Suitability of CRSEs/wild cluster bootstrap-t for mixed panel/cross-sectional DiD analysis
Dear Stata list,
I've been landed with analysing a treatment effect on a binary and an effectively continuous outcome in the context of a simple difference-in-differences design: there are two treatment groups (intervention and control) and two time periods (pre and post), and treatment allocation is also clustered, so that there are 4 intervention clusters and 4 control clusters with about 15 units (healthcare providers) per cluster per period.
The problem is some healthcare providers were measured at pre and post periods but some only during the post period, and there is no way to identify who were measured repeatedly or not!
I have identified two possible solutions and would welcome any advice or suggestions.
First: analyse using a standard linear regression based DiD estimator and rely on cluster robust standard errors, clustered at the treatment allocation cluster level, to account for the mixed panel and cross-sectional data, which would imply serial correlation of some units/healthcare providers' outcomes across time (when they were measured at pre and post) and not others (when they were only measured at one time period). Or use the wild cluster bootstrap-t in a similar way.
As per Brewer et al. 2017 "inference with difference-in-differences revisited" both methods should allow analysis that is theoretically robust to heteroscedasticity and arbitrary patterns of error correlation within cluster, which I believe would cover my issue, but I can't find anywhere that explicitly states this and that always makes me nervous. Any views on this are greatly appreciated.
Second: following Donald and Lang 2007 "inference with difference-in-differences and other panel data" I thought an alternative approach is to aggregate observations into clusters based on treatment group, period, and other relevant characteristics (e.g. here say sex, type of provider etc) and analyse the group means using a standard DiD linear regression approach.
Thanks for any advice.
I've been landed with analysing a treatment effect on a binary and an effectively continuous outcome in the context of a simple difference-in-differences design: there are two treatment groups (intervention and control) and two time periods (pre and post), and treatment allocation is also clustered, so that there are 4 intervention clusters and 4 control clusters with about 15 units (healthcare providers) per cluster per period.
The problem is some healthcare providers were measured at pre and post periods but some only during the post period, and there is no way to identify who were measured repeatedly or not!
I have identified two possible solutions and would welcome any advice or suggestions.
First: analyse using a standard linear regression based DiD estimator and rely on cluster robust standard errors, clustered at the treatment allocation cluster level, to account for the mixed panel and cross-sectional data, which would imply serial correlation of some units/healthcare providers' outcomes across time (when they were measured at pre and post) and not others (when they were only measured at one time period). Or use the wild cluster bootstrap-t in a similar way.
As per Brewer et al. 2017 "inference with difference-in-differences revisited" both methods should allow analysis that is theoretically robust to heteroscedasticity and arbitrary patterns of error correlation within cluster, which I believe would cover my issue, but I can't find anywhere that explicitly states this and that always makes me nervous. Any views on this are greatly appreciated.
Second: following Donald and Lang 2007 "inference with difference-in-differences and other panel data" I thought an alternative approach is to aggregate observations into clusters based on treatment group, period, and other relevant characteristics (e.g. here say sex, type of provider etc) and analyse the group means using a standard DiD linear regression approach.
Thanks for any advice.
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