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Dynamic covariate balancing: estimating treatment effects over time with potential local projections

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  • Davide Viviano
  • Jelena Bradic

Abstract

This paper studies the estimation and inference of treatment histories in panel data settings when treatments change dynamically over time. We propose a method that allows for (i) treatments to be assigned dynamically over time based on high-dimensional covariates, past outcomes and treatments; (ii) outcomes and time-varying covariates to depend on treatment trajectories; (iii) heterogeneity of treatment effects. Our approach recursively projects potential outcomes' expectations on past histories. It then controls the bias by balancing dynamically observable characteristics. We study the asymptotic and numerical properties of the estimator and illustrate the benefits of the procedure in an empirical application.

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  • Davide Viviano & Jelena Bradic, 2021. "Dynamic covariate balancing: estimating treatment effects over time with potential local projections," Papers 2103.01280, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2103.01280
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    1. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
    2. Athey, Susan. & Stern, Scott, 1969-, 1998. "An empirical framework for testing theories about complementarity in orgaziational design," Working papers WP 4022-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Card, David & Krueger, Alan B, 1994. "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania," American Economic Review, American Economic Association, vol. 84(4), pages 772-793, September.
    4. Christopher Blattman & Julian C. Jamison & Margaret Sheridan, 2017. "Reducing Crime and Violence: Experimental Evidence from Cognitive Behavioral Therapy in Liberia," American Economic Review, American Economic Association, vol. 107(4), pages 1165-1206, April.
    5. Giavazzi, Francesco & Tabellini, Guido, 2005. "Economic and political liberalizations," Journal of Monetary Economics, Elsevier, vol. 52(7), pages 1297-1330, October.
    6. Joshua D. Angrist & Òscar Jordà & Guido M. Kuersteiner, 2018. "Semiparametric Estimates of Monetary Policy Effects: String Theory Revisited," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 371-387, July.
    7. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    8. repec:fth:prinin:315 is not listed on IDEAS
    9. David Card & Alan 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..
    10. David Card, 1990. "The Impact of the Mariel Boatlift on the Miami Labor Market," ILR Review, Cornell University, ILR School, vol. 43(2), pages 245-257, January.
    11. Halbert White & Xun Lu, 2010. "Granger Causality and Dynamic Structural Systems," Journal of Financial Econometrics, Oxford University Press, vol. 8(2), pages 193-243, spring.
    12. Alexandre Belloni & Victor Chernozhukov & Christian Hansen & Damian Kozbur, 2016. "Inference in High-Dimensional Panel Models With an Application to Gun Control," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 590-605, October.
    13. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72, Elsevier.
    14. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
    15. 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(1), pages 25-46, January.
    16. Kosuke Imai & Marc Ratkovic, 2015. "Robust Estimation of Inverse Probability Weights for Marginal Structural Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1013-1023, September.
    17. Iavor Bojinov & Neil Shephard, 2019. "Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1665-1682, October.
    18. Heckman, James J. & Humphries, John Eric & Veramendi, Gregory, 2016. "Dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 191(2), pages 276-292.
    19. Daron Acemoglu & Suresh Naidu & Pascual Restrepo & James A. Robinson, 2019. "Democracy Does Cause Growth," Journal of Political Economy, University of Chicago Press, vol. 127(1), pages 47-100.
    20. Craig Garthwaite & Tal Gross & Matthew J. Notowidigdo, 2014. "Public Health Insurance, Labor Supply, and Employment Lock," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(2), pages 653-696.
    21. Heckman, James J. & Navarro, Salvador, 2007. "Dynamic discrete choice and dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 136(2), pages 341-396, February.
    22. Athey, Susan & Imbens, Guido W., 2022. "Design-based analysis in Difference-In-Differences settings with staggered adoption," Journal of Econometrics, Elsevier, vol. 226(1), pages 62-79.
    23. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    24. Amy Finkelstein & Sarah Taubman & Bill Wright & Mira Bernstein & Jonathan Gruber & Joseph P. Newhouse & Heidi Allen & Katherine Baicker, 2012. "The Oregon Health Insurance Experiment: Evidence from the First Year," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1057-1106.
    25. Baqun Zhang & Anastasios A. Tsiatis & Eric B. Laber & Marie Davidian, 2013. "Robust estimation of optimal dynamic treatment regimes for sequential treatment decisions," Biometrika, Biometrika Trust, vol. 100(3), pages 681-694.
    26. Joshua D. Angrist & Guido M. Kuersteiner, 2011. "Causal Effects of Monetary Shocks: Semiparametric Conditional Independence Tests with a Multinomial Propensity Score," The Review of Economics and Statistics, MIT Press, vol. 93(3), pages 725-747, August.
    27. Sean Yiu & Li Su, 2018. "Covariate association eliminating weights: a unified weighting framework for causal effect estimation," Biometrika, Biometrika Trust, vol. 105(3), pages 709-722.
    28. James H. Stock & Mark W. Watson, 2018. "Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments," Economic Journal, Royal Economic Society, vol. 128(610), pages 917-948, May.
    29. Tingting Zhou & Michael R. Elliott & Roderick J. A. Little, 2019. "Penalized Spline of Propensity Methods for Treatment Comparison: Rejoinder," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 35-38, January.
    30. Nikolay Doudchenko & Guido W. Imbens, 2016. "Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis," NBER Working Papers 22791, National Bureau of Economic Research, Inc.
    31. 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, January.
    32. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    33. José R. Zubizarreta, 2015. "Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 910-922, September.
    34. Georgia Papadogeorgou & Fan Li, 2019. "Discussion of “Penalized Spline of Propensity Methods for Treatment Comparison”," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 32-35, January.
    35. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    36. Casey B. Mulligan & Ricard Gil & Xavier Sala-i-Martin, 2004. "Do Democracies Have Different Public Policies than Nondemocracies?," Journal of Economic Perspectives, American Economic Association, vol. 18(1), pages 51-74, Winter.
    37. Max Tabord-Meehan, 2023. "Stratification Trees for Adaptive Randomisation in Randomised Controlled Trials," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(5), pages 2646-2673.
    38. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    39. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
    40. Manuel Arellano & Stèphane Bonhomme, 2011. "Nonlinear Panel Data Analysis," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 395-424, September.
    41. 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.
    42. Audrey Boruvka & Daniel Almirall & Katie Witkiewitz & Susan A. Murphy, 2018. "Assessing Time-Varying Causal Effect Moderation in Mobile Health," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1112-1121, July.
    43. Susan Athey & Scott Stern, 1998. "An Empirical Framework for Testing Theories About Complimentarity in Organizational Design," NBER Working Papers 6600, National Bureau of Economic Research, Inc.
    44. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
    45. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    46. Matthew Blackwell, 2013. "A Framework for Dynamic Causal Inference in Political Science," American Journal of Political Science, John Wiley & Sons, vol. 57(2), pages 504-520, April.
    47. Blackwell, Matthew & Glynn, Adam N., 2018. "How to Make Causal Inferences with Time-Series Cross-Sectional Data under Selection on Observables," American Political Science Review, Cambridge University Press, vol. 112(4), pages 1067-1082, November.
    48. Tingting Zhou & Michael R. Elliott & Roderick J. A. Little, 2019. "Penalized Spline of Propensity Methods for Treatment Comparison," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 1-19, January.
    49. Shi, Chengchun & Fan, Ailin & Song, Rui & Lu, Wenbin, 2018. "High-dimensional A-learning for optimal dynamic treatment regimes," LSE Research Online Documents on Economics 102113, London School of Economics and Political Science, LSE Library.
    50. Fan Li & Kari Lock Morgan & Alan M. Zaslavsky, 2018. "Balancing Covariates via Propensity Score Weighting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 390-400, January.
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    Cited by:

    1. Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.
    2. Yuqian Zhang & Weijie Ji & Jelena Bradic, 2021. "Dynamic treatment effects: high-dimensional inference under model misspecification," Papers 2111.06818, arXiv.org, revised Jun 2023.

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