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The identification power of smoothness assumptions in models with counterfactual outcomes

反事实结果模型中平滑性假设的识别能力

In this paper, we investigate what can be learned about average counterfactual outcomes as well as average treatment effects when it is assumed that treatment response functions are smooth. We obtain a set of new partial identification results for both the average treatment response and the average treatment effect. In particular, we find that the monotone treatment response and monotone treatment selection bound of Manski and Pepper, 2000 can be further tightened if we…

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Information structure and statistical information in discrete response models

离散响应模型中的信息结构与统计信息

Strategic interaction parameters characterize the impact of actions of one economic agent on the payoff of another economic agent, and are of great interest in both theoretical and empirical work. In this paper, by considering econometric models involving simultaneous discrete systems of equations, we study how the information available to economic agents regarding other economic agents can influence whether or not these strategic information parameters can be inferred from…

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On two-stage estimation of structural instrumental variable models

结构工具变量模型的两阶段估计

Two-stage least squares estimation is popular for structural equation models with unmeasured confounders. In such models, both the outcome and the exposure are assumed to follow linear models conditional on the measured confounders and instrumental variable, which is related to the outcome only via its relation with the exposure. We consider data where both the outcome and the exposure may be incompletely observed, with particular attention to the case where both are…

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Doubly robust nonparametric inference on the average treatment effect

平均处理效应的双重稳健非参数推断

Summary Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average…

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A $C_p$ criterion for semiparametric causal inference

半参数因果推断中的 Cp 模型选择准则

Summary For marginal structural models, which play an important role in causal inference, we consider a model selection problem within a semiparametric framework using inverse-probability-weighted estimation or doubly robust estimation. In this framework, the modelling target is a potential outcome that may be missing, so there is no classical information criterion. We define a mean squared error for treating the potential outcome and derive an asymptotic unbiased estimator…

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Extended conditional independence and applications in causal inference

扩展条件独立及其在因果推断中的应用

The goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence. We show that under appropriate assumptions the calculus that applies for the two cases separately (axioms of a separoid) still applies for the extended case. These results provide a rigorous basis for a wide range of statistical concepts, including ancillarity and sufficiency, and,…

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Targeted sequential design for targeted learning inference of the optimal treatment rule and its mean reward

最优治疗规则及其平均回报推断的靶向序贯设计

, assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adaptive statistical parameter is worthy of interest on its own. Our main result is a central limit theorem which enables the…

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Volatile Top Income Shares in Switzerland? Reassessing the Evolution between 1981 and 2010

瑞士顶端收入份额波动吗?重新评估1981—2010年的演变

In the past twenty years, the share of top incomes in Switzerland has risen, while exhibiting large variations. Switzerland is similar to European countries for the top 1% but closer to the United States for higher top income groups. With the synthetic control method, we close a time gap in the tax data, exploiting the fact that Swiss cantons changed their tax system at different points in time. Using social security data, which cover all top labor incomes, we document the…

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Direct and Indirect Treatment Effects–Causal Chains and Mediation Analysis with Instrumental Variables

直接与间接处理效应:工具变量下的因果链与中介分析

Summary The paper discusses the non-parametric identification of causal direct and indirect effects of a binary treatment based on instrumental variables. We identify the indirect effect, which operates through a mediator (i.e. intermediate variable) that is situated on the causal path between the treatment and the outcome, as well as the unmediated direct effect of the treatment by using distinct instruments for the endogenous treatment and the endogenous mediator. We…

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Rank-Based Procedures in Factorial Designs: Hypotheses About Non-Parametric Treatment Effects

因子设计中的秩方法:关于非参数处理效应的假设检验

Summary Existing tests for factorial designs in the non-parametric case are based on hypotheses formulated in terms of distribution functions. Typical null hypotheses, however, are formulated in terms of some parameters or effect measures, particularly in heteroscedastic settings. Here this idea is extended to non-parametric models by introducing a novel non-parametric analysis-of-variance type of statistic based on ranks or pseudoranks which is suitable for testing…

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Concordance-Assisted Learning for Estimating Optimal Individualized Treatment Regimes

用于估计最优个体化治疗规则的一致性辅助学习

Summary We propose new concordance-assisted learning for estimating optimal individualized treatment regimes. We first introduce a type of concordance function for prescribing treatment and propose a robust rank regression method for estimating the concordance function. We then find treatment regimes, up to a threshold, to maximize the concordance function, named the prescriptive index. Finally, within the class of treatment regimes that maximize the concordance function, we…

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Robust Estimation of Encouragement Design Intervention Effects Transported Across Sites

跨站点迁移鼓励设计干预效应的稳健估计

Summary We develop robust targeted maximum likelihood estimators (TMLEs) for transporting intervention effects from one population to another. Specifically, we develop TMLEs for three transported estimands: the intent-to-treat average treatment effect (ATE) and complier ATE, which are relevant for encouragement design interventions and instrumental variable analyses, and the ATE of the exposure on the outcome, which is applicable to any randomized or observational study. We…

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Regression discontinuity with categorical outcomes

分类结果变量的回归不连续设计

We consider the regression discontinuity (RD) design with categorical outcomes, and exploit the possibility of adapting well-developed microeconometric models to the RD setting. The channels through which the forcing variable affects the potential outcome distributions are constrained to be minimal, to preserve the nonparametric feature of the RD design. Focusing on general categorical outcomes (nominal or ordinal), we develop a new RD estimator based on a nonparametric…

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The triangular model with random coefficients

随机系数三角模型

The triangular model is a very popular way to allow for causal inference in the presence of endogeneity. In this model, an outcome is determined by an endogenous regressor, which in turn is first caused by an instrument. We study the triangular model with random coefficients and additional exogenous regressors in both equations, and establish non-identification of the joint distribution of random coefficients. This implies that counterfactual outcomes are not identified…

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Doubly robust uniform confidence band for the conditional average treatment effect function

条件平均处理效应函数的双重稳健一致置信带

Summary In this paper, we propose a doubly robust method to estimate the heterogeneity of the average treatment effect with respect to observed covariates of interest. We consider a situation where a large number of covariates are needed for identifying the average treatment effect but the covariates of interest for analyzing heterogeneity are of much lower dimension. Our proposed estimator is doubly robust and avoids the curse of dimensionality. We propose a uniform…

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Estimating the economic costs of organized crime by synthetic control methods

用合成控制法估计有组织犯罪的经济成本

Summary The economic costs of organized crime have been estimated for the case of southern Italy by Pinotti ( Economic Journal 2015; 125 , F203–F232, 2015): using synthetic control methods, he finds that, due to the advent of the Italian Mafia in the regions Apulia and Basilicata, GDP per capita dropped by 16%. Replicating this study in a narrow sense by estimating the same model with the same data, but using different software implementations, we observe minor differences…

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Unobserved selection heterogeneity and the gender wage gap

未观测的选择异质性与性别工资差距

Summary Selection correction methods usually make assumptions about selection itself. In the case of gender wage gap estimation, those assumptions are especially tenuous because of high female nonparticipation and because selection could be different in different parts of the labor market. This paper proposes an estimator for the wage gap that allows for arbitrary and unobserved heterogeneity in selection. It applies to the subpopulation of “always employed” women, which is…

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Dynamic skill accumulation, education policies, and the return to schooling

动态技能积累、教育政策与 schooling 回报

Using a dynamic skill accumulation model of schooling and labor supply with learning-by-doing, we decompose early life-cycle wage growth of U.S. white males into four main sources: education, hours worked, cognitive skills (Armed Forces Qualification Tests scores), and unobserved heterogeneity, and evaluate the effect of compulsory high school graduation and a reduction in the cost of college. About 60 percent of the differences in slopes of early life-cycle wage profiles…

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Quantifying an Adherence Path-Specific Effect of Antiretroviral Therapy in the Nigeria PEPFAR Program

尼日利亚 PEPFAR 项目中抗逆转录病毒治疗经依从性传导的路径特定效应

Since the early 2000s, evidence has accumulated for a significant differential effect of first-line antiretroviral therapy (ART) regimens on human immunodeficiency virus (HIV) viral load suppression. This finding was replicated in our data from the Harvard President's Emergency Plan for AIDS Relief (PEPFAR) program in Nigeria. Investigators were interested in finding the source of these differences, i.e., understanding the mechanisms through which one regimen outperforms…

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General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference

有限总体中心极限定理的一般形式及其因果推断应用

Frequentists’ inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point estimators, which, in many but not all cases, are related to asymptotic Normal distributions ensured by central limit theorems. Although previous literature has established various forms of central limit theorems for statistical inference in…

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Bootstrap Inference of Matching Estimators for Average Treatment Effects

平均处理效应匹配估计量的自助法推断

It is known that the naive bootstrap is not asymptotically valid for a matching estimator of the average treatment effect with a fixed number of matches. In this article, we propose asymptotically valid inference methods for matching estimators based on the weighted bootstrap. The key is to construct bootstrap counterparts by resampling based on certain linear forms of the estimators. Our weighted bootstrap is applicable for the matching estimators of both the average…

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Information-regret compromise in covariate-adaptive treatment allocation

协变量自适应治疗分配中的信息与遗憾权衡

Covariate-adaptive treatment allocation is considered in the situation when a compromise must be made between information (about the dependency of the probability of success of each treatment upon influential covariates) and cost (in terms of number of subjects receiving the poorest treatment). Information is measured through a design criterion for parameter estimation, the cost is additive and is related to the success probabilities. Within the framework of approximate…

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Identification of peer effects through social networks using variance restrictions

利用方差限制识别社会网络中的同伴效应

This paper presents a novel method to identify peer effects through exploiting fluctuations in the variances and covariances of outcomes over a social network. Endogenous and contextual peer effects can be disentangled by contrasting the covariances of the outcomes of peers with the covariances of the outcomes of peers of peers. Correlated effects are incorporated by allowing for unrestricted network level heterogeneity. The method is applied to the Project STAR data to…

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Modeling heaped duration data: An application to neonatal mortality

堆积报告的持续时间数据建模:新生儿死亡率应用

In 2005, the Indian Government launched a conditional cash-incentive program to encourage institutional delivery. This paper studies the effects of the program on neonatal mortality using district-level household survey data. We model mortality using survival analysis, paying special attention to substantial heaping, a form of measurement error, present in the data. The main objective of this paper is to provide a set of sufficient conditions for identification and…

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