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What do instrumental variable models deliver with discrete dependent variables?

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  • Andrew Chesher
  • Adam Rosen

Abstract

We study models with discrete endogenous variables and compare the use of two stage least squares (2SLS) in a linear probability model with bounds analysis using a nonparametric instrumental variable model.2SLS has the advantage of providing an easy to compute point estimator of a slope coefficient which can be interpreted as a local average treatment effect (LATE). However, the 2SLS estimator does not measure the value of other useful treatment effect parameters without invoking untenable restrictions.The nonparametric instrumental variable (IV) model has the advantage of being weakly restrictive, so more generally applicable, but it usually delivers set identification. Nonetheless it can be used to consistently estimate bounds on many parameters of interest including, for example, average treatment effects. We illustrate using data from Angrist & Evans (1998) and study the effect of family size on female employment.This October 2015 version corrects an error in the paper, as explained in footnote 1. The original version of the working paper is available here.

Suggested Citation

  • Andrew Chesher & Adam Rosen, 2013. "What do instrumental variable models deliver with discrete dependent variables?," CeMMAP working papers 10/13, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:10/13
    DOI: 10.1920/wp.cem.2013.1013
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    1. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    2. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131, September.
    3. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 45(3), pages 809-829, August.
    4. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    5. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    6. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735, September.
    7. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124, September.
    8. 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, September.
    9. 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.
    10. Angrist, Joshua D & Evans, William N, 1998. "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size," American Economic Review, American Economic Association, vol. 88(3), pages 450-477, June.
    11. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    12. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728, September.
    13. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, March.
    14. 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, May.
    15. Andrew Chesher & Adam M. Rosen, 2013. "What Do Instrumental Variable Models Deliver with Discrete Dependent Variables?," American Economic Review, American Economic Association, vol. 103(3), pages 557-562, May.
    16. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742, September.
    17. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117, September.
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    2. Andrew Chesher & Adam M. Rosen, 2013. "What Do Instrumental Variable Models Deliver with Discrete Dependent Variables?," American Economic Review, American Economic Association, vol. 103(3), pages 557-562, May.
    3. Ainhoa Aparicio-Fenoll & Veruska Oppedisano, 2016. "Should I stay or should I go? Sibling effects in household formation," Review of Economics of the Household, Springer, vol. 14(4), pages 1007-1027, December.
    4. Alexander Torgovitsky, 2019. "Partial identification by extending subdistributions," Quantitative Economics, Econometric Society, vol. 10(1), pages 105-144, January.
    5. Andrew Chesher & Adam Rosen, 2018. "Generalized instrumental variable models, methods, and applications," CeMMAP working papers CWP43/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Porgo, Mohamed & Kuwornu, John K.M. & Zahonogo, Pam & Jatoe, John Baptist D. & Egyir, Irene S., 2018. "Credit constraints and cropland allocation decisions in rural Burkina Faso," Land Use Policy, Elsevier, vol. 70(C), pages 666-674.
    7. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    8. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    9. Manuel Denzer, 2019. "Estimating Causal Effects in Binary Response Models with Binary Endogenous Explanatory Variables - A Comparison of Possible Estimators," Working Papers 1916, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    10. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2023. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," Econometrica, Econometric Society, vol. 91(1), pages 107-146, January.
    11. Blunch, Niels-Hugo & Datta Gupta, Nabanita, 2020. "Mothers’ health knowledge gap for children with diarrhea: A decomposition analysis across caste and religion in India," World Development, Elsevier, vol. 126(C).
    12. Stephan, Gesine & van den Berg, Gerard & Homrighausen, Pia, 2016. "Randomizing information on a targeted wage support program for older workers: A field experiment," VfS Annual Conference 2016 (Augsburg): Demographic Change 145487, Verein für Socialpolitik / German Economic Association.
    13. Li, Chuhui & Poskitt, D.S. & Zhao, Xueyan, 2019. "The bivariate probit model, maximum likelihood estimation, pseudo true parameters and partial identification," Journal of Econometrics, Elsevier, vol. 209(1), pages 94-113.
    14. Öberg, Stefan, 2021. "The casual effect of fertility: The multiple problems with instrumental variables for the number of children in families," SocArXiv peuvz, Center for Open Science.

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    JEL classification:

    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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