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Econometrics
"On ne voit bien qu´avec le coeur. L´essentiel est invisible pour les yeux." Antoine de Saint-Exupéry The average treatment effect (ATE) is a measure used to compare treatments (or 'interventions) in randomized experiments, evaluation of policy interventions, and medical trials. The ATE measures the average causal difference in outcomes under the treatment and under the control. In a randomized trial (i.e., experiment), the average treatment effect can be estimated using a comparison in means (or medians) between treated and untreated units. However, the ATE is a causal estimand defined without reference to the study design or estimation procedure, and both observational and experimental designs may attempt to estimate an ATE in a variety of ways. In order to define formally the ATE, we define two potential outcomes : y0i is the value of the outcome variable for individual i if he is not treated, y1i is the value of the outcome variable for individual i if he is treated. For example, y0i is the health status of the individual if he is not administered the drug under study and y1i is the health status if he is administered the drug. The treatment effect for individual i is given by y1i − y0i = βi. In the general case, there is no reason to expect this effect to be constant across individuals. Estimation Depending on the data and its underlying circumstances, many methods can be used to estimate the ATE. The most common ones are
Once a policy change occurs on a population, a regression can be run controlling for the treatment. 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.
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