All simulators
The Wald & Grouping Estimator
Draft-lottery groups: the slope through group means estimates the effect of service; veterans-versus-others does not.
Day 62: The Wald EstimatorWald estimate
-2.78
veterans vs others
-2.34
truth
-2.80
Lottery groups differ only in their draft risk. Each dot is a group: its veteran share (x) and mean earnings (y). The slope through the group means is the Wald estimate (2 groups) or the grouping (2SLS) estimate (more groups). Comparing veterans with non-veterans instead mixes in volunteers, who would earn more anyway.