Math for Causal Inference
All simulators

Triple Differences

A state shock biases DiD for the targeted group; subtracting other workers in the same state removes it.

Day 72: Triple Differences & Changes-in-Changes
-3.0treated stateaffected3.0comparison statesaffected-1.0treated stateothers2.0comparison statesothers
DiD, affected group
-6.00
DiD, other workers
-3.00
DDD
-3.00
truth
-3.00

Changes in log wages (%) before and after a state mandate that raises costs of employing married women aged 20–40 (the affected group). A state-wide shock hits everyone in the treated state; a national trend hits the affected group everywhere. DiD for the affected group picks up the state shock; DDD subtracts it using other workers in the same state. Only a shock specific to the treated state and the affected group (the violation) biases DDD.