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Instrumental variables with unrestricted heterogeneity and continuous treatment

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  • Kasy, Maximilian

Abstract

This paper discusses identification in continuous triangular systems without restrictions on heterogeneity or functional form. In particular, we do not assume separability of structural functions, restrictions on the dimensionality of unobservables, or monotonicity in unobservables. We do maintain monotonicity of the first stage relationship in the instrument and consider the case of real-valued treatment. We show that under these conditions alone, and given rich enough support of the data, we can achieve point identification of potential outcome distributions, and in particular of the average structural function and quantile structural functions. If the support of the continuous instrument is not large enough potential outcome distributions are partially identified. If the instrument is discrete identification fails completely. If treatment is multidimensional, additional exclusion restrictions allow to achieve identification. The setup discussed in this paper covers important cases not covered by existing approaches such as conditional moment restrictions (cf. Newey and Powell 2003) and control variables (cf. Imbens and Newey 2009). It covers, in particular, random coefficient models, as well as models arising as the reduced form of a system of structural equations.

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Paper provided by Harvard University OpenScholar in its series Working Paper with number 33257.

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Handle: RePEc:qsh:wpaper:33257

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  1. Eric Gautier & Yuichi Kitamura, 2013. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Econometrica, Econometric Society, vol. 81(2), pages 581-607, 03.
  2. Eric Gautier & Stefan Hoderlein, 2012. "A Triangular Treatment Effect Model With Random Coefficients In The Selection Equation," Boston College Working Papers in Economics 838, Boston College Department of Economics.
  3. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, 09.
  4. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, 05.
  5. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, 03.
  6. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
  7. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  8. Jean-Pierre Florens & James J. Heckman & Costas Meghir & Edward J. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects," NBER Working Papers 14002, National Bureau of Economic Research, Inc.
  9. Kasy, Maximilian, 2011. "Identification In Triangular Systems Using Control Functions," Econometric Theory, Cambridge University Press, vol. 27(03), pages 663-671, June.
  10. Stefan Hoderlein & Yuya Sasaki, 2013. "Outcome Conditioned Treatment Effects," Boston College Working Papers in Economics 840, Boston College Department of Economics.
  11. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-60, September.
  12. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, April.
  13. Schennach, Susanne & White, Halbert & Chalak, Karim, 2012. "Local indirect least squares and average marginal effects in nonseparable structural systems," Journal of Econometrics, Elsevier, vol. 166(2), pages 282-302.
  14. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
  15. Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  16. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
  17. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, 09.
  18. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, 05.
  19. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  20. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June.
  21. Heckman, James J & Smith, Jeffrey, 1997. "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 487-535, October.
  22. Jun, Sung Jae & Pinkse, Joris & Xu, Haiqing, 2011. "Tighter bounds in triangular systems," Journal of Econometrics, Elsevier, vol. 161(2), pages 122-128, April.
  23. Jinyong Hahn & Geert Ridder, 2011. "Conditional Moment Restrictions and Triangular Simultaneous Equations," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 683-689, May.
  24. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
  25. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, 09.
  26. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
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