The Resolution of Causal Heterogeneity

• URL: http://arxiv.org/abs/2607.17280v1
• Date: Sun, 19 Jul 2026 14:56:06 GMT
• Title: The Resolution of Causal Heterogeneity
• Abstract summary: Causal subgroup analyses often report a small number of groups summarizing treatment effect heterogeneity, as if that number were a well-defined estimand.<n>We replace it with a new population estimand, the resolution profile, a functional of the causal feature law.<n>Inference is organized around one cross-fitted Bayesian-bootstrap posterior for a single structured moment process.
• Score: 5.222979968110479
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Causal subgroup analyses often report a small number of groups summarizing treatment effect heterogeneity, as if that number were a well-defined estimand. Outside genuinely latent class populations, however, a ``true'' subgroup count is model dependent rather than a population functional. We replace it with a new population estimand, the resolution profile, a functional of the causal feature law giving the fewest groups explaining a prescribed fraction of causal heterogeneity, defined for every population without latent structure. Inference is organized around one cross-fitted Bayesian-bootstrap posterior for a single structured moment process, its scores corrected with influence functions, so that paths, profiles, fixed-resolution summaries, and subgroup effects follow by composition. A uniform conditional Bernstein--von Mises theorem over a loss class containing the nonsmooth quantization losses shows this posterior merges with the efficient Gaussian limit under stated nuisance-rate and margin conditions. Subgroup-number uncertainty is not model selection but threshold nonregularity, the profile being an integer-valued threshold of a continuous path, discontinuous in the law at each knot. At these knots no single-valued selector is locally uniformly consistent over root-$n$ neighborhoods, and the set-valued report obtained by inverting a simultaneous band retains locally uniform validity over exactly the same perturbations. Simulations support the approximations, and an analysis of the MineThatData e-mail experiment illustrates the resolution-indexed report, in which two to three groups summarize the visit response while finer structure falls below a noise-floor diagnostic.

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