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Robust Permutation Tests in Linear Instrumental Variables Regression

线性工具变量回归的稳健置换检验

This paper develops permutation versions of identification-robust tests in linear instrumental variables (IV) regression. Unlike the existing randomization and rank-based tests in which independence between the instruments and the error terms is assumed, the permutation Anderson- Rubin (AR), Lagrange Multiplier (LM) and Conditional Likelihood Ratio (CLR) tests are asymptotically similar and robust to conditional heteroskedasticity under standard exclusion restriction i.e.…

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Estimating Higher-Order Mixed Memberships via the l2,∞ Tensor Perturbation Bound

利用逐行张量扰动界估计高阶混合社群成员关系

Higher-order multiway data is ubiquitous in machine learning and statistics and often exhibits community-like structures, where each component (node) along each different mode has a community membership associated with it. In this article we propose the sub-Gaussian) tensor mixed-membership blockmodel, a generalization of the tensor blockmodel positing that memberships need not be discrete, but instead are convex combinations of latent communities. We establish the…

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A Model-Agnostic Graph Neural Network for Integrating Local and Global Information

整合局部与全局信息的模型无关图神经网络

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to their black-box nature, and an inability to learn representations of varying orders. To tackle these issues, we propose a novel Model-agnostic Graph Neural Network (MaGNet) framework, which is able to effectively integrate information of…

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Model-Based Causal Feature Selection for General Response Types

面向一般响应类型的模型化因果特征选择

Discovering causal relationships from observational data is a fundamental yet challenging task. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings and exploits that causal models are invariant. ICP has been extended to general additive noise models and to nonparametric settings using conditional independence tests. However, the latter often suffer from low power (or poor type I error…

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Mediation Analysis with the Mediator and Outcome Missing Not at Random

中介变量与结果非随机缺失时的中介分析

Mediation analysis is widely used for investigating direct and indirect causal pathways through which an effect arises. However, many mediation analysis studies are challenged by missingness in the mediator and outcome. In general, when the mediator and outcome are missing not at random, the direct and indirect effects are not identifiable without further assumptions. We study the identifiability of the direct and indirect effects under some interpretable mechanisms that…

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A Heteroscedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates

高维协变量下对异方差稳健的过度识别约束检验

This paper proposes an overidentifying restriction test for high-dimensional linear instrumental variable models. The novelty of the proposed test is that it allows the number of covariates and instruments to be larger than the sample size. The test is scale-invariant and robust to heteroskedastic errors. To construct the final test statistic, we first introduce a test based on the maximum norm of multiple parameters that could be high-dimensional. The theoretical power…

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Statistical Identification of Independent Shocks with Kernel-based Maximum Likelihood Estimation and an Application to the Global Crude Oil Market

独立冲击的核最大似然统计识别及全球原油市场应用

Independent component analysis has emerged as a promising approach for revealing structural relationships in multivariate dynamic systems, particularly in scenarios with limited knowledge of causal patterns. This article introduces a robust kernel-based maximum likelihood (KML) estimation method that accommodates the distributional characteristics of the structural sources of data variation. Our Monte Carlo study demonstrates the superior performance of the KML estimator…

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Probability of Causation with Sample Selection: A Reanalysis of the Impacts of Jóvenes en Acción on Formality

样本选择下的因果发生概率:重新分析 Jóvenes en Acción 对正规就业的影响

This paper identifies the probability of causation when there is sample selection. We show that the probability of causation is partially identified for individuals who are always observed regardless of treatment status and derive sharp bounds under three increasingly restrictive sets of assumptions. The first set imposes an exogenous treatment and a monotone sample selection mechanism. To tighten these bounds, the second set also imposes the monotone treatment response…

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Efficient estimation for functional accelerated failure time models

函数型加速失效时间模型的有效估计

Summary We propose a functional accelerated failure time model to characterize the effects of both functional and scalar covariates on the time to event of interest, and provide regularity conditions to guarantee model identifiability. For efficient estimation of model parameters, we develop a sieve maximum likelihood approach where parametric and nonparametric coefficients are bundled with an unknown baseline hazard function in the likelihood function. Not only do the…

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Randomization inference when N equals one

样本单位数为一时的随机化推断

Summary For decades, $ N $-of-1 experiments, where a unit serves as its own control and treatment in different time windows, have been used in certain medical contexts. However, due to effects that accumulate over long time windows and interventions that have complex evolution, a lack of robust inference tools has limited the widespread applicability of such $ N $-of-1 designs. This work combines techniques from experimental design in causal inference and system…

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Noise-induced randomization in regression discontinuity designs

断点回归设计中由噪声诱导的随机化

Summary Regression discontinuity designs assess causal effects in settings where treatment is determined by whether an observed running variable crosses a prespecified threshold. Here, we propose a new approach to identification, estimation and inference in regression discontinuity designs that uses knowledge about exogenous noise (e.g., measurement error) in the running variable. In our strategy, we weight treated and control units to balance a latent variable, of which the…

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An omitted variable bias framework for sensitivity analysis of instrumental variables

工具变量敏感性分析的遗漏变量偏误框架

Abstract We develop an omitted variable bias framework for sensitivity analysis of instrumental variable estimates that naturally handles multiple side effects (violations of the exclusion restriction assumption) and confounders (violations of the ignorability of the instrument assumption) of the instrument, exploits expert knowledge to bound sensitivity parameters and can be easily implemented with standard software. Specifically, we introduce sensitivity statistics for…

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Two-sample distribution tests in high dimensions via max-sliced Wasserstein distance and bootstrapping

基于最大切片 Wasserstein 距离与自助法的高维两样本分布检验

Summary Two-sample hypothesis testing is a fundamental statistical problem for inference about two populations. In this paper, we construct a novel test statistic to detect high-dimensional distributional differences based on the max-sliced Wasserstein distance to mitigate the curse of dimensionality. By exploiting an intriguing link between the distance and suprema of empirical processes, we develop an effective bootstrapping procedure to approximate the null distribution…

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Randomization-based Z -estimation for evaluating average and individual treatment effects

评估平均与个体处理效应的随机化 Z 估计

Summary Randomized experiments have been the gold standard for drawing causal inference. The conventional model-based approach has been one of the most popular methods of analysing treatment effects from randomized experiments, which is often carried out through inference for certain model parameters. In this paper, we provide a systematic investigation of model-based analyses for treatment effects under the randomization-based inference framework. This framework does not…

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Philip G. Wright, directed acyclic graphs, and instrumental variables

This Special Issue celebrates the seminal contributions of Philip G. Wright to causal inference in economics and puts them in a modern perspective. At its core is a reproduction of Online Appendix B in Wright’s 1928 book The Tariff on Animal and Vegetable Oils.1 This book deals with demand for and supply of oils and butter. In its Online Appendix B, Wright made several fundamental contributions to causal inference. He introduced a structural equation model of demand and…

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Effects of a duty on price and output with special reference to butter and flaxseed

关税对价格与产出的影响:以黄油和亚麻籽为重点

Editorial statement: This is a reproduction of Appendix B in Wright, P. G. (1928). The Tariff on Animal and Vegetable Oils, 286–319. New York: The Macmillan Company. We have corrected four minor errors in its mathematical expressions: We have made further typographical changes to improve readability: We (i) have placed all footnotes, some of which are long and contain graphics, in a new section at the end; (ii) have reconstructed all graphics using TikZ, with some added…

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Extending the scope of instrumental variable methods

拓展工具变量方法的适用范围

Summary Since Philip Wright’s proposal of the linear instrumental variables (IV) estimator in 1928, the scope of application of IV models has greatly expanded. There are now nonlinear IV models in use with both additive and nonadditive latent variables, employing both semiparametric and nonparametric specifications. A notable feature of Wright’s linear IV estimator is that it is applicable to incomplete models that leave the genesis of endogenous explanatory variables…

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Design-based identification with formula instruments: a review

公式型工具变量的设计型识别:综述

Summary Many studies in economics use instruments or treatments that combine a set of exogenous shocks with other predetermined variables via a known formula. Examples include shift-share instruments and measures of social or spatial spillovers. We review recent econometric tools for this setting, which leverage the assignment process of the exogenous shocks and the structure of the formula for identification. We compare this design-based approach with conventional…

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Causal inference and data fusion in econometrics

计量经济学中的因果推断与数据融合

Summary Learning about cause and effect is arguably the main goal in applied econometrics. In practice, the validity of these causal inferences is contingent on a number of critical assumptions regarding the type of data that has been collected, and the substantive knowledge that is available about the phenomenon under investigation. For instance, unobserved confounding factors threaten the internal validity of estimates; data availability is often limited to nonrandom,…

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Identifying the volatility risk price through the leverage effect

通过杠杆效应识别波动率风险价格

In asset pricing models with stochastic volatility, uncertainty about volatility affects risk premia through two channels: aversion to decreasing returns and aversion to increasing volatility. We analyze the identification of and robust inference for structural parameters measuring investors’ aversions to these risks: the return risk price and the volatility risk price. In the presence of a leverage effect (instantaneous causality between the asset return and its…

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Identification-robust and simultaneous inference in multifactor asset pricing models

多因子资产定价模型中识别稳健的同时推断

This paper proposes exact identification-robust confidence sets for the zero-beta rate and ex-post factor prices in asset pricing models. Exploiting the information from the cross-sectional intercept allows us to impose or formally test model-consistent restrictions, including those resulting from traded factors in excess of the zero beta-rate or from return spreads. Analytical projection-based solutions for confidence set outcomes are developed. The proposed procedures are…

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Weak identification in discrete choice models

离散选择模型中的弱识别

We study the impact of weak identification in discrete choice models, and provide insights into the determinants of identification strength in these models. Using these insights, we propose a novel test that can consistently detect weak identification in commonly applied discrete choice models, such as probit, logit, and many of their extensions. Furthermore, we demonstrate that when the null hypothesis of weak identification is rejected, Wald-based inference can be carried…

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Exogeneity tests and weak identification in IV regressions: Asymptotic theory and point estimation

IV 回归中的外生性检验与弱识别:渐近理论及点估计

This paper provides new insights on exogeneity tests in linear IV models and their use for estimation, when identification fails or may not be strong. We make two main contributions. First, we show that Durbin–Wu–Hausman (DWH) and Revankar–Hartley (RH) exogeneity tests have correct level asymptotically, even when the first-stage coefficient matrix (which controls identification) is rank-deficient. We provide necessary and sufficient conditions under which these tests are…

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The chained difference-in-differences

链式双重差分

This paper studies the identification, estimation, and inference of long-term (binary) treatment effect parameters when balanced panel data is not available, or consists of only a subset of the available data. We develop a new estimator: the chained difference-in-differences, which leverages the overlapping structure of many unbalanced panel data sets. This approach consists in aggregating a collection of short-term treatment effects estimated on multiple incomplete panels.…

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