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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

Slawa Rokicki (), Jessica Cohen, Günther Fink, Joshua A. Salomon and Mary Beth Landrum
Additional contact information
Jessica Cohen: Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, MA.
Günther Fink: Swiss Tropical and Public Health Institute and University of Basel, Basel, Switzerland
Joshua A. Salomon: Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, MA.
Mary Beth Landrum: Department of Health Care Policy, Harvard Medical School, Boston, MA

No 201802, Working Papers from Geary Institute, University College Dublin

Abstract: Background - 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. Methods - 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). Results - 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. Conclusions - In DID estimation with a small number of groups, analysis using aggregation, permutation tests, wild cluster bootstrap, or bias-adjusted GEE is recommended.

Keywords: difference-in-differences; clustered standard errors; inference; Monte Carlo simulation; GEE (search for similar items in EconPapers)
Date: 2018-01-16
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Working Paper: Inference with difference-in-differences with a small number of groups: a review, simulation study and empirical application using SHARE data (2018) Downloads
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