Potential Outcomes Framework

Understanding the Causal Effects in Potential Outcomes Framework

Potential Outcome Framework has helped in giving causal effects very precise definitions.

The Potential outcome is the outcome that would be observed if an individual is given a specific value of the treatment. It is the study of the effect of treatment at an individual level. For every Individual one can not simultaneously observe the 2 potential Outcomes, we can only observe one. Here, the unobserved outcome is called the "Counterfactual Outcome ".

Two possible treatments, T - Treatment received or not received(Placebo)

$$T ∈ \{0,1\}$$

Two possible outcomes, Y - the outcome is there or not there

$$\{Y_i (0) ,Y_i(1)\}$$

Note: Quantities we are trying to measure here is not observable!!

Example: What is the causal effect of doing a Master's degree and getting a high paying job?

• Treatment: doing Master's (T=1) & not doing Master's (T=0)

• Every individual person has 2 potential outcomes, Yt=0 & Yt=1 .

• Yt=0 -> Potential Outcome when not doing Masters

• Yt=1 -> Potential Outcome when doing Masters

ITE

**Individual Treatment Effect is the difference between the 2 potential outcomes for a particular individual. We cannot measure ICE as we would need counterfactual value for the individual.

$$ICE = Y1 - Y0$$

ATE

Average Treatment Effect is the average difference between the 2 potential outcomes averaged over the entire population of interest. It is the population level average of the Individual Causal Effect(ICE).

$$ATE = E[Yi1] - E[Yi0]$$

• Note: Even though an Individual Causal Effect is non zero, the Average causal effect can be Zero.