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Covariate-assisted bounds on causal effects with instrumental variables

协变量辅助的工具变量因果效应界限

Abstract When an exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs relies on strong untestable structural assumptions. When one is unwilling to assert such structure, IVs can nonetheless be used to construct bounds on the ATE. Famously, Alexander Balke and Judea Pearl proved tight bounds on the ATE for a…

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A statistical view of column subset selection

列子集选择的统计视角

Abstract We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as column subset selection (CSS). Meanwhile, the typical statistical formalization is to find an information-maximizing set of principal variables. This paper shows that these two approaches are equivalent, and moreover, both can be viewed as maximum-likelihood…

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Finite Sample Inference for the Maximum Score Estimand

最大得分目标参数的有限样本推断

Abstract We provide a finite sample inference method for the structural parameters of Manski's semiparametric binary response model under a conditional median restriction. This is achieved by exploiting distributional properties of observable outcomes conditional on the observed sequence of exogenous variables. Moment inequalities conditional on the size n sequence of exogenous covariates are constructed, and the proposed test statistic is a monotone function of violations…

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Addressing endogeneity issues in a spatial autoregressive model using copulas

利用 Copula 处理空间自回归模型中的内生性

This paper develops a novel, instrument-free semiparametric copula framework for a spatial autoregressive (SAR) model to address endogeneity arising from an endogenous spatial weights matrix, endogenous regressors, or both. Moving beyond conventional Gaussian copulas, we develop a flexible estimator based on the Student’s t copula with an unknown degrees-of-freedom (df) parameter, which nests the Gaussian case and allows the data to determine the presence of tail dependence.…

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Estimation of spatial autoregressive panel data models with nonparametric endogenous effect

含非参数内生效应的空间自回归面板模型估计

This paper proposes a sieve generalized method of moments (GMM) method for the estimation of spatial autoregressive panel data models with nonparametric endogenous effect. The new estimator incorporates both linear moments based on the orthogonality of the exogenous regressors with the model disturbances and quadratic moments based on the properties of idiosyncratic errors. We establish the consistency and asymptotic normality of the sieve GMM estimator and show that it is…

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Inference on model parameters with many L-moments

使用大量 L 矩的模型参数推断

This paper studies parameter estimation using L-moments, an alternative to traditional moments with attractive statistical properties. The estimation of model parameters by matching sample L-moments is known to outperform maximum likelihood estimation (MLE) in small samples from popular distributions. The choice of the number of L-moments used in estimation remains ad-hoc, though: researchers typically set the number of L-moments equal to the number of parameters, which is…

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Nonparametric regression under cluster sampling

聚类抽样下的非参数回归

This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya–Watson kernel regression, and local linear estimation. Our theory accommodates growing and heterogeneous cluster sizes. We derive asymptotic conditional bias and variance, establish uniform consistency, and prove asymptotic normality. Our findings reveal that under heterogeneous cluster sizes, the…

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Measuring the effects of segregation in the presence of social spillovers: A nonparametric approach

社会溢出下隔离效应的非参数测量

In this paper we nonparametrically analyze the effects of reallocating individuals across social groups in the presence of social spillovers. Individuals are either 'high' or 'low' types. Own outcomes may vary with the fraction of high types in one's social group. We characterize the average outcome and inequality effects of small increases in segregation by type. We also provide a measure of average spillover strength. We generalize the setup used by Benabou (1996) and…

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Estimating high dimensional monotone index models by iterative convex optimization

通过迭代凸优化估计高维单调指标模型

In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric transformation, and duration models. A main advantage of our approach is computational. For instance, rank estimation procedures such as those proposed in [13] and [7] that optimize a nonsmooth, nonconvex objective function are difficult to use…

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Nonlinear budget set regressions in random utility models: Theory and application to taxable income

随机效用模型中的非线性预算集回归:理论与应税收入应用

This paper is about the nonparametric regression of a choice variable on a nonlinear budget set under utility maximization with general heterogeneity, i.e. in the random utility model (RUM). We show that utility maximization and convex budget sets make this regression three dimensional with a more parsimonious specification than previously derived. We show that nonconvexities in the budget set will have little effect on these results in important cases. We characterize all…

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Identification and estimation of partial effects in nonlinear semiparametric panel models

非线性半参数面板模型中偏效应的识别与估计

Average partial effects (APEs) are often not point identified in panel models with unrestricted unobserved individual heterogeneity, such as a binary response panel model with fixed effects and logistic errors as a special case. This lack of point identification occurs despite the identification of these models' common coefficients. We provide a unified framework to establish the point identification of various partial effects in a wide class of nonlinear semiparametric…

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Higher-order refinements of small bandwidth asymptotics for density-weighted average derivative estimators

密度加权平均导数估计量的小带宽渐近理论的高阶改进

The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter restrictions and model assumptions that imply an asymptotic linear representation of the point estimator. These conditions can be restrictive, and the resulting distributional approximation may not be representative of the actual sampling…

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Improved estimation of semiparametric dynamic copula models with filtered nonstationarity

过滤非平稳成分后的半参数动态 Copula 模型改进估计

This paper considers estimation of short-run dynamics in time series that contain a nonstationary component. We assume that appropriate preliminary methods can be applied to the observed time series to separate short-run elements from long-run slowly evolving secular components, and focus on estimation of the short-run dynamics based on the filtered data. We use a flexible copula-generated Markov model to capture the nonlinear temporal dependence in the short-run component…

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Estimation of wage inequality in the UK by quantile regression with censored selection

利用删失选择分位数回归估计英国工资不平等

Arellano and Bonhomme (2017) proposed a quantile selection model to study the evolution of wage inequality in the UK, which specifies a binary selection equation and requires an exclusion restriction. In this paper we propose a quantile selection model with a more informative censored selection equation. Following Heckman (1974, 1979), Heckman and Sedlacek (1990), and Blundell et al. (2003), among others, the employment selection equation could be equivalently modeled by an…

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Phase transitions in nonparametric regressions

非参数回归中的相变

When the unknown regression function of a single variable is known to have derivatives up to the (γ+1)th order bounded in absolute values by a common constant everywhere or a.e. (i.e., (γ+1)th degree of smoothness), the minimax optimal rate of the mean integrated squared error (MISE) is stated as 1n2γ+22γ+3 in the literature. This paper shows that: (i) if n≤γ+12γ+3, the minimax optimal MISE rate is lognnlog(logn) and the optimal degree of smoothness to exploit is roughly…

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Identification of time-varying counterfactual parameters in nonlinear panel models

非线性面板模型中时变反事实参数的识别

We develop a general framework for the identification of counterfactual parameters in a class of nonlinear semiparametric panel models with fixed effects and time effects. Our method applies to models for discrete outcomes (e.g., two-way fixed effects binary choice) or continuous outcomes (e.g., censored regression), with discrete or continuous regressors. Our results do not require parametric assumptions on the error terms or time-homogeneity on the outcome equation. Our…

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Loss aversion and the welfare ranking of policy interventions

损失厌恶与政策干预的福利排序

This paper develops theoretical criteria and econometric methods to rank policy interventions in terms of welfare when individuals are loss-averse. Our new criterion for “loss aversion-sensitive dominance” defines a weak partial ordering of the distributions of policy-induced gains and losses. It applies to the class of welfare functions which model individual preferences with non-decreasing and loss-averse attitudes towards changes in outcomes. We also develop new…

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AVERAGING ESTIMATORS OF HETEROGENEOUS TREATMENT EFFECTS UNDER ADDITIVE MODELS

加性模型下异质处理效应估计量的模型平均

We consider spline-based additive models for estimation of conditional treatment effects. To handle the uncertainty due to variable selection, we propose a method of model averaging with weights obtained by minimizing a J -fold cross-validation criterion, in which a nearest neighbor matching is used to approximate the unobserved potential outcomes. We show that the proposed method is asymptotically optimal in the sense of achieving the lowest possible squared loss in some…

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The inverse Kalman filter

逆卡尔曼滤波器

Summary We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman filter with the conjugate gradient algorithm, which substantially accelerates the computation of matrix inversion for a general form of covariance matrix, where other approximation approaches may not be directly applicable. We…

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A semiparametric instrumented difference-in-differences approach to policy learning

用于政策学习的半参数工具变量双重差分方法

Summary Recently, there has been a surge in methodological development for the difference-in-differences approach to evaluate causal effects. Standard methods in the literature rely on the parallel-trend assumption to identify the average treatment effect on the treated. However, the parallel-trend assumption may be violated in the presence of unmeasured confounding, and the average treatment effect on the treated may not be useful in learning a treatment assignment policy…

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ESTIMATION OF INTEGRATED VOLATILITY FUNCTIONALS WITH KERNEL SPOT VOLATILITY ESTIMATORS

基于核现货波动率估计量的积分波动率泛函估计

For a multidimensional Itô semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013, The Annals of Statistics 41(3), 1462–1484) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated functional and a spot volatility estimator with a forward uniform kernel. Motivated by recent results that show that spot volatility estimators with general two-sided kernels of unbounded support are…

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Mixture Models: Parametric, Semiparametric, and New Directions

混合模型:参数、半参数与新方向

Weixin Yao and Sijia Xiang. Boca Raton, FL: Chapman & Hall/CRC Press, 2024, xvii + 379 pp., $130.00(H), ISBN: 978-0-367-48182-7.The mixture modeling framework has become a mainstay in the toolkit o...

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Boosting AI-Generated Biomedical Images with Confidence through Advanced Statistical Inference

利用统计推断增强 AI 生成生物医学图像的可信度

Generative artificial intelligence (AI) has transformed the biomedical imaging field through image synthesis, addressing challenges of data availability, privacy, and diversity in biomedical research. This paper proposes a novel nonparametric method within the functional data framework to discern significant differences between the mean and covariance functions of original and synthetic biomedical imaging data, thereby enhancing the fidelity and utility of synthetic data.…

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Adaptation Using Spatially Distributed Gaussian Processes

利用空间分布式高斯过程实现自适应

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that this approximate posterior retains the rate of recovery of the full data posterior distribution, where the rate of recovery adapts to the smoothness of the true regression function. As particular examples we consider Gaussian process…

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