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From Late to Mte

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Advanced LATE concept in econometrics
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  Forschungsinstitut zur Zukunft der ArbeitInstitute for the Study of Labor    D   I   S   C   U   S   S   I   O   N    P   A   P   E   R    S   E   R   I   E   S From Late to MTE: Alternative Methods for theEvaluation of Policy Interventions IZA DP No. 10056July 2016Thomas CornelissenChristian DustmannAnna RauteUta Schönberg    From Late to MTE: Alternative Methods for    the Evaluation of Policy Interventions Thomas Cornelissen University of York Christian Dustmann University College London and CReAM  Anna Raute University of Mannheim   Uta Schönberg University College London, CReAM, IAB and IZA   Discussion Paper No. 10056 July 2016 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: iza@iza.org  Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The IZA research network is committed to the IZA Guiding Principles of Research Integrity. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) srcinal and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author.  IZA Discussion Paper No. 10056 July 2016  ABSTRACT From Late to MTE: Alternative Methods for the Evaluation of Policy Interventions 1   This paper provides an introduction into the estimation of Marginal Treatment Effects (MTE). Compared to the existing surveys on the subject, our paper is less technical and speaks to the applied economist with a solid basic understanding of econometric techniques who would like to use MTE estimation. Our framework of analysis is a generalized Roy model based on the potential outcomes framework, within which we define different treatment effects of interest, and review the well-known case of IV estimation with a discrete instrument resulting in a local average treatment effect (LATE). Turning to IV estimation with a continuous instrument we demonstrate that the 2SLS estimator may be viewed as a weighted average of LATEs, and discuss MTE estimation as an alternative and more informative way of exploiting a continuous instrument. We clarify the assumptions underlying the MTE framework and illustrate how the MTE estimation is implemented in practice. JEL Classification: C26, I26 Keywords: marginal treatment effects, instrumental variables, heterogeneous effects Corresponding author: Uta Schönberg Department of Economics University College London 30 Gordon Street London WC1H 0AX United Kingdom E-mail: u.schoenberg@ucl.ac.uk  1  Christian Dustmann acknowledges funding from the European Research Council (ERC) under  Advanced Grant No. 323992. An improved and edited version of this article appears in Labour Economics , see http://dx.doi.org/10.1016/j.labeco.2016.06.004.  2 Contents 2   Introduction 3   3   Instrumental variables estimation with heterogeneous treatment effects 6   3.1   Framework of analysis and definition of treatment effects 6   3.2   IV with a binary instrument and LATE 11   3.2.1   Covariate-Specific IV 12   3.2.2   Aggregating covariate-specific LATEs into one IV effect 14   3.3   IV with a continuous instrument 16   3.3.1   Pairwise Covariate-specific LATEs 16   3.3.2   Aggregating Pairwise (covariate-specific) LATEs into one Effect 18   3.4   Control Function Approach: The Correlated Random Coefficients Model 19   4   Definition of Marginal Treatment Effects (MTE) and Relation to LATE 21   4.1   Definition 21   4.2   Relation to LATE and the importance of a continuous instrument 23   5   Estimation of MTE 25   5.1   The fully parametric normal model 25   5.2   Minimal assumptions and nonparametric estimation (the ideal case) 27   5.3   Strengthening assumptions for estimation in less ideal cases 28   5.4   Aggregating the MTE into treatment parameters 31   6   Two examples from the applied literature 34   6.1   Example of MTE applied to returns to college education 34   6.2   Example of MTE applied to returns to preschool education 36   7   Conclusions 38   References 40   APPENDIX 44   A.   Policy-Relevant Treatment Effects 44   B.   Sketch of common estimation methods for the MTE 45   B.1   Semi-parametric estimation 45   B.2   Parametric polynomial estimation 45   C.   Computation of IV weights in the linear separable model 46  
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