IDEAS home Printed from https://ideas.repec.org/p/qub/charms/1801.html
   My bibliography  Save this paper

Inference with difference-in-differences with a small number of groups: a review, simulation study and empirical application using SHARE data

Author

Listed:
  • Slawa Rokicki
  • Jessica Cohen
  • Gunther Fink
  • Joshua Salomon
  • Mary Beth Landrum

Abstract

Difference-in-differences (DID) estimation has become increasingly popular as an approach to evaluate the effect of a group-level policy on individual-level outcomes. Several statistical methodologies have been proposed to correct for the within-group correlation of model errors resulting from the clustering of data. Little is known about how well these corrections perform with the often small number of groups observed in health research using longitudinal data. First, we review the most commonly used modelling solutions in DID estimation for panel data, including generalized estimating equations (GEE), permutation tests, clustered standard errors (CSE), wild cluster bootstrapping, and aggregation. Second, we compare the empirical coverage rates and power of these methods using a Monte Carlo simulation study in scenarios in which we vary the degree of error correlation, the group size balance, and the proportion of treated groups. Third, we provide an empirical example using the Survey of Health, Ageing and Retirement in Europe (SHARE). When the number of groups is small, CSE are systematically biased downwards in scenarios when data are unbalanced or when there is a low proportion of treated groups. This can result in over-rejection of the null even when data are composed of up to 50 groups. Aggregation, permutation tests, bias-adjusted GEE and wild cluster bootstrap produce coverage rates close to the nominal rate for almost all scenarios, though GEE may suffer from low power. In DID estimation with a small number of groups, analysis using aggregation, permutation tests, wild cluster bootstrap, or bias-adjusted GEE is recommended.

Suggested Citation

  • Slawa Rokicki & Jessica Cohen & Gunther Fink & Joshua Salomon & Mary Beth Landrum, 2018. "Inference with difference-in-differences with a small number of groups: a review, simulation study and empirical application using SHARE data," CHaRMS Working Papers 18-01, Centre for HeAlth Research at the Management School (CHaRMS).
  • Handle: RePEc:qub:charms:1801
    as

    Download full text from publisher

    File URL: ftp://ftp.qub.ac.uk/pub/users/repec/qub/charms/MS_WPS_CHARMS_18_01.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Jessica Cohen & Pascaline Dupas, 2008. "Free Distribution or Cost-Sharing? Evidence from a Malaria Prevention Experiment," NBER Working Papers 14406, National Bureau of Economic Research, Inc.
    2. Guido W. Imbens & Michal Kolesár, 2016. "Robust Standard Errors in Small Samples: Some Practical Advice," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 701-712, October.
    3. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    4. Avendano, Mauricio & Berkman, Lisa F. & Brugiavini, Agar & Pasini, Giacomo, 2015. "The long-run effect of maternity leave benefits on mental health: Evidence from European countries," Social Science & Medicine, Elsevier, vol. 132(C), pages 45-53.
    5. Joan Costa‐Font & Martin Karlsson & Henning Øien, 2016. "Careful in the Crisis? Determinants of Older People's Informal Care Receipt in Crisis‐Struck European Countries," Health Economics, John Wiley & Sons, Ltd., vol. 25, pages 25-42, November.
    6. Lloyd A. Mancl & Timothy A. DeRouen, 2001. "A Covariance Estimator for GEE with Improved Small-Sample Properties," Biometrics, The International Biometric Society, vol. 57(1), pages 126-134, March.
    7. A. Colin Cameron & Douglas L. Miller, 2010. "Robust Inference with Clustered Data," Working Papers 107, University of California, Davis, Department of Economics.
    8. Michael P. Fay & Barry I. Graubard, 2001. "Small-Sample Adjustments for Wald-Type Tests Using Sandwich Estimators," Biometrics, The International Biometric Society, vol. 57(4), pages 1198-1206, December.
    9. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
    10. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    11. Brewer, Mike & Crossley, Thomas F. & Joyce, Robert, 2013. "Inference with Difference-in-Differences Revisited," IZA Discussion Papers 7742, Institute for the Study of Labor (IZA).
    12. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Difference-in-differences; Clustered standard errors; Inference; Monte Carlo simulation; GEE;

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • I10 - Health, Education, and Welfare - - Health - - - General

    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:qub:charms:1801. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mark McGovern). General contact details of provider: http://edirc.repec.org/data/dequbuk.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.