & Economic Statistics 20, 518–529.10.1198/073500102288618658Google Scholar
Stock, J.H. & Yogo, M. (2005) Asymptotic distributions of instrumental variables statistics with many weak instruments. In Andrews, D.W.K. & Stock, J.H. (eds.) Identification and Inference in Econometric Models: Essays in Honor of Thomas J. Rothenberg, pp. 109–120. Cambridge University Press.10.1017/CBO9780511614491.007Google Scholar
van der Ploeg, J. & Bekker, P.A. (1995) Efficiency Bounds for Instrumental Variable Estimators under Group-Asymptotics. Working paper, University of Groningen.Google Scholar
van der Vaart, A.W. (1991) An asymptotic representation theorem. International Statistical Review 59, 97–121.10.2307/1403577Google Scholar
van der Vaart, A.W. (1998) Asymptotic Statistics. Cambridge University Press.10.1017/CBO9780511802256CrossRefGoogle Scholar