Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2405.14104

On the Identifying Power of Generalized Monotonicity for Average Treatment Effects

Yuehao Bai·Shunzhuang Huang·Sarah Moon·Azeem M. Shaikh·Edward J. Vytlacil
View original source ↗Read source document ↗Export metadata ↓

Abstract

In the context of a binary outcome, treatment, and instrument, Balke and Pearl (1993, 1997) es- tablish that the monotonicity condition of Imbens and Angrist (1994) has no identifying power beyond instrument exogeneity for average potential outcomes and average treatment effects in the sense that adding it to instrument exogeneity does not decrease the identified sets for those parameters whenever those restrictions are consistent with the distribution of the observable data. This paper shows that this phenomenon holds in a broader setting with a multi-valued outcome, treatment, and instrument, under an extension of the monotonicity condition that we refer to as generalized monotonicity. We further show that this phenomenon holds for any restriction on treatment response that is stronger than generalized monotonicity provided that these stronger restrictions do not restrict potential outcomes. Importantly, many models of potential treatments previously considered in the literature imply generalized monotonic- ity, including the types of monotonicity restrictions considered by Kline and Walters (2016), Kirkeboen et al. (2016), and Heckman and Pinto (2018), and the restriction that treatment selection is determined by particular classes of additive random utility models. We show through a series of examples that restrictions on potential treatments can provide identifying power beyond instrument exogeneity for av- erage potential outcomes and average treatment effects when the restrictions imply that the generalized monotonicity condition is violated. In this way, our results shed light on the types of restrictions required for help in identifying average potential outcomes and average treatment effects.

Explore related subjects

econ.EMstat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yuehao Bai, Shunzhuang Huang, Sarah Moon, Azeem M. Shaikh, Edward J. Vytlacil. 2025-11-18. On the Identifying Power of Generalized Monotonicity for Average Treatment Effects. https://doi.org/10.1080/01621459.2026.2620141

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

KEEP EXPLORING

Related papers

arXiv2026

Conditional-Moment Estimation and Inference in the BLP Model

The random-coefficient demand model of Berry, Levinsohn, and Pakes (1995) is commonly estimated by the generalized method of moments (GMM), using an unconditional moment restriction with a fixed set of instruments. Identification of the model, however, rests on a conditional moment restriction. The two are not equivalent: the unconditional restriction may admit additional parameter values. We construct a counterexample in which the model is identified by the conditional restriction yet standard GMM is not, even with the optimal instrument. Building directly on the identifying restriction, we propose a two-step estimator, following Ai and Chen (2003), that first estimates the relevant conditional expectations nonparametrically and then selects the structural parameters by a conditional-variance-weighted minimum-distance criterion; standard GMM is recovered as the special case of a linear projection onto finitely many instruments. We establish root-T asymptotic normality for the proposed estimator, and we develop the theory for both kernel and series implementations of the first stage. The two implementations share a common limiting distribution, attaining the semiparametric efficiency bound. Simulation evidence illustrates the consequences of the identification gap and demonstrates that the proposed estimator outperforms standard GMM in finite samples.

econ.EM↗
arXiv2026

Generic Covariate Adjustment for Regression Discontinuity Designs

It is standard practice to include covariates in regression discontinuity designs (RDDs) and regression kink designs (RKDs), but the theoretical justification for doing so does not generally extend beyond linear estimands. This paper proposes a novel entropy balancing reweighting approach for covariate adjustment within a general framework of RDDs and RKDs. While conventional regression-based covariate adjustment methods generally fail to deliver consistent estimation for nonlinear estimands such as quantile treatment effects, our reweighting approach achieves consistency while improving efficiency. Moreover, even in settings where the regression-based covariate adjustment method already improves efficiency, our approach can deliver additional efficiency gains. Simulation studies corroborate these theoretical findings. We present an empirical application in which our covariate adjustment yields statistically significant results that would not be obtained without covariate adjustment.

econ.EM↗
arXiv2026

Kernel Balancing in Tree-based Methods

Studying heterogeneous treatment effects has become essential in experimental and observational studies. A critical assumption for obtaining reliable treatment effect estimates is overlap, which requires that treated and control units have sufficiently similar covariate distributions. Poor overlap may limit the effectiveness of estimators, especially those based on propensity scores, potentially leading to unreliable results. We investigate the effectiveness of kernel balancing (KBal) (Hazlett, 2020) as an alternative to propensity score methods for conditional average treatment effect (CATE) estimation, particularly in settings with overlap violations. Building on optimization-based balancing approaches, we integrate KBal weights into tree-based methods, specifically, causal forests (Athey et al., 2019) and the X-Learner (XRF) (Künzel et al., 2019), to assess their impact on bias reduction and estimation precision. Monte Carlo evidence shows that KBal achieves near-exact balance in a transformed feature space, thereby improving treatment effect estimation in cases where traditional reweighting methods struggle due to extreme weights, finite-sample bias, or insufficient removal of pre-existing confounding bias. We apply the proposed methods to the semi-synthetic IHDP benchmark dataset. Overall, the results indicate that KBal leads to performance improvements, especially in settings with nonlinear treatment effects and limited overlap, making it a useful alternative to propensity score methods.

econ.EM↗