IDEAS home Printed from https://ideas.repec.org/a/inm/ormksc/v43y2024i2p267-279.html
   My bibliography  Save this article

Frontiers: A Simple Forward Difference-in-Differences Method

Author

Listed:
  • Kathleen T. Li

    (McCombs School of Business, University of Texas at Austin, Austin, Texas 78712)

Abstract

The difference-in-differences (DID) method is the most widely used tool to answer causal questions from quasiexperimental data in marketing and the broader social sciences. Because assignment to treatment in quasiexperiments is not random, the selection of proper control units is critically important for estimating the causal effect. DID requires that the treatment unit’s outcomes would have been parallel to the average of the control units’ outcomes in the absence of treatment. However, this DID parallel trends assumption is likely to be violated when assignment to the treatment and control groups is not random. We propose a simple forward difference-in-differences (Forward DID) method that uses a forward selection algorithm to flexibly select a relevant subset of control units. The Forward DID has several advantages. First, it can be widely applied and suitable even when DID is too restrictive. Second, Forward DID can accommodate any number of control units. Third, there are no overfitting concerns because Forward DID only needs to estimate one parameter after identifying a subset of control units. Fourth, Forward DID has computational advantages over algorithms that consider all possible subsets of control units. Finally, we establish consistency and develop inference theory, which is applicable to both stationary and nonstationary data. We demonstrate the usefulness of the Forward DID method and compare it with the alternative methods using simulations and an application to store openings.

Suggested Citation

  • Kathleen T. Li, 2024. "Frontiers: A Simple Forward Difference-in-Differences Method," Marketing Science, INFORMS, vol. 43(2), pages 267-279, March.
    • Handle: RePEc:inm:ormksc:v:43:y:2024:i:2:p:267-279
    DOI: 10.1287/mksc.2022.0212
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mksc.2022.0212
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mksc.2022.0212?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Garrett A. Johnson & Scott K. Shriver & Shaoyin Du, 2020. "Consumer Privacy Choice in Online Advertising: Who Opts Out and at What Cost to Industry?," Marketing Science, INFORMS, vol. 39(1), pages 33-51, January.
    2. Stéphane Bonhomme & Elena Manresa, 2015. "Grouped Patterns of Heterogeneity in Panel Data," Econometrica, Econometric Society, vol. 83(3), pages 1147-1184, May.
    3. Matthew Chesnes & Weijia (Daisy) Dai & Ginger Zhe Jin, 2017. "Banning Foreign Pharmacies from Sponsored Search: The Online Consumer Response," Marketing Science, INFORMS, vol. 36(6), pages 879-907, November.
    4. Kathleen T. Li, 2020. "Statistical Inference for Average Treatment Effects Estimated by Synthetic Control Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 2068-2083, December.
    5. Liangjun Su & Zhentao Shi & Peter C. B. Phillips, 2016. "Identifying Latent Structures in Panel Data," Econometrica, Econometric Society, vol. 84, pages 2215-2264, November.
    6. Avi Goldfarb & Catherine E. Tucker, 2011. "Privacy Regulation and Online Advertising," Management Science, INFORMS, vol. 57(1), pages 57-71, January.
    7. 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.
    8. Benny Mantin & Eran Rubin, 2016. "Fare Prediction Websites and Transaction Prices: Empirical Evidence from the Airline Industry," Marketing Science, INFORMS, vol. 35(4), pages 640-655, July.
    9. 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.
    10. 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.
    11. Jura Liaukonyte & Thales Teixeira & Kenneth C. Wilbur, 2015. "Television Advertising and Online Shopping," Marketing Science, INFORMS, vol. 34(3), pages 311-330, May.
    12. Xu, Yiqing, 2017. "Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models," Political Analysis, Cambridge University Press, vol. 25(1), pages 57-76, January.
    13. Tomohiro Ando & Jushan Bai, 2016. "Panel Data Models with Grouped Factor Structure Under Unknown Group Membership," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(1), pages 163-191, January.
    14. David R. Bell & Santiago Gallino & Antonio Moreno, 2018. "Offline Showrooms in Omnichannel Retail: Demand and Operational Benefits," Management Science, INFORMS, vol. 64(4), pages 1629-1651, April.
    15. Seshadri Tirunillai & Gerard J. Tellis, 2017. "Does Offline TV Advertising Affect Online Chatter? Quasi-Experimental Analysis Using Synthetic Control," Marketing Science, INFORMS, vol. 36(6), pages 862-878, November.
    16. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    17. Yang Wang & Marco Shaojun Qin & Xueming Luo & Yu (Eric) Kou, 2022. "Frontiers: How Support for Black Lives Matter Impacts Consumer Responses on Social Media," Marketing Science, INFORMS, vol. 41(6), pages 1029-1044, November.
    18. Shi, Zhentao & Huang, Jingyi, 2023. "Forward-selected panel data approach for program evaluation," Journal of Econometrics, Elsevier, vol. 234(2), pages 512-535.
    19. Joan Calzada & Ricard Gil, 2020. "What Do News Aggregators Do? Evidence from Google News in Spain and Germany," Marketing Science, INFORMS, vol. 39(1), pages 134-167, January.
    20. 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.
    21. 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.
    22. Dinesh Puranam & Vishal Narayan & Vrinda Kadiyali, 2017. "The Effect of Calorie Posting Regulation on Consumer Opinion: A Flexible Latent Dirichlet Allocation Model with Informative Priors," Marketing Science, INFORMS, vol. 36(5), pages 726-746, September.
    23. 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.
    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. Luya Wang & Jeffrey S. Racine & Qiaoyu Wang, 2024. "Bootstrap Inference on a Factor Model Based Average Treatment Effects Estimator," Department of Economics Working Papers 2024-03, McMaster University.
    3. Andrii Melnychuk, 2024. "Synthetic Controls with spillover effects: A comparative study," Papers 2405.01645, arXiv.org.
    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. 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.
    6. Bai, Jushan & Wang, Peng, 2024. "Causal inference using factor models," MPRA Paper 120585, University Library of Munich, Germany.
    7. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    8. Pier Basaglia & Sophie M. Behr & Moritz A. Drupp, 2023. "De-Fueling Externalities: How Tax Salience and Fuel Substitution Mediate Climate and Health Benefits," Discussion Papers of DIW Berlin 2041, DIW Berlin, German Institute for Economic Research.
    9. Ignacio Martinez & Jaume Vives-i-Bastida, 2022. "Bayesian and Frequentist Inference for Synthetic Controls," Papers 2206.01779, arXiv.org, revised Jul 2024.
    10. Luis Costa & Vivek F. Farias & Patricio Foncea & Jingyuan (Donna) Gan & Ayush Garg & Ivo Rosa Montenegro & Kumarjit Pathak & Tianyi Peng & Dusan Popovic, 2023. "Generalized Synthetic Control for TestOps at ABI: Models, Algorithms, and Infrastructure," Interfaces, INFORMS, vol. 53(5), pages 336-349, September.
    11. Pier Basaglia & Sophie M. Behr & Moritz A. Drupp, 2023. "De-Fueling Externalities: Causal Effects of Fuel Taxation and Mediating Mechanisms for Reducing Climate and Pollution Costs," CESifo Working Paper Series 10508, CESifo.
    12. Rong J. B. Zhu, 2023. "Synthetic Regressing Control Method," Papers 2306.02584, arXiv.org, revised Oct 2023.
    13. Maximiliano Marzetti & Rok Spruk, 2023. "Long-Term Economic Effects of Populist Legal Reforms: Evidence from Argentina," Comparative Economic Studies, Palgrave Macmillan;Association for Comparative Economic Studies, vol. 65(1), pages 60-95, March.
    14. 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.
    15. Xiong, Ruoxuan & Pelger, Markus, 2023. "Large dimensional latent factor modeling with missing observations and applications to causal inference," Journal of Econometrics, Elsevier, vol. 233(1), pages 271-301.
    16. Tomasz Serwach, 2023. "The European Union and within‐country income inequalities. The case of the new member states," The World Economy, Wiley Blackwell, vol. 46(7), pages 1890-1939, July.
    17. Stefano, Roberta di & Mellace, Giovanni, 2020. "The inclusive synthetic control method," Discussion Papers on Economics 14/2020, University of Southern Denmark, Department of Economics.
    18. Tomasz Serwach, 2022. "The European Union and within-country income inequalities. The case of the New Member States," Working Papers hal-03548416, HAL.
    19. 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.
    20. Lucke, Bernd, 2022. "Growth Effects of European Monetary Union: A Synthetic Control Approach," MPRA Paper 115373, University Library of Munich, Germany.

    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:inm:ormksc:v:43:y:2024:i:2:p:267-279. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.