Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T18:47:42.389Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE ASYMPTOTIC SIZE DISTORTION OF TESTS WHEN INSTRUMENTS LOCALLY VIOLATE THE EXOGENEITY ASSUMPTION

Published online by Cambridge University Press:  13 September 2011

Patrik Guggenberger
Patrik Guggenberger*
Affiliation:
University of California San Diego
*
*Address correspondence to Patrik Guggenberger, University of California San Diego, Dept. of Economics, Room 315, 9500 Gilman Dr., La Jolla, CA 92093-0508; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

In the linear instrumental variables model with possibly weak instruments we derive the asymptotic size of testing procedures when instruments locally violate the exogeneity assumption. We study the tests by Anderson and Rubin (1949, The Annals of Mathematical Statistics 20, 46–63), Moreira (2003, Econometrica 71, 1027–1048), and Kleibergen (2005, Econometrica 73, 1103–1123) and their generalized empirical likelihood versions. These tests have asymptotic size equal to nominal size when the instruments are exogenous but are size distorted otherwise. While in just-identified models all the tests that we consider are equally size-distorted asymptotically, the Anderson-Rubin type tests are less size-distorted than the tests of Moreira (2003) and Kleibergen in over-identified situations. On the other hand, we also show that there are parameter sequences under which the former test asymptotically overrejects more frequently. Given that strict exogeneity of instruments is often a questionable assumption, our findings should be important to applied researchers who are concerned about the degree of size distortion of their inference procedure. We suggest robustness of asymptotic size under local model violations as a new alternative measure to choose among competing testing procedures. We also investigate the subsampling and hybrid tests introduced in Andrews and Guggenberger (2010a, Journal of Econometrics 158, 285–305) and show that they do not offer any improvement in terms of size-distortion reduction over the Anderson-Rubin type tests.

Type
ARTICLES
Information
Econometric Theory , Volume 28 , Issue 2 , April 2012 , pp. 387 - 421
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Acemoglu, D., Johnson, S., & Robinson, J.A. (2001) The colonial origins of comparative development: An empirical investigation. American Economic Review 91, 1369–1401.CrossRefGoogle Scholar
Anderson, T.W. & Rubin, H. (1949) Estimation of the parameters of a single equation in a complete set of stochastic equations. The Annals of Mathematical Statistics 20, 46–63.CrossRefGoogle Scholar
Andrews, D.W.K., Cheng, X., & Guggenberger, P. (2009) Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests. Working paper, Yale University.Google Scholar
Andrews, D.W.K. & Guggenberger, P. (2009a) Hybrid and size-corrected subsampling methods. Econometrica 77, 721–762.Google Scholar
Andrews, D.W.K. & Guggenberger, P. (2009b) Validity of subsampling and "plug-in asymptotic"inference for parameters defined by moment inequalities. Econometric Theory 25, 669–709.CrossRefGoogle Scholar
Andrews, D.W.K. & Guggenberger, P. (2010a) Applications of hybrid and size-corrected subsampling methods. Journal of Econometrics 158, 285–305.CrossRefGoogle Scholar
Andrews, D.W.K. & Guggenberger, P. (2010b) Asymptotic size and a problem with subsampling and the m out of n bootstrap. Econometric Theory 26, 426–468.CrossRefGoogle Scholar
Andrews, D.W.K., Moreira, M., & Stock, J.H. (2006) Optimal invariant similar tests for instrumental variables regression. Econometrica 74, 715–752.CrossRefGoogle Scholar
Andrews, D.W.K. & Soares, G. (2010) Inference for parameters defined by moment inequalities using generalized moment selection. Econometrica 78, 119–157.Google 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 of the Econometric Society, vol. III. Cambridge University Press.Google Scholar
Angrist, J.D. (1990) Lifetime earnings and the Vietnam era draft lottery: Evidence from Social Security administrative records. American Economic Review 80, 313–336.Google Scholar
Angrist, J.D. & Krueger, A. (1991) Does compulsory school attendance affect schoolings and earnings? Quarterly Journal of Economics 106, 979–1014.CrossRefGoogle Scholar
Berkowitz, D., Caner, M., & Fang, Y. (2008) Are “nearly exogenous instruments” reliable? Economics Letters 101, 20–23.CrossRefGoogle Scholar
Bound, J., Jaeger, D., & Baker, R. (1995) Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variables is weak. Journal of American Statistical Association 90, 443–50.Google Scholar
Breusch, T.S. & Pagan, A.R. (1980) The Lagrange multiplier test and its applications to model specifications in econometrics. Review of Economic Studies 47, 239–253.CrossRefGoogle Scholar
Bugni, F., Canay, I., & Guggenberger, P. (2009) Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models. Working paper, University of California San Diego.Google Scholar
Caner, M. (2007) Near Exogeneity and Weak Identification in Generalized Empirical Likelihood Estimators: Many Moment Asymptotics. Working paper, North Carolina State University.CrossRefGoogle Scholar
Card, D. (1995) Using geographic variation in college proximity to estimate the return to schooling. In Christofides, L.N., Grant, E.K., & Swidinsky, R. (eds.), Aspects of Labor Market Behaviour: Essays in Honour of John Vanderkamp. University of Toronto Press.Google Scholar
Chao, J.C. & Swanson, N.R. (2005) Consistent estimation with a large number of weak instruments. Econometrica 73, 1673–1692.CrossRefGoogle Scholar
Chernozhukov, V., Hong, H., & Tamer, E. (2007) Parameter set inference in a class of econometric models. Econometrica 75, 1243–1284.CrossRefGoogle Scholar
Conley, T., Hansen, C., & Rossi, P.E. (2011) Plausibly exogenous. Review of Economics and Statistics, forthcoming.Google Scholar
Doko, F. & Dufour, J.M. (2008) Instrument endogeneity and identification-robust tests: Some analytical results. Journal of Statistical Planning and Inference 138, 2649–2661.CrossRefGoogle Scholar
Dufour, J.M. (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 1365–1387.CrossRefGoogle Scholar
Fang, Y. (2006) GMM with Weak Identification and Near Exogeneity. Working paper, Xiamen University.Google Scholar
Frankel, J.A. & Romer, D. (1999) Does trade cause growth? American Economic Review 89, 379–399.CrossRefGoogle Scholar
Glaeser, E., La Porta, R., Lopez-de-Silanes, F., & Shleifer, A. (2004) Do institutions cause growth? Journal of Economic Growth 9, 271–303.CrossRefGoogle Scholar
Guggenberger, P. (2003) Econometric Essays on Generalized Empirical Likelihood, Long-Memory Time Series, and Volatility. Ph.D. dissertation, Yale University.Google Scholar
Guggenberger, P. (2010) A Note on the (In)Consistency of the Test of Overidentifying Restrictions and the Concepts of True and Pseudo-True Parameters. Working paper, University of California San Diego.Google Scholar
Guggenberger, P. & Kumar, G. (2011) On the size distortion of tests after an overidentifying restrictions pretest. Journal of Applied Econometrics, forthcoming.Google Scholar
Guggenberger, P., Ramalho, J.J.S., & Smith, R.J. (2008) GEL Statistics under Weak Identification. Working paper, Cambridge University.Google Scholar
Guggenberger, P. & Smith, R.J. (2005) Generalized empirical likelihood estimators and tests under partial, weak and strong identification. Econometric Theory 21, 667–709.CrossRefGoogle Scholar
Han, C. & Phillips, P.C.B. (2006) GMM with many moment conditions. Econometrica 74, 147–192.CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Hansen, L.P., Heaton, J., & Yaron, A. (1996) Finite-sample properties of some alternative GMM estimators. Journal of Business & Economic Statistics 14, 262–280.Google Scholar
Imbens, G. (1997) One-step estimators for over-identified generalized method of moments models. Review of Economic Studies 64, 359–383.CrossRefGoogle Scholar
Imbens, G., Spady, R.H., & Johnson, P. (1998) Information theoretic approaches to inference in moment condition models. Econometrica 66, 333–357.CrossRefGoogle Scholar
Kane, T.J. & Rouse, C. (1995) Labor market returns to two-year and four-year college. American Economic Review 85, 600–614.Google Scholar
Kitamura, Y. (2001) Asymptotic optimality of empirical likelihood for testing moment restrictions. Econometrica 69, 1661–1672.CrossRefGoogle Scholar
Kitamura, Y. & Stutzer, M. (1997) An information-theoretic alternative to generalized method of moments estimation. Econometrica 65, 861–874.CrossRefGoogle Scholar
Kleibergen, F. (2005) Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1123.CrossRefGoogle Scholar
Kleibergen, F. & Mavroeidis, S. (2009) Inference on Subsets of Parameters in GMM Without Assuming Identification. Working paper, Brown University.Google Scholar
Kraay, A. (2011) Instrumental variables regressions with uncertain exclusion restrictions: A Bayesian approach. Journal of Applied Econometrics, forthcoming.Google Scholar
Miguel, E., Satyanath, S., & Sergenti, E. (2004) Economic shocks and civil conflict: An instrumental variables approach. Journal of Political Economy 112, 725–753.CrossRefGoogle Scholar
Mikusheva, A. (2010) Robust confidence sets in the presence of weak instruments. Journal of Econometrics 157, 236–247.CrossRefGoogle Scholar
Moreira, M.J. (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048.CrossRefGoogle Scholar
Moreira, M.J. (2009) Tests with correct size when instruments can be arbitrarily weak. Journal of Econometrics 152, 131–140.CrossRefGoogle Scholar
Nevo, A. & Rosen, A. (2011) Identification with imperfect instruments. Review of Economics and Statistics, forthcoming.Google Scholar
Otsu, T. (2006) Generalized empirical likelihood inference for nonlinear and time series models under weak identification. Econometric Theory 22, 513–527.CrossRefGoogle Scholar
Owen, A. (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75, 237–249.CrossRefGoogle Scholar
Politis, D.N. & Romano, J.P. (1994) Large sample confidence regions based on subsamples under minimal assumptions. Annals of Statistics 22, 2031–2050.CrossRefGoogle Scholar
Qin, J. & Lawless, J. (1994) Empirical likelihood and general estimating equations. Annals of Statistics 22, 300–325.CrossRefGoogle Scholar
Rajan, R. & Zingales, L. (1998) Financial dependence and growth. American Economic Review 88, 559–586.Google Scholar
Smith, R.J. (1997) Alternative semi-parametric likelihood approaches to generalized method of moments estimation. Economic Journal 107, 503–519.CrossRefGoogle Scholar
Staiger, D. & Stock, J.H. (1997) Instrumental variables regression with weak instruments. Econometrica 65, 557–586.CrossRefGoogle Scholar
Stock, J.H. & Wright, J. (2000) GMM with weak identification. Econometrica 68, 1055–1096.CrossRefGoogle Scholar