Advertisement

Local Average Treatment Effect and Regression-Discontinuity-Design

  • Giovanni Cerulli
Chapter
  • 2.7k Downloads
Part of the Advanced Studies in Theoretical and Applied Econometrics book series (ASTA, volume 49)

Abstract

This chapter addresses two different but related approaches, both widely used within the literature on the econometrics of program evaluation: the Local average treatment effect (LATE) and the Regression-discontinuity-design (RDD). Considered as nearly quasi-experimental methods, these approaches have recently been the subject of a vigorous interest as tools for detecting treatment effects within special statistical settings. The first part of the chapter covers the theory behind LATE, thus illustrating how such approach can be embedded within the setting of a randomized experiment with imperfect compliance. The discussion then goes on to present the Wald estimator of LATE, and to extend LATE to the case of multiple instruments and multiple treatments. The second part of the chapter illustrates the RDD econometric theoretical background; in particular, it discusses separately sharp RDD and fuzzy RDD, and suggests a protocol for the empirical implementation of such approaches. The chapter ends with some illustrative empirical implementation of both LATE and RDD performed using Stata on both real and simulative examples.

References

  1. Abadie, A. (2003). Semiparametric instrumental variable estimation of treatment response models. Journal of Econometrics, 113, 231–263. doi: 10.1016/S0304-4076(02)00201-4.CrossRefGoogle Scholar
  2. Abadie, A., Angrist, J., & Imbens, G. (2002). Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica, 70, 91–117. doi: 10.1111/1468-0262.00270.CrossRefGoogle Scholar
  3. Angrist, J. D. (1990). Lifetime earnings and the Vietnam era draft lottery: Evidence from social security administrative records. American Economic Review, 80, 313–336.Google Scholar
  4. Angrist, J. D., & Evans, W. N. (1998). Children and their parents’ labor supply: Evidence from exogenous variation in family size. American Economic Review, 88, 450–477.Google Scholar
  5. Angrist, J. D., & Imbens, G. W. (1995). Two-stage least squares estimation of average causal effects in models with variable treatment intensity. Journal of the American Statistical Association, 90, 431–442. doi: 10.1080/01621459.1995.10476535.CrossRefGoogle Scholar
  6. Angrist, J. D., & Lavy, V. (1999). Using Maimonides’ rule to estimate the effect of class size on scholastic achievement. Quarterly Journal of Economics, 114, 533–575.CrossRefGoogle Scholar
  7. Angrist, J. D., & Pischke, J.-S. (2008). Mostly harmless econometrics: An empiricist’s companion. Princeton, NJ: Princeton University Press.Google Scholar
  8. Bloom, H. S. (1984). Accounting for no-shows in experimental evaluation designs. Evaluation Review, 8, 225–246. doi: 10.1177/0193841X8400800205.CrossRefGoogle Scholar
  9. Cook, T. D. (2008). “Waiting for life to arrive”: A history of the regression-discontinuity design in psychology, statistics and economics. Journal of Econometrics, 142, 636–654. doi: 10.1016/j.jeconom.2007.05.002.CrossRefGoogle Scholar
  10. Fan, J., & Gijbels, I. (1996). Local polynomial modelling and its applications: Monographs on statistics and applied probability (Vol. 66). Boca Raton, FL: CRC Press.Google Scholar
  11. Hahn, J., Todd, P., & Van der Klaauw, W. (2001). Identification and estimation of treatment effects with a regression-discontinuity design. Econometrica, 69, 201–209. doi: 10.1111/1468-0262.00183.CrossRefGoogle Scholar
  12. Härdle, W. (1991). Applied nonparametric regression. Cambridge: Cambridge University Press.Google Scholar
  13. Härdle, W., & Marron, J. S. (1985). Optimal bandwidth selection in nonparametric regression function estimation. Annals of Statistics, 13, 1465–1481.CrossRefGoogle Scholar
  14. Imbens, G. W., & Angrist, J. D. (1994). Identification and estimation of local average treatment effects. Econometrica, 62, 467–475. doi: 10.2307/2951620.CrossRefGoogle Scholar
  15. Imbens, G., & Kalyanaraman, K. (2012). Optimal bandwidth choice for the regression discontinuity estimator. Review of Economic Studies, 79, 933–959.CrossRefGoogle Scholar
  16. Imbens, G. W., & Lemieux, T. (2008). Regression discontinuity designs: A guide to practice. Journal of Econometrics, 142, 615–635. doi: 10.1016/j.jeconom.2007.05.001.CrossRefGoogle Scholar
  17. Lee, D. S., & Lemieux, T. (2009). Regression discontinuity designs in economics (NBER Working Paper No. 14723). National Bureau of Economic Research, Inc.Google Scholar
  18. Lee, D. S., Moretti, E., & Butler, M. J. (2004). Do voters affect or elect policies? Evidence from the U. S. House. Quarterly Journal of Economics, 119, 807–859.CrossRefGoogle Scholar
  19. Ludwig, J., & Miller, D. L. (2007). Does head start improve children’s life chances? Evidence from a regression discontinuity design. Quarterly Journal of Economics, 122, 159–208. doi: 10.1162/qjec.122.1.159.CrossRefGoogle Scholar
  20. McCrary, J. (2008). Manipulation of the running variable in the regression discontinuity design: A density test. Journal of Econometrics, 142, 698–714.CrossRefGoogle Scholar
  21. Nichols, A. (2007). Causal inference with observational data: Regression discontinuity and related methods in Stata (North American Stata Users’ Group Meetings 2007 No. 2). Stata Users Group.Google Scholar
  22. Pagan, A., & Ullah, A. (1999). Nonparametric econometrics. Cambridge: Cambridge University Press.Google Scholar
  23. Porter, J. (2003). Estimation in the regression discontinuity model. Dep. Econ. Univ. Wis. Mimeo.Google Scholar
  24. Stone, C. J. (1982). Optimal global rates of convergence for nonparametric regression. Annals of Statistics, 10, 1040–1053.CrossRefGoogle Scholar
  25. Thistlethwaite, D. L., & Campbell, D. T. (1960). Regression-discontinuity analysis: An alternative to the ex post facto experiment. Journal of Education & Psychology, 51, 309–317. doi: 10.1037/h0044319.CrossRefGoogle Scholar
  26. Van Der Klaauw, W. (2002). Estimating the effect of financial aid offers on college enrollment: A regression-discontinuity approach. International Economic Review, 43, 1249–1287. doi: 10.1111/1468-2354.t01-1-00055.CrossRefGoogle Scholar
  27. Van Der Klaauw, W. (2008). Regression-discontinuity analysis: A survey of recent developments in economics. Labour, 22, 219–245. doi: 10.1111/j.1467-9914.2008.00419.x.CrossRefGoogle Scholar
  28. Wald, A. (1940). The fitting of straight lines if both variables are subject to error. Annals of Mathematical Statistics, 11, 284–300. doi: 10.1214/aoms/1177731868.CrossRefGoogle Scholar
  29. Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. Cambridge, MA: MIT Press.Google Scholar
  30. Yang, M. (2013). Treatment effect analyses through orthogonality conditions implied by a fuzzy regression discontinuity design, with two empirical studies. Dep. Econ. Rauch Bus. Cent. Lehigh Univ., Bethlehem, PA.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Giovanni Cerulli
    • 1
  1. 1.Research Institute on Sustainable Economic GrowthCNR-IRCrES National Research Council of ItalyRomaItaly

Personalised recommendations