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Estimating and improving dynamic treatment regimes with a time-varying instrumental variable

利用时变工具变量估计与改进动态治疗方案

Abstract Estimating dynamic treatment regimes (DTRs) from retrospective observational data is challenging as some degree of unmeasured confounding is often expected. In this work, we develop a framework of estimating properly defined ‘optimal’ DTRs with a time-varying instrumental variable (IV) when unmeasured covariates confound the treatment and outcome, rendering the potential outcome distributions only partially identified. We derive a novel Bellman equation under…

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Causal inference on distribution functions

以分布函数为结果的因果推断

Abstract Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space Rp. However, it is increasingly common that complex datasets are best summarized as data points in nonlinear spaces. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in…

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Estimating the efficiency gain of covariate-adjusted analyses in future clinical trials using external data

利用外部数据估计未来临床试验中协变量调整的效率增益

Abstract We present a framework for using existing external data to identify and estimate the relative efficiency of a covariate-adjusted estimator compared to an unadjusted estimator in a future randomized trial. Under conditions, these relative efficiencies approximate the ratio of sample sizes needed to achieve a desired power. We develop semiparametrically efficient estimators of the relative efficiencies for several treatment effect estimands of interest with either…

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Estimating heterogeneous treatment effects with right-censored data via causal survival forests

利用因果生存森林估计右删失数据中的异质性处理效应

Abstract Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in survival and observational setting where outcomes may be right-censored. Our approach relies on orthogonal estimating equations to robustly adjust for both censoring and selection effects under unconfoundedness. In our experiments,…

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Common Ownership, Competition, and Top Management Incentives

共同所有权、竞争与高管激励

We present a mechanism based on managerial incentives through which common ownership affects product market outcomes. Firm-level variation in common ownership causes variation in managerial incentives and productivity across firms, which leads to intraindustry and intrafirm cross-market variation in prices, output, markups, and market shares that is consistent with empirical evidence. The organizational structure of multiproduct firms and the passivity of common owners…

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Rejective Sampling, Rerandomization, and Regression Adjustment in Survey Experiments

调查实验中的拒绝式抽样、再随机化与回归调整

Classical randomized experiments, equipped with randomization-based inference, provide assumption-free inference for treatment effects. They have been the gold standard for drawing causal inference and provide excellent internal validity. However, they have also been criticized for questionable external validity, in the sense that the conclusion may not generalize well to a larger population. The randomized survey experiment is a design tool that can help mitigate this…

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Identification, Semiparametric Efficiency, and Quadruply Robust Estimation in Mediation Analysis with Treatment-Induced Confounding

存在处理诱导混杂的中介分析:识别、半参数效率与四重稳健估计

Natural mediation effects are often of interest when the goal is to understand a causal mechanism. However, most existing methods and their identification assumptions preclude treatment-induced confounders often present in practice. To address this fundamental limitation, we provide a set of assumptions that identify the natural direct effect in the presence of treatment-induced confounders. Even when some of those assumptions are violated, the estimand still has an…

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Rerandomization in Stratified Randomized Experiments

分层随机实验中的再随机化

Stratification and rerandomization are two well-known methods used in randomized experiments for balancing the baseline covariates. Renowned scholars in experimental design have recommended combining these two methods; however, limited studies have addressed the statistical properties of this combination. This article proposes two rerandomization methods to be used in stratified randomized experiments, based on the overall and stratum-specific Mahalanobis distances. The…

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Assumption-Lean Analysis of Cluster Randomized Trials in Infectious Diseases for Intent-to-Treat Effects and Network Effects

传染病簇随机试验中意向治疗效应与网络效应的弱假设分析

Cluster randomized trials (CRTs) are a popular design to study the effect of interventions in infectious disease settings. However, standard analysis of CRTs primarily relies on strong parametric methods, usually mixed-effect models to account for the clustering structure, and focuses on the overall intent-to-treat (ITT) effect to evaluate effectiveness. The article presents two assumption-lean methods to analyze two types of effects in CRTs, ITT effects and network effects…

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Model-Robust Inference for Clinical Trials that Improve Precision by Stratified Randomization and Covariate Adjustment

结合分层随机化与协变量调整的临床试验模型稳健推断

Two commonly used methods for improving precision and power in clinical trials are stratified randomization and covariate adjustment. However, many trials do not fully capitalize on the combined precision gains from these two methods, which can lead to wasted resources in terms of sample size and trial duration. We derive consistency and asymptotic normality of model-robust estimators that combine these two methods, and show that these estimators can lead to substantial…

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Matching One Sample According to Two Criteria in Observational Studies

观察性研究中兼顾两类准则的样本匹配

Multivariate matching has two goals: (i) to construct treated and control groups that have similar distributions of observed covariates, and (ii) to produce matched pairs or sets that are homogeneous in a few key covariates. When there are only a few binary covariates, both goals may be achieved by matching exactly for these few covariates. Commonly, however, there are many covariates, so goals (i) and (ii) come apart, and must be achieved by different means. As is also true…

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Noncompliance and Instrumental Variables for 2 K Factorial Experiments

多因素析因实验中的不依从与工具变量

Factorial experiments are widely used to assess the marginal, joint, and interactive effects of multiple concurrent factors. While a robust literature covers the design and analysis of these experiments, there is less work on how to handle treatment noncompliance in this setting. To fill this gap, we introduce a new methodology that uses the potential outcomes framework for analyzing 2K factorial experiments with noncompliance on any number of factors. This framework builds…

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Nonparametric Causal Effects Based on Longitudinal Modified Treatment Policies

基于纵向修正处理政策的非参数因果效应

Most causal inference methods consider counterfactual variables under interventions that set the exposure to a fixed value. With continuous or multi-valued treatments or exposures, such counterfactuals may be of little practical interest because no feasible intervention can be implemented that would bring them about. Longitudinal modified treatment policies (LMTPs) are a recently developed nonparametric alternative that yield effects of immediate practical relevance with an…

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Estimating Density Ratio of Marginals to Joint: Applications to Causal Inference

边际密度乘积与联合密度之比的估计:因果推断应用

In various fields of data science, researchers often face problems of estimating the ratios of two probability densities.Particularly in the context of causal inference, the product of marginals for a treatment variable and covariates to their joint density ratio typically emerges in the process of constructing causal effect estimators.This article applies the general least square density ratio estimation methodology by Kanamori, Hido and Sugiyama to the product of marginals…

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Multi-Threshold Structural Equation Model

多阈值结构方程模型

In this article, we consider the instrumental variable estimation for causal regression parameters with multiple unknown structural changes across subpopulations. We propose a multiple change point detection method to determine the number of thresholds and estimate the threshold locations in the two-stage least square procedure. After identifying the estimated threshold locations, we use the Wald method to estimate the parameters of interest, that is, the regression…

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Twisting the demand curve: Digitalization and the older workforce

扭转需求曲线:数字化与年长劳动力

Software represents a major and fast-growing share of firms’ capital investment, impacting demand for labor and what workers do on their jobs. Using U.S. Census Bureau panel data that link firms and workers, this paper estimates the effect of firm software capital on the earnings of workers by age group. We extend the AKM framework to include job-spell fixed effects that account for potential correlation between the worker–firm match and employee age, as well as including…

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Estimation of spillover effects with matched data or longitudinal network data

利用匹配数据或纵向网络数据估计溢出效应

Social interactions often play a key role in determining the impact of policies, but measuring the magnitude of spillover effects empirically is notoriously challenging because, in most applications, a person’s relationships are likely to reflect her own characteristics (homophily), and people who are connected are likely to be affected by the same shocks (common factors). In addition, a significant share of social interactions is likely to occur through variables that are…

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Testing identifying assumptions in bivariate probit models

双变量 probit 模型识别假设的检验

Summary This paper considers the bivariate probit model's identifying assumptions: linear index specification, joint normality of errors, instrument exogeneity, and relevance. First, we develop sharp testable equalities that detect all possible observable violations of the assumptions. Second, we propose an easy‐to‐implement testing procedure for the model's validity using existing inference methods for intersection bounds. The test achieves correct empirical size and…

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Testing random assignment to peer groups

同伴群体随机分配的检验

Summary Identification of peer effects is complicated by the fact that the individuals under study may select their peers. Random assignment to peer groups has proven useful to sidestep such a concern. In the absence of a formal randomization mechanism, it needs to be argued that assignment is “as good as” random. This paper introduces a simple yet powerful test to do so. We provide theoretical results for this test. As a by‐product, we equally obtain such results for an…

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Inference in difference‐in‐differences: How much should we trust in independent clusters?

双重差分推断:独立聚类假设有多可信?

Summary We analyze the challenges for inference in difference‐in‐differences (DID) when there is spatial correlation. We present novel theoretical insights and empirical evidence on the settings in which ignoring spatial correlation should lead to more or less distortions in DID applications. We show that details, such as the time frame used in the estimation, the choice of the treated and control groups, and the choice of the estimator, are key determinants of distortions…

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The employment effects of the minimum wage: A selection ratio approach to measuring treatment effects

最低工资的就业效应:基于选择比率的处理效应测量

Summary I develop a method for measuring a binary treatment's effects when more than one control group is available but each control group is imperfect. To study effects of the minimum wage, for example, I compare border counties where the minimum wage increases to the set of neighboring counties, the set of neighbor‐of‐neighboring counties, and so forth. The key innovation is to model the ratio of the biases present in these comparisons. Crucially, the model contains a…

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Tax Policy and Lumpy Investment Behaviour: Evidence from China’s VAT Reform

税收政策与企业非连续大额投资:中国增值税改革的证据

Abstract We incorporate the lumpy nature of firm-level investment into the study of how tax policy affects investment behaviour. We show that tax policies can directly impact the lumpiness of investment. Extensive-margin responses to tax policy are key to understanding the effects of different tax reforms and to designing effective stimulus policies. We illustrate these results by studying China’s 2009 VAT reform, which lowered the tax cost of investment and reduced partial…

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Large dimensional latent factor modeling with missing observations and applications to causal inference

含缺失观测的高维潜在因子模型及其因果推断应用

This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal component analysis to an adjusted covariance matrix estimated from partially observed panel data. We derive the asymptotic distribution for the estimated factors, loadings and the imputed values under an approximate factor model and general…

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Treatment effects in interactive fixed effects models with a small number of time periods

少量时间期数下交互固定效应模型的处理效应

This paper considers identifying and estimating the Average Treatment Effect on the Treated (ATT) when untreated potential outcomes are generated by an interactive fixed effects model. That is, in addition to time-period and individual fixed effects, we consider the case where there is an unobserved time invariant variable whose effect on untreated potential outcomes may change over time and which can therefore cause outcomes (in the absence of participating in the…

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