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Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models

非随机缺失下的矩阵补全及其在因果面板模型中的应用

This paper develops an inferential framework for matrix completion when missing is not at random and without the requirement of strong signals. Our development is based on the observation that if the number of missing entries is small enough compared to the panel size, then they can be estimated well even when missing is not at random. Taking advantage of this fact, we divide the missing entries into smaller groups and estimate each group via nuclear norm regularization. In…

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On the instrumental variable estimation with many weak and invalid instruments

众多弱工具变量与无效工具变量下的工具变量估计

Abstract We discuss the fundamental issue of identification in linear instrumental variable (IV) models with unknown IV validity. With the assumption of the ‘sparsest rule’, which is equivalent to the plurality rule but becomes operational in computation algorithms, we investigate and prove the advantages of non-convex penalized approaches over other IV estimators based on two-step selections, in terms of selection consistency and accommodation for individually weak IVs.…

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GENIUS-MAWII: for robust Mendelian randomization with many weak invalid instruments

GENIUS-MAWII:应对大量弱且无效工具变量的稳健孟德尔随机化

Abstract Mendelian randomization (MR) addresses causal questions using genetic variants as instrumental variables. We propose a new MR method, G-Estimation under No Interaction with Unmeasured Selection (GENIUS)-MAny Weak Invalid IV, which simultaneously addresses the 2 salient challenges in MR: many weak instruments and widespread horizontal pleiotropy. Similar to MR-GENIUS, we use heteroscedasticity of the exposure to identify the treatment effect. We derive influence…

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Doubly robust calibration of prediction sets under covariate shift

协变量漂移下预测集的双重稳健校准

Abstract Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semi-parametric efficiency theory for more efficient uncertainty quantification. We consider the problem of obtaining well-calibrated prediction regions that can data adaptively account for a shift in the distribution of covariates between training and test data. Under a…

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Fixed Effects and the Generalized Mundlak Estimator

固定效应与广义 Mundlak 估计量

Abstract We develop a new approach for estimating average treatment effects in observational studies with unobserved group-level heterogeneity. We consider a general model with group-level unconfoundedness and provide conditions under which aggregate balancing statistics—group-level averages of functions of treatments and covariates—are sufficient to eliminate differences between groups. Building on these results, we re-interpret commonly used linear fixed-effect regression…

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Graphical tools for selecting conditional instrumental sets

选择条件工具变量集合的图形工具

Summary We consider the efficient estimation of total causal effects in the presence of unmeasured confounding using conditional instrumental sets. Specifically, we consider the two-stage least-squares estimator in the setting of a linear structural equation model with correlated errors that is compatible with a known acyclic directed mixed graph. To set the stage for our results, we characterize the class of linearly valid conditional instrumental sets that yield consistent…

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Estimation of continuous-time linear DSGE models from discrete-time measurements

利用离散时间观测估计连续时间线性 DSGE 模型

We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from discrete-time data. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, hence avoiding discretization errors. We construct the exact likelihood for data sampled either as stocks or flows, based on the Kalman filter, and provide necessary and sufficient conditions for local identification of the frequency-invariant…

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Part‐time subsidies and maternal reemployment: Evidence from a difference‐in‐differences analysis

兼职补贴与母亲再就业:双重差分分析的证据

Summary Employment interruptions of mothers are still one of the main causes for different labour market outcomes between women and men. Employment subsidies can incentivise mothers to shorten employment interruptions after childbirth. We examine a German parental leave reform incentivising an early return to part‐time work. Exploiting the exogenous variation defined by the child's birthday, we apply unconditional difference‐in‐differences (DiD) estimation using…

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Identifying program benefits when participation is misreported

参与情况误报时的项目收益识别

Summary In cases of noncompliance with an assigned treatment, estimates of causal effects typically rely on instrumental variables (IV). However, when participation is also misreported, the IV estimand may become a nonconvex combination of local average treatment effects that fails to satisfy even a minimal condition for being causal. The aim of our paper is to generalize the MR‐LATE approach. This is an alternative IV estimand that is more robust in cases of noncompliance…

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Quantiles of the gain distribution of an early childhood intervention

早期儿童干预收益分布的分位数

Summary We investigate the distribution of gains among participants in the Infant Health and Development Program, an understudied randomized controlled trial that targets infants with low birth weight. Our primary focus is on assessing the effects in cognitive and health outcomes within distinct subgroups, which we define based on the outcomes that would occur in the absence of program participation. We propose a strategy to estimate the distribution of gains from the…

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Instrument-Based Estimation of Full Treatment Effects with Partial Compliers

存在部分服从者时完整处理效应的工具变量估计

Abstract The effect of the full treatment is a primary parameter of interest in policy evaluation, while often the effect of a subset of treatment is estimated. We partially identify the local average treatment effect of receiving full treatment (LAFTE) using an instrumental variable that may induce individuals into subsets of treatment (partial compliers). We show that partial compliers violate the standard exclusion restriction, necessary conditions on the absence of…

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A nonparametric doubly robust test for a continuous treatment effect

连续处理效应的非参数双重稳健检验

The vast majority of literature on evaluating the significance of a treatment effect based on observational data has been confined to discrete treatments. These methods are not applicable to drawing inference for a continuous treatment, which arises in many important applications. To adjust for confounders when evaluating a continuous treatment, existing inference methods often rely on discretizing the treatment or using (possibly misspecified) parametric models for the…

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One-step estimation of differentiable Hilbert-valued parameters

可微 Hilbert 空间值参数的一步估计

rate estimators and corresponding confidence sets. These estimators correspond to generalizations of cross-fitted one-step estimators based on Hilbert-valued efficient influence functions. We give theoretical guarantees even when arbitrary estimators of nuisance functions are used, including those based on machine learning techniques. We show that these results naturally extend to Hilbert spaces that lack a reproducing kernel, as long as the parameter has an efficient…

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Identification and estimation of unconditional policy effects of an endogenous binary treatment: An unconditional MTE approach

内生二元处理的无条件政策效应:无条件 MTE 方法

This paper studies the identification and estimation of policy effects when treatment status is binary and endogenous. We introduce a new class of marginal treatment effects (MTEs) based on the influence function of the functional underlying the policy target. We show that an unconditional policy effect can be represented as a weighted average of the newly defined MTEs over the individuals who are indifferent about their treatment status. We provide conditions for point…

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High-dimensional model-assisted inference for treatment effects with multi-valued treatments

多值处理效应的高维模型辅助推断

Consider estimation of average treatment effects with multi-valued treatments using augmented inverse probability weighted (IPW) estimators, depending on outcome regression and propensity score models in high-dimensional settings. These regression models are often fitted by regularized likelihood-based estimation, while ignoring how the fitted functions are used in the subsequent inference about the treatment parameters. Such separate estimation can be associated with known…

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Heterogeneous treatment effect bounds under sample selection with an application to the effects of social media on political polarization

样本选择下的异质处理效应界:社交媒体与政治极化应用

We propose a method for estimation and inference for bounds for heterogeneous causal effect parameters in general sample selection models where the treatment can affect whether an outcome is observed and no exclusion restrictions are available. The method provides conditional effect bounds as functions of policy relevant pre-treatment variables. It allows for conducting valid statistical inference on the unidentified conditional effects. We use a flexible debiased/double…

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A method of moments approach to asymptotically unbiased Synthetic Controls

以矩方法构造渐近无偏的合成控制

A common approach to constructing a Synthetic Control unit is to fit on the outcome variable and covariates in pre-treatment time periods, but it has been shown by Ferman and Pinto (2021) that this approach does not provide asymptotic unbiasedness when the fit is imperfect and the number of controls is fixed. Many related panel methods have a similar limitation when the number of units is fixed. I introduce and evaluate a new method in which the Synthetic Control is…

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Tuning-parameter-free propensity score matching approach for causal inference under shape restriction

形状约束下无需调参的倾向得分匹配因果推断

Propensity score matching (PSM) is a pseudo-experimental method that uses statistical techniques to construct an artificial control group by matching each treated unit with one or more untreated units of similar characteristics. To date, the problem of determining the optimal number of matches per unit, which plays an important role in PSM, has not been adequately addressed. We propose a tuning-parameter-free PSM approach to causal inference based on the nonparametric…

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Terrorism and education: Evidence from instrumental variables estimators

恐怖主义与教育:工具变量估计的证据

Summary This paper estimates the effect of exposure to terrorist violence on education. Since terrorists may choose targets endogenously, we construct a set of novel instruments. To that end, we leverage exogenous variation from a local terrorist group's revenues and its affiliation with al‐Qaeda. Across several Kenyan datasets, we find that attacks suppress school enrolment more than predicted by difference‐in‐differences‐type estimators. This indicates that terrorists…

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Rajendra Bhansali’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez

Rajendra Bhansali 对《因果模型的参数化与模拟》的讨论意见

Contribution: My own introduction to the subject area of this paper is through the notion of Granger causality, a topic which has attracted much attention in time series analysis and related disciplines, including signal processing. The authors have proposed a new approach to causal models. However, this involves working with full density functions. It seems to me that, from a data analysis point of view, the authors’ approach might be a bit too general, and it might be…

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Heather Battey’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez

Heather Battey对《因果模型的参数化与模拟》的讨论评论

My brief comment relates to the inferential discussion of Section 5. The sample-space factorization of the joint probability from the marginal structural model induces a parameter-space factorization of the likelihood function, with the implication that θZX is orthogonal to (⁠θY|X*,ϕYZ|X*⁠) in the sense of, e.g. Cox and Reid (1987), and leading to the simplified asymptotic covariance matrix of Theorem 5.1. The parameter cut discussed at the beginning of Section 5 also…

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Richard Guo’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez

Richard Guo 对《因果模型的参数化与模拟》的讨论:两种分解与密度比

I congratulate Evans and Didelez warmly on this innovative and inspiring paper. Here, I offer my interpretation of the approach in terms of two factorizations and a density ratio. Any distribution over Z,X,Y can be factorized in two ways: Factorization C−1 is the usual one; it is factorization A−1 that is the focus of the two authors. More concretely, suppose ϕZY∣X(z,y∣x) is a conditional copula density, i.e. for every value of x, (z,y)↦ϕZY∣X(z,y∣x) is a density function…

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Torben Martinussen’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez

马丁努森对《因果模型的参数化与模拟》的讨论

I congratulate the authors on an interesting and useful contribution to the literature on causal inference. The authors propose a nice way of generating data so that a given causal structure of interest is preserved. This is a handy tool to have when for instance one needs to generate data to investigate small sample performance of a new inference procedure. I find it less attractive to use the suggested procedure for estimation purposes as is also alluded to in the paper…

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A. Philip Dawid’s contribution to the Discussion of ‘Parameterizing and simulating from causal models’ by Evans and Didelez

A. Philip Dawid对《因果模型的参数化与模拟》的讨论意见

When discussing causal inference in sequential problems, the authors only consider interventions that set their target variables to pre-specified fixed values. A more practically relevant aim, as considered by Dawid and Didelez (2010), is to assess the effect of a pre-specified dynamic treatment strategy, which details how each decision is to depend (possibly even stochastically) on previously observed variables. Can the methods of this paper be applied to this case?

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