Computing Synthetic Controls Using Bilevel Optimization

Malo, Pekka and Eskelinen, Juha and Zhou, Xun and Kuosmanen, Timo (2020): Computing Synthetic Controls Using Bilevel Optimization.

Abstract

The synthetic control method (SCM) is a major innovation in the estimation of causal effects of policy interventions and programs in a comparative case study setting. In this paper, we demonstrate that the data-driven approach to SCM requires solving a bilevel optimization problem. We show how the SCM problem can be solved using iterative algorithms based on Tykhonov descent or KKT approximations.

• Item Type: MPRA Paper
• Language: English
• Keywords: Causal effects; Comparative case studies; Policy impact assessment
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C54 - Quantitative Policy Modeling; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling

References

Abadie, A. (2019). Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects. Journal of Economic Literature.

Abadie, A., Diamond, A., & Hainmueller, J. (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), 493-505.

Abadie, A., Diamond, A., & Hainmueller, J. (2015). Comparative Politics and the Synthetic Control Method. American Journal of Political Science, 59 (2), 495-510.

Abadie, A., & Gardeazabal, J. (2003). The Economic Costs of Conflict: A Case Study of the Basque Country. American Economic Review, 93 (1), 113-132.

Abadie, A., & L'Hour, J. (2020). A Penalized Synthetic Control Estimator for Disaggregated Data. Work. Pap., Mass. Inst. Technol., Cambridge, MA.

Acemoglu, D., Johnson, S., Kermani, A., Kwak, J., & Mitton, T. (2016). The value of connections in turbulent times: Evidence from the United States. Journal of Financial Economics, 121 (2), 368-391.

Amjad, M., Shah, D., & Shen, D. (2018). Robust synthetic control. Journal of Machine Learning Research, 19 (1), 802-852.

Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. (2018). Synthetic Difference in Differences. arXiv preprint arXiv:1812.09970.

Athey, S., & Imbens, G. W. (2017). The state of applied econometrics: Causality and policy evaluation. Journal of Economic Perspectives, 31 (2), 3-32.

Bank, B., Guddat, J., Klatte, D., Kummer, B., & Tammer, K. (1982). Non-Linear Parametric Optimization. Akademie-Verlag, Berlin.

Becker, M., & Klössner, S. (2017). Estimating the economic costs of organized crime by synthetic control methods. Journal of Applied Econometrics, 32 (7), 1367-1369.

Becker, M., & Klössner, S. (2018). Fast and reliable computation of generalized synthetic controls. Econometrics and Statistics, 5, 1-19.

Becker, M., Klössner, S., & Pfeifer, G. (2018). Cross-validating synthetic controls. Economics Bulletin, 38 (1), 603-609.

Ben-Michael, E., Feller, A., & Rothstein, J. (2018). The Augmented Synthetic Control Method. arXiv preprint arXiv:1811.04170.

Cavallo, E., Galiani, S., Noy, I., & Pantano, J. (2013). Catastrophic natural disasters and economic growth. Review of Economics and Statistics, 95 (5), 1549-1561.

Charnes, A. (1952). Optimality and Degeneracy in Linear Programming. Econometrica, 20 (2), 160-170.

Cherchye, L., Knox Lovell, C. A., Moesen, W., & Van Puyenbroeck, T. (2007). One market, one number? A composite indicator assessment of EU internal market dynamics. European Economic Review, 51 (3), 749-779.

Dempe, S., & Franke, S. (2019). Solution of bilevel optimization problems using the KKT approach. Optimization, 68 (8), 1471-1489.

Dempe, S., & Schmidt, H. (1996). On an algorithm solving two-level programming problems with nonunique lower level solutions. Computational Optimization and Applications, 6 (3), 227-249.

Dempe, S. (2010). Foundations of Bilevel Programming. Kluwer Academic Publishers.

Doudchenko, N., & Imbens, G. W. (2017). Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis. arXiv preprint arXiv:1610.07748.

Gobillon, L., & Magnac, T. (2016). Regional policy evaluation: Interactive fixed effects and synthetic controls. Review of Economics and Statistics, 98 (3), 535-551.

Hansen, P., Jaumard, B., & Savard, G. (1992). New Branch-and-Bound Rules for Linear Bilevel Programming. SIAM Journal on Scientific and Statistical Computing, 13 (5), 1194-1217.

Kaul, A., Klössner, S., Pfeifer, G., & Schieler, M. (2015). Synthetic Control Methods: Never Use All Pre-Intervention Outcomes Together With Covariates. MPRA Paper 83790.

Kleven, H. J., Landais, C., & Saez, E. (2013). Taxation and international migration of superstars: Evidence from the European football market. American Economic Review, 103 (5), 1892-1924.

Klössner, S., Kaul, A., Pfeifer, G., & Schieler, M. (2018). Comparative politics and the synthetic control method revisited: A note on Abadie et al. (2015). Swiss Journal of Economics and Statistics, 154 (1), 11.

Klössner, S., & Pfeifer, G. (2015). Synthesizing Cash for Clunkers: Stabilizing the Car Market, Hurting the Environment. Beitrage zur Jahrestagung des Vereins für Socialpolitik 2015: Okonomische Entwicklung - Theorie und Politik - Session: Automobiles and the Environment, F13-V1.

Mersha, A. G., & Dempe, S. (2011). Direct search algorithm for bilevel programming problems. Computational Optimization and Applications, 49 (1), 1-15.

Sinha, A., Malo, P., & Deb, K. (2013). Efficient Evolutionary Algorithm for Single-Objective Bilevel Optimization. arXiv preprint arXiv:1303.3901.

Vicente, L., Savard, G., & Judice, J. (1994). Descent approaches for quadratic bilevel programming. Journal of Optimization Theory and Applications, 81 (2), 379-399.

Xu, Y. (2017). Generalized synthetic control method: Causal inference with interactive fixed effects models. Political Analysis, 25 (1), 57-76.