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Intersection bounds: estimation and inference

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Author Info

  • Victor Chernozhukov

    ()
    (Institute for Fiscal Studies and MIT)

  • Sokbae 'Simon' Lee

    ()
    (Institute for Fiscal Studies and Seoul National University)

  • Adam Rosen

    ()
    (Institute for Fiscal Studies and University College London)

Abstract

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. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for 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 size of the identified set, we also offer a median-bias-corrected estimator of such bounds as a by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP33/12.

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Date of creation: Oct 2012
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Handle: RePEc:ifs:cemmap:33/12

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Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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Related research

Keywords: Bound analysis; conditional moments; partial identi cation; strong approximation; infi nite dimensional constraints; linear programming; concentration inequalities; anti-concentration inequalities; non-Donsker empirical process methods; moderate deviations; adaptive moment selection.;

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References

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  1. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2006. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," CIRJE F-Series CIRJE-F-420, CIRJE, Faculty of Economics, University of Tokyo.
  2. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2012. "Intersection bounds: estimation and inference," CeMMAP working papers CWP33/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Lee, Sokbae & Wilke, Ralf A., 2009. "Reform of Unemployment Compensation in Germany: A Nonparametric Bounds Analysis Using Register Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 193-205.
  4. Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010. "Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1529-1564, October.
  5. 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.
  6. Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Gonzalez, Libertad, 2004. "Nonparametric Bounds on the Returns to Language Skills," IZA Discussion Papers 1098, Institute for the Study of Labor (IZA).
  8. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, 03.
  9. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
  10. 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.
  11. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
  12. 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.
  13. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  14. 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.
  15. 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.
  16. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  17. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
  18. 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.
  19. 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.
  20. 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.
  21. 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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