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COMPARISON OF INFERENTIAL METHODS IN PARTIALLY IDENTIFIED MODELS IN TERMS OF ERROR IN COVERAGE PROBABILITY

Published online by Cambridge University Press:  13 November 2014

Federico A. Bugni
Federico A. Bugni*
Affiliation:
Duke University
*
*Address correspondence to Federico Bugni, Department of Economics, Duke University, 213 Social Sciences, Box 90097, Durham, NC, 27708; phone: 919-660-1887; e-mail: [email protected].
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Abstract

This paper considers the problem of coverage of the elements of the identified set in a class of partially identified econometric models with a prespecified probability. In order to conduct inference in partially identified econometric models defined by moment (in)equalities, the literature has proposed three methods: bootstrap, subsampling, and asymptotic approximation. The objective of this paper is to compare these methods in terms of the rate at which they achieve the desired coverage level, i.e., in terms of the rate at which the error in the coverage probability (ECP) converges to zero.

Under certain conditions, we show that the ECP of the bootstrap and the ECP of the asymptotic approximation converge to zero at the same rate, which is a faster rate than that of the ECP of subsampling methods. As a consequence, under these conditions, the bootstrap and the asymptotic approximation produce inference that is more precise than subsampling. A Monte Carlo simulation study confirms that these results are relevant in finite samples.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 1 , February 2016 , pp. 187 - 242
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Andrews, D.W.K. (2000) Inconsistency of the bootstrap when a parameter is on the boundary of the parameter space. Econometrica 68, 399–405.Google Scholar
Andrews, D.W.K., Berry, S., & Jia-Barwick, P. (2004) Confidence Regions for Parameters in Discrete Games with Multiple Equilibria with an Application to Discount Chain Store Location. Mimeo, Yale University and M.I.T.Google Scholar
Andrews, D.W.K. & Guggenberger, P. (2009) 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. & Jia-Barwick, P. (2012) Inference for parameters defined by moment inequalities: A recommended moment selection procedure. Econometrica 80, 2805–2826.Google Scholar
Andrews, D.W.K. & Shi, X. (2013) Inference based on conditional moment inequalities. Econometrica 81, 609–666.Google 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
Armstrong, T.B. (2012) Asymptotically Exact Inference in Conditional Moment Inequality Models. Mimeo, Yale University.Google Scholar
Armstrong, T.B. (2014) Weighted KS statistics for inference on conditional moment inequalities. Journal of Econometrics 181, 92–116.Google Scholar
Babu, G.J. & Singh, K. (1985) Edgeworth expansions for sampling without replacement from finite populations. Journal of Multivariate Analysis 17, 261–278.Google Scholar
Beran, R. (1987) Prepivoting to reduce level error of confidence sets. Biometrika 74, 457–468.Google Scholar
Beran, R. (1988) Prepivoting test statistics: A bootstrap view of asymptotic refinements. Journal of the American Statistical Association 83, 687–697.Google Scholar
Beresteanu, A. & Molinari, F. (2008) Asymptotic properties for a class of partially identified models. Econometrica 76, 763–814.Google Scholar
Bhattacharya, R.N. & Rao, R.R. (1976) Normal Approximation and Asymptotic Expansions. Wiley.Google Scholar
Bickel, P. & Freedman, R. (1981) Some asymptotic theory for the bootstrap. Annals of Statistics 9, 1196–1217.CrossRefGoogle Scholar
Bontemps, C., Magnac, T., & Maurin, E. (2012) Set identified linear models. Econometrica 80, 1129–1155.Google Scholar
Bugni, F.A. (2010) Bootstrap inference in partially identified models defined by moment inequalities: Coverage of the identified set. Econometrica 78, 735–753.Google Scholar
Bugni, F.A. (2014) Supplemental Material to “Comparison of inferential methods in partially identified models in terms of error in coverage probability”. Accepted for electronic publication in Econometric Theory on August 11, 2014.Google Scholar
Bugni, F.A., Canay, I.A., & Guggenberger, P. (2012) Distortions of asymptotic confidence size in locally misspecified moment inequality models. Econometrica 80, 1741–1768.Google Scholar
Canay, I.A. (2010) E.L. inference for partially identified models: Large deviations optimality and bootstrap validity. Journal of Econometrics 156, 408–425.Google Scholar
Chernozhukov, V., Hong, H., & Tamer, E. (2007) Estimation and confidence regions for parameter sets in econometric models. Econometrica 75, 1243–1284.Google Scholar
Chernozhukov, V., Lee, S., & Rosen, A.M. (2013) Intersection bounds: Estimation and inference. Econometrica 81, 667–737.Google Scholar
Chetverikov, D. (2012) Adaptive Test of Conditional Moment Inequalities. Mimeo, MIT.Google Scholar
Davydov, Y.A., Lifshits, M.A., & Smorodina, N.V. (1995) Local Properties of Distributions of Stochastic Functionals. Translations of Mathematical Monographs, vol. 173. American Mathematical Society.Google Scholar
Galichon, A. & Henry, M. (2006) Inference in Incomplete Models. Mimeo, Ecole Polytechnique, Paris - Department of Economic Sciences and Pennsylvania State University.Google Scholar
Galichon, A. & Henry, M. (2013) Dilation bootstrap. Journal of Econometrics 177, 109–115.Google Scholar
Hall, P. (1992) The Bootstrap and Edgeworth Expansion. Springer Series in Statistics. Springer.Google Scholar
Horowitz, J.L. (2001) The bootstrap. In Heckman, J.J. and Leamer, E. (eds.), Handbook of Econometrics, vol. 4, chap. 52, pp. 3159–3228. Elsevier Science B.V.Google Scholar
Hüsler, J., Liu, R., & Singh, K. (2002) A formula for the tail probability of a multivariate normal distribution and its applications. Journal of Multivariate Analysis 82, 422–430.Google Scholar
Imbens, G. & Manski, C.F. (2004) Confidence Intervals for Partially Identified Parameters. Econometrica 72, 1845–1857.Google Scholar
Joag-Dev, K. & Proschan, F. (1983) Negative association of random variables with applications. Annals of Statistics 11, 286–295.Google Scholar
Kim, K. (2008) Set Estimation and Inference with Models Characterized by Conditional Moment Inequalities. Mimeo, Michigan State University.Google Scholar
Manski, C.F. (1995) Identification Problems in the Social Sciences. Harvard University Press.Google Scholar
Pakes, A., Porter, J., Ho, K., & Ishii, J. (2014) Moment Inequalities and Their Application. http://dx.doi.org/10.1920/wp.cem.2007.1607.Google Scholar
Politis, D.N., Romano, J.P., & Wolf, M. (1999) Subsampling. Springer.Google Scholar
Ponomareva, M. (2010) Inference in Models Defined by Conditional Moment Inequalities with Continuous Covariates. Mimeo, Northern Illinois University.Google Scholar
Romano, J.P. & Shaikh, A.M. (2008) Inference for identifiable parameters in partially identified econometric models. Journal of Statistical Planning and Inference 138, 2786–2807.Google Scholar
Romano, J.P. & Shaikh, A.M. (2010) Inference for the identified set in partially identified econometric models. Econometrica 78, 169–211.Google Scholar
Romano, J.P., Shaikh, A.M., & Wolf, M. (2014) A practical two-step method for testing moment inequalities. Econometrica 82, 1979–2002.Google Scholar
Rosen, A.M. (2008) Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities. Journal of Econometrics 146, 107–117.CrossRefGoogle Scholar
Stoye, J. (2009) More on confidence intervals for partially identified parameters. Econometrica 77, 299–1315.Google Scholar
Tamer, E. (2003) Incomplete simultaneous discrete response model with multiple equilibria. Review of Economic Studies 70, 147–165.Google Scholar
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