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GMM 与矩条件:广义矩估计、条件矩限制与经验似然。
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Conditional Selective Inference for the Selected Groups in Panel Data

面板数据中所选群组的条件选择后推断

We consider the problem of testing for differences in group-specific slopes between the selected groups in panel data identified via k-means clustering. In this setting, the classical Wald-type test statistic is problematic because it produces an extremely inflated type I error probability. The underlying reason is that the same dataset is used to identify the group structure and construct the test statistic, simultaneously. This creates dependence between the selection and…

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Counterexamples and Sufficient Conditions: Comments on "Optimally-Transported Generalized Method of Moments"

反例与充分条件:对“最优传输广义矩估计”的评论

We comment on the optimally-transported generalized method of moments (OTGMM) estimator proposed by Schennach & Starck (2026a) and give counterexamples to Theorems 2-6 under their stated assumptions. First, the assumptions used in the small-error analysis are insufficient for consistency in Theorem 2 and asymptotic normality in Theorem 3. Next, we consider the large-error analysis, in which Theorem 4 states that the OTGMM estimator is equivalent to a GMM estimator with…

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Large sample properties of GMM estimators under second-order identification

二阶识别下 GMM 估计量的大样本性质

Dovonon and Hall (Journal of Econometrics, 2018) proposed a limiting distribution theory for GMM estimators for a p - dimensional globally identified parameter vector φ when local identification conditions fail at first-order but hold at second-order. They assumed that the first-order underidentification is due to the expected Jacobian having rank p-1 at the true value φ_{0}, i.e., having a rank deficiency of one. After reparametrizing the model such that the last column of…

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Estimating Social Effects with Randomized and Observational Network Data

利用随机分配与观察网络数据估计社会效应

This paper introduces an innovative approach to identifying and estimating the parameters of interest in the widely recognized linear-in-means regression model under conditions where the initial randomization of peers determines the observed network. We assert that peers who are initially randomized do not produce social effects. However, after randomization, agents can endogenously develop significant connections that potentially generate peer influences. We present a…

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Dynamic Local Average Treatment Effects in Time Series

时间序列中的动态局部平均处理效应

This paper discusses identification, estimation, and inference on dynamic local average treatment effects (LATEs) in instrumental variables (IVs) settings. First, we show that compliers--observations whose treatment status is affected by the instrument--can be identified individually in time series data using smoothness assumptions and local comparisons of treatment assignments. Second, we show that this result enables not only better interpretability of IV estimates but…

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Unified Inference on Moment Restrictions with Nuisance Parameters

含干扰参数的矩约束统一推断

This paper proposes a simple unified inference approach on moment restrictions in the presence of nuisance parameters. The proposed test is constructed based on a new characterization that avoids the estimation of nuisance parameters and can be broadly applied across diverse settings. Under suitable conditions, the test is shown to be asymptotically size controlled and consistent for both independent and dependent samples. Monte Carlo simulations show that the test performs…

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Debiased Machine Learning: Identification, Estimation, and Shape Constraints

去偏机器学习:识别、估计与形状约束

We develop a general framework of identification and estimation for automatic debiased machine learning (DML) where the parameter of interest $θ_0$ is identified by a moment condition involving a nuisance $γ_0$ that may be high dimensional. We establish conditions under which the Riesz representer $α_0$, which is at the core of DML, is identified, and show that the identification occurs precisely when $α_0$ uniquely optimizes a quadratic functional. This characterization…

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On Robust Empirical Likelihood for Nonparametric Regression with Application to Regression Discontinuity Designs

非参数回归的稳健经验似然及其断点回归应用

Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these settings using local linear smoothers, with Wilks' theorem holding only when an undersmoothed bandwidth is selected. However, the generalization of bias-corrected versions of empirical likelihood under more realistic conditions is non-trivial…

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Arellano-Bond LASSO Estimator for Dynamic Linear Panel Models

动态线性面板模型的 Arellano–Bond LASSO 估计量

The Arellano-Bond estimator is a fundamental method for dynamic panel data models, widely used in practice. It can be severely biased when the time series dimension of the data, $T$, is long. The source of the bias is the large degree of overidentification. We propose a simple two-step approach to deal with this problem. The first step applies LASSO to the cross-section data at each time period to select the most informative moment conditions, exploiting the approximately…

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Locally Robust Kernel Specification Tests for Conditional Moment Restrictions

条件矩限制的局部稳健核设定检验

We develop kernel-based specification tests for semiparametric conditional moment models with high-dimensional nuisance parameters, extending existing conditional moment tests---which typically require asymptotically linear nuisance estimators---to accommodate modern machine-learning methods. The proposed locally robust kernel tests combine Neyman-orthogonal moments, cross-fitting, and reproducing kernel Hilbert space methods, yielding inference that is first-order…

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Partial Identification with Auxiliary Moment Restrictions

辅助矩约束下的部分识别

Partial identification is often set aside in practice because the identification regions it delivers are too wide to be useful, pushing researchers toward strong assumptions that buy point identification at the cost of credibility. We show that a source of information already sitting in most interval-valued datasets can fix this without adding any assumption at all. When an outcome is reported only as an interval---because a data custodian bracketed, top-coded, or formally…

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Estimating Network Spillovers under Dense Measurement Error

稠密测量误差下的网络溢出效应估计

This paper analyzes spillover effects in spatial (network) models when the neighborhood (adjacency) matrix is contaminated by measurement error from reporting, aggregation, or disclosure imperfections, leading to inconsistent estimation of network effects. We introduce a regularization framework for the latent network that allows for sparse and/or low-rank structure and accommodates potential correlation between measurement errors and outcomes. We propose two estimators: (i)…

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Kernel Minimum Distance Estimation and Testing with Conditional Moment Restrictions: A Unified Framework

条件矩约束下核最小距离估计与检验的统一框架

We propose a unified Kernel Minimum Distance (KMD) framework for estimating and testing models defined by conditional moment restrictions. By embedding conditional moments into a Reproducing Kernel Hilbert Space (RKHS), we construct a closed-form $V$-statistic objective function that quantifies the distance from the restrictions. We establish the $\sqrt{n}$-consistency and asymptotic normality of the associated minimum distance estimator. Within this framework, the minimized…

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Orthogonal Integrated Conditional Moment Tests for Treatment Effect Heterogeneity

处理效应异质性的正交积分条件矩检验

We propose a nonparametric integrated conditional moment (ICM) test for treatment effect heterogeneity across subpopulations defined by a given covariate subvector. Under unconfoundedness, the null is recast as a conditional moment restriction based on a Neyman-orthogonal score, which reduces the first-order sensitivity of the empirical process to nuisance parameter estimation. The test statistics are constructed as continuous functionals of a marked empirical process. We…

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Detecting changes in the mean of spatial random fields on a regular grid

规则网格上空间随机场均值变化的检测

We propose statistical procedures for detecting changes in the mean of spatial random fields observed on regular grids. The proposed framework provides a general approach to change detection in spatial processes. Extending a block-based method originally developed for time series, we introduce two test statistics, one based on Gini's mean difference and a novel variance-based variant. Under mild moment conditions, we derive asymptotic normality of the variance-based…

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Quasi-Bayesian Hierarchical Models

准贝叶斯层次模型

We develop the Quasi-Bayesian Hierarchical Model (QBHM) for grouped GMM settings. The framework combines Bayesian hierarchical modelling with Laplace-type estimation: it preserves each group-specific objective function, while introducing a pooling term for economically comparable parameters. When the number of studies is fixed, the QBHM estimator-the quasi-posterior mean-has the same asymptotic distribution as GMM when estimating strongly identified study parameters. For…

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Design-Based Inference for Time-Series GMM

时间序列 GMM 的设计型推断

This paper studies inference for time-series GMM when uncertainty comes from shock assignment within a realized historical episode. Rather than treating the data as one random draw from a population of hypothetical economies, the framework conditions on the historical environment and considers alternative realizations of shocks and instruments. For locally correctly specified GMM estimators, the centered moment has design long-run variance $Ω_R$, which determines the…

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Asymmetric GARCH modelling without moment conditions

无矩条件下的非对称 GARCH 建模

Heavy tails and stability are two persistent challenges in modelling financial time series, yet most existing approaches rely on finite-moment assumptions and pay insufficient attention to stability issues. To bridge this gap, we propose an asymmetric GARCH model with standardized non-Gaussian stable innovations (sAGARCH), which accommodates infinite variance and even infinite mean. We establish a comprehensive inference framework for both stationary and explosive cases,…

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Sensitivity, Informativeness, and Misspecification in GMM Estimation

GMM 估计中的敏感性、信息含量与模型误设

This paper develops misspecification-robust sensitivity and informativeness diagnostics for GMM estimators, evaluated at pseudo-true values. The sensitivity matrix nests that of Andrews, Gentzkow, and Shapiro (2017) under correct specification. The informativeness $Δ$ measures the share of an estimator's asymptotic variance explained by sampling variation in the moments, a notion of structural efficiency that equals one under correct specification and can fall below one…

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Causal Inference with the Napkin Graph

Napkin 因果图下的因果推断

Unmeasured confounding can render identification strategies based on adjustment functionals invalid. We study the "Napkin" graph, a causal structure that encapsulates features of M-bias, instrumental variables, and classical back-door and front-door settings, yet identifies the average treatment effect through a nonstandard ratio of two g-formulas. We develop influence-function-based estimators for this functional, including doubly-robust one-step and targeted minimum…

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Orthogonalized Synthetic Controls

正交化合成控制

When conducting inference for the average treatment effect on the treated with a Synthetic Control Estimator, the vector of control weights is a nuisance parameter that is often constrained, high-dimensional, and may be only partially identified even when the average treatment effect on the treated is point-identified. All three of these features of a nuisance parameter can lead to failure of asymptotic normality for the estimate of the parameter of interest when using…

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Bounds for Standard Errors in Combined Data

组合数据中标准误的界限

We propose methods for constructing lower bounds on the standard errors of parameters estimated from moment conditions obtained across different samples. Sharp explicit bounds are derived by exploiting geometric inequalities when no information about correlations across samples is available. Furthermore, we develop computationally tractable sharp bounds for more general settings with no or partial correlation information, which can be obtained by solving a simple…

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Semi-nonparametric estimation of spatial dynamic panel data models with nonparametric spatial weights

采用非参数空间权重的空间动态面板模型半非参数估计

We develop a semi-nonparametric framework for spatial dynamic panel data (SDPD) models with two-way fixed effects when the spatial interaction structure is unknown beyond a distance measure. This is accomplished by modelling spatial weights in the outcome, lagged-outcome, and disturbance channels as unknown functions of underlying economic distances. These enter the SDPD system through matrix-function operators, providing a unified approach that accommodates both spatial…

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Distributional Granger Causality: Identification, Sequential Inference, and Adaptive Testing

分布格兰杰因果:识别、序贯推断与自适应检验

Predictive dependence in time series need not be confined to the conditional mean. Outside the Gaussian setting, causal content may arise through conditional scale, tail behavior, asymmetry, or other distributional features, implying that no single Granger-type test provides a complete characterization of predictive dependence. This paper develops a framework for distributional Granger causality based on a finite collection of channel-specific restrictions. Under suitable…

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