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MODEL AVERAGING FOR TREATMENT EFFECT ESTIMATION WITH HETEROGENEITY AND HETEROSKEDASTICITY

异质处理效应与异方差下的模型平均估计

The primary focus of this article is to capture heterogeneous treatment effects measured by the conditional average treatment effect. A model averaging estimation scheme is proposed with multiple candidate linear regression models under heteroskedastic errors, and the properties of this scheme are explored analytically. First, it is shown that our proposal is asymptotically optimal in the sense of achieving the lowest possible squared error. Second, the convergence of the…

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REGRESSION DISCONTINUITY DESIGN WITH POTENTIALLY MANY COVARIATES

可能包含大量协变量的断点回归设计

This article examines high-dimensional covariates in regression discontinuity design (RDD) analysis. We introduce estimation and inference methods for the RDD models that incorporate covariate selection while maintaining stability across various numbers of covariates. The proposed methods combine a localization approach using kernel weights with $\ell _{1}$ -penalization to handle high-dimensional covariates. We provide both theoretical and numerical evidence demonstrating…

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FUNCTIONAL INSTRUMENTAL VARIABLE REGRESSION WITH AN APPLICATION TO ESTIMATING THE IMPACT OF IMMIGRATION ON NATIVE WAGES

函数型工具变量回归及移民对本土工资影响的估计

Functional linear regression has gained popularity as a statistical tool for studying the relationship between function-valued variables. However, in practice, it is hard to expect that the explanatory variables of interest are strictly exogenous, due to, for example, the presence of omitted variables and measurement error. This issue of endogeneity remains insufficiently explored, in spite of its empirical importance. To fill this gap, this article proposes new consistent…

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WELFARE ANALYSIS VIA MARGINAL TREATMENT EFFECTS

通过边际处理效应进行福利分析

We consider a causal structure with endogeneity, i.e., unobserved confoundedness, where an instrumental variable is available. In this setting, we show that the mean social welfare function can be identified and represented via the marginal treatment effect as the operator kernel. This representation result can be applied to a variety of statistical decision rules for treatment choice, including plug-in rules, Bayes rules, and empirical welfare maximization rules. Focusing…

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Estimating Endogenous Effects on Ordinal Outcomes

有序结果中内生变量效应的估计

Abstract We examine the use of instrumental variable (IV) methods to measure the effect of a ceteris paribus change in an endogenous variable on an ordered outcome. Specifically, we use these methods to investigate the effect of neighborhood characteristics on subjective well-being (SWB) among participants in the Moving to Opportunity (MTO) housing voucher experiment. We find that the estimated positive effect of a decrease in neighborhood poverty on SWB is sensitive to the…

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ISOTONIC PROPENSITY SCORE MATCHING

保序倾向得分匹配

We propose a one-to-many matching estimator of the average treatment effect based on propensity scores estimated by isotonic regression. This approach is predicated on the assumption of monotonicity in the propensity score function, a condition that can be justified in many economic applications. We show that the nature of the isotonic estimator can help us to fix many problems of existing matching methods, including efficiency, choice of the number of matches, choice of…

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Semiparametric localized principal stratification analysis with continuous strata

连续主层的半参数局部化主分层分析

Abstract Principal stratification is essential for revealing causal mechanisms involving post-treatment intermediate variables, in real-world applications like surrogate marker evaluation. Principal stratification analysis with continuous intermediate variables is increasingly common but challenging due to the infinite principal strata and the nonidentifiability and nonregularity of principal causal effects (PCEs). Inspired by recent research, we resolve these challenges by…

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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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Job Displacement, Unemployment Benefits and Domestic Violence

失业冲击、失业救济与家庭暴力

Abstract We estimate impacts of male job loss, female job loss, and male unemployment benefits on domestic violence (DV) in Brazil. We merge individual-level employment and welfare registers with different measures of DV: judicial cases brought to criminal courts, the use of public shelters by victims, and mandatory DV notifications by health providers. Leveraging mass layoffs for identification, we first show that both male and female job loss, independently, lead to large,…

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Inference with a Single Treated Cluster

仅有一个处理簇时的统计推断

Abstract I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in difference-in-differences estimation, but the test developed here applies more broadly. I show that the test controls size and has power under asymptotics where the number of observations within each cluster is large but the number of clusters is fixed.…

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Causal inference in network experiments: Regression-based analysis and design-based properties

网络实验中的因果推断:回归分析与基于设计的性质

Network experiments are powerful tools for studying spillover effects, which avoid endogeneity by randomly assigning treatments to units over networks. However, it is non-trivial to analyze network experiments properly without imposing strong modeling assumptions. We show that regression-based point estimators and standard errors can have strong theoretical guarantees if the regression functions and robust standard errors are carefully specified to accommodate the…

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Shrinkage methods for treatment choice

处理选择中的收缩方法

This study examines the problem of determining whether to treat individuals based on observed covariates. The most common decision rule is the conditional empirical success (CES) rule proposed by Manski (2004), which assigns individuals to treatments that yield the best experimental outcomes conditional on the observed covariates. Conversely, using shrinkage estimators, which shrink unbiased but noisy preliminary estimates toward the average of these estimates, is a common…

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Quantile graphical models: Prediction and conditional independence with applications to systemic risk

分位数图模型:预测、条件独立与系统性风险应用

We propose two types of Quantile Graphical Models: (i) Conditional Independence Quantile Graphical Models (CIQGMs) characterize the conditional independence by evaluating the distributional dependence structure at each quantile index, as such, those can be used for validation of the graph structure in the causal graphical models; (ii) Prediction Quantile Graphical Models (PQGMs) characterize the statistical dependencies through the graphs of the best linear predictors under…

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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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Statistical inference for the low dimensional parameters of linear regression models in the presence of high-dimensional data: An orthogonal projection approach

高维线性回归中低维参数推断的正交投影方法

We consider the estimation and statistical inference for low dimensional parameters for a regression model with covariates whose dimension increases with sample size. We suggest a computationally simple one stage orthogonal projection approach to estimate the low dimensional parameters under strict or approximate sparsity conditions. The orthogonal projection approach is simple to implement and the inference for the low dimensional parameters is straightforward to derive…

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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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Financial constraints and the racial housing gap

融资约束与种族住房差距

We show that financial constraints lead to spatial misallocation and contribute to racial disparities in housing and wealth accumulation. Using bunching and difference-in-differences designs, we document that down payment constraints disproportionately limit the ability of Black households to access housing in high-opportunity areas. We build a dynamic life-cycle model to examine the long-term wealth effects of these leverage distortions on group differences in wealth…

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A Local Projections Approach to Difference‐in‐Differences

基于局部投影的双重差分方法

ABSTRACT We propose a local projections (LPs)‐based difference‐in‐differences (DiD) approach that subsumes many of the recent solutions proposed in the literature to address possible biases arising from negative weighting. We combine LPs with a flexible “clean control” condition to define appropriate sets of treated and control units. Our proposed LP‐DiD estimator can be implemented with various weighting and normalization schemes for different target estimands, can be…

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Difference‐in‐Difference Causal Forests With an Application to Payroll Tax Incidence in Norway

双重差分因果森林及其在挪威工资税负担归宿中的应用

ABSTRACT This paper introduces the difference‐in‐difference causal forest (DiDCF) method, which extends the causal‐forest technique for estimating heterogeneous treatment effects to settings with dynamic treatment effects. Regular causal forests require independence between treatment assignment and the outcome variable (after conditioning out observables). In contrast, DiDCFs provide consistent estimates with a parallel trend assumption. DiDCFs can be used to create…

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When Should Public Programs Be Privately Administered? Theory and Evidence from the Paycheck Protection Program

公共项目何时应由私人机构执行?工资保障计划的理论与证据

Abstract When should private companies allocate public resources? In our model, delegation is attractive when delay is costly, the impact of funds is similar across firms, and government and private objectives are aligned. We use novel firm-level survey data to measure heterogeneity in the impact of the Paycheck Protection Program and to assess whether banks targeted loans to high-impact firms. Banks did target loans to their most valuable pre-existing customers. However, we…

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Signaling Specific Skills and the Labor Market of College Graduates

特定技能信号与大学毕业生劳动力市场

Abstract Using administrative data and a regression discontinuity design, we study the labor market effects of a government-sponsored award given to top-performing students on Colombia’s national college exit exam. The award signals field-specific skills, leading recipients to earn seven to ten percent more than comparable peers without the signal. The benefits are concentrated among graduates from lowerreputation institutions, who enter the market with weaker signals and…

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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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Sensitivity analysis for observational studies with flexible matched designs

灵活匹配设计下观察性研究的敏感性分析

Abstract Observational studies provide invaluable opportunities to draw causal inference, but they may suffer from biases due to pretreatment differences between treated and control units. Matching is a popular approach to reduce observed covariate imbalance. To tackle unmeasured confounding, a sensitivity analysis is often conducted to investigate how robust a causal conclusion is to the strength of unmeasured confounding. For matched observational studies, Rosenbaum…

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On the asymptotic validity of confidence sets for linear functionals of solutions to integral equations

积分方程解的线性泛函置信集合的渐近有效性

Summary This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of $ W $ and $ X $ whose conditional mean given $ Z $ and $ X $ equals the conditional mean of another variable $ Y $ given $ Z $ and $ X $. Many estimands of interest in causal inference can be expressed in this form, including the average treatment effect in proximal causal inference and treatment effect contrasts in instrumental variable models. We…

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