Intersection Bounds: Estimation and Inference

Econometrica

Volumn 81, Issue 2, 2013, Pages 667-737

  Chernozhukov, Victor ^a   Lee, Sokbae ^b   Rosen, Adam M ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b Seoul National University   (South Korea)

^c UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Adaptive moment selection; Anti concentration inequalities; Bound analysis; Concentration inequalities; Conditional moments; Infinite dimensional constraints; Linear programming; Moderate deviations; Non Donsker empirical process methods; Partial identification; Strong approximation

Indexed keywords

EID: 84875481261     PISSN: 00129682     EISSN: 14680262     Source Type: Journal    
DOI: 10.3982/ECTA8718     Document Type: Article

References (75)

1. Andrews, D. W. K. (1991): "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models, " Econometrica, 59 (2), 307-345. DOI: 10.2307/2938259
2. Andrews, D. W. K., and P. Guggenberger (2009): "Validity of Subsampling and Plug-In Asymptotic Inference for Parameters Defined by Moment Inequalities, " Econometric Theory, 25, 669-709. DOI: 10.1017/S0266466608090257
3. Andrews, D. W. K., and S. Han (2009): "Invalidity of the Bootstrap and m Out of n Bootstrap for Interval Endpoints Defined by Moment Inequalities, " Econometrics Journal, 12 (s1), S172-S199. DOI: 10.1111/j.1368-423X.2008.00265.x
4. Andrews, D. W. K., and P. Jia (2012): "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure, " Econometrica, 80 (6), 2805-2826. DOI: 10.3982/ECTA8166
5. Andrews, D. W. K., and X. Shi (2011): "Nonparametric Inference Based on Conditional Moment Inequalities, " Discussion Paper 1840, Cowles Foundation.
6. Andrews, D. W. K., and X. Shi (2013): "Inference for Parameters Defined by Conditional Moment Inequalities, " Econometrica (forthcoming).
7. Andrews, D. W. K., and G. Soares (2010): "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection, " Econometrica, 78 (1), 119-157. DOI: 10.3982/ECTA7502
8. Armstrong, T. B. (2011a): "Asymptotically Exact Inference in Conditional Moment Inequality Models, " Working Paper, Stanford University.
9. Armstrong, T. B. (2011b): "Weighted KS Statistics for Inference on Conditional Moment Inequalities, " Working Paper, Stanford University.
10. Belloni, A., V. Chernozhukov, and I. Fernandez-Val (2011): "Conditional Quantile Processes Under Increasing Dimensions, " Working Paper CWP19/11, CeMMAP.
11. Belloni, A., V. Chernozhukov, and K. Kato (2010): "(Some) New Asymptotic Theory for Linear Series Estimators, " Working Paper, MIT.
12. Beresteanu, A., and F. Molinari (2008): "Asymptotic Properties for a Class of Partially Identified Models, " Econometrica, 76 (4), 763-814. DOI: 10.1111/j.1468-0262.2008.00859.x
13. Berry, S. T., and E. Tamer (2007): "Identification in Models of Oligopoly Entry, " in Advances in Econometrics, Ninth World Congress, Vol. 2, ed. by R. Blundell, W. Newey, and T. Persson. Cambridge: Cambridge University Press, 46-85.
14. Bickel, P. J., and M. Rosenblatt (1973): "On Some Global Measures of the Deviations of Density Function Estimates, " The Annals of Statistics, 1 (6), 1071-1095. DOI: 10.1214/aos/1176342558
15. Bierens, H. (1982): "Consistent Model Specification Tests, " Journal of Econometrics, 20, 105-134. DOI: 10.1016/0304-4076(82)90105-1
16. Blundell, R., A. Gosling, H. Ichimura, and C. Meghir (2007): "Changes in the Distribution of Male and Female Wages Accounting for Unemployment Composition Using Bounds, " Econometrica, 75 (2), 323-363. DOI: 10.1111/j.1468-0262.2006.00750.x
17. Bugni, F. (2010): "Bootstrap Inference for Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set, " Econometrica, 78 (2), 735-753. DOI: 10.3982/ECTA8056
18. Canay, I. (2010): "EL Inference for Partially Identified Models: Large Deviations Optimality and Bootstrap Validity, " Journal of Econometrics, 156 (2), 408-425. DOI: 10.1016/j.jeconom.2009.11.009
19. Carneiro, P., and S. Lee (2009): "Estimating Distributions of Potential Outcomes Using Local Instrumental Variables With an Application to Changes in College Enrollment and Wage Inequality, " Journal of Econometrics, 149, 191-208. DOI: 10.1016/j.jeconom.2009.01.011
20. Chen, X. (2007): "Large Sample Sieve Estimation of Semi-Nonparametric Models (Chapter 76), " in Handbook of Econometrics, Vol. 6. Amsterdam: Elsevier, 5549-5632.
21. Chernozhukov, V., Chetverikov, D., and K. Kato (2011): "Anti-Concentration and Honest Adaptive Confidence Bands, " Working Paper, Hiroshima University.
22. Chernozhukov, V., H. Hong, and E. Tamer (2007): "Estimation and Confidence Regions for Parameter Sets in Econometric Models, " Econometrica, 75 (5), 1243-1284. DOI: 10.1111/j.1468-0262.2007.00794.x
23. Chernozhukov, V., S. Lee, and A. Rosen (2009): "Intersection Bounds: Estimation and Inference, " Working Paper CWP19/09, CeMMAP.
24. Chernozhukov, V., S. Lee, and A. Rosen (2013): "Supplement to 'Intersection Bounds: Estimation and Inference', " Econometrica Supplementary Material, 81, http://www.econometricsociety.org/ecta/Supmat/8718_proofs.pdf; http://www.econometricsociety.org/ecta/Supmat/8718_data_and_programs.zip.
25. Chernozhukov, V., R. Rigobon, and T. Stoker (2010): "Set Identification and Sensitivity Analysis With Tobin Regressors, " Quantitative Economics, 1 (2), 255-277. DOI: 10.3982/QE1
26. Chesher, A. D. (2010): "Instrumental Variable Models for Discrete Outcomes, " Econometrica, 78 (2), 575-601. DOI: 10.3982/ECTA7315
27. Chetverikov, D. (2011): "Adaptive Rate Optimal Test of Conditional Moment Inequalities, " Working Paper, MIT.
28. Chetverikov, D. (2012): "Testing Regression Monotonicity in Econometric Models, " Working Paper, MIT.
29. Dudley, R., and W. Philipp (1983): "Invariance Principles for Sums of Banach Space Valued Random Elements and Empirical Processes, " Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 62, 509-552. DOI: 10.1007/BF00534202
30. Fan, J., and I. Gijbels (1996): Local Polynomial Modelling and Its Applications. London, U.K.: Chapman & Hall.
31. Fan, Y., and S. Park (2011): "Bias-Correction and Confidence Sets Under IV and MIV Assumptions, " Working Paper, Vanderbilt University.
32. Galichon, A., and M. Henry (2009): "A Test of Non-Identifying Restrictions and Confidence Regions for Partially Identified Parameters, " Journal of Econometrics, 159 (2), 186-196. DOI: 10.1016/j.jeconom.2009.01.010
33. Gonzalez, L. (2005): "Nonparametric Bounds on the Returns to Language Skills, " Journal of Applied Econometrics, 20, 771-795. DOI: 10.1002/jae.795
34. Haile, P. A., and E. Tamer (2003): "Inference With an Incomplete Model of English Auctions, " Journal of Political Economy, 111 (1), 1-51. DOI: 10.1086/344801
35. Härdle, W., and E. Mammen (1993): "Comparing Nonparametric versus Parametric Regression Fits, " The Annals of Statistics, 21 (4), 1926-1947. DOI: 10.1214/aos/1176349403
36. Heckman, J. J., and E. J. Vytlacil (1999): "Local Instrumental Variables and Latent Variable Models for Identifying and Bounding Treatment Effects, " Proceedings of the National Academy of Sciences, 96, 4730-4734. DOI: 10.1073/pnas.96.8.4730
37. Heckman, J. J., J. Smith, and N. Clements (1997): "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts, " Review of Economic Studies, 64, 487-537. DOI: 10.2307/2971729
38. Hirano, K., and J. R. Porter (2012): "Impossibility Results for Nondifferentiable Functionals, " Econometrica, 80 (4), 1769-1790. DOI: 10.3982/ECTA8681
39. Horowitz, J., and V. G. Spokoiny (2001): "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model Against a Nonparametric Alternative, " Econometrica, 69 (3), 599-631. DOI: 10.1111/1468-0262.00207
40. Imbens, G., and C. F. Manski (2004): "Confidence Intervals for Partially Identified Parameters, " Econometrica, 72 (6), 1845-1857. DOI: 10.1111/j.1468-0262.2004.00555.x
41. Kim, K. i. (2009): "Set Estimation and Inference With Models Characterized by Conditional Moment Inequalities, " Working Paper, University of Minnesota.
42. Koenker, R. (2005): Quantile Regression. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511754098
43. Kong, E., O. Linton, and Y. Xia (2010): "Uniform Bahadur Representation for Local Polynomial Estimates of m-Regression and Its Application to the Additive Model, " Econometric Theory, 26, 1529-1564. DOI: 10.1017/S0266466609990661
44. Kreider, B., and J. Pepper (2007): "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors, " Journal of the American Statistical Association, 102 (478), 432-441. DOI: 10.1198/016214506000000997
45. Lee, S., and R. Wilke (2009): "Reform of Unemployment Compensation in Germany: A Nonparametric Bounds Analysis Using Register Data, " Journal of Business & Economic Statistics, 27 (2), 193-205. DOI: 10.1198/jbes.2009.0014
46. Lee, S., K. Song, and Y.-J. Whang (2013): "Testing Functional Inequalities, " Journal of Econometrics, 172, 14-32. DOI: 10.1016/j.jeconom.2012.08.006
47. Manski, C. F. (1989): "Anatomy of the Selection Problem, " The Journal of Human Resources, 24 (3), 343-360. DOI: 10.2307/145818
48. Manski, C. F. (1990): "Nonparametric Bounds on Treatment Effects, " American Economic Review, 80 (2), 319-323.
49. Manski, C. F. (1997): "Monotone Treatment Response, " Econometrica, 65 (6), 1311-1334. DOI: 10.2307/2171738
50. Manski, C. F. (2003): Partial Identification of Probability Distributions. New York: Springer-Verlag.
51. Manski, C. F., and J. V. Pepper (2000): "Monotone Instrumental Variables: With an Application to the Returns to Schooling, " Econometrica, 68 (4), 997-1010. DOI: 10.1111/1468-0262.00144
52. Manski, C. F., and J. V. Pepper (2009): "More on Monotone Instrumental Variables, " Econometrics Journal, 12 (s1), S200-S216. DOI: 10.1111/j.1368-423X.2008.00262.x
53. Masry, E. (1996): "Multivariate Local Polynomial Regression for Time Series: Uniform Strong Consistency and Rates, " Journal of Time Series Analysis, 17, 571-599. DOI: 10.1111/j.1467-9892.1996.tb00294.x
54. Massart, P. (1989): "Strong Approximation for Multivariate Empirical and Related Processes, via KMT Constructions, " The Annals of Probability, 17 (1), 266-291. DOI: 10.1214/aop/1176991508
55. Menzel, K. (2009): "Estimation and Inference With Many Weak Moment Inequalities, " Working Paper, MIT.
56. Nevo, A., and A. M. Rosen (2012): "Identification With Imperfect Instruments, " Review of Economics and Statistics, 94 (3), 659-671. DOI: 10.1162/REST\_a\_00171
57. Newey, W. K. (1995): "Convergence Rates for Series Estimators, " in Statistical Methods of Economics and Quantitative Economics: Essays in Honor of C.R. Rao, ed. by G. Maddalla, P. Phillips, and T. Srinavasan. Cambridge, MA: Blackwell, 254-275.
58. Newey, W. K. (1997): "Convergence Rates and Asymptotic Normality for Series Estimators, " Journal of Econometrics, 79, 147-168. DOI: 10.1016/S0304-4076(97)00011-0
59. Nicoletti, C., F. Foliano, and F. Peracchi (2011): "Estimating Income Poverty in the Presence of Missing Data and Measurement Error Problems, " Journal of Business & Economic Statistics, 29 (1), 61-72. DOI: 10.1198/jbes.2010.07185
60. Pakes, A., J. Porter, K. Ho, and J. Ishii (2005): "The Method of Moments With Inequality Constraints, " Working Paper, Harvard University.
61. Pollard, D. (2002): A User's Guide to Measure Theoretic Probability. Cambridge: Cambridge University Press.
62. Ponomareva, M. (2010): "Inference in Models Defined by Conditional Moment Inequalities With Continuous Covariates, " Working Paper, University of Western Ontario.
63. Powell, J. L. (1984): "Least Absolute Deviations Estimation for the Censored Regression Model, " Journal of Econometrics, 25 (3), 303-325. DOI: 10.1016/0304-4076(84)90004-6
64. Rio, E. (1994): "Local Invariance Principles and Their Application to Density Estimation, " Probability Theory and Related Fields, 98, 21-45. DOI: 10.1007/BF01311347
65. Romano, J. P., and A. M. Shaikh (2008): "Inference for Identifiable Parameters in Partially Identified Econometric Models, " Journal of Statistical Planning and Inference, 138 (9), 2786-2807. DOI: 10.1016/j.jspi.2008.03.015
66. Romano, J. P., and A. M. Shaikh (2010): "Inference for the Identified Set in Partially Identified Econometric Models, " Econometrica, 78 (1), 169-211. DOI: 10.3982/ECTA6706
67. Rosen, A. M. (2008): "Confidence Sets for Partially Identified Parameters that Satisfy a Finite Number of Moment Inequalities, " Journal of Econometrics, 146, 107-117. DOI: 10.1016/j.jeconom.2008.08.001
68. Shaikh, A. M., and E. J. Vytlacil (2011): "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables, " Econometrica, 79 (3), 949-955. DOI: 10.3982/ECTA9082
69. Skorohod, A. (1956): "Limit Theorems for Stochastic Processes, " Theory of Probability and Its Applications, 1, 261-290. DOI: 10.1137/1101022
70. Stone, C. J. (1982): "Optimal Global Rates of Convergence for Nonparametric Regression, " The Annals of Statistics, 10 (4), 1040-1053. DOI: 10.1214/aos/1176345969
71. Stoye, J. (2009): "More on Confidence Regions for Partially Identified Parameters, " Econometrica, 77 (4), 1299-1315. DOI: 10.3982/ECTA7347
72. Tsybakov, A. B. (2009): Introduction to Nonparametric Estimation. New York: Springer. DOI: 10.1007/b13794
73. Van der Vaart, A. W., and J. A. Wellner (1996): Weak Convergence and Empirical Processes. New York: Springer-Verlag.
74. White, H. (1984): Asymptotic Theory for Econometricians. New York: Academic Press.
75. Yurinskii, V. (1977): "On the Error of the Gaussian Approximation for Convolutions, " Theory of Probability and Its Applications, 22, 236-247. DOI: 10.1137/1122030