All simulators
The Roy Model of Self-Selection
Workers enrol when their gain beats the cost: decompose the naive gap into ATE, selection bias and heterogeneity bias.
Day 34: The Fundamental Problem & Selection BiasATE
2.02
ATT
3.19
theory 3.28
ATC
-1.80
naive
-0.06
selection bias
-3.25
heterogeneity bias
1.17
Check: ATE + SB + HB = -0.06 ≈ naive -0.06. Share enrolled 0.76.
Each dot is a worker: earnings without training (Y0) against the gain from training. Workers enrol when the gain exceeds the cost (dashed line). The naive comparison = ATE + selection bias (enrollees' Y0 differs) + heterogeneity bias (enrollees gain more).