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识别与工具变量:工具变量、弱识别、部分识别与识别条件。
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The Proximal Surrogate Index: Long-Term Treatment Effects under Unobserved Confounding

近端替代指标:未观测混杂下的长期处理效应

We study the identification and estimation of long-term treatment effects under unobserved confounding by combining an experimental sample, where the long-term outcome is missing, with an observational sample, where the treatment assignment is unobserved. While standard surrogate index methods fail when unobserved confounders exist, we establish novel identification results by leveraging proxy variables for the unobserved confounders. We further develop multiply robust…

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Statistical Decisions and Partial Identification: With Application to Boundary Discontinuity Design

统计决策与部分识别:边界不连续设计的应用

We are delighted to respond to the excellent surveys by Cattaneo et al. (2026) and Hirano (2026). Our discussion will attempt two things: first, we show how statistical decision theory can be applied to situations with partial identification; second, we connect the surveys' themes by applying these insights to an imagined policy experiment in one of Cattaneo et al.'s (2025) applications. To do so, we lay out a stylized scenario of statistical decision making under partial…

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Efficient Difference-in-Differences Estimation when Outcomes are Missing at Random

结果随机缺失时的有效双重差分估计

The Difference-in-Differences (DiD) method is a fundamental tool for causal inference, yet its application is often complicated by missing data. Although recent work has developed robust DiD estimators for complex settings like staggered treatment adoption, these methods typically assume complete data and fail to address the critical challenge of outcomes that are missing at random (MAR) -- a common problem that invalidates standard estimators. We develop a rigorous…

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Recovering Counterfactual Distributions via Wasserstein GANs

通过 Wasserstein 生成对抗网络恢复反事实分布

Standard Distributional Synthetic Controls (DSC) estimate counterfactual distributions by minimizing the Euclidean $L_2$ distance between quantile functions. We demonstrate that this geometric reliance renders estimators fragile: they lack informative gradients under support mismatch and produce structural artifacts when outcomes are multimodal. This paper proposes a robust estimator grounded in Optimal Transport (OT). We construct the synthetic control by minimizing the…

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Differentiable Cyclic Causal Discovery Under Unmeasured Confounders

未观测混杂下的可微循环因果发现

Understanding causal relationships between variables is fundamental across scientific disciplines. Most causal discovery algorithms rely on two key assumptions: (i) all variables are observed, and (ii) the underlying causal graph is acyclic. While these assumptions simplify theoretical analysis, they are often violated in real-world systems, such as biological networks. Existing methods that account for confounders either assume linearity or struggle with scalability. To…

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Bayesian Nonparametric Causal Inference for High-Dimensional Nutritional Data via Factor-Based Exposure Mapping

通过因子暴露映射对高维营养数据开展贝叶斯非参数因果推断

Diet plays a crucial role in health, and understanding the causal effects of dietary patterns is essential for informing public health policy and personalized nutrition strategies. However, causal inference in nutritional epidemiology faces several challenges: (i) high-dimensional and correlated food/nutrient intake data induce massive treatment levels; (ii) nutritional studies are interested in latent dietary patterns rather than single food items; and (iii) the goal is to…

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Bayesian Joint Additive Factor Models for Multiview Learning

用于多视图学习的贝叶斯联合加性因子模型

It is increasingly common to collect data of multiple different types on the same set of samples. Our focus is on studying relationships between such multiview features and responses. A motivating application arises in the context of precision medicine where multi-omics data are collected to correlate with clinical outcomes. It is of interest to infer dependence within and across views while combining multimodal information to improve the prediction of outcomes. The…

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Three's a crowd: Identification challenges in the triple difference model with spillover effects

三者成群:存在溢出效应时三重差分模型的识别挑战

The paper studies identification in triple-difference designs when spillover effects contaminate one or more control groups. We show that, under conventional identifying assumptions, the triple-difference model fails to identify both the treatment effect and the spillover effect under such interference. To overcome this limitation, we propose an alternative specification, the double-triple-difference model, and explicitly formalize identifying assumptions and spillover…

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What Impulse Response Do Instrumental Variables Identify?

工具变量究竟识别哪一种脉冲响应?

The local projection-instrumental variable (LP-IV) literature has been largely silent on cases in which impulse responses are set-identified, arising when the shock of interest is composite and instruments are correlated with multiple components. We demonstrate that LP-IV estimands constructed using one instrument at a time identify affine combinations of impulse responses to structural shock components with instrument-specific and potentially negative weights, challenging…

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On the falsification of instrumental variable models for heterogeneous treatment effects

异质性处理效应工具变量模型的可证伪性

In this paper I derive a set of testable implications for econometric models defined by three assumptions: (i) the existence of strictly exogenous discrete instruments, (ii) restrictions on how the instruments affect adoption of a finite number of treatment types (such as monotonicity), and (iii) the assumption that the instruments only affect outcomes through their effect on treatment adoption (i.e. an exclusion restriction). The testable implications aggregate (via…

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Assessing Utility of Differential Privacy for RCTs

评估差分隐私对随机对照试验分析的实用性

Randomized controlled trials (RCTs) have become powerful tools for assessing the impact of interventions and policies in many contexts. They are considered the gold standard for causal inference in the biomedical fields and many social sciences. Researchers have published an increasing number of studies that rely on RCTs for at least part of their inference. These studies typically include the response data that has been collected, de-identified, and sometimes protected…

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Identification in Multiple Treatment Models under Discrete Variation

离散变动下多处理模型的识别

We develop a marginal treatment effect based method to learn about causal effects in multiple treatment models with discrete instruments. We allow selection into treatment to be governed by a general class of threshold crossing models that permit multidimensional unobserved heterogeneity. An inherent complication is that the primitives characterizing the selection model are not generally point-identified. Allowing these primitives to be point-identified up to a…

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Interpolated stochastic interventions based on propensity scores, target policies and treatment-specific costs

基于倾向得分、目标政策与处理成本的插值随机干预

We introduce two families of stochastic interventions with discrete treatments that connect causal modeling to cost-sensitive decision making. The interventions arise from a cost-penalized information projection of the independent product of the organic propensity scores and a reference policy, yielding closed-form Boltzmann-Gibbs couplings. The induced marginals define modified stochastic policies that interpolate smoothly, via a tilt parameter, from the organic law or from…

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Probabilistic Forecasting of Climate Policy Uncertainty: The Role of Macro-financial Variables and Google Search Data

气候政策不确定性的概率预测:宏观金融变量与谷歌搜索数据

Accurately forecasting Climate Policy Uncertainty (CPU) is essential for designing climate strategies that balance economic growth with environmental objectives. Elevated CPU levels can delay regulatory implementation, hinder investment in green technologies, and amplify public resistance to policy reforms, particularly during periods of economic stress. Despite the growing literature documenting the economic relevance of CPU, forecasting its evolution and understanding the…

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Partial Identification under Stratified Randomization

分层随机化下的部分识别与推断

This paper develops a unified framework for partial identification and inference in stratified experiments with attrition, accommodating both equal and heterogeneous treatment shares across strata. For equal-share designs, we apply recent theory for finely stratified experiments to Lee bounds, yielding closed-form, design-consistent variance estimators and properly sized confidence intervals. Simulations show that the conventional formula can overstate uncertainty, while our…

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Nonlinear Dynamic Factor Analysis With a Transformer Network

基于 Transformer 网络的非线性动态因子分析

The paper develops a Transformer architecture for estimating dynamic factors from multivariate time series data under flexible identification assumptions. Performance on small datasets is improved substantially by using a conventional factor model as prior information via a regularization term in the training objective. The results are interpreted with Attention matrices that quantify the relative importance of variables and their lags for the factor estimate. Time variation…

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Revisiting the Identification of the Conduct Parameter in Homogeneous Goods Markets

重新审视同质产品市场中行为参数的识别

We revisit the identification of the conduct parameter in homogeneous goods markets. Lau (1982) argues that the conduct parameter is not identified if and only if the inverse demand function is separable, except for a specific separable function. This result has been regarded as an extension of the result in Bresnahan (1982) to more general settings. However, we show that Lau's claim is incorrect and provide a new characterization of the non-identification. Our…

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Policy Learning under Endogeneity Using Instrumental Variables

利用工具变量在内生性下学习政策规则

I propose a framework for learning individualized policy rules in observational data settings characterized by endogenous treatment selection and the availability of an instrumental variable. I introduce encouragement rules that manipulate the instrument. By incorporating the marginal treatment effect (MTE) as a policy invariant parameter, I establish the identification of the social welfare criterion for the optimal encouragement rule. Focusing on binary encouragement…

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Beyond Validity: SVAR Identification Through the Proxy Zoo

超越有效性:利用多种代理变量识别结构向量自回归

This paper develops a framework for robust identification in SVARs when researchers face a zoo of proxy variables. Instead of imposing exact exogeneity, we introduce generalized ranking restrictions (GRR) that bound the relative correlation of each proxy with the target and non-target shocks through a continuous proxy-quality parameter. Combining GRR with standard sign and narrative restrictions, we characterize identified sets for structural impulse responses and show how…

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Uncovering Sparse Financial Networks with Information Criteria

利用信息准则识别稀疏金融网络

Empirical measures of financial connectedness based on Forecast Error Variance Decompositions (FEVDs) often yield dense network structures that obscure true transmission channels and complicate the identification of systemic risk. This paper proposes a novel information-criterion-based approach to uncover sparse, economically meaningful financial networks. By reformulating FEVD-based connectedness as a regression problem, we develop a model selection framework that…

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Chasing Opportunity: Spillovers and Drivers of U.S. State Population Growth

追逐机会:美国州人口增长的溢出效应与驱动因素

We study the drivers and spatial diffusion of U.S. state population growth using a dynamic spatial model for 49 states, 1965-2017. Methodologically, we recover the spatial network structure from the data, rather than imposing it a priori via contiguity or distance, and combine this with an IV estimator that permits heterogeneous slopes and interactive fixed effects. This unified design delivers consistent estimation and inference in a flexible spatial panel model with…

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Difference-in-Differences with Time-varying Continuous Treatments using Double/Debiased Machine Learning

基于双重/去偏机器学习的时变连续处理双重差分

We propose a difference-in-differences (DiD) framework designed for time-varying continuous treatments across multiple periods. Specifically, we estimate the average treatment effect on the treated (ATET) by comparing distinct non-zero treatment intensities. Identification rests on a conditional parallel trends assumption that accounts for observed covariates and past treatment histories. Our approach allows for lagged treatment effects and, in repeated cross-sectional…

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The drift burst hypothesis

漂移爆发假说

The drift burst hypothesis postulates the existence of short-lived locally explosive trends in the price paths of financial assets. The recent U.S. equity and treasury flash crashes can be viewed as two high-profile manifestations of such dynamics, but we argue that drift bursts of varying magnitude are an expected and regular occurrence in financial markets that can arise through established mechanisms of liquidity provision. We show how to build drift bursts into the…

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Lee Bounds for Random Objects

随机对象的 Lee 界

In applied research, Lee (2009) bounds are widely applied to bound the average treatment effect in the presence of selection bias. This paper extends the methodology of Lee bounds to accommodate outcomes in a general metric space, such as compositional and distributional data. By exploiting a representation of the Fréchet mean of the potential outcome via embedding in an Euclidean or Hilbert space, we present a feasible characterization of the identified set of the causal…

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