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Front-door identification

If one or more unblocked bach-door paths connect a causal variable to an outcome variable, the causal effect is identified by conditioning on a set of observed variables \(\{M\}\), that make up an identifying mechanism if

  • Condition 1 (exhaustiveness) The variables in the set \(\{M\}\) intercept all directed paths from the causal variable to the outcome variable.

  • Condition 2 (isolation) No unblocked back-door paths connect the causal variable to the variables in the set \(\{M\}\), and all back-door paths from the variables in the set \(\{M\}\) to the outcome variable can be blocked by conditioning on the causal variable.