Estimation
Depending on the data and its underlying circumstances, many methods can be used to estimate the ATE. The most common ones are
- Natural experiment and the similar quasi-experiment,
- Difference in differences or its short version: diff-in-diffs,
- the Regression discontinuity design method,
- matching method,
- methods based on the theory of local IVs (in a strict sense regression discontinuity design belongs here as well)
Once a policy change occurs on a population, a regression can be run controlling for the treatment. The resulting equation would be
where y is the response variable and measures the effects of the policy change on the population.
The difference in differences equation would be
where T is the treatment group and C is the control group. In this case the measures the effects of the treatment on the average outcome and is the average treatment effect.
From the diffs-in-diffs example we can see the main problems of estimating treatment effects. As we can not observe the same individual as treated and non-treated at the same time, we have to come up with a measure of counterfactuals to estimate the average treatment effect.
Read more about this topic: Average Treatment Effect
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