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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
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    References listed on IDEAS

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    2. Walsh, Brendan & Nolan, Anne & Brick, Aoife & Keegan, Conor, 2019. "Did the expansion of free GP care impact demand for Emergency Department attendances? A difference-in-differences analysis," Social Science & Medicine, Elsevier, vol. 222(C), pages 101-111.
    3. Walsh, Brendan & Wren, Maev-Ann & Smith, Samantha & Lyons, Seán & Eighan, James & Morgenroth, Edgar, 2019. "An analysis of the effects on Irish hospital care of the supply of care inside and outside the hospital," Research Series, Economic and Social Research Institute (ESRI), number RS91.

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    More about this item

    Keywords

    Difference-in-differences; Clustered standard errors; Inference; Monte Carlo simulation; GEE;
    All these keywords.

    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

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