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Intersection Bounds: estimation and inference

  • Victor Chernozhukov

    ()

    (Institute for Fiscal Studies and Massachusetts Institute of Technology)

  • Sokbae 'Simon' Lee

    ()

    (Institute for Fiscal Studies and University College London)

  • Adam Rosen

    ()

    (Institute for Fiscal Studies and University College London)

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with a potentially infinite constraint set. Our approach is especially convenient in models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are non-separable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the length of the identified set, we also offer a (downward/upward) median unbiased estimator of these (upper/lower) bounds as a natural by-product of our inferential procedure. Furthermore, our method appears to be the first and currently only method for inference in nonparametric models with a continuum of inequalities. We develop asymptotic theory for our method based on the strong approximation of a sequence of studentized empirical processes by a sequence of Gaussian or other pivotal processes. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for general series estimators, which may be of independent interest. We illustrate the usefulness of our method with Monte Carlo experiments and an empirical example.

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File URL: http://cemmap.ifs.org.uk/wps/cwp1909.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP19/09.

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Date of creation: Jul 2009
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Handle: RePEc:ifs:cemmap:19/09
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  1. Lee, Sokbae & Wilke, Ralf A., 2005. "Reform of Unemployment Compensation in Germany: A Nonparametric Bounds Analysis Using Register Data," ZEW Discussion Papers 05-29, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  2. Gonzalez, Libertad, 2004. "Nonparametric Bounds on the Returns to Language Skills," IZA Discussion Papers 1098, Institute for the Study of Labor (IZA).
  3. Donald W.K. Andrews, 1988. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Cowles Foundation Discussion Papers 874R, Cowles Foundation for Research in Economics, Yale University, revised May 1989.
  4. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  5. Donald W.K. Andrews & Panle Jia, 2008. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Cowles Foundation Discussion Papers 1676, Cowles Foundation for Research in Economics, Yale University.
  6. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2006. "Testing for stochastic monotonicity," LSE Research Online Documents on Economics 4425, London School of Economics and Political Science, LSE Library.
  7. repec:att:wimass:8909 is not listed on IDEAS
  8. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, 03.
  9. Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Charles F. Manski & John V. Pepper, 1998. "Monotone Instrumental Variables: With an Application to the Returns to Schooling," Virginia Economics Online Papers 308, University of Virginia, Department of Economics.
  11. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2009. "Intersection Bounds: estimation and inference," CeMMAP working papers CWP19/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  12. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, 01.
  13. Kreider, Brent & Pepper, John V., 2003. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Staff General Research Papers 10229, Iowa State University, Department of Economics.
  14. Philip Haile, 2000. "Inference with an Incomplete Model of English Auctions," Econometric Society World Congress 2000 Contributed Papers 1546, Econometric Society.
  15. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
  16. Pedro Carneiro & Sokbae 'Simon' Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  17. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
  18. Efang Kong & Oliver Linton & Yingcun Xia, 2009. "Uniform Bahadur Representation for LocalPolynomial Estimates of M-Regressionand Its Application to The Additive Model," STICERD - Econometrics Paper Series /2009/535, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  19. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
  20. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  21. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  22. Charles F. Manski & John V. Pepper, 2009. "More on monotone instrumental variables," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages S200-S216, 01.
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