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Identifying the Average Treatment Effect in a Two Threshold Model

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  • Arthur Lewbel

    ()
    (Boston College)

  • Thomas Tao Yang

    (Boston College)

Abstract

Assume individuals are treated if a latent variable, containing a continuous instrument, lies between two thresholds. We place no functional form restrictions on the latent errors. Here unconfoundedness does not hold and identification at infinity is not possible. Yet we still show nonparametric point identification of the average treatment effect. We provide an associated root-n consistent estimator. We apply our model to reinvestigate the inverted-U relationship between competition and innovation, estimating the impact of moderate competitiveness on innovation without the distributional assumptions required by previous analyses. We find no evidence of an inverted-U in US data.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 825.

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Date of creation: 01 Jul 2013
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Handle: RePEc:boc:bocoec:825

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Related research

Keywords: Average treatment effect; Ordered choice model; Special regressor; Semiparametric; Competition and innovation; Identification.;

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  1. Yingying Dong & Arthur Lewbel, 2004. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Boston College Working Papers in Economics 604, Boston College Department of Economics, revised 15 Jun 2012.
  2. Heckman, James J. & Urzua, Sergio & Vytlacil, Edward, 2006. "Understanding Instrumental Variables in Models with Essential Heterogeneity," IZA Discussion Papers 2320, Institute for the Study of Labor (IZA).
  3. Guido Imbens & Jeffrey Wooldridge, 2008. "Recent developments in the econometrics of program evaluation," CeMMAP working papers CWP24/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Arthur Lewbel, 2000. "Endogenous Selection Or Treatment Model Estimation," Boston College Working Papers in Economics 462, Boston College Department of Economics, revised 13 Jun 2007.
  5. Aamir Rafique Hashmi, 2011. "Competition and Innovation: The Inverted-U Relationship Revisited," Departmental Working Papers wp1101, National University of Singapore, Department of Economics.
  6. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  7. Marianne Bertrand, 2004. "From the Invisible Handshake to the Invisible Hand? How Import Competition Changes the Employment Relationship," Journal of Labor Economics, University of Chicago Press, vol. 22(4), pages 723-766, October.
  8. Philippe Aghion & Nicholas Bloom & Richard Blundell & Rachel Griffith & Peter Howitt, 2002. "Competition and Innovation: An Inverted U Relationship," NBER Working Papers 9269, National Bureau of Economic Research, Inc.
  9. Card, David & Krueger, Alan B, 1994. "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania," American Economic Review, American Economic Association, vol. 84(4), pages 772-93, September.
  10. Eric Gautier & Stefan Hoderlein, 2012. "A triangular treatment effect model with random coefficients in the selection equation," CeMMAP working papers CWP39/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Revenga, Ana L, 1992. "Exporting Jobs? The Impact of Import Competition on Employment and Wages in U.S. Manufacturing," The Quarterly Journal of Economics, MIT Press, vol. 107(1), pages 255-84, February.
  12. Bo E. Honore & Arthur Lewbel, 1998. "Semiparametric Binary Choice Panel Data Models without Strictly Exogeneous Regressors," Boston College Working Papers in Economics 455, Boston College Department of Economics, revised 22 Sep 2001.
  13. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Viewpoint: Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics, Canadian Economics Association, vol. 45(3), pages 809-829, August.
  14. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
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