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Methods Based on Selection on Observables

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

Abstract

This chapter deals with the estimation of average treatment effects (ATEs) under the assumption of “selection on observables”, and provides a systematic account of the meaning and scope of such an assumption in program evaluation analysis. It illustrates a number of econometric methods developed in the literature to provide correct inference for causal parameters under selection on observables. In particular, it illustrates and discusses the four most popular approaches used in applications: Regression-adjustment, Matching, Reweighting, and the Doubly-robust estimator. In the final part, the chapter also offers a number of applications of these econometric methods in a comparative perspective using built-in and user-written Stata commands on real datasets.

References

  1. Abadie, A., Drukker, D., Herr, H., & Imbens, G. (2004). Implementing matching estimators for average treatment effects in Stata. The Stata Journal, 4, 290–311.Google Scholar
  2. Abadie, A., & Imbens, G. W. (2006). Large sample properties of matching estimators for average treatment effects. Econometrica, 74(1), 235–267.Google Scholar
  3. Abadie, A., & Imbens, G. W. (2008). On the failure of the bootstrap for matching estimators. Econometrica, 76(6), 1537–1557.CrossRefGoogle Scholar
  4. Abadie, A., & Imbens, G. (2011). Bias-corrected matching estimators for average treatment effects. Journal of Business & Economic Statistics, 29, 1–11.CrossRefGoogle Scholar
  5. Abadie, A., & Imbens, G. W. (2012). Matching on the estimated propensity score. Harvard University and National Bureau of Economic Research.Google Scholar
  6. Becker, S. O., & Caliendo, M. (2007). Sensitivity analysis for average treatment effects. The Stata Journal, 7(1), 71–83.Google Scholar
  7. Becker, S., & Ichino, A. (2002). Estimation of average treatment effects based on propensity scores. The Stata Journal, 2, 358–377.Google Scholar
  8. Blackwell, M., Iacus, S. M., King, G., & Porro, G. (2009). CEM: Coarsened exact matching. The Stata Journal, 9, 524–546.Google Scholar
  9. Brunell, T. L., & DiNardo, J. E. (2004). A propensity score reweighting approach to estimating the partisan effects of full turnout in American presidential elections. Political Analysis, 12, 28–45.CrossRefGoogle Scholar
  10. Busso, M., DiNardo, J., & McCrary, J. (2009). New evidence on the finite sample properties of propensity score matching and reweighting estimators. Unpublished manuscript, Dept. Of Economics, UC Berkeley.Google Scholar
  11. Caliendo, M., & Kopeinig, S. (2008). Some practical guidance for the implementation of propensity score matching. Journal of Economic Surveys, 22, 31–72.CrossRefGoogle Scholar
  12. Cameron, A. C., & Trivedi, P. K. (2005). Microeconometrics: Methods and applications. New York: Cambridge University Press.CrossRefGoogle Scholar
  13. Cattaneo, M. D. (2010). Efficient semiparametric estimation of multi–valued treatment effects under ignorability. Journal of Econometrics, 155, 138–154.CrossRefGoogle Scholar
  14. Cerulli, G. (2014a). TREATREW: A user–written Stata routine for estimating average treatment effects by reweighting on propensity score. The Stata Journal, 14(3), 541–561.Google Scholar
  15. Cerulli, G. (2014b). IVTREATREG: A new Stata routine for estimating binary treatment models with heterogeneous response to treatment and unobservable selection. The Stata Journal, 14(3), 453–480.Google Scholar
  16. Cochran, W. G., & Rubin, D. B. (1973). Controlling bias in observational studies: A review. Sankhya, Series A, 35, 417–446.Google Scholar
  17. Dehejia, R., & Wahba, S. (1999). Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs. Journal of the American Statistical Association, 94, 1053–1062.CrossRefGoogle Scholar
  18. Dehejia, R., & Wahba, S. (2002). Propensity score–matching methods for nonexperimental causal studies. The Review of Economics and Statistics, 84, 151–161.CrossRefGoogle Scholar
  19. DiPrete, T., & Gangl, M. (2004). Assessing bias in the estimation of causal effects: Rosenbaum bounds on matching estimators and instrumental variables estimation with imperfect instruments. Sociological Methodology, 34, 271–310.CrossRefGoogle Scholar
  20. Fan, J. (1992). Local linear regression smoothers and their minimax efficiencies. Annals of Statistics, 21, 196–216.CrossRefGoogle Scholar
  21. Gangl, M. (2004). RBOUNDS: Stata module to perform Rosenbaum sensitivity analysis for average treatment effects on the treated. Statistical Software Components S438301, Boston College Department of Economics.Google Scholar
  22. Hahn, J. (1998). On the role of the propensity score in efficient semiparametric estimation of average treatment effects. Econometrica, 66(2), 315–332.CrossRefGoogle Scholar
  23. Heckman, J. J., Ichimura, H., & Todd, P. E. (1997). Matching as an econometric evaluation estimator: Evidence from evaluating a job training programme. Review of Economic Studies, 64(4), 605–54.CrossRefGoogle Scholar
  24. Heckman, J. J., Ichimura, H., & Todd, P. (1998). Matching as an econometric evaluation estimator. Review of Economic Studies, 65(2), 261–94.CrossRefGoogle Scholar
  25. Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient estimation of average treatment effects using the estimated propensity score. Econometrica, 71(4), 1161–1189.CrossRefGoogle Scholar
  26. Horvitz, D. G., & Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe source. Journal of the American Statistical Association, 47, 663–685.CrossRefGoogle Scholar
  27. Iacus, S. M., King, G., & Porro, G. (2012). Causal inference without balance checking: Coarsened exact matching. Political Analysis, 20, 1–24.CrossRefGoogle Scholar
  28. Imbens, G. W. (2004). Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and Statistics, 86(1), 4–29.CrossRefGoogle Scholar
  29. Imbens, G. W., & Rubin, D. (forthcoming). Causal inference in statistics. Cambridge: Cambridge University Press.Google Scholar
  30. Johnston, J., & DiNardo, J. E. (1996). Econometric methods. New York: McGraw-Hill.Google Scholar
  31. LaLonde, R. (1986). Evaluating the econometric evaluations of training programs with experimental data. American Economic Review, 76, 604–620.Google Scholar
  32. Lechner, M. (2008). A note on the common support problem in applied evaluation studies. Annals of Economics and Statistics/Annales d’Économie et de Statistique, 91/92, 217–235.Google Scholar
  33. Leuven, E., & Sianesi, B. (2003). PSMATCH2: Stata module to perform full Mahalanobis and propensity score matching, common support graphing, and covariate imbalance testing. Statistical Software Components S432001, Boston College Department of Economics, revised 12 Feb 2014.Google Scholar
  34. Li, Q., Racine, J. S., & Wooldridge, J. M. (2009). Efficient estimation of average treatment effects with mixed categorical and continuous data. Journal of Business and Economic Statistics, 27, 206–223.CrossRefGoogle Scholar
  35. Lunceford, J. K., & Davidian, M. (2004). Stratification and weighting via the propensity score in estimation of causal treatment effects: A comparative study. Statistics in Medicine, 15, 2937–2960.CrossRefGoogle Scholar
  36. Nannicini, T. (2007). Simulation–based sensitivity analysis for matching estimators. The Stata Journal, 7, 3.Google Scholar
  37. Newey, W. K. (1997). Convergence rates and asymptotic normality for series estimators. Journal of Applied Econometrics, 5, 99–135.CrossRefGoogle Scholar
  38. Robins, J. M., Hernan, M. A., & Brumback, B. A. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology, 11, 550–560.CrossRefGoogle Scholar
  39. Robins, J., & Rotnitzky, A. (1995). Semiparametric efficiency in multivariate regression models with missing data. Journal of the American Statistical Association, 90, 122–129.CrossRefGoogle Scholar
  40. Robins, J., Rotnitzky, A., & Zhao, L. P. (1994). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89, 846–866.CrossRefGoogle Scholar
  41. Rosenbaum, P. R. (2002). Observational studies (2nd ed.). New York: Springer.CrossRefGoogle Scholar
  42. Rosenbaum, P. R. (2005). Sensitivity analysis in observational studies. In B. S. Everitt & D. C. Howell (Eds.), Encyclopedia of statistics in behavioral science (Vol. 4, pp. 1809–1814). Chichester, UK: Wiley.Google Scholar
  43. Rosenbaum, P., & Rubin, D. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41–55.CrossRefGoogle Scholar
  44. Rosenbaum, P. R., & Rubin, D. B. (1984). Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association, 79(387), 147–156.Google Scholar
  45. Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola, S. (2008). Global sensitivity analysis. The primer. Chichester, UK: Wiley.Google Scholar
  46. Seifert, B., & Gasser, T. (2000). Data adaptive ridging in local polynomial regression. Journal of Computational and Graphical Statistics, 9, 338–360.Google Scholar
  47. Smith, J. A., & Todd, P. E. (2005). Does matching overcome LaLonde’s critique of nonexperimental estimators? Journal of Econometrics, 125, 305–353.CrossRefGoogle Scholar
  48. StataCorp. (2013). Stata 13 Treatment-effects reference manual. College Station, TX: Stata Press.Google Scholar
  49. Stuart, E. A. (2010). Matching methods for causal inference: A review and a look forward. Statistical Science, 25(1), 1–21.CrossRefGoogle Scholar
  50. Wooldridge, J. M. (2007). Inverse probability weighted estimation for general missing data problems. Journal of Econometrics, 141, 1281–1301.CrossRefGoogle Scholar
  51. Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data (Vol. 2). Cambridge, MA: MIT Press. Chapter 21.Google Scholar
  52. Wooldridge, J. M. (2013). Introductory econometrics: A modern approach (5th ed.). Mason, OH: South-Western.Google Scholar
  53. Zhao, Z. (2004). Using matching to estimate treatment effects: data requirements, matching metrics, and Monte Carlo evidence. Review of Economics and Statistics, 86, 91–107.CrossRefGoogle 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

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