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Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis

Listed author(s):
  • Nikolay Doudchenko
  • Guido W. Imbens

In a seminal paper Abadie et al (2010) develop the synthetic control procedure for estimating the effect of a treatment, in the presence of a single treated unit and a number of control units, with pre-treatment outcomes observed for all units. The method constructs a set of weights such that covariates and pre-treatment outcomes of the treated unit are approximately matched by a weighted average of control units. The weights are restricted to be nonnegative and sum to one, which allows the procedure to obtain the weights even when the number of lagged outcomes is modest relative to the number of control units, a setting that is not uncommon in applications. In the current paper we propose a more general class of synthetic control estimators that allows researchers to relax some of the restrictions in the ADH method. We allow the weights to be negative, do not necessarily restrict the sum of the weights, and allow for a permanent additive difference between the treated unit and the controls, similar to difference-in-difference procedures. The weights directly minimize the distance between the lagged outcomes for the treated and the control units, using regularization methods to deal with a potentially large number of possible control units.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 22791.

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Date of creation: Oct 2016
Handle: RePEc:nbr:nberwo:22791
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  1. Bryan S. Graham & Cristine Campos de Xavier Pinto & Daniel Egel, 2008. "Inverse Probability Tilting for Moment Condition Models with Missing Data," NBER Working Papers 13981, National Bureau of Economic Research, Inc.
  2. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
  3. Orley Ashenfelter & David Card, 1984. "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs," NBER Working Papers 1489, National Bureau of Economic Research, Inc.
  4. David Card, 1989. "The Impact of the Mariel Boatlift on the Miami Labor Market," Working Papers 633, Princeton University, Department of Economics, Industrial Relations Section..
  5. Alexis Diamond & Jasjeet S. Sekhon, 2013. "Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 932-945, July.
  6. Susan Athey & Guido Imbens, 2003. "Identification and Inference in Nonlinear Difference-in-Differences Models," Levine's Working Paper Archive 506439000000000079, David K. Levine.
  7. Bruce D. Meyer & W. Kip Viscusi & David L. Durbin, 1990. "Workers' Compensation and Injury Duration: Evidence from a Natural Experiment," NBER Working Papers 3494, National Bureau of Economic Research, Inc.
  8. David Card & Alan B. Krueger, 1993. "Minimum Wages and Employment: A Case Study of the Fast Food Industry in New Jersey and Pennsylvania," Working Papers 694, Princeton University, Department of Economics, Industrial Relations Section..
  9. Ferman, Bruno & Pinto, Cristine, 2016. "Revisiting the Synthetic Control Estimator," MPRA Paper 73982, University Library of Munich, Germany.
  10. Hainmueller, Jens, 2012. "Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies," Political Analysis, Cambridge University Press, vol. 20(01), pages 25-46, December.
  11. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, 01.
  12. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
  13. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, 01.
  14. Giovanni Peri & Vasil Yasenov, 2015. "The Labor Market Effects of a Refugee Wave: Applying the Synthetic Control Method to the Mariel Boatlift," NBER Working Papers 21801, National Bureau of Economic Research, Inc.
  15. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, December.
  16. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2002. "How Much Should We Trust Differences-in-Differences Estimates?," NBER Working Papers 8841, National Bureau of Economic Research, Inc.
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