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Limit Theory for U-Statistics under Clustered and Weakly Dependent Data

聚类与弱依赖数据下 U 统计量的极限理论

This paper develops asymptotic theory and feasible inference for unbounded-kernel order-k U-statistics under clustered sampling and weakly dependent time-series. The analysis first builds the complete order-2 pipeline, moving from clustered data to exact $m$-dependence and then to near-epoch dependence. The same logic is subsequently extended to general order k greater or equal to 2. Under clustered sampling, the theory allows arbitrary within-cluster dependence and growing,…

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A Grid-Rate Condition for Valid Uniform Inference

有效一致推断的网格增长速率条件

Conducting uniform inference on a continuous functional F defined on a compact subset X of R^d involves specifying L_n^d nodes for estimation and the construction of confidence bands. While asymptotically valid inference requires L_n to increase with n, existing fixed-L rules of thumb and heuristic data-driven approaches lack formal justification. This paper shows that, for functions within a Donsker class, the simple grid-growth condition r_n^(1/4)/L_n -> 0, equivalently…

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Quantile and Distribution Treatment Effects on the Treated with Possibly Non-Continuous Outcomes

可能非连续结局下处理组的分位数与分布处理效应

Applied Difference-in-Differences studies often involve outcomes that are discrete, mixed, censored, or otherwise non-continuously distributed, while policy questions frequently concern distributional effects rather than mean effects alone. This paper develops a distributional DiD framework for identifying and conducting uniform inference on distribution and quantile treatment effects on the treated in such settings under stated identifying and regularity conditions.…

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Difference-in-differences with as few as two cross-sectional units -- A new perspective to the democracy-growth debate

仅需两个截面单位的双重差分:民主与增长的新视角

Pooled panel analyses often mask heterogeneity in unit-specific treatment effects. This challenge, for example, crops up in studies of the impact of democracy on economic growth, where findings vary substantially due to differences in country composition. To address this challenge, this paper introduces the Temporal Difference-in-Differences (T-DiD) estimator that leverages temporal variation in the data to estimate unit-specific average treatment effects on the treated…

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A Consistent ICM-based $χ^2$ Specification Test

基于积分条件矩的一致卡方设定检验

In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, they are not commonly used in empirical practice owing to features such as the non-pivotality of the test and the high computational cost of available bootstrap schemes, especially in large samples. This paper proposes specification and mean independence tests based on ICM metrics. The proposed test exhibits consistency, asymptotic $χ^2$-distribution under the null hypothesis, and…

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A Distance Covariance-based Estimator

基于距离协方差的估计量

This paper proposes an estimator that relaxes the conventional relevance condition in instrumental variable (IV) analyses. The method allows endogenous covariates to be weakly correlated, uncorrelated, or even mean-independent -- though not independent -- of the instruments, enabling the use of the maximal set of relevant instruments in a given application. Identification is attainable without exclusion restrictions and without finite-moment assumptions on the disturbance…

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Clustered Covariate Regression

聚类协变量回归

High covariate dimensionality is increasingly occurrent in model estimation, and existing techniques to address this issue typically require sparsity or discrete heterogeneity of the \emph{unobservable} parameter vector. However, neither restriction may be supported by economic theory in some empirical contexts, leading to severe bias and misleading inference. The clustering-based grouped parameter estimator (GPE) introduced in this paper drops both restrictions and…

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Treatment Effects in Staggered Adoption Designs with Non-Parallel Trends

非平行趋势下交错采用设计的处理效应

This paper considers identifying and estimating causal effect parameters in a staggered treatment adoption setting -- that is, where a researcher has access to panel data and treatment timing varies across units. We consider the case where untreated potential outcomes may follow non-parallel trends over time across groups. This implies that the identifying assumptions of leading approaches such as difference-in-differences do not hold. We mainly focus on the case where…

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Feasible IV Regression without Excluded Instruments

无需排除型工具变量的可行工具变量回归

The relevance condition of Integrated Conditional Moment (ICM) estimators is significantly weaker than the conventional IV's in at least two respects: (1) consistent estimation without excluded instruments is possible, provided endogenous covariates are non-linearly mean-dependent on exogenous covariates, and (2) endogenous covariates may be uncorrelated with but mean-dependent on instruments. These remarkable properties notwithstanding, multiplicative-kernel ICM estimators…

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