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Set identified linear models

  • Christian Bontemps

    (Institute for Fiscal Studies and Toulouse)

  • Thierry Magnac

    ()

    (Institute for Fiscal Studies and Toulouse)

  • Eric Maurin

    (Institute for Fiscal Studies)

We analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictions E(z T (x β−y)) = E(z Tu(z)) where z is a set of instruments and u(z) an unknown bounded scalar function. We first provide empirically relevant examples of such a set-up. Second, we show that these conditions set identify β where the identified set B is bounded and convex. We provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest but also in the case in which the number of conditions is strictly larger than the number of parameters. We derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar Sargan condition. Third, we provide new results on the asymptotics of analog estimates constructed from the identification results. When B is a strictly convex set, we also construct a test of the null hypothesis, β 0 ε B, whose size is asymptotically correct and which relies on the minimization of the support function of the set B − { β 0 }. Results of some Monte Carlo experiments are presented.

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File URL: http://cemmap.ifs.org.uk/wps/cwp1311.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 CWP13/11.

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Date of creation: Apr 2011
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Handle: RePEc:ifs:cemmap:13/11
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  1. Ridder, Geert & Moffitt, Robert, 2007. "The Econometrics of Data Combination," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 75 Elsevier.
  2. Elie Tamer & Federico Ciliberto, 2004. "Market Structure and Multiple Equilibria in Airline Markets," 2004 Meeting Papers 52, Society for Economic Dynamics.
  3. 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.
  4. Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, 03.
  6. Charles F. Manski & John V. Pepper, 2009. "More on monotone instrumental variables," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages S200-S216, 01.
  7. Edward Leamer, 1906. "Errors in Variables in Linear Systems," UCLA Economics Working Papers 406, UCLA Department of Economics.
  8. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
  9. Hans Peter Gruner & Giacomo Corneo, 2000. "Social Limits to Redistribution," American Economic Review, American Economic Association, vol. 90(5), pages 1491-1507, December.
  10. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
  11. Bo E. Honore & Adriana Lleras Muney, 2004. "Bounds in Competing Risks Models and the War on Cancer," NBER Working Papers 10963, National Bureau of Economic Research, Inc.
  12. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 835-864.
  13. 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.
  14. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
  15. Klepper, Steven & Leamer, Edward E, 1984. "Consistent Sets of Estimates for Regressions with Errors in All Variables," Econometrica, Econometric Society, vol. 52(1), pages 163-83, January.
  16. Arthur Lewbel & Oliver Linton & Daniel McFadden, 2001. "Estimating features of a distribution from binomial data," CeMMAP working papers CWP07/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  17. 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.
  18. 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.
  19. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Validity of Subsampling and "Plug-in Asymptotic" Inference for Parameters Defined by Moment Inequalities," Cowles Foundation Discussion Papers 1620, Cowles Foundation for Research in Economics, Yale University.
  20. 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.
  21. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
  22. 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.
  23. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
  24. Erickson, Timothy, 1993. "Restricting Regression Slopes in the Errors-in-Variables Model by Bounding the Error Correlation," Econometrica, Econometric Society, vol. 61(4), pages 959-69, July.
  25. Bollinger, Christopher R., 1996. "Bounding mean regressions when a binary regressor is mismeasured," Journal of Econometrics, Elsevier, vol. 73(2), pages 387-399, August.
  26. repec:bla:restud:v:75:y:2008:i:3:p:835-864 is not listed on IDEAS
  27. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  28. Bo E. Honoré & Adriana Lleras-Muney, 2004. "Bounds in Competing Risks Models and the War on Cancer," CAM Working Papers 2004-08, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics.
  29. Guido Imbens & Charles F. Manski, 2003. "Confidence intervals for partially identified parameters," CeMMAP working papers CWP09/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  30. 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.
  31. Thomas Piketty, 2005. "Top Income Shares in the Long Run: An Overview," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 382-392, 04/05.
  32. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(03), pages 931-951, June.
  33. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, 07.
  34. 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.
  35. Vazquez-Alvarez, R. & Melenberg, B. & van Soest, A.H.O., 2001. "Nonparametric Bounds in the Presence of Item Nonresponse, Unfolding Brackets and Anchoring," Discussion Paper 2001-67, Tilburg University, Center for Economic Research.
  36. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
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