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Inference for best linear approximations to set identified functions

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Author Info

  • Arun Chandrasekhar
  • Victor Chernozhukov

    ()
    (Institute for Fiscal Studies and MIT)

  • Francesca Molinari

    ()
    (Institute for Fiscal Studies and Cornell University)

  • Paul Schrimpf

Abstract

This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any functions, including ones carrying an index, which can be estimated parametrically or non-parametrically. The identification region of the parameters of the best linear approximation is characterised via its support function, and limit theory is developed for the latter. We prove that the support function approximately converges to a Gaussian process, and validity of the Bayesian bootstrap is established. The paper nests as special cases the canonical examples in the literature: mean regression with interval valued outcome data and interval valued regressor data. Because the bounds may carry an index, the paper covers problems beyond mean regression; the framework is extremely versatile. Applications include quantile and distribution regression with interval valued data, sample selection problems, as well as mean, quantile and distribution treatment effects. Moreover, the framework can account for the availability of instruments. An application is carried out, studying female labor force participation along the lines of Mulligan and Rubinstein (2008).

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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 CWP43/12.

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Date of creation: Dec 2012
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Handle: RePEc:ifs:cemmap:43/12

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Related research

Keywords: Set identified function; best linear approximation; partial identification; support function; bayesian bootstrap; convex set;

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References

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  1. Blundell, Richard William & Gosling, Amanda & Ichimura, Hidehiko & Meghir, Costas, 2004. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," CEPR Discussion Papers 4705, C.E.P.R. Discussion Papers.
  2. Han, Aaron & Hausman, Jerry A, 1990. "Flexible Parametric Estimation of Duration and Competing Risk Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(1), pages 1-28, January-M.
  3. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, 03.
  4. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, 05.
  5. Thierry Magnac & Eric Maurin, 2004. "Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data," Working Papers 2004-11, Centre de Recherche en Economie et Statistique.
  6. 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.
  7. 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.
  8. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, April.
  9. Casey B. Mulligan & Yona Rubinstein, 2008. "Selection, Investment, and Women's Relative Wages Over Time," The Quarterly Journal of Economics, MIT Press, vol. 123(3), pages 1061-1110, August.
  10. Patrick Kline & Andres Santos, 2013. "Sensitivity to missing data assumptions: Theory and an evaluation of the U.S. wage structure," Quantitative Economics, Econometric Society, vol. 4(2), pages 231-267, 07.
  11. Liran Einav & Amy Finkelstein & Stephen P. Ryan & Paul Schrimpf & Mark R. Cullen, 2011. "Selection on Moral Hazard in Health Insurance," NBER Working Papers 16969, National Bureau of Economic Research, Inc.
  12. Foresi, S. & Paracchi, F., 1992. "The Conditional Distribution of Excess Returns: An Empirical Analysis," Working Papers 92-49, C.V. Starr Center for Applied Economics, New York University.
  13. repec:bla:restud:v:75:y:2008:i:3:p:835-864 is not listed on IDEAS
  14. 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.
  15. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
  16. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  17. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, 03.
  18. Maria Ponomareva & Elie Tamer, 2011. "Misspecification in moment inequality models: back to moment equalities?," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 186-203, 07.
  19. He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
  20. 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.
  21. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
  22. 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.
  23. Jasso, Guillermina & Rosenzweig, Mark R., 2008. "Selection Criteria and the Skill Composition of Immigrants: A Comparative Analysis of Australian and U.S. Employment Immigration," IZA Discussion Papers 3564, Institute for the Study of Labor (IZA).
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Citations

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Cited by:
  1. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
  2. Karun Adusumilli & Taisuke Otsu, 2014. "Empirical Likelihood for Random Sets," STICERD - Econometrics Paper Series /2014/574, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. Hoshino, Tadao, 2013. "Partial identification in binary response models with nonignorable nonresponses," Economics Letters, Elsevier, vol. 121(1), pages 74-78.

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