Title: Generalized Encouragement-Based Instrumental Variables for Counterfactual Regression
Primary area: causal reasoning
Keywords: Encouragement Design, Causal Inference, Instrumental Variable, Data Fusion

Abstract: In causal inference, encouragement designs (EDs) are widely used to analyze causal effects, when randomized controlled trials (RCTs) are impractical or compliance to treatment cannot be perfectly enforced. Unlike RCTs, which directly allocate treatments, EDs randomly assign encouragement policies that positively motivate individuals to engage in a specific treatment. These random encouragements act as instrumental variables (IVs), facilitating the identification of causal effects through leveraging exogenous perturbations in discrete treatment scenarios. However, real-world implementations of EDs often deviate from ideal conditions. Specifically, encouragements are frequently nonrandom, the number of available encouragement policies is limited, and sample sizes are often small—posing significant challenges to reliable causal estimation. To address this, we propose a novel identifiability theory that leverages variations in encouragement to identify the Conditional Average Treatment Effect (CATE). Building on this foundation, we develop a new IV estimator, named Encouragement-based Counterfactual Regression (EnCounteR), to effectively estimate causal effects even when the number of instruments is smaller than the number of treatments. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of the proposed EnCounteR.