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The wild bootstrap for few (treated) clusters

处理簇很少时的野生自助法

Inference based on cluster‐robust standard errors in linear regression models, using either the Student's t‐distribution or the wild cluster bootstrap, is known to fail when the number of treated clusters is very small. We propose a family of new procedures called the subcluster wild bootstrap, which includes the ordinary wild bootstrap as a limiting case. In the case of pure treatment models, where all observations within clusters are either treated or not, the latter…

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Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics

利用 L 统计量对(条件)分位数差与分位距进行非参数推断

We provide novel, high‐order accurate methods for non‐parametric inference on quantile differences between two populations in both unconditional and conditional settings. These quantile differences correspond to (conditional) quantile treatment effects under (conditional) independence of a binary treatment and potential outcomes. Our methods use the probability integral transform and a Dirichlet (rather than Gaussian) reference distribution to pick appropriate L‐statistics…

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Efficient propensity score regression estimators of multivalued treatment effects for the treated

多值处理下受处理者效应的有效倾向得分回归估计

When a multivalued treatment is randomly assigned conditional on observables, valid causal comparisons for a subpopulation treated at a particular treatment level require two propensity scores—one for the treated level and one for the counterfactual level. We contribute efficient propensity score regression estimators to a class of treatment effects for the treated, under the cases when the propensity scores are unknown and when they are known. Our efficient estimator…

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ON NONPARAMETRIC INFERENCE IN THE REGRESSION DISCONTINUITY DESIGN

断点回归设计中的非参数推断

This paper studies the validity of nonparametric tests used in the regression discontinuity design. The null hypothesis of interest is that the average treatment effect at the threshold in the so-called sharp design equals a pre-specified value. We first show that, under assumptions used in the majority of the literature, for any test the power against any alternative is bounded above by its size. This result implies that, under these assumptions, any test with nontrivial…

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Minimum distance approach to inference with many instruments

多工具变量推断的最小距离方法

I analyze a linear instrumental variables model with a single endogenous regressor and many instruments. I use invariance arguments to construct a new minimum distance objective function. With respect to a particular weight matrix, the minimum distance estimator is equivalent to the random effects estimator of Chamberlain and Imbens (2004), and the estimator of the coefficient on the endogenous regressor coincides with the limited information maximum likelihood estimator.…

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Labor Misallocation and Mass Mobilization: Russian Agriculture during the Great War

劳动力错配与大规模动员:第一次世界大战期间的俄国农业

We exploit a quasi-natural experiment of military draftees in Russia during World War I to examine the effects of a massive, negative labor shock on agricultural production. Employing a novel district-level panel data set, we find that mass mobilization produces a dramatic decrease in cultivated area. Surprisingly, farms with communal land tenure exhibit greater resilience to the labor shock than private farms. The resilience stems from peasants reallocating labor in favor…

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Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes

工具变量下平均处理效应的部分识别:二元工具、处理与结果的方法综述

Several methods have been proposed for partially or point identifying the average treatment effect (ATE) using instrumental variable (IV) type assumptions. The descriptions of these methods are widespread across the statistical, economic, epidemiologic, and computer science literature, and the connections between the methods have not been readily apparent. In the setting of a binary instrument, treatment, and outcome, we review proposed methods for partial and point…

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A Permutation Test for the Regression Kink Design

回归折点设计的置换检验

The regression kink (RK) design is an increasingly popular empirical method for estimating causal effects of policies, such as the effect of unemployment benefits on unemployment duration. Using simulation studies based on data from existing RK designs, we empirically document that the statistical significance of RK estimators based on conventional standard errors can be spurious. In the simulations, false positives arise as a consequence of nonlinearities in the underlying…

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Using Standard Tools From Finite Population Sampling to Improve Causal Inference for Complex Experiments

运用有限总体抽样工具改进复杂实验的因果推断

This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling, an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments. This framework extends classical methods by allowing the possibility of randomization…

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Bayesian Inference for Assessing Effects of Email Marketing Campaigns

评估电子邮件营销活动效果的贝叶斯推断

Email marketing has been an increasingly important tool for today’s businesses. In this article, we propose a counting-process-based Bayesian method for quantifying the effectiveness of email marketing campaigns in conjunction with customer characteristics. Our model explicitly addresses the seasonality of data, accounts for the impact of customer characteristics on their purchasing behavior, and evaluates effects of email offers as well as their interactions with customer…

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Bayesian Factor Model Shrinkage for Linear IV Regression With Many Instruments

多工具变量线性 IV 回归的贝叶斯因子模型收缩

A Bayesian approach for the many instruments problem in linear instrumental variable models is presented. The new approach has two components. First, a slice sampler is developed, which leverages a decomposition of the likelihood function that is a Bayesian analogue to two-stage least squares. The new sampler permits nonconjugate shrinkage priors to be implemented easily and efficiently. The new computational approach permits a Bayesian analysis of problems that were…

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Measuring Nonlinear Granger Causality in Mean

均值中非线性Granger因果性的度量

We propose model-free measures for Granger causality in mean between random variables. Unlike the existing measures, ours are able to detect and quantify nonlinear causal effects. The new measures are based on nonparametric regressions and defined as logarithmic functions of restricted and unrestricted mean square forecast errors. They are easily and consistently estimated by replacing the unknown mean square forecast errors by their nonparametric kernel estimates. We derive…

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Fuzzy Differences-in-Differences

模糊双重差分

Difference-in-differences (DID) is a method to evaluate the effect of a treatment. In its basic version, a “control group” is untreated at two dates, whereas a “treatment group” becomes fully treated at the second date. However, in many applications of the DID method, the treatment rate only increases more in the treatment group. In such fuzzy designs, a popular estimator of the treatment effect is the DID of the outcome divided by the DID of the treatment. We show that this…

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A Simple Adjustment for Bandwidth Snooping

带宽窥探的简单校正

Kernel-based estimators such as local polynomial estimators in regression discontinuity designs are often evaluated at multiple bandwidths as a form of sensitivity analysis. However, if in the reported results, a researcher selects the bandwidth based on this analysis, the associated confidence intervals (CIs) may not have correct coverage, even if the estimator is unbiased. This article proposes a simple adjustment that gives correct coverage in such situations: replace the…

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Frequency domain minimum distance inference for possibly noninvertible and noncausal ARMA models

可能不可逆与非因果 ARMA 模型的频域最小距离推断

This article introduces frequency domain minimum distance procedures for performing inference in general, possibly non causal and/or noninvertible, autoregressive moving average (ARMA) models. We use information from higher order moments to achieve identification on the location of the roots of the AR and MA polynomials for non-Gaussian time series. We propose a minimum distance estimator that optimally combines the information contained in second, third, and fourth moments.…

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Identification issues in the public/private wage gap, with an application to Italy

公私部门工资差距的识别问题:意大利应用

Summary This paper reviews some of the standard assumptions that are imposed in order to estimate the average public/private wage gap and that are mainly related to the possible selection of the sector. There are two contributions to the existing public/private wage gap literature. One is a better understanding of the identified parameters: standard estimators identify a local effect (LATE), which in general cannot be generalized to the entire population, as instead is…

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Self‐employment among women: Do children matter more than we previously thought?

女性自雇:子女的影响是否比我们此前认为的更大?

Summary This paper presents an estimation approach that addresses the problems of sample selection and endogeneity of fertility decisions when estimating the effect of young children on women's self‐employment. Using data from the National Longitudinal Survey of Youth 1979, 1982–2006, we find that ignoring self‐selection and endogeneity leads to underestimating the effect of young children. Once both sources of biases are accounted for, the estimated effect of young children…

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On causal estimation using $U$-statistics

基于 U 统计量的因果估计

We introduce a general class of causal estimands which extends the familiar notion of average treatment effect. The class is defined by a contrast function, prespecified to quantify the relative favourability of one outcome over another, averaged over the marginal distributions of two potential outcomes. Natural estimators arise in the form of |$U$|-statistics. We derive both a naive inverse propensity score weighted estimator and a class of locally efficient and doubly…

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Kernel-based covariate functional balancing for observational studies

观察性研究中基于核的协变量函数平衡

Covariate balance is often advocated for objective causal inference since it mimics randomization in observational data. Unlike methods that balance specific moments of covariates, our proposal attains uniform approximate balance for covariate functions in a reproducing-kernel Hilbert space. The corresponding infinite-dimensional optimization problem is shown to have a finite-dimensional representation in terms of an eigenvalue optimization problem. Large-sample results are…

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Simple least squares estimator for treatment effects using propensity score residuals

利用倾向得分残差估计处理效应的简单最小二乘方法

Propensity score matching is widely used to control covariates when analysing the effects of a nonrandomized binary treatment. However, it requires several arbitrary decisions, such as how many matched subjects to use and how to choose them. In this paper a simple least squares estimator is proposed, where the treatment, and possibly the response variable, is replaced by the propensity score residual. The proposed estimator controls covariates semiparametrically if the…

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A randomization-based perspective on analysis of variance: a test statistic robust to treatment effect heterogeneity

随机化视角下的方差分析:对处理效应异质性稳健的检验统计量

Fisher randomization tests for Neyman’s null hypothesis of no average treatment effect are considered in a finite-population setting associated with completely randomized experiments involving more than two treatments. The consequences of using the |$F$| statistic to conduct such a test are examined, and we argue that under treatment effect heterogeneity, use of the |$F$| statistic in the Fisher randomization test can severely inflate the Type I error under Neyman’s null…

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Threshold regression with endogeneity

存在内生性的门槛回归

This paper studies estimation in threshold regression with endogeneity in the regressors and thresholding variable. Three key results differ from those in regular models. First, both the threshold point and the threshold effect parameters are shown to be identified without the need for instrumentation. Second, in partially linear threshold models, both parametric and nonparametric components rely on the same data, which prima facie suggests identification failure. But, as…

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Board diversity, firm risk, and corporate policies

董事会多样性、企业风险与公司政策

We examine the effects of diversity in the board of directors on corporate policies and risk. Using a multidimensional measure, we find that greater board diversity leads to lower volatility and better performance. The lower risk levels are largely due to diverse boards adopting more persistent and less risky financial policies. However, consistent with diversity fostering more efficient (real) risk-taking, firms with greater board diversity also invest persistently more in…

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Testing Rank Similarity

秩相似性检验

We introduce a test of the rank invariance or rank similarity assumption common in treatment effects and instrumental variables models. The test probes the implication that the conditional distribution of ranks should be identical across treatment states using a regression-based test statistic. We apply the test to data from the Tennessee STAR class-size reduction experiment and show that systematic slippages in rank can be important statistically and economically.

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