Average treatment effects

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Average treatment effects (ATE) is an econometric measure of treatments used in from policy evaluation to medicine. Depending on the data and its underlying circumstances, many methods can be used to estimate the ATE. The most common ones are

natural experiment (also known as a quasi-experiment),
difference in differences or its short version: diffs-in-diffs,
the Regression Discontinuity Design method,
matching method,
methods based on the theory of local IVs (in a strict sense Regression Discontinuity Desing 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 $y = \Beta_{0} + \delta_{0}d2 + \Beta_{1}dT + \delta_{1}d2 \cdot dT$ where y is the response variable and $δ 1$ measures the effects of the policy change on the population.

The difference in differences equation would be $\hat \delta_{1} = (\bar y_{2,T} - \bar y_{2,C}) - (\bar y_{1,T} - \bar y_{1,C})$ where T is the treatment group and C is the control group. In this case the $δ 1$ 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.