arXiv subjects

Peter Hull

Publications and source records attributed to Peter Hull.

11 recordsLinked to original sources

arXiv2026

Optimal Experimental Design and Estimation when Potential Outcomes are Bounded

I study the optimal design and analysis of randomized experiments for estimating finite-population average treatment effects when potential outcomes are known to be bounded, as with binary outcomes. Among all assignment mechanisms and a broad class of affine estimators, worst-case mean-squared error (MSE) is minimized by independent random assignment and an unconventional regression of the support-midpoint-centered outcome on the recentered treatment, with no intercept. This contrasts with the usual prescription of balanced complete randomization and difference-in-means estimation: when outcomes are bounded, randomness in the realized treatment share is informative. The worst-case gain over full-sample complete randomization is asymptotically small, but gains can be first-order relative to other designs: complete within-pair randomization and pair-fixed-effect regression have twice the worst-case MSE. I extend the result to allow for arbitrary estimators. Independent random assignment remains optimal, and the generally-nonlinear optimal estimator can meaningfully reduce worst-case MSE.

econ.EM↗

arXiv2026

Robust Signal Maximization in Spillover Experiments

We study the optimal design and analysis of experiments for estimating spillover effects. Assuming a known (e.g., linear) exposure mapping, we characterize the treatment-assignment distribution and regression-based estimator that minimize worst-case asymptotic variance against a broad class of distributions of unobservables. The design problem yields an intuitive solution in which the planner trades off spillover signal strength against diffusion of spillover variation. The analysis problem yields a simple recentered instrumental variable estimator to best leverage this variation. This framework produces natural solutions in several benchmark cases - such as clustered exposure - and suggests computationally tractable approximations for general networks, including bipartite settings. We illustrate these new tools in semi-synthetic experiments based on two applications from development economics. Our approach yields large standard error reductions in both experiments, increasing effective sample sizes by 50-100% or more.

econ.EM↗

arXiv2026

Long-Term Causal Inference with Many Noisy Proxies

We propose a method for estimating long-term treatment effects with many short-term proxy outcomes: a central challenge when experimenting on digital platforms. We formalize this challenge as a latent variable problem where observed proxies are noisy measures of a low-dimensional set of unobserved surrogates that mediate treatment effects. Through theoretical analysis and simulations, we demonstrate that regularized regression methods substantially outperform naive proxy selection. We show in particular that the bias of Ridge regression decreases as more proxies are added, with closed-form expressions for the bias-variance tradeoff. We illustrate our method with an empirical application to the California GAIN experiment.

econ.EM↗

arXiv2025

Nonparametric Identification of Demand without Exogenous Product Characteristics

We study identification of differentiated product demand from market-level data when product characteristics can be endogenous. Past work suggests nonparametric identification may be impossible: that is, in addition to standard price instruments, exogenous characteristic-based instruments are essentially necessary to identify sufficiently flexible demand models with standard index restrictions. We show, however, that price counterfactuals are nonparametrically identified using recentered instruments -- which combine exogenous price instruments with possibly endogenous product characteristics -- under a weaker index restriction and a new condition we term faithfulness. We argue that faithfulness, like the usual completeness condition for nonparametric instrumental variable identification, is best viewed as a technical requirement on the strength of identifying variation rather than a substantive economic or statistical restriction. We show the two conditions are closely related, though generally distinct. We conclude with several practical implications for the parametric estimation of demand counterfactuals.

econ.EM↗

arXiv2025

Leniency Designs: An Operator's Manual

We develop a step-by-step guide to leniency (a.k.a. judge or examiner instrument) designs, drawing on recent econometric literatures. The unbiased jackknife instrumental variables estimator (UJIVE) is purpose-built for leveraging exogenous leniency variation, avoiding subtle biases even in the presence of many decision-makers or controls. We show how UJIVE can also be used to assess key assumptions underlying leniency designs, including quasi-random assignment and average first-stage monotonicity, and to probe the external validity of treatment effect estimates. We further discuss statistical inference, arguing that non-clustered standard errors are often appropriate. A reanalysis of Farre-Mensa et al. (2020), using quasi-random examiner assignment to estimate the value of patents to startups, illustrates our checklist.

econ.EM↗

arXiv2025

Estimating Demand with Recentered Instruments

We develop a new approach to estimating flexible demand models with exogenous supply-side shocks. Our approach avoids conventional assumptions of exogenous product characteristics, putting no restrictions on product entry, despite using instrumental variables that incorporate characteristic variation. The proposed instruments are model-predicted responses of endogenous variables to the exogenous shocks, recentered to avoid bias from endogenous characteristics. We illustrate the approach in a series of Monte Carlo simulations.

econ.EM↗

arXiv2025

Instrumental Variables with Time-Varying Exposure: Dynamic Effects of Revascularization on Quality of Life

This paper develops instrumental variables (IV) estimators for dynamic causal effects in randomized trials with imperfect compliance. These methods are applied to a randomized trial that assigned patients with ischemic heart disease to either an invasive treatment arm centered on revascularization or a control group meant to receive non-invasive medical therapy. As is common in such ``strategy trials,'' many participants assigned to treatment remained untreated while many assigned to control crossed over into treatment. Protocol non-compliance causes ITT estimates to diverge from the effect of treatment received, while conventional per-protocol analyses that condition on treatment received are compromised by selection bias. Extending the static potential-outcomes IV framework, the methods here identify average causal effects of treatment for dynamic compliers, the set of trial participants who comply with trial protocol at different follow-up horizons. IV estimates of revascularization effects on compliers' quality of life are markedly larger and more sustained than previously reported ITT and per-protocol estimates. We also show how to estimate average characteristics and marginal potential outcome means for dynamic compliers. These results are used to explain confounding in as-treated per-protocol estimates.

econ.EM↗

arXiv2022

Labour by Design: Contributions of David Card, Joshua Angrist, and Guido Imbens

The 2021 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel was awarded to David Card "for his empirical contributions to labour economics" and to Joshua Angrist and Guido Imbens "for their methodological contributions to the analysis of causal relationships." We survey these contributions of the three laureates, and discuss how their empirical and methodological insights transformed the modern practice of applied microeconomics. By emphasizing research design and formalizing the causal content of different econometric procedures, the laureates shed new light on key questions in labour economics and advanced a robust toolkit for empirical analyses across many fields.

econ.GN↗

arXiv2021

Contamination Bias in Linear Regressions

We study regressions with multiple treatments and a set of controls that is flexible enough to purge omitted variable bias. We show that these regressions generally fail to estimate convex averages of heterogeneous treatment effects -- instead, estimates of each treatment's effect are contaminated by non-convex averages of the effects of other treatments. We discuss three estimation approaches that avoid such contamination bias, including the targeting of easiest-to-estimate weighted average effects. A re-analysis of nine empirical applications finds economically and statistically meaningful contamination bias in observational studies; contamination bias in experimental studies is more limited due to smaller variability in propensity scores.

econ.EM↗

arXiv2018

Quasi-Experimental Shift-Share Research Designs

Many studies use shift-share (or ``Bartik'') instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shift-share instrument and an unobserved residual can be represented as the orthogonality between the underlying shocks and a shock-level unobservable. SSIV regression coefficients can similarly be obtained from an equivalent shock-level regression, motivating shock-level conditions for their consistency. We discuss and illustrate several practical insights of this framework in the setting of Autor et al. (2013), estimating the effect of Chinese import competition on manufacturing employment across U.S. commuting zones.

econ.EM↗

arXiv2018

Estimating Treatment Effects in Mover Designs

Researchers increasingly leverage movement across multiple treatments to estimate causal effects. While these "mover regressions" are often motivated by a linear constant-effects model, it is not clear what they capture under weaker quasi-experimental assumptions. I show that binary treatment mover regressions recover a convex average of four difference-in-difference comparisons and are thus causally interpretable under a standard parallel trends assumption. Estimates from multiple-treatment models, however, need not be causal without stronger restrictions on the heterogeneity of treatment effects and time-varying shocks. I propose a class of two-step estimators to isolate and combine the large set of difference-in-difference quasi-experiments generated by a mover design, identifying mover average treatment effects under conditional-on-covariate parallel trends and effect homogeneity restrictions. I characterize the efficient estimators in this class and derive specification tests based on the model's overidentifying restrictions. Future drafts will apply the theory to the Finkelstein et al. (2016) movers design, analyzing the causal effects of geography on healthcare utilization.

econ.EM↗