When unobserved causes may connect a treatment to an outcome, an instrumental variable estimand uses variation from an instrument to identify a causal effect. In the online-game example, Side-Quest Group Assignment and Customization Level serve as instruments for Side-Quest Engagement and its effect on In-Game Purchases. section 11.3 section 11.3.2
Treat an instrument as valid only when the causal graph supports both requirements:
- As-if-random: backdoor paths between the instrument and outcome can be blocked; other causes of the outcome do not also cause the instrument. section 11.3.2
- Exclusion: the instrument affects the outcome only through the treatment, with no non-treatment-mediated causal path. section 11.3.2
- Add a parametric assumption for estimation: DoWhy defaults to linearity and fits linear regression models to derive the effect. section 11.3.2
Choosing an estimand under hidden confounding
If Prior Experience directly affects both Side-Quest Engagement and In-Game Purchases, a backdoor estimand may fail because the confounder is unobserved. An instrumental variable estimand remains an option when its as-if-random and exclusion assumptions are credible. section 11.3.4
### Estimand : 2 Estimand name: iv Estimand expression:⎡-1⎤⎢d⎛d⎞⎥E⎢──────────(IGP)⋅───────────([SQE])⎥⎣d[SQGA CL]⎝d[SQGA CL]⎠⎦Estimand assumption 1, As-if-random: If U→→IGP then ¬(U →→{SQGA,CL}) Estimand assumption 2, Exclusion: If we remove {SQGA,CL}→{SQE} then ¬({SQGA,CL}→IGP)
Inspect the identified instrumental-variable expression and its two graphical assumptions for the game example. section 11.3.2
