Primary Submission Category: Algorithmic Causal Inference
An Efficient Algorithm for Closed-Form Partial Identification of Causal Quantities
Authors: Guilherme Duarte,
Presenting Author: Guilherme Duarte*
Since the groundbreaking contributions of Manski (1990) and Balke and Pearl (1994) concerning bounds on causal quantities, scholars have directed their attention toward scenarios marked by the non-existence of point-identification solutions. Rather than capitulating or modifying their original inquiries to align with more tractable estimands, researchers have endeavored to derive ranges of potential values that conform to their assumptions and empirical data. For instance, in experimental settings characterized by imperfect compliance, the reliance on estimands like the Local Average Treatment Effect – which is point-identifiable but lacks a straightforward interpretation – can be supplanted by the estimation of sharp bounds for the non-identifiable Average Treatment Effect. However, while partial identification represents a preferable strategy, its implementation often proves challenging. Complete algorithmic solutions typically resort to numeric methods (Duarte et al., 2023), introducing complications for subsequent inference. To address these challenges, we present an efficient algorithm capable of providing closed-form solutions for causal-complete problems with symmetric constraints. These problems encapsulate a substantial portion of problems encountered in causal inference. Significantly, our algorithm not only cuts down on computation time compared to existing solutions but also unveils novel solutions previously unknown.