Inverse Probability Weighting — how does it work?

hard

Answer

$Weight each treated unit by 1/e(x) and each control by 1/(1-e(x)) \to weighted population is balanced on X.$
$(T_{i}\;Y_{i}\; / \;e_{i})\; - \;{\Sigma}$
$Consistent under unconfoundedness + overlap + correct e(x) model.$
$Weakness: high-variance when e(x) near 0 or 1 \to truncate weights or use stabilized IPW / doubly robust estimators.$
$Standard in observational causal inference.$

Check yourself — multiple choice

Random
Weight treated by 1/e, control by 1/(1-e) → balances X on average; consistent under unconfoundedness + overlap + correct e model; variance blows up near e ∈ {0,1}
Same as OLS
Not real

IPW: reweight by 1/e or 1/(1-e); consistent under unconfoundedness + overlap.

#causal-inference

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