BGM-IV: an AI-powered Bayesian generative modeling approach for instrumental variable analysis

The instrumental-variables (IV) setting is standard for partial identification of causal effects when unobserved confounding makes point identification impossible. Existing approaches face methodological bottlenecks: closed-form bound estimands are required -- e.g., Balke-Pearl equations in binary IV -- and even when available, designing accurate estimators requires manual effort tailored to each estimand. While direct Bayesian inference of the causal effects, instead of the bounds, circumvents these challenges, it is often computationally intensive and suffers from high prior sensitivity or under-dispersed posteriors. As a remedy, we introduce IV-ICL, an amortized Bayesian in-context learning method that learns the marginal posterior distribution of the causal effects directly and derives bounds as its quantiles. Unlike standard variational inference that optimizes exclusive KL divergence, amortized Bayesian inference minimizes the expected inclusive KL, a mass-covering objective. We empirically observe that optimizing inclusive KL can recover the entire identified set across diverse data-generating processes, while exclusive-KL (e.g. with variational inference) of the same Bayesian formulation collapses onto a single mode and fails to cover the identified set. We evaluate IV-ICL on synthetic and semi-synthetic IV benchmarks and show it produces intervals that are more reliably valid and more informative compared to efficient semi-parametric, Bayesian, and plug-in baselines, at 20-500x lower inference time. Beyond methodology, we propose a procedure to convert randomized controlled trials into IV benchmarks with provably preserved ground-truth causal effects that enables a more realistic evaluation of partial-identification methods.

This work proposes deep nonparametric Instrumental variable quantile regression (IVQR), a two-stage estimator that combines conditional diffusion modeling with a kernel-smoothed conditional moment formulation. In the first stage, we estimate the joint conditional distribution of the outcome and endogenous covariates given the instrument using a variance-preserving conditional diffusion model. In the second stage, we approximate the conditional moment operator through Monte Carlo sampling and a kernel-smoothed surrogate for the indicator function, and then estimate the structural quantile function by empirical risk minimization over deep neural networks. We establish an excess-risk bound for the proposed estimator and derive end-to-end total variation guarantees for the conditional diffusion model under unbounded support, explicitly accounting for score estimation, early stopping, and discretization errors. Our theory is developed under a polynomial-tail envelope on the data distribution and degenerates continuously to the exponential setting: as the tail index grows, the obtained excess-risk rate converges to the minimax-optimal rate of nonparametric regression, thus our heavy-tailed theory covers the classical light-tailed nonparametric guarantees as a limiting case. Simulation studies and a real-data application demonstrate that the proposed method outperforms existing nonparametric IVQR approaches, with gains that become increasingly pronounced as the dimensionality of the covariates and instruments increases.

We study linear regression when the regressor is latent and observed only through multiple noisy measurements, each a smooth but possibly nonlinear function of the latent variable. The problem is acute in the measurement of occupational exposure to artificial intelligence, where competing scores yield downstream estimates that differ by a factor of eleven. A regression on any single measurement recovers a source-specific coefficient rather than the structural one. We fix the latent scale by requiring the consensus measurement function to be linear and bound the remaining curvature heterogeneity across sources relative to slope. Under this bound, the structural coefficient lies in a closed-form interval centered at a symmetric cross-source estimator. The interval is invariant to unknown source loadings, and its half-width is second order in the curvature bound and sharp to the same order. With at least four measurements, the bound is estimable from the joint distribution of the sources through a split-instrument auxiliary regression, and Imbens-Manski confidence intervals with the Stoye critical value attain uniform coverage over the curvature class, including at the point-identified boundary. The application matches six exposure measures to an American Community Survey panel of 8.88 million person-year observations for 2015 to 2024. The post-2022 employment coefficient changes sign between the language-model measures and the Webb patent-text measure, and an ex ante factor-analytic rule separates the Webb measure as a distinct construct. The five retained sources yield a loading-invariant consensus coefficient of -0.239, with a partial-identification half-width of 1.23 percent of the point estimate, or 1.88 percent at the one-sided 95 percent upper bound on the curvature. We read the application as measurement reconciliation rather than as a causal estimate of AI displacement.