IDEAS home Printed from https://ideas.repec.org/p/kan/wpaper/202305.html
   My bibliography  Save this paper

A Quasi Synthetic Control Method for Nonlinear Models With High-Dimensional Covariates

Author

Listed:
  • Zongwu Cai

    (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA)

  • Ying Fang

    (The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China and Department of Statistics & Data Science, School of Economics, Xiamen University, Xiamen, Fujian 361005, China)

  • Ming Lin

    (The Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen, Fujian 361005, China and Department of Statistics and Data Science, School of Economics, Xiamen University, Xiamen, Fujian 361005, China)

  • Zixuan Wu

    (Department of Statistics and Data Science, School of Economics, Xiamen University, Xiamen, Fujian 361005, China)

Abstract

To make the conventional synthetic control method more flexible to estimate the average treatment effect, this article proposes a quasi synthesis control method for nonlinear models under the index model framework with possible high-dimensional covariates, together with a suggestion of using the minimum average variance estimation method to estimate parameters and the LASSO type procedure to choose covariates. Also, we derive the asymptotic distribution of the proposed estimators. A properly designed Bootstrap method is proposed to obtain confidence intervals and its theoretical justification is provided. Finally, Monte Carlo simulation studies are conducted to illustrate the finite sample performance and an empirical application to re-analyze the data from the National Supported Work Demonstration is also considered to demonstrate the proposed model to be practically useful.

Suggested Citation

  • Zongwu Cai & Ying Fang & Ming Lin & Zixuan Wu, 2023. "A Quasi Synthetic Control Method for Nonlinear Models With High-Dimensional Covariates," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202305, University of Kansas, Department of Economics, revised Aug 2023.
    • Handle: RePEc:kan:wpaper:202305
    as

    Download full text from publisher

    File URL: http://www2.ku.edu/~kuwpaper/2023Papers/202305.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Azeem M. Shaikh & Panos Toulis, 2021. "Randomization Tests in Observational Studies With Staggered Adoption of Treatment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1835-1848, October.
    2. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2021. "The Augmented Synthetic Control Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1789-1803, October.
    3. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    4. Jushan Bai & Serena Ng, 2021. "Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1746-1763, October.
    5. 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.
    6. 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.
    7. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    9. Matias D. Cattaneo & Yingjie Feng & Rocio Titiunik, 2021. "Prediction Intervals for Synthetic Control Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1865-1880, October.
    10. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353.
    11. Bruno Ferman, 2021. "On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1764-1772, October.
    12. Victor Chernozhukov & Kaspar Wüthrich & Yinchu Zhu, 2021. "An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1849-1864, October.
    13. Wan, Shui-Ki & Xie, Yimeng & Hsiao, Cheng, 2018. "Panel data approach vs synthetic control method," Economics Letters, Elsevier, vol. 164(C), pages 121-123.
    14. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    15. Maxwell Kellogg & Magne Mogstad & Guillaume A. Pouliot & Alexander Torgovitsky, 2021. "Combining Matching and Synthetic Control to Tradeoff Biases From Extrapolation and Interpolation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1804-1816, October.
    16. Alberto Abadie & Alexis Diamond & Jens Hainmueller, 2015. "Comparative Politics and the Synthetic Control Method," American Journal of Political Science, John Wiley & Sons, vol. 59(2), pages 495-510, February.
    17. Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    18. Rajeev H. Dehejia & Sadek Wahba, 2002. "Propensity Score-Matching Methods For Nonexperimental Causal Studies," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 151-161, February.
    19. Cheng Hsiao & H. Steve Ching & 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, John Wiley & Sons, Ltd., vol. 27(5), pages 705-740, August.
    20. Cai, Zongwu & Juhl, Ted & Yang, Bingduo, 2015. "Functional index coefficient models with variable selection," Journal of Econometrics, Elsevier, vol. 189(2), pages 272-284.
    21. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1112-1137, December.
    22. Ricardo Masini & Marcelo C. Medeiros, 2021. "Counterfactual Analysis With Artificial Controls: Inference, High Dimensions, and Nonstationarity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1773-1788, October.
    23. Anish Agarwal & Devavrat Shah & Dennis Shen & Dogyoon Song, 2021. "On Robustness of Principal Component Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1731-1745, October.
    24. Alberto Abadie, 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects," Journal of Economic Literature, American Economic Association, vol. 59(2), pages 391-425, June.
    25. Alberto Abadie & Matias D. Cattaneo, 2021. "Introduction to the Special Section on Synthetic Control Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1713-1715, October.
    26. James J. Heckman & Hidehiko Ichimura & Petra Todd, 1998. "Matching As An Econometric Evaluation Estimator," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(2), pages 261-294.
    27. Alberto Abadie & Jérémy L’Hour, 2021. "A Penalized Synthetic Control Estimator for Disaggregated Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1817-1834, October.
    28. Efang Kong & Yingcun Xia, 2007. "Variable selection for the single‐index model," Biometrika, Biometrika Trust, vol. 94(1), pages 217-229.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Xingyu & Shen, Yan & Zhou, Qiankun, 2024. "Confidence intervals of treatment effects in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 240(1).
    2. Dennis Shen & Peng Ding & Jasjeet Sekhon & Bin Yu, 2022. "Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data," Papers 2207.14481, arXiv.org, revised Oct 2022.
    3. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    4. David Gilchrist & Thomas Emery & Nuno Garoupa & Rok Spruk, 2023. "Synthetic Control Method: A tool for comparative case studies in economic history," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 409-445, April.
    5. Stefano, Roberta di & Mellace, Giovanni, 2020. "The inclusive synthetic control method," Discussion Papers on Economics 14/2020, University of Southern Denmark, Department of Economics.
    6. Alberto Abadie & Jaume Vives-i-Bastida, 2022. "Synthetic Controls in Action," Papers 2203.06279, arXiv.org.
    7. Ignacio Martinez & Jaume Vives-i-Bastida, 2022. "Bayesian and Frequentist Inference for Synthetic Controls," Papers 2206.01779, arXiv.org, revised Jul 2024.
    8. Guillaume Allaire Pouliot & Zhen Xie, 2022. "Degrees of Freedom and Information Criteria for the Synthetic Control Method," Papers 2207.02943, arXiv.org.
    9. Nuno Garoupa & Rok Spruk, 2024. "Populist Constitutional Backsliding and Judicial Independence: Evidence from Turkiye," Papers 2410.02439, arXiv.org.
    10. Michael Funke & Kadri Männasoo & Helery Tasane, 2023. "Regional Economic Impacts of the Øresund Cross-Border Fixed Link: Cui Bono?," CESifo Working Paper Series 10557, CESifo.
    11. Rong J. B. Zhu, 2023. "Synthetic Regressing Control Method," Papers 2306.02584, arXiv.org, revised Oct 2023.
    12. Matias D. Cattaneo & Yingjie Feng & Filippo Palomba & Rocio Titiunik, 2022. "scpi: Uncertainty Quantification for Synthetic Control Methods," Papers 2202.05984, arXiv.org, revised Oct 2022.
    13. Joseph Fry, 2023. "A Method of Moments Approach to Asymptotically Unbiased Synthetic Controls," Papers 2312.01209, arXiv.org, revised Mar 2024.
    14. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    15. Wei Tian & Seojeong Lee & Valentyn Panchenko, 2023. "Synthetic Controls with Multiple Outcomes," Papers 2304.02272, arXiv.org, revised Jul 2024.
    16. Guido W. Imbens & Davide Viviano, 2023. "Identification and Inference for Synthetic Controls with Confounding," Papers 2312.00955, arXiv.org.
    17. Masahiro Kato & Akari Ohda & Masaaki Imaizumi, 2023. "Asymptotically Unbiased Synthetic Control Methods by Distribution Matching," Papers 2307.11127, arXiv.org, revised May 2024.
    18. Guido Imbens & Nathan Kallus & Xiaojie Mao, 2021. "Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models," Papers 2108.03849, arXiv.org.
    19. Alberto Abadie & Jinglong Zhao, 2021. "Synthetic Controls for Experimental Design," Papers 2108.02196, arXiv.org, revised Sep 2024.
    20. Jiafeng Chen, 2023. "Synthetic Control as Online Linear Regression," Econometrica, Econometric Society, vol. 91(2), pages 465-491, March.

    More about this item

    Keywords

    Average treatment effect; Bootstrap inference; Index model; Minimum average variance estimation method; Semiparametric estimation; Synthetic control method;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kan:wpaper:202305. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Professor Zongwu Cai (email available below). General contact details of provider: https://edirc.repec.org/data/deuksus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.