Partial Identification

Definition

When point identification is impossible due to a lack of assumptions, we only know that the parameter lies in the identified set $\Theta_I$ (often an interval $[\theta_L,\theta_U]$) compatible with the data plus assumptions. Manski’s assumption-free / worst-case bounds are the starting point. sharp bounds = the smallest set that uses all available information. Inference targets the set: Imbens–Manski (2004) is the standard for confidence intervals on the parameter (not the set).

Intuitive Understanding

“Honest agnosticism” — instead of a single number under untestable assumptions, report the range that the data can support. Adding assumptions narrows the set (the assumptions↔precision trade-off).

Related Concepts

• Proximal Causal Inference (the fallback point when point identification fails) · Negative Control Outcome · Sensitivity Analysis

Key Papers

• Manski, “Nonparametric Bounds on Treatment Effects”, AER P&P 80(2):319–323, 1990
• Imbens & Manski, Econometrica 72(6):1845–1857, 2004 — CIs for partially identified parameters
• Dorn & Guo, “Sharp Sensitivity Analysis for IPW”, JASA 118(544), 2023