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Identification and Estimation of Causal Effects in High-Frequency Event Studies

高频事件研究中因果效应的识别与估计

We provide precise conditions for nonparametric identification of causal effects by high-frequency event study regressions, which have been used widely in the recent macroeconomics, financial economics and political economy literatures. The high-frequency event study method regresses changes in an outcome variable on a measure of unexpected changes in a policy variable in a narrow time window around an event or a policy announcement (e.g., a 30-minute window around an FOMC…

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Nonparametric "rich covariates" without saturation

无需饱和设定的非参数“丰富协变量”方法

We consider two nonparametric approaches to ensure that linear instrumental variables estimators satisfy the rich-covariates condition emphasized by Blandhol et al. (2025), even when the instrument is not unconditionally randomly assigned and the model is not saturated. Both approaches start with a nonparametric estimate of the expectation of the instrument conditional on the covariates, and ensure that the rich-covariates condition is satisfied either by using as the…

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Doubly robust estimation of optimal treatment regimes for survival data using an instrumental variable

利用工具变量双重稳健估计生存数据的最优治疗规则

In survival contexts, substantial literature exists on estimating optimal treatment regimes, where treatments are assigned based on personal characteristics to maximize the survival probability. These methods assume that a set of covariates is sufficient to deconfound the treatment-outcome relationship. However, this assumption can be limited in observational studies or randomized trials in which non-adherence occurs. Therefore, we propose a novel approach to estimating…

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Bayesian causal discovery: Posterior concentration and optimal detection

贝叶斯因果发现:后验集中与最优检测

We consider the problem of Bayesian causal discovery for the standard model of linear structural equations with equivariant Gaussian noise. A uniform prior is placed on the space of directed acyclic graphs (DAGs) over a fixed set of variables and, given the graph, independent Gaussian priors are placed on the associated linear coefficients of pairwise interactions. We show that the rate at which the posterior on model space concentrates on the true underlying DAG depends…

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Identifying Conditional Causal Effects in MPDAGs

最大定向部分有向无环图中的条件因果效应识别

We consider identifying a conditional causal effect when a graph is known up to a maximally oriented partially directed acyclic graph (MPDAG). An MPDAG represents an equivalence class of graphs that is restricted by background knowledge and where all variables in the causal model are observed. We provide three results that address identification in this setting: an identification formula when the conditioning set is unaffected by treatment, a generalization of the well-known…

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Bayesian implementation of Targeted Maximum Likelihood Estimation for uncertainty quantification in causal effect estimation

用于因果效应不确定性量化的贝叶斯目标极大似然估计

Robust decision making involves making decisions in the presence of uncertainty and is often used in critical domains such as healthcare, supply chains, and finance. Causality plays a crucial role in decision-making as it predicts the change in an outcome (usually a key performance indicator) due to a treatment (also called an intervention). To facilitate robust decision making using causality, this paper proposes three Bayesian approaches of the popular Targeted Maximum…

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The Win Ratio at the Design Stage of Clinical Trials

临床试验设计阶段的胜率比

The win ratio offers a flexible approach to incorporate the hierarchy of clinical outcomes into the analysis of a composite endpoint, enabling simultaneous consideration of multiple outcome types, unlike traditional time-to-first-event (TTFE) analysis or focus on a single outcome. We examined the statistical power of the win ratio compared to single-endpoint analyses and TTFE analysis through a case study and simulation studies. Furthermore, we provide a novel formula to…

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Detecting and Understanding the Difference between Natural Mediation Effects and Their Randomized Interventional Analogues

自然中介效应与随机干预类比量差异的检测与理解

In causal mediation analysis, the natural direct and indirect effects (natural effects) are nonparametrically unidentifiable in the presence of treatment-induced confounding, which motivated the development of randomized interventional analogues (RIAs) of the natural effects. Being easier to identify, the RIAs are becoming widely used in practice. However, applied researchers often interpret RIA estimates as if they were the natural effects, even though the RIAs can be poor…

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Causal Mediation Analysis for Zero-inflated Mixture Mediators

零膨胀混合中介变量的因果中介分析

Causal mediation analysis is an important statistical tool to quantify effects transmitted by intermediate variables from a cause to an outcome. There is a gap in mediation analysis methods to handle mixture mediator data that are zero-inflated with multi-modality and atypical behaviors. We propose an innovative way to model zero-inflated mixture mediators from the perspective of finite mixture distributions to flexibly capture such mediator data. Multiple data types are…

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Assessing the Impact of Covariate Distribution and Positivity Violation on Weighting-Based Indirect Comparisons: a Simulation Study

协变量分布与正值性违反对加权间接比较的影响:模拟研究

Population-Adjusted Indirect Comparisons (PAICs) are used to estimate treatment effects when direct comparisons are infeasible and individual patient data (IPD) are only available for one trial. Among PAIC methods, Matching-Adjusted Indirect Comparison (MAIC) is the most widely used. However, little is known about how MAIC performs under challenging conditions such as limited covariate overlap or markedly non-normal covariate distributions. We conducted a Monte Carlo…

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Leveraging Covariates in Regression Discontinuity Designs

在回归不连续设计中有效利用协变量

It is common practice to incorporate additional covariates in empirical economics. In the context of Regression Discontinuity (RD) designs, covariate adjustment plays multiple roles, making it essential to understand its impact on analysis and conclusions. Typically implemented via local least squares regressions, covariate adjustment can serve three main distinct purposes: (i) improving the efficiency of RD average causal effect estimators, (ii) learning about heterogeneous…

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Better Understanding Triple Differences Estimators

更好地理解三重差分估计量

Triple Differences (DDD) designs are widely used in empirical work to relax parallel trends assumptions in Difference-in-Differences (DiD) settings. This paper highlights that common DDD implementations -- such as taking the difference between two DiDs or applying three-way fixed effects regressions -- are generally invalid when identification requires conditioning on covariates. In staggered adoption settings, the common DiD practice of pooling all not-yet-treated units as…

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Revisiting Randomization with the Cube Method

用立方体方法重新审视实验随机化

We introduce a new randomization procedure for experiments based on the cube method, which achieves near-exact covariate balance. This ensures compliance with standard balance tests and allows for balancing on many covariates, enabling more precise estimation of treatment effects using pre-experimental information. We derive theoretical bounds on imbalance as functions of sample size and covariate dimension, and establish consistency and asymptotic normality of the resulting…

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A regression-based approach for bidirectional proximal causal inference in the presence of unmeasured confounding

未观测混杂下双向近端因果推断的回归方法

Proxy variables are commonly used in causal inference when unmeasured confounding exists. While most existing proximal methods assume a unidirectional causal relationship between two primary variables, many social and biological systems exhibit complex feedback mechanisms that imply bidirectional causality. In this paper, using regression-based models, we extend the proximal framework to identify bidirectional causal effects in the presence of unmeasured confounding. We…

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Statistical inference of heterogeneous treatment effects using semiparametric single-index model

半参数单指标模型下异质性处理效应的统计推断

In recent years, with the rapid development of science and technology, heterogeneous treatment effects have emerged as a focal research topic in statistics, econometrics, and sociology. This paper investigates HTE through semiparametric single-index models based on doubly robust estimation. Departing from conventional approaches, we neither impose boundedness constraints on the link function in single-index models nor restrict its support range. By employing the sieve method…

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Revisiting the Berkeley Admissions data: Statistical Tests for Causal Hypotheses

重访伯克利录取数据:因果假设的统计检验

Reasoning about fairness through correlation-based notions is rife with pitfalls. The 1973 University of California, Berkeley graduate school admissions case from Bickel et. al. (1975) is a classic example of one such pitfall, namely Simpson's paradox. The discrepancy in admission rates among males and female applicants, in the aggregate data over all departments, vanishes when admission rates per department are examined. We reason about the Berkeley graduate school…

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Formalising causal inference as prediction on a target population

将因果推断形式化为目标总体上的预测

The standard approach to causal modelling especially in social and health sciences is the potential outcomes framework due to Neyman and Rubin. In this framework, observations are thought to be drawn from a distribution over variables of interest, and the goal is to identify parameters of this distribution. Even though the stated goal is often to inform decision making on some target population, there is no straightforward way to include these target populations in the…

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Nonlinear Fore(Back)casting and Innovation Filtering for Causal-Noncausal VAR Models

因果—非因果VAR模型的非线性预测、回溯预测与创新过滤

We show that the mixed causal-noncausal Vector Autoregressive (VAR) processes satisfy the Markov property in both calendar and reverse time. Based on that property, we introduce closed-form formulas of forward and backward predictive densities for point and interval forecasting and backcasting out-of-sample. The backcasting formula is used for adjusting the forecast interval to obtain a desired coverage level when the tail quantiles are difficult to estimate. A confidence…

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Just Trial Once: Ongoing Causal Validation of Machine Learning Models

只试验一次:机器学习模型更新的持续因果验证

Machine learning (ML) models are increasingly used as decision-support tools in high-risk domains. Evaluating the causal impact of deploying such models can be done with a randomized controlled trial (RCT) that randomizes users to ML vs. control groups and assesses the effect on relevant outcomes. However, ML models are inevitably updated over time, and we often lack evidence for the causal impact of these updates. While the causal effect could be repeatedly validated with…

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A general Bayesian approach to design adaptive clinical trials with time-to-event outcomes

事件时间结局自适应临床试验设计的一般贝叶斯方法

Clinical trials are an integral component of medical research. Trials require careful design to, for example, maintain the safety of participants, use resources efficiently and allow clinically meaningful conclusions to be drawn. Adaptive clinical trials (i.e. trials that can be altered based on evidence that has accrued) are often more efficient, informative and ethical than standard or non-adaptive trials because they require fewer participants, target more promising…

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Policy Learning with New Treatments

包含新处理选项的政策学习

I study the problem of a decision maker choosing a policy which allocates treatment to a heterogeneous population on the basis of experimental data that includes only a subset of possible treatment values. The effects of new treatments are partially identified by shape restrictions on treatment response. Policies are compared according to the minimax regret criterion, and I show that the empirical analog of the population decision problem has a tractable linear- and…

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Constructing targeted minimum loss/maximum likelihood estimators: a simple illustration to build intuition

构造目标最小损失/最大似然估计量:建立直觉的简单示例

Use of machine learning to estimate nuisance functions (e.g. outcomes models, propensity score models) in estimators used in causal inference is increasingly common, as it can mitigate bias due to model misspecification. However, it can be challenging to achieve valid inference (e.g., estimate valid confidence intervals). The efficient influence function (EIF) provides a recipe to go from a statistical estimand relevant to our causal question, to an estimator that can…

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Dynamic Causal Effects in a Nonlinear World: the Good, the Bad, and the Ugly

非线性世界中的动态因果效应:稳健解释与识别隐患

Applied macroeconomists frequently use impulse response estimators motivated by linear models. We study whether the estimands of such procedures have a causal interpretation when the true data generating process is in fact nonlinear. We show that vector autoregressions and linear local projections onto observed shocks or proxies identify weighted averages of causal effects regardless of the extent of nonlinearities. By contrast, identification approaches that exploit…

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Interpretational challenges of the Win Ratio in analyzing Hierarchical Composite Endpoints in Chronic Kidney Disease

慢性肾病分层复合终点分析中胜率比的解释难题

Win statistics based methods have gained traction as a method for analyzing Hierarchical Composite Endpoints (HCEs) in randomized clinical trials, particularly in cardiovascular and kidney disease research. HCEs offer several key advantages, including increased statistical power, mitigation of competing risks, and hierarchical ranking of clinical outcomes. While, as summary measures, the win ratio (WR) along with the Net Benefit (NB) and the Win Odds (WO) provide a…

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