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Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models

Abstract

Difference-in-differences (DID) is commonly used for causal inference in time-series cross-sectional data. It requires the assumption that the average outcomes of treated and control units would have followed parallel paths in the absence of treatment. In this paper, we propose a method that not only relaxes this often-violated assumption, but also unifies the synthetic control method (Abadie, Diamond, and Hainmueller 2010) with linear fixed effects models under a simple framework, of which DID is a special case. It imputes counterfactuals for each treated unit using control group information based on a linear interactive fixed effects model that incorporates unit-specific intercepts interacted with time-varying coefficients. This method has several advantages. First, it allows the treatment to be correlated with unobserved unit and time heterogeneities under reasonable modeling assumptions. Second, it generalizes the synthetic control method to the case of multiple treated units and variable treatment periods, and improves efficiency and interpretability. Third, with a built-in cross-validation procedure, it avoids specification searches and thus is easy to implement. An empirical example of Election Day Registration and voter turnout in the United States is provided.

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Copyright
Corresponding author
* Email: yiqingxu@ucsd.edu
Footnotes
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Author’s note: The author is indebted to Matt Blackwell, Devin Caughey, Justin Grimmer, Jens Hainmueller, Danny Hidalgo, Simon Jackman, Jonathan Katz, Luke Keele, Eric Min, Molly Roberts, Jim Snyder, Brandon Stewart, Teppei Yamamoto, as well as seminar participants at the 2015 MPSA Annual Meeting and 2015 APSA Annual Meeting for helpful comments and suggestions. The author thanks the editor, Mike Alvarez, and two anonymous reviewers for their extremely helpful suggestions. He also thanks Jushan Bai for generously sharing the Matlab codes used in Bai (2009) and Melanie Springer for kindly providing the state-level voter turnout data (1920–2000). The source code and data used in the paper can be downloaded from the Political Analysis Dataverse at dx.doi.org/10.7910/DVN/8AKACJ (Xu 2016) as well as the author’s website.
Contributing Editor: R. Michael Alvarez
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Alberto Abadie . 2005. Semiparametric difference-in-differences estimators. The Review of Economic Studies 72(1):119.

Alberto Abadie , Alexis Diamond , and Jens Hainmueller . 2010. Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program. Journal of the American Statistical Association 105(490):493505.

Alberto Abadie , Alexis Diamond , and Jens Hainmueller . 2015. Comparative politics and the synthetic control method. American Journal of Political Science 59(2):495510.

Daron Acemoglu , Simon Johnson , Amir Kermani , James Kwak , and Todd Mitton . 2016. The value of connections in turbulent times: Evidence from the United States. Journal of Financial Economics 121(2):368391.

Jushan Bai . 2003. Theory for factor models of large dimensions. Econometrica 71(1):135137.

Nathaniel Beck , and Jonathan N. Katz . 1995. What to do (and not to do) with time-series cross-section data. American Political Science Review 89(3):634647.

Craig Leonard Brians , and Bernard Grofman . 2001. Election day registration’s effect on US voter turnout. Social Science Quarterly 82(1):170183.

Kay H. Brodersen , Fabian Gallusser , Jim Koehler , Nicolas Remy , and Steven L. Scott . 2014. Inferring causal impact using Bayesian structural time-series models. Annals of Applied Statistics 9(1):247274.

Brad Efron . 2012. The estimation of prediction error. Journal of the American Statistical Association 99(467):619632.

Brad Efron , and Rob Tibshirani . 1993. An introduction to the bootstrap . New York: Chapman & Hall.

Mark J. Fenster 1994. The impact of allowing day of registration voting on turnout in US elections from 1960 to 1992 A research note. American Politics Research 22(1):7487.

Laurent Gobillon , and Thierry Magnac . 2016. Regional policy evaluation: Interactive fixed effects and synthetic controls. The Review of Economics and Statistics 98(3):535551.

Michael J. Hanmer 2009. Discount voting: Voter registration reforms and their effects . New York: Cambridge University Press.

Benjamin Highton . 1997. Easy registration and voter turnout. The Journal of Politics 59(2):565575.

Benjamin Highton . 2004. Voter registration and turnout in the United States. Perspectives on Politics 2(3):507515.

Paul W. Holland 1986. Statistics and causal inference. Journal of American Statistical Association 81(8):945960.

Cheng Hsiao , Steve H. Ching , and Shui Ki Wan . 2012. A panel data approach for program evaluation: Measuring the benefits of political and economic integration of Hong Kong with Mainland China. Journal of Applied Econometrics 27(5):705740.

Chi Huang , and Todd G. Shields . 2000. Interpretation of interaction effects in logit and probit analyses reconsidering the relationship between registration laws, education, and voter turnout. American Politics Research 28(1):8095.

Dukpa Kim , and Tatsushi Oka . 2014. Divorce law reforms and divorce rates in the USA: An interactive fixed-effects approach. Journal of Applied Econometrics 29(2):231245.

James D. King , and Rodney A. Wambeam . 1995. Impact of election day registration on voter turnout: A quasi-experimental analysis. Policy Studies Review 14(3):263278.

Stephen Knack . 2001. Election-day registration The second wave. American Politics Research 29(1):6578.

Stephen Knack , and James White . 2000. Election-day registration and turnout inequality. Political Behavior 22(1):2944.

Jan E. Leighley , and Jonathan Nagler . 2013. Who votes now? Demographics, issues, inequality, and turnout in the United States . Princeton, NJ: Princeton University Press.

Glenn E. Mitchell , and Christopher Wlezien . 1995. The impact of legal constraints on voter registration, turnout, and the composition of the American electorate. Political Behavior 17(2):179202.

Hyungsik Roger Moon , and Martin Weidner . 2015. Dynamic linear panel regression models with interactive fixed effects. Econometric Theory 33(1):158195.

J. R. Neiheisel , and B. C. Burden . 2012. The impact of election day registration on voter turnout and election outcomes. American Politics Research 40(4):636664.

Jong Hee Park . 2010. Structural change in US presidents’ use of force. American Journal of Political Science 54(3):766782.

Jong Hee Park . 2012. A unified method for dynamic and cross-sectional heterogeneity: Introducing hidden Markov panel models. American Journal of Political Science 56(4):10401054.

Staci L. Rhine 1992. An analysis of the impact of registration factors on turnout in 1992. Political Behavior 18(2):171185.

Melanie Jean Springer . 2014. How the states shaped the nation: American electoral institutions and voter turnout, 1920–2000 . Chicago, IL: University of Chicago Press.

Richard J. Timpone 1998. Structure, behavior, and voter turnout in the United States. The American Political Science Review 92(1):145.

Richard J. Timpone 2002. Estimating aggregate policy reform effects: New baselines for registration, participation, and representation. Political Analysis 10(2):154177.

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Political Analysis
  • ISSN: 1047-1987
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