I am trying to find causal effects of a policy change in one county in Spain on the absence of certain types of cancer in 2008. My idea was to compare pre- and post-treatment prevalence rates in this county with the national rates (maybe also compare to the prevalence rates of peer counties). (treated vs non-treated ofcourse)

My data are aggregated, meaning I have cancer rates per year from 2000 until 2014 for each and every county (89 in total), see http://imgur.com/XKAxGGD with only 3 counties as an example.

If I plot my data over time ("county1" vs "mean rates of every other county"), the common trends assumption seems to be met, and you can also see the effect of the treatment pretty good.

My question is the following: since my data are not on an individual basis, is it even appropriate/possible to use the regression formulation of diff-in-diff? I don´t see how it would be possible to get sstandard errors off that.

Thank you so much!

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    – Sycorax
    Feb 16 '16 at 13:22

You can use the standard difference in differences framework. Given that you treatment happens at the county level, the aggregate regression will estimate the same coefficient as the individual level regression. If $g = 1$ is a dummy for people who live in the treated county ($g=0$ are the control counties) and $t = 1$ is the post treatment period (with $t=0$ being the pre-treatment period), your difference in differences estimate is $$ E[y_i|g=1, t=1] - E[y_i|g=1, t=0] - (E[y_i|g=0, t=1] - E[y_i|g=0, t=0])$$

where $y_i$ is the outcome of interest and $E$ is the expectations operator. So you take the difference of the pre- and post-treatment period average of the outcome in the treatment group and subtract from that the difference of the pre- and post-treatment period average in the control group.

Whether you do this at the individual level or county level will give the same point estimate but the standard errors will not be the same. As long as you cluster the standard errors at the county level this should not be a problem though.

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    – Andy
    Mar 19 '16 at 18:54

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