control function

TL;DR Athey, Chetty, and Imbens develop a new method to estimate treatment effects on primary outcomes (like graduation rates) by combining experimental data where treatment is randomized but only secondary outcomes are observed (like test scores) with observational data where both primary and secondary outcomes are measured but treatment is not randomized.

Motivation Endogeneity: When an explanatory variable (treatment) is correlated with the unobserved error term (e.g., due to omitted variables, measurement error, or simultaneity). Consequence: Standard regression (e.g., OLS) yields biased estimates.