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IDENTIFICATION AND INFERENCE ON REGRESSIONS WITH MISSING COVARIATE DATA

Published online by Cambridge University Press:  02 September 2015

Esteban M. Aucejo
Affiliation:
London School of Economics and Political Science
Federico A. Bugni*
Affiliation:
Duke University
V. Joseph Hotz
Affiliation:
Duke University, NBER, and IZA
*
*Address correspondence to Federico A. Bugni, Department of Economics, Duke University, 213 Social Sciences, Box 90097, Durham, NC, 27708; e-mail: federico.bugni@duke.edu.

Abstract

This paper examines the problem of identification and inference on a conditional moment condition model with missing data, with special focus on the case when the conditioning covariates are missing. We impose no assumption on the distribution of the missing data and we confront the missing data problem by using a worst case scenario approach.

We characterize the sharp identified set and argue that this set is usually too complex to compute or to use for inference. Given this difficulty, we consider the construction of outer identified sets (i.e. supersets of the identified set) that are easier to compute and can still characterize the parameter of interest. Two different outer identification strategies are proposed. Both of these strategies are shown to have nontrivial identifying power and are relatively easy to use and combine for inferential purposes.

Type
ARTICLES
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

We thank useful comments and suggestions from Arie Beresteanu, Ivan Canay, Shakeeb Khan, and the participants at the presentations in the 2010 World Congress in Shanghai, the 2010 Triangle Econometrics Conference, the 2011 Joint Statistical Meetings in Miami, and at the Statistics Seminar at Duke University. Bugni thanks the National Science Foundation for research support via grant SES-1123771. We also thank the co-editors and the two anonymous referees for several comments and suggestions that have significantly improved this paper. Takuya Ura provided excellent research assistance. Any and all errors are our own.

References

Abrevaya, J. (2001) The effects of demographics and maternal behavior on the distribution of birth outcomes. Empirical Economics 26, 247257.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.CrossRefGoogle 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, 669709.CrossRefGoogle Scholar
Andrews, D.W.K. & Jia-Barwick, P. (2012) Inference for parameters defined by moment inequalities: A recommended moment selection procedure. Econometrica 80, 28052826.Google Scholar
Andrews, D.W.K. & Shi, X. (2013) Inference based on conditional moment inequalities. Econometrica 81, 609666.Google Scholar
Andrews, D.W.K. & Soares, G. (2010) Inference for parameters defined by moment inequalities using generalized moment selection. Econometrica 78, 119157.Google Scholar
Arcidiacono, P., Aucejo, E., Coate, P., & Hotz, V.J. (2012) Affirmative Action and University Fit: Evidence from Proposition 209. NBER Working paper #18523.CrossRefGoogle 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, 92116.CrossRefGoogle Scholar
Armstrong, T.B. & Chan, H.P. (2012) Multiscale Adaptive Inference on Conditional Moment Inequalities. Mimeo, Yale University and National University of Singapore.Google Scholar
Aucejo, E.M., Bugni, F.A., & Hotz, V.J. (2015a) The determinants of graduation outcomes at the University of California before and after Proposition 209. Mimeo, London School of Economics and Political Science and Duke University.Google Scholar
Aucejo, E.M., Bugni, F.A., & Hotz, V.J. (2015b) Online Supplemental Material to “Identification and Inference on Regressions with Missing Covariate Data”. Mimeo, London School of Economics and Political Science and Duke University.Google Scholar
Beresteanu, A. & Molinari, F. (2008) Asymptotic properties for a class of partially identified models. Econometrica 76, 763814.CrossRefGoogle Scholar
Beresteanu, A., Molinari, F., & Molchanov, I. (2011) Sharp identification regions in models with convex predictions. Econometrica 79, 17851821.Google Scholar
Bontemps, C., Magnac, T., & Maurin, E. (2012) Set identified linear models. Econometrica 80, 11291155.Google Scholar
Bugni, F.A. (2010) Bootstrap inference in partially identified models defined by moment inequalities: Coverage of the identified set. Econometrica 78, 735753.Google Scholar
Bugni, F.A. (2015) A comparison of inferential methods in partially identified models in terms of error in coverage probability (formerly circulated as “Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Elements of the Identified Set”). Econometric Theory FirstView, 156.Google Scholar
Bugni, F.A., Canay, I.A., & Shi, X. (2015) Specification tests for partially identified models defined by moment inequalities. Journal of Econometrics 185, 259282.Google Scholar
Canay, I.A. (2010) E.L. inference for partially identified models: Large deviations optimality and bootstrap validity. Journal of Econometrics 156, 408425.CrossRefGoogle Scholar
Chernozhukov, V., Hong, H., & Tamer, E. (2007) Estimation and confidence regions for parameter sets in econometric models. Econometrica 75, 12431284.CrossRefGoogle Scholar
Chernozhukov, V., Lee, S., & Rosen, A.M. (2013) Intersection bounds: Estimation and inference. Econometrica 81, 667737.Google Scholar
Chesher, A. & Rosen, A. (2014a) Generalized Instrumental Variable Models. Mimeo, CeMMAP working paper CWP04/14.CrossRefGoogle Scholar
Chesher, A. & Rosen, A. (2014b) An instrumental variable random coefficients model for binary outcomes. Econometrics Journal 17, S1S19.CrossRefGoogle Scholar
Chesher, A., Rosen, A., & Smolinski, K. (2013) An instrumental variable model for multiple discrete choice. Quantitative Economics 4, 157196.CrossRefGoogle Scholar
Chetverikov, D. (2013) Adaptive test of conditional moment inequalities. Unpublished manuscript.CrossRefGoogle Scholar
Domínguez, M. & Lobato, I.N. (2004) Consistent estimation of models defined by conditional moment restrictions. Econometrica 72, 16011615.CrossRefGoogle 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. (2011) Set identification in models with multiple equilibria. Journal of Econometrics 78, 12641298.Google Scholar
Galichon, A. & Henry, M. (2013) Dilation bootstrap: A methodology for constructing confidence regions with partially identified models. Journal of Econometrics 177, 109115.Google Scholar
Horowitz, J.L. & Manski, C.F. (1995) Identification and robustness with contaminated and corrupted data. Econometrica 63, 281302.CrossRefGoogle Scholar
Horowitz, J.L. & Manski, C.F. (1998) Censoring of outcomes and regressors due to survey nonresponse: Identification and estimation using weights and imputations. Journal of Econometrics 84, 3758.CrossRefGoogle Scholar
Horowitz, J.L. & Manski, C.F. (2000) Nonparametric analysis of randomized experiments with missing covariate and outcome data. Journal of the American Statistical Association 95, 7788.CrossRefGoogle Scholar
Horowitz, J.L. & Manski, C.F. (2006) Identification and estimation of statistical functionals using incomplete data. Journal of Econometrics 132, 445459.CrossRefGoogle Scholar
Horowitz, J.L., Manski, C.F., Ponomareva, M., & Stoye, J. (2003) Computation of bounds on population parameters when the data are incomplete. Reliable Computing 9, 419440.CrossRefGoogle Scholar
Imbens, G. & Manski, C.F. (2004) Confidence intervals for partially identified parameters. Econometrica 72, 18451857.CrossRefGoogle Scholar
Kim, K. (2008) Set Estimation and Inference with Models Characterized by Conditional Moment Inequalities. Mimeo, Michigan State University.Google Scholar
Lewbel, A. (2002) Estimation of average treatment effects with misclassification. Econometrica 75, 537551.CrossRefGoogle Scholar
Lundberg, S. (1988) Labor supply of husbands and wives: A simultaneous equations approach. The Review of Economics and Statistics 70, 224235.CrossRefGoogle Scholar
Mahajan, A. (2006) Identification and estimation of regression models with missclassification. Econometrica 74, 631665.CrossRefGoogle Scholar
Manski, C.F. (2003) Partial Identification of Probability Distributions. Springer-Verlag.Google Scholar
Manski, C.F. & Tamer, E. (2002) Inference of regressions with interval data on a regressor or outcome. Econometrica 70, 519546.CrossRefGoogle Scholar
Molinari, F. (2008) Partial identification of probability distributions with misclassified data. Journal of Econometrics 144, 81117.CrossRefGoogle Scholar
Pakes, A., Porter, J., Ho, K., & Ishii, J. (2014) Moment inequalities and their application. Econometrica 83, 315334.CrossRefGoogle Scholar
Pollard, D. (1990) Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probability and Statistics, vol. 2.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, 27862807.Google Scholar
Romano, J.P. & Shaikh, A.M. (2010) Inference for the identified set in partially identified econometric models. Econometrica 78, 169211.Google Scholar
Rosen, A.M. (2008) Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities. Journal of Econometrics 146, 107117.CrossRefGoogle Scholar
Stoye, J. (2009) More on confidence intervals for partially identified parameters. Econometrica 77, 2991315.Google Scholar
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