Inference With Difference-in-Differences With a Small Number of Groups: A Review, Simulation Study, and Empirical Application Using SHARE Data.
- Rokicki S Interfaculty Initiative in Health Policy, Harvard University, Cambridge, MA.
- Cohen J Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, MA.
- Fink G Swiss Tropical and Public Health Institute and University of Basel, Basel, Switzerland.
- Salomon JA Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Boston, MA.
- Landrum MB Department of Health Care Policy, Harvard Medical School, Boston, MA.
- 2017-11-08
Published in:
- Medical care. - 2018
Bias
Cluster Analysis
Computer Simulation
Europe
Humans
Models, Statistical
Monte Carlo Method
Patient Outcome Assessment
Statistics as Topic
English
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 modeling 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.
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.
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 modeling 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.
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.
- Language
-
- English
- Open access status
- green
- Identifiers
-
- DOI 10.1097/MLR.0000000000000830
- PMID 29112050
- Persistent URL
- https://sonar.ch/global/documents/232191
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