All simulators
Manski & Lee Bounds
Worst-case bounds, monotonicity assumptions that shrink them, and Lee bounds by trimming.
Day 79: Bounds & Partial Identification (Manski, Lee)naive difference
70
Lee bounds width
100
= trim share × wage range
Left: worst-case bounds on the average effect of a programme on a binary outcome use only the data and the outcome's range [0, 1]; their width is always 1. Monotone treatment response (no one is harmed) raises the lower bound to 0; monotone treatment selection (participants would do better anyway) caps the upper bound at the naive difference. Right: Lee bounds when wages are seen only for the employed and treatment raises employment.