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Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem

含社会互动的内生处理模型:运动对自尊影响的应用

We address the estimation of endogenous treatment models with social interactions in both the treatment and outcome equations. We model the interactions between individuals via a game theoretic approach based on discrete Bayesian games. We employ a nested pseudo joint likelihood algorithm when obtaining the model’s parameters and provide relevant treatment effects and procedures for their estimation. Our empirical application examines the impact of an individual’s exercise…

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The informativeness of combined experimental and observational data under dynamic selection

动态选择下实验与观察数据结合的信息价值

The Average Treatment Effect on the Treated Survivors (ATETS; Vikström et al., 2018) captures a composite effect of time-varying treatment and dynamic selection into the survivor population. We address the problem of identifying this treatment-effect parameter in the absence of long-term experimental data, utilizing available long-term observational data instead. This poses a nontrivial challenge in practice, as dynamic selection compounds static selection in observational…

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Regularizing fairness in optimal policy learning with distributional targets

分布目标下最优政策学习的公平性正则化

A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an “optimal” predicted outcome distribution according to some target functional. Nevertheless, a fairness-aware decision maker may not be satisfied achieving said optimality at the cost of being “unfair” against a subgroup of the population, in the sense that the outcome distribution in that subgroup…

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Minimax rates of convergence for nonparametric location-Scale models

非参数位置—尺度模型的极小极大收敛速率

This paper studies minimax rates of convergence for nonparametric location-scale models, which include mean, quantile, expectile and momentile regression settings. Under Hellinger differentiability on the error distribution and other mild conditions, we show that the minimax rate of convergence for estimating the regression function under the squared L2 loss is determined by the metric entropy of the nonparametric function class. Different error distributions, including…

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Unveiling Plant‐Product Productivity via First‐Order Conditions: Robust Replication of Orr (2022)

通过一阶条件揭示工厂—产品生产率:对 Orr(2022)的稳健复现

ABSTRACT We assess the replicability of Orr's (2022) method for estimating within‐plant productivity across product lines, which combines demand estimation with cost minimization. The original study uses input price shocks in other output markets as instrumental variables, with exclusion restrictions based on downstream purchase shares. Reconstructing the original dataset of Indian machinery producers from 2000–2007, we reproduce the main productivity patterns and…

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The PCDID Approach to Treatment Effects Estimation: A Further Investigation

处理效应估计的 PCDID 方法:进一步考察

ABSTRACT In the present paper, we study the so‐called “PCDID” approach to treatment effects estimation in panels with interactive effects where the factors represent trends whose effect need not be parallel across the cross‐sectional units. Our interest in this step‐wise approach originates with the observation that the interactive effects are ignored in the first step, which should not be possible without affecting subsequent steps. We confirm that the estimated second‐step…

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Decision Theory for Treatment Choice Problems with Partial Identification

部分识别下处理选择问题的决策理论

Abstract We apply classical statistical decision theory to a large class of treatment choice problems with partial identification. We show that, in a general class of problems with Gaussian likelihood, all decision rules are admissible; it is maximin-welfare optimal to ignore all data; and, for severe enough partial identification, there are infinitely many minimax-regret optimal decision rules, all of which sometimes randomize the policy recommendation. We uniquely…

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Perturbation Analysis of Randomized SVD and its Applications to Statistics

随机化奇异值分解的扰动分析及统计应用

Randomized singular value decomposition (RSVD) is a class of computationally efficient algorithms for computing the truncated SVD of large data matrices. Given an m×n matrix M̂, the prototypical RSVD algorithm outputs an approximation of the k leading left singular vectors of M̂ by computing the SVD of M̂(M̂⊤M̂)gG; here g≥1 is an integer and G∈Rn×k˜ is a random Gaussian sketching matrix with k˜≥k. In this paper we derive upper bounds for the l2 and l2,∞ distances between the…

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Scalable Estimation of Multinomial Response Models with Random Consideration Sets

随机考虑集多项响应模型的可扩展估计

A common assumption in the fitting of unordered multinomial response models for $J$ mutually exclusive categories is that the responses arise from the same set of $J$ categories across subjects. However, when responses measure a choice made by the subject, it is more appropriate to condition the distribution of multinomial responses on a subject-specific consideration set, drawn from the power set of $\{1,2,\ldots,J\}$. This leads to a mixture of multinomial response models…

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A Conditional Ordinal Stereotype Model to Estimate Police Officers’ Propensity to Escalate Force

估计警员武力升级倾向的条件有序刻板模型

This article introduces a conditional ordinal stereotype model for estimating a police officer’s latent propensity to escalate to higher-severity force options during an encounter. Propensity to escalate is the likelihood of selecting a more serious force category than peer officers confronting the same circumstances, not necessarily implying that such force is excessive or contrary to policy. The associated conditional likelihood depends solely on data from the times and…

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An average-case sensitivity analysis for unmeasured confounding

未观测混杂的平均强度敏感性分析

Summary Sensitivity analysis for the unconfoundedness assumption is crucial in observational studies. For this purpose, the marginal sensitivity model has gained popularity in recent years owing to its good interpretability and mathematical properties. However, most existing models only consider a worst-case parameter that bounds the logit difference between the observed-data and full-data propensity scores, which may not fully capture the extent of unmeasured confounding.…

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Nonparametric efficient estimation of marginal structural models with continuous time-varying treatments

连续时变处理下边际结构模型的非参数有效估计

Summary Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable nonparametric estimator exists for marginal structural models with multi-valued or continuous time-varying treatments. In this paper, we combine flexible, data-adaptive regression methods, including ensemble learning techniques, with recent developments in semiparametric efficiency theory for longitudinal…

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Dynamic clustering for heterophilic stochastic block models with time-varying node memberships

节点归属随时间变化的异配随机块模型动态聚类

Summary We consider a time-ordered sequence of networks stemming from stochastic block models in which nodes gradually change their membership over time, and no network at any single time-point contains sufficient signal strength to recover its community structure. To estimate the time-varying community structure, we develop the kernel-debiased sum of squares method that performs spectral clustering after a debiased sum-of-squared aggregation of adjacency matrices. Our…

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Comparing causal parameters with many treatments and positivity violations

多处理与正值性违背下的因果参数比较

Summary Comparing outcomes across treatments is essential in medicine and public policy. To do so, researchers typically estimate a set of parameters, possibly counterfactual, each targeting adifferent treatment. Treatment-specific means are commonly used, but their identification requires a positivity assumption: every subject has a nonzero probability of receiving each treatment. This assumption is often implausible, especially when treatment can take many values. Causal…

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Dynamic covariate balancing: estimating treatment effects over time with potential local projections

动态协变量平衡:利用潜在结果局部投影估计跨期处理效应

Abstract This article concerns the estimation and inference of treatment effects in panel data settings when treatments change dynamically over time. We propose a balancing method that allows for (i) treatments to be assigned dynamically over time based on high-dimensional covariates, past outcomes and treatments; (ii) outcomes and time-varying covariates to depend on the trajectory of all past treatments; and (iii) heterogeneity of treatment effects. Our approach…

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Design-based causal inference for incomplete block designs

不完全区组设计的设计型因果推断

Summary Researchers often turn to block randomization to increase the precision of their inference or for practical reasons, such as in multi-site trials. However, if the number of treatments under consideration is large, it may not be feasible or practical to assign all treatments within each block. We develop novel inference results under the finite-population, design-based framework for natural alternatives to the complete block design that do not require reducing the…

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Parameterizing the effect of a continuous treatment using average derivative effects

用平均导数效应参数化连续处理的影响

Summary The average treatment effect is commonly used to quantify the main effect of a binary treatment on an outcome. Extensions to continuous treatments are usually based on the dose-response curve or shift interventions, but both require strong overlap conditions, and the resulting curves may be difficult to summarize. This article focuses instead on average derivative effects, which are scalar estimands related to infinitesimal shift interventions requiring only local…

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Randomization-based confidence sets for the local average treatment effect

局部平均处理效应的随机化置信集合

Summary We consider the problem of generating confidence sets in randomized experiments with noncompliance. We show that a refinement of a randomization-based procedure proposed by Imbens & Rosenbaum (2005) has desirable properties. Specifically, we show that using a studentized Anderson–Rubin statistic as a test statistic yields confidence sets that are finite-sample exact under treatment effect homogeneity and remain asymptotically valid for the local average treatment…

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Treatment choice with nonlinear regret

非线性遗憾下的处理选择

Summary Following Savage (1951)and Manski (2004), the literature on statistical treatment choice focuses on the mean of welfare regret. Ignoring other features of the regret distribution, however, can lead to a rule that is sensitive to sampling uncertainty. We propose to minimize the mean of a nonlinear transformation of regret and show that singleton rules are not essentially complete for nonlinear regret. Focusing on mean-square regret, we derive closed-form fractions for…

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Assumption-lean post-integrated inference with surrogate-control outcomes

利用代理控制结局的数据整合后推断

Summary Data integration methods aim to extract low-dimensional embeddings from high-dimensional outcomes to remove unwanted variation, such as batch effects and unmeasured covariates, across heterogeneous datasets. However, multiple hypothesis testing after integration can be biased due to data-dependent processes. We introduce a robust post-integrated inference method that accounts for latent heterogeneity by leveraging control outcomes. Using causal interpretations, we…

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Testing for latent structure via the Wilcoxon–Wigner random matrix of normalized rank statistics

基于标准化秩统计量的 Wilcoxon–Wigner 矩阵潜在结构检验

Summary This paper considers the problem of testing for latent structure in large symmetric data matrices. The goal is to develop statistically principled methodology that is flexible in its applicability, computationally efficient and insensitive to extreme data variation, thereby overcoming limitations of existing approaches. To this end, we introduce and systematically study certain symmetric matrices, called Wilcoxon–Wigner random matrices, whose entries are normalized…

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Calibrated sensitivity models

校准敏感性模型

Summary In causal inference, sensitivity models are used to assess how unmeasured confounders could alter causal analyses, but the sensitivity parameter (which quantifies the degree of unmeasured confounding) is often difficult to interpret. For this reason, researchers sometimes compare the sensitivity parameter to an estimate of measured confounding, a process known as calibration or benchmarking. However, calibrated estimates are not always interpreted correctly, and…

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On the consistency of bootstrap for matching estimators

匹配估计量的自助法一致性

Summary In a landmark paper, Abadie & Imbens (2008)showed that the naive bootstrap is inconsistent when applied to nearest neighbour matching estimators of the average treatment effect with a fixed number of matches. Since then, this finding has inspired numerous efforts to address the inconsistency issue, typically by employing alternative bootstrap methods. In contrast, in this work we show that the naive bootstrap is provably consistent for the original matching…

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Bounds on causal effects in $ 2^{K} $ factorial experiments with noncompliance

存在不依从时二水平多因素实验的因果效应界

Summary Factorial experiments are ubiquitous in the social and biomedical sciences, but when units fail to comply with each assigned factor, identification and estimation of the average treatment effects become impossible without strong assumptions. Leveraging an instrumental variables approach, previous studies have shown how to define and estimate the causal effect of treatment uptake among respondents who comply with treatment. A major caveat is that these results rely on…

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