Questions: Causal Inference from Observational Data

Question 1

A researcher adds a new control variable to a regression model. The variable is a collider — it is caused by both the treatment variable and the outcome variable. What happens to the causal estimate?

• A. It improves, because more variance is explained
• B. It is unaffected, because colliders are neutral controls
• C. It becomes biased, because conditioning on a collider opens a previously blocked non-causal path
• D. The standard errors decrease, making the estimate more reliable

Answer: (C)

Conditioning on a collider opens a backdoor path between treatment and outcome that was previously blocked, inducing a spurious correlation and biasing the causal estimate. This is the key reason 'add more controls' is not always the right strategy. Proper causal analysis requires mapping the data-generating process (via a DAG) before deciding what to condition on.

Question 2

If a study finds a statistically significant association between X and Y after controlling for most available observed confounders, we can conclude that X causes Y.

• T. True
• F. False

Answer: False

Unconfoundedness — the assumption that no unmeasured confounders exist — cannot be verified from data alone. Even after controlling for every observed covariate, unmeasured variables may still confound the relationship. Causal identification requires a credible design argument about the data-generating process, not just statistical significance after observed controls.

Question 3

What is the potential outcomes framework, and why is the fundamental problem of causal inference called 'fundamental'?

Model answer: The potential outcomes framework defines the causal effect of treatment T on unit i as Y_i(1) − Y_i(0): what would happen if treated minus what would happen if untreated. It is called fundamental because we can only ever observe one of these two outcomes for any individual — the other is an unobservable counterfactual. This is a logical impossibility, not a data limitation, and cannot be solved by collecting more observations on the same unit.

The impossibility of observing both potential outcomes simultaneously is not a measurement problem — it is a structural fact about causality. All causal inference strategies (randomization, instrumental variables, difference-in-differences, regression discontinuity) are attempts to credibly estimate the missing counterfactual under different sets of identifying assumptions. Understanding this frames why each design requires its own specific assumptions.