Constrained Design of a Binary Instrument in a Partially Linear Model

Area of Science:

• Econometrics
• Causal Inference
• Experimental Design

Background:

• Randomized encouragement designs are used to estimate treatment effects when compliance is imperfect.
• Assigning nudges effectively is crucial for accurate estimation of the local average treatment effect (LATE).
• Existing methods may not be optimal for covariate-dependent nudge assignment.

Purpose of the Study:

• To develop an optimal strategy for assigning nudges based on covariates in randomized encouragement studies.
• To improve the estimation of the local average treatment effect (LATE) under a partially linear model.
• To provide a flexible design criterion that accommodates practical constraints.

Main Methods:

• A two-stage procedure is proposed for consistent and optimal LATE estimation.
• A partially linear model is assumed, with a non-parametric baseline and linear treatment effect.
• A finite sample approximation of the LATE variance is derived to create a convex design criterion for minimization.

Main Results:

• The proposed two-stage method consistently and optimally estimates the LATE.
• The derived design criterion is convex, allowing for incorporation of budgetary or ethical constraints.
• The method demonstrated significant gains compared to a regression discontinuity design in a semi-synthetic emergency department triage example.

Conclusions:

• The developed two-stage procedure offers an optimal approach for nudge assignment in randomized encouragement studies.
• The method provides a practical and efficient way to estimate LATE, even with constraints.
• This approach shows promise for improving causal inference in observational and experimental settings.