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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. 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 natural 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 CWP34/11.

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Date of creation: Nov 2011
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Handle: RePEc:ifs:cemmap:34/11

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  1. 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.
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  3. 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.
  4. Gonzalez, Libertad, 2004. "Nonparametric Bounds on the Returns to Language Skills," IZA Discussion Papers 1098, Institute for the Study of Labor (IZA).
  5. Andrews, Donald W K, 1991. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Econometrica, Econometric Society, vol. 59(2), pages 307-45, March.
  6. 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.
  7. 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.
  8. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  9. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  10. 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.
  11. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
  12. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
  13. Charles F. Manski & John V. Pepper, 2009. "More on monotone instrumental variables," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages S200-S216, 01.
  14. 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.
  15. 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.
  16. 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.
  17. Blundell, Richard & Gosling, Amanda & Ichimura, Hidehiko & Meghir, Costas, 2004. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," IZA Discussion Papers 1350, Institute for the Study of Labor (IZA).
  18. 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.
  19. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2011. "Intersection bounds: estimation and inference," CeMMAP working papers CWP34/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  20. Philip Haile, 2000. "Inference with an Incomplete Model of English Auctions," Econometric Society World Congress 2000 Contributed Papers 1546, Econometric Society.
  21. Kreider, Brent & Pepper, John V., 2007. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 432-441, June.
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