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Unformatted text preview: APPLICATIONS OF SUBSAMPLING, HYBRID, AND SIZECORRECTION METHODS By Donald W. K. Andrews and Patrik Guggenberger May 2007 COWLES FOUNDATION DISCUSSION PAPER NO. 1608 COWLES FOUNDATION FOR RESEARCH IN ECONOMICS YALE UNIVERSITY Box 208281 New Haven, Connecticut 065208281 http://cowles.econ.yale.edu/ Applications of Subsampling, Hybrid, and SizeCorrection Methods Donald W. K. Andrews ∗ Cowles Foundation for Research in Economics Yale University Patrik Guggenberger Department of Economics UCLA November 2005 Revised: May 2007 ∗ Andrews gratefully acknowledges the research support of the National Science Foundation via grant number SES0417911. Guggenberger gratefully acknowledges research support from a faculty research grant from UCLA in 2005. The authors thank the participants at a number of seminars and conferences at which the paper was presented for comments. Abstract This paper analyzes the properties of subsampling, hybrid subsampling, and size correction methods in two nonregular models. The latter two procedures are intro duced in Andrews and Guggenberger (2005b). The models are nonregular in the sense that the test statistics of interest exhibit a discontinuity in their limit distribu tion as a function of a parameter in the model. The f rst model is a linear instrumental variables (IV) model with possibly weak IVs estimated using twostage least squares (2SLS). In this case, the discontinuity occurs when the concentration parameter is zero. The second model is a linear regression model in which the parameter of interest may be near a boundary. In this case, the discontinuity occurs when the parameter is on the boundary. The paper shows that in the IV model onesided and equaltailed twosided sub sampling tests and con f dence intervals (CIs) based on the 2SLS t statistic do not have correct asymptotic size. This holds for both fully and partiallystudentized t statistics. But, subsampling procedures based on the partiallystudentized t statistic can be sizecorrected. On the other hand, symmetric twosided subsampling tests and CIs are shown to have (essentially) correct asymptotic size when based on a partiallystudentized t statistic. Furthermore, all types of hybrid subsampling tests and CIs are shown to have correct asymptotic size in this model. The above results are consistent with “impossibility” results of Dufour (1997) because subsampling and hybrid subsampling CIs are shown to have in f nite length with positive probability. Subsampling CIs for a parameter that may be near a lower boundary are shown to have incorrect asymptotic size for upper onesided and equaltailed and symmetric twosided CIs. Again, sizecorrection is possible. In this model as well, all types of hybrid subsampling CIs are found to have correct asymptotic size....
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 Fall '08
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 Economics, Statistics, Normal Distribution, Regression Analysis, Statistical hypothesis testing, Tn

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