Instrumental Variable Estimation

Information systems (IS) researchers increasingly use quasi-experimental methods such as difference-in-differences (DiD) and instrumental variables (IV) to recover causal effects from observational panel data. Power calculations that justify these designs assume i.i.d. errors, but the deeper problem is what even a cluster-robust calculator cannot see. We report a Monte Carlo study over 9837 parameter conditions (approx 9.8 million datasets) and decompose the planned-versus-achieved power gap. The serial-correlation component is recoverable by an AR(1)-aware calculator when rho is known, and partially when rho must be estimated from short pre-periods, but panel attrition, staggered-adoption bias, and parallel-trends pretesting are captured by no closed-form formula; exogenous attrition alone costs approx 8 to 11 percentage points at the few-hundred-to-thousand sample sizes IS studies use. Treatment-correlated, outcome-dependent attrition instead induces bias, not just power loss. For IV, holding first-stage F fixed, larger N neither raises power nor curbs exclusion bias, though with a fixed instrument more data does sharpen the first stage, so identification rests on instrument strength, not sample size.

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.

Control-function instrumental variable estimators need a first-stage residual, not merely a first-stage prediction. High-capacity first stages can interpolate treatment and leave too little residual information for the outcome equation. We study Adaptive Anisotropic Instrumental Heat Flow (A-IHF), a deterministic graph-diffusion residual extractor for flexible control functions. A-IHF treats treatment as a signal on a graph of first-stage features, uses pilot diffusion to detect large treatment jumps, attenuates conductance across those jumps, and computes the generated control with a sparse graph resolvent. Its observational selection rule uses only $(Z,X)$, combining graph generalized cross-validation, roughness, residualized-treatment relevance, and graph-admissibility filtering. The analysis decomposes error into structural leakage, residual attenuation, and residualized treatment variation, yielding finite-sample bounds, graph-admissibility rates under latent piecewise-smooth geometry, and finite-path selection calibration. Across 54 synthetic benchmark cells with tuned graph, kernel, tree, boosting, series, and neural control-function baselines, guarded observational A-IHF has the lowest average structural-response MSE; the A-IHF family beats the best non-A-IHF baseline in 32 cells. Performance is strongest when the graph captures piecewise-smooth first-stage structure.

We introduce a perturbative approach for nonparametric instrumental variable (NPIV) estimation. By drawing inspiration from perturbation theory in physics, we extend standard kernel ridge methods with systematic higher perturbation order corrections that significantly improve estimation accuracy. Spectrally, the perturbation introduces mixing between different eigenmodes of the expectation integral operator, which becomes especially useful when the integral equation is ill-defined. One source for such ill-definedness can be the curse of dimensionality. Our method performs across various dimensionality regimes, particularly when the dimensionality parameter $β$ which is defined through the number of samples $n$ and dimension $d$ as $n^β= d$, becomes large. Experimental results show that our first-order perturbative corrections can reduce prediction error by up to 99% in high-dimensional ill-defined cases ($β> 0.7$) compared to standard ridge regression approaches. The performance improvement is maintained across a wide range of dimensions, with the advantage becoming more pronounced as dimensionality increases.

Public service programs often allocate limited resources under uncertainty about their benefits, creating a need for randomization to support credible evaluation. In practice, however, applicants commonly enter waitlists where resources are prioritized toward individuals judged to have higher need through tiered priority queues, making direct randomization difficult. Motivated by this, we develop an experimental design framework for learning treatment effects while treating those most in need where incoming applicants are randomized into priority queues based on their assessed risk scores. Treatments are then provided across queues in priority order and first-in-first-out within queue as budget becomes available. Our contributions are two-fold. First, we characterize what causal effects are identified under this priority-queue allocation. When arrivals are exogenous, treatments are conditionally randomized, and hence standard estimands are identified; when arrivals are endogenous, queue randomization instead provides an instrument for treatment, identifying local treatment effects induced by the queuing process. Second, we develop optimized queue-assignment designs that trade off statistical efficiency against prioritizing higher-need applicants. We show in the process that, despite dependence in treatment assignments induced by the design, usual iid efficiency bounds remain well-justified design objectives. We illustrate the proposed designs using data from a housing allocation program in a large U.S. county.

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.

Instrumental-variable (IV) regression enables causal estimation under endogeneity, but modern IV problems often involve nonlinear structural effects and high-dimensional covariates. Existing methods typically operate in observed or generic learned feature spaces, and they often yield point estimates without uncertainty quantification. We introduce BGM-IV, a Bayesian generative modeling approach that performs nonlinear IV regression through posterior inference in a causally structured latent space. BGM-IV separates covariate variation by the role in the treatment and outcome mechanism, and accounts for endogeneity through an IV-integrated pseudo-likelihood that averages over instrument-induced treatment variation. The resulting model provides both structural-function estimates and predictive intervals for outcomes under intervention. Across various benchmark datasets, BGM-IV outperforms existing nonlinear IV methods overall, with significant gains in high-dimensional settings, while achieving near-nominal predictive coverage. These results highlight structured latent generative modeling as a flexible approach to uncertainty-aware IV inference with rich covariates. The code of BGM-IV is available at https://github.com/liuq-lab/BGM-IV.

Instrumental variable (IV) and control function (CF) methods are powerful tools for causal effect estimation in the presence of unmeasured confounding, yet most existing approaches target only mean effects and/or demand substantial fitting and tuning effort. In this paper, we introduce a simple method, TabCF, for control function regression using tabular foundation models, which enables accurate, fast, identification-transparent, and tuning-light causal estimation of distributional quantities, such as interventional means and quantiles; we also propose a copula-based approximation for multivariate outcomes. TabCF performs favorably against representative methods across a broad range of small- to medium-sized synthetic and real data scenarios. The central message is two-fold: for practitioners, it highlights that TabCF is an effective tool for distributional causal inference; for researchers, it suggests that the proposed approach could be considered a strong baseline for future method development. Code is available at https://github.com/GepingChen/TabCF.

We study the pricing behavior of third-party platforms facing strategic agents. Assuming the platform is a revenue maximizer, it observes market features that generally affect demand. Since only transacted quantities and prices can be observed, this presents a general demand learning problem under confounding. Mathematically, we develop an algorithm with optimal regret of $\Tilde{\mathcal{O}}(\sqrt{T}\wedgeσ_S^{-2})$. Our results reveal that supply-side noise fundamentally affects the learnability of demand, leading to a phase transition in regret. Technically, we show that non-i.i.d. actions can serve as instrumental variables for learning demand. We also propose a novel homeomorphic construction that allows us to establish estimation bounds without assuming star-shapedness, providing the first efficiency guarantee for learning demand with deep neural networks. Finally, we use simulations and offline counterfactuals from Talabat and Lyft data to illustrate the potential revenue implications of our approach.