Comparing Two Proxy Methods for Causal Identification
This work provides insights for researchers in causal inference, but it is incremental as it compares existing methods without introducing new techniques.
The paper tackled the challenge of identifying causal effects with unmeasured variables by comparing two proxy methods: bridge equation and array decomposition, analyzing their model restrictions and assumptions to clarify applicability.
Identifying causal effects in the presence of unmeasured variables is a fundamental challenge in causal inference, for which proxy variable methods have emerged as a powerful solution. We contrast two major approaches in this framework: (1) bridge equation methods, which leverage solutions to integral equations to recover causal targets, and (2) array decomposition methods, which recover latent factors composing counterfactual quantities by exploiting unique determination of eigenspaces. We compare the model restrictions underlying these two approaches and provide insight into implications of the underlying assumptions, clarifying the scope of applicability for each method.