Discussing the concept of bias in causality
An estimator is a tool used to measure specific parameters, such as the average effect of a treatment. When an estimator is biased, it means it regularly deviates from the true value it’s supposed to measure. In terms of ATE, a biased estimator either consistently overestimates or underestimates the actual impact of the treatment. This concept is crucial in separating mere associations in data from true causation. Bias becomes apparent when the estimates we get from the data do not match the actual causal effects we are interested in.
Estimating ATE involves a thought experiment. We need to imagine two scenarios:
- Scenario 1, what would have happened to the treated group if they hadn’t received the treatment?
- Scenario 2, what would have happened to the untreated group if they had received the treatment?
In statistical terms, we represent these hypothetical outcomes as 
for the treated group without treatment...
