Subsampling Applications Hybrid Methods

Subsampling Applications Hybrid Methods - APPLICATIONS OF...

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Unformatted text preview: APPLICATIONS OF SUBSAMPLING, HYBRID, AND SIZE-CORRECTION 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 06520-8281 http://cowles.econ.yale.edu/ Applications of Subsampling, Hybrid, and Size-Correction 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 SES-0417911. 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 non-regular models. The latter two procedures are intro- duced in Andrews and Guggenberger (2005b). The models are non-regular 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 two-stage 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 one-sided and equal-tailed two-sided 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 partially-studentized t statistics. But, subsampling procedures based on the partially-studentized t statistic can be size-corrected. On the other hand, symmetric two-sided subsampling tests and CIs are shown to have (essentially) correct asymptotic size when based on a partially-studentized 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 one-sided and equal-tailed and symmetric two-sided CIs. Again, size-correction is possible. In this model as well, all types of hybrid subsampling CIs are found to have correct asymptotic size....
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Subsampling Applications Hybrid Methods - APPLICATIONS OF...

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