Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.40719

Weak Identification in Bunching Designs: Rare Events and Counterfactual Uncertainty

Kun Huang
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study shrinking tax kinks when the counterfactual density is locally Hölder continuous and may be accompanied by a known background atom at the threshold. Small policy incentives create two distinct obstacles: few behavioral bunchers and an unobserved relocation interval. For the complete observed distribution, we establish matching minimax bounds for elasticity estimation and honest confidence-set diameter. With kink size $d$, background mass $γ$, and smoothness $0<s\leq1$, the rate is $\min\{1,\sqrt{(γ+d)/(nd^2)}+d^s\}$. The stochastic component has a rare-event scale when the background mass is of the kink order or smaller and a conventional weak-signal scale when it remains positive. The extrapolation component follows from observationally equivalent counterfactual densities, rather than sampling error. We derive normal and Poisson limits for a conventional bunching ratio, show a coverage failure of its Wald interval, and give finite-sample confidence sets by exact binomial inversion with a deterministic smoothness allowance. The procedure estimates the counterfactual density from an unaffected bin and covers the entire population identified set uniformly, including zero policy incentives. A likelihood-ratio calculation establishes a finite-parameter Poisson limit for a smooth, known counterfactual submodel. Structural Monte Carlo experiments document both coverage protection and its cost in set length. The results apply to the stated exact-atom observation model; general rounding and optimization frictions require additional assumptions.

Explore related subjects

econ.EM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Kun Huang. 2026-10-29. Weak Identification in Bunching Designs: Rare Events and Counterfactual Uncertainty. https://arxiv.org/abs/2610.40719

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Model Selection in High-Dimensional Linear Regression using Boosting with Multiple Testing

This paper studies model selection in high dimensional regression settings. We propose a Boosting with Multiple Testing (BMT) approach designed to address proxy signal contamination in environments with strongly correlated regressors, including settings driven by latent common factors. At each stage, at most one regressor is selected conditional on those already included, using a multiple testing threshold for the remaining candidates. Under stated dependence, detectability and design conditions, BMT recovers the exact true model with probability approaching one. A separate extension permits growing signal counts under additional restrictions. For fixed numbers of signals and proxies, we also establish recovery of an approximating model containing all true signals and no noise variables under a separate set of conditions. Following exact selection, fixed dimensional least squares has the oracle asymptotic distribution under the stated moment conditions. A theoretical comparison identifies designs and tuning sequences for which BMT is consistent while the Lasso is not. In the main Monte Carlo comparison, BMT has the highest median Matthews correlation coefficient and exact recovery rate and the lowest median coefficient root mean squared error among the compared specifications. Applications to U.S. emissions and inflation show that BMT combines sparse specifications with favourable forecast performance, including the lowest emissions forecasting errors in the reported comparisons and the best one quarter ahead forecasts in the baseline inflation comparison.

econ.EM↗
arXiv2026

Sharp Identification for Regressions with Interval-Observed and Missing Covariates

Researchers frequently estimate regressions when key variables are missing or observed only through intervals. Imputation or assumptions about the observation process can yield seemingly precise but misleading conclusions. We develop methods for identification and inference that remain robust to such incomplete data. For a broad class of conditional moment models, we characterize the sharp identified set, the set of all parameter values consistent with the observed data and maintained regression model, without restricting how incomplete observations arise. We establish Hausdorff-consistent estimation and uniformly valid confidence regions, and develop computationally tractable implementations for common regression models. In an application relating interval-elicited discount rates to on-time high-school graduation, conventional inference excludes zero, whereas our interval-data-robust confidence regions include it. Exploiting sharp identification nevertheless yields substantially tighter confidence regions than non-sharp alternatives.

econ.EM↗
arXiv2026

Regret-based Characterization, Information Limits, and the Sample Complexity of Auditing Adaptive Policies

A policy can earn its performance by where it locates on average or by reacting to information. For any Markov policy $π$ in a finite-horizon MDP, let $ν$ be its open-loop marginal, which plays $π$'s average action distribution at each step. We show that $J(π)-J(ν)$ equals $\sum_t tr Cov(Q^ν_t,π_t)$ under endogenous dynamics. Audits based on immediate costs alone can have the wrong sign. Writing the covariance as a joint-versus-product gap gives the bound $|J(π)-J(ν)|\le\sum_t span_t\sqrt{I(s_t;a_t)/2}$, with a sharp constant. Hence, an MDP's adaptivity gap is bounded by the information that its optimal policy uses. Estimating $J(π)-J(ν)$ from $π$'s own bandit-feedback logs takes $Θ(\barχ^2 \log(1/η)/δ^2)$ rounds, where $\barχ^2$ is an average $χ^2$-divergence. At the same time, deterministic non-constant policies cannot be audited at all. We also provide an importance-sampling auditor for episodic MDPs.

econ.EM↗