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Randomization Tests in Observational Studies With Staggered Adoption of Treatment

交错采用处理的观察性研究中的随机化检验

This article considers the problem of inference in observational studies with time-varying adoption of treatment. In addition to an unconfoundedness assumption that the potential outcomes are independent of the times at which units adopt treatment conditional on the units’ observed characteristics, our analysis assumes that the time at which each unit adopts treatment follows a Cox proportional hazards model. This assumption permits the time at which each unit adopts…

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Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data

矩阵补全、反事实与缺失数据的因子分析

This paper proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it is shown that the common component can be consistently estimated at four different rates of convergence without requiring regularization or iteration. An asymptotic analysis of the…

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On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls

大量时期与大量对照单位下合成控制估计量的性质

We consider the asymptotic properties of the synthetic control (SC) estimator when both the number of pretreatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which the SC unit asymptotically recovers the factor structure of the treated unit, even when the pretreatment fit is imperfect. This happens when there are weights diluted among an increasing number of control units such that a weighted average…

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Counterfactual Analysis With Artificial Controls: Inference, High Dimensions, and Nonstationarity

人工对照的反事实分析:推断、高维与非平稳性

Recently, there has been growing interest in developing statistical tools to conduct counterfactual analysis with aggregate data when a single “treated” unit suffers an intervention, such as a policy change, and there is no obvious control group. Usually, the proposed methods are based on the construction of an artificial counterfactual from a pool of “untre ated” peers, organized in a panel data structure. In this article, we consider a general framework for counterfactual…

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The Augmented Synthetic Control Method

增广合成控制法

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The “synthetic control” is a weighted average of control units that balances the treated unit’s pretreatment outcomes and other covariates as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pretreatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings…

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On Robustness of Principal Component Regression

主成分回归的稳健性

Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy, missing, and mixed-valued, that is, discrete and continuous, covariates is not understood and remains an important open challenge. As the main contribution of this work, we establish the robustness of PCR, without any change, in this respect…

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An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls

反事实与合成控制的精确稳健共形推断方法

We introduce new inference procedures for counterfactual and synthetic control methods for policy evaluation. We recast the causal inference problem as a counterfactual prediction and a structural breaks testing problem. This allows us to exploit insights from conformal prediction and structural breaks testing to develop permutation inference procedures that accommodate modern high-dimensional estimators, are valid under weak and easy-to-verify conditions, and are provably…

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Matrix Completion Methods for Causal Panel Data Models

因果面板数据模型的矩阵补全方法

In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated unit/period combinations. We propose a class of matrix completion estimators that uses the observed elements of the matrix of control outcomes corresponding to untreated unit/periods to impute the "missing" elements of the control outcome matrix,…

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A Bayesian Hierarchical CACE Model Accounting for Incomplete Noncompliance With Application to a Meta-analysis of Epidural Analgesia on Cesarean Section

处理不完整依从信息的贝叶斯分层 CACE 模型:硬膜外镇痛与剖宫产的荟萃分析

Noncompliance with assigned treatments is a common challenge in analyzing and interpreting randomized clinical trials (RCTs). One way to handle noncompliance is to estimate the complier-average causal effect (CACE), the intervention's efficacy in the subpopulation that complies with assigned treatment. In a two-step meta-analysis, one could first estimate CACE for each study, then combine them to estimate the population-averaged CACE. However, when some trials do not report…

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Biased Encouragements and Heterogeneous Effects in an Instrumental Variable Study of Emergency General Surgical Outcomes

急诊普外科结局工具变量研究中的偏倚鼓励与异质性效应

We investigate the efficacy of surgical versus nonsurgical management for two gastrointestinal conditions, colitis and diverticulitis, using observational data. We deploy an instrumental variable design with surgeons’ tendencies to operate as an instrument. Assuming instrument validity, we find that nonsurgical alternatives can reduce both hospital length of stay and the risk of complications, with estimated effects larger for septic patients than for nonseptic patients. The…

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Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs

多阈值回归不连续设计中的处理效应外推

In non-experimental settings, the Regression Discontinuity (RD) design is one of the most credible identification strategies for program evaluation and causal inference. However, RD treatment effect estimands are necessarily local, making statistical methods for the extrapolation of these effects a key area for development. We introduce a new method for extrapolation of RD effects that relies on the presence of multiple cutoffs, and is therefore design-based. Our approach…

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Randomization Tests for Weak Null Hypotheses in Randomized Experiments

随机实验中弱零假设的随机化检验

The Fisher randomization test (FRT) is appropriate for any test statistic, under a sharp null hypothesis that can recover all missing potential outcomes. However, it is often sought after to test a weak null hypothesis that the treatment does not affect the units on average. To use the FRT for a weak null hypothesis, we must address two issues. First, we need to impute the missing potential outcomes although the weak null hypothesis cannot determine all of them. Second, we…

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A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models

在线性模型中引出、纳入并约束识别信念的框架

To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of interest. Yet beliefs about instrument validity do not exist in isolation. Applied researchers often discuss the likely direction of selection and the potential for measurement error in their articles but lack formal tools for incorporating…

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Measuring Granger Causality in Quantiles

分位数格兰杰因果性的度量

We consider measures of Granger causality in quantiles, which detect and quantify both linear and nonlinear causal effects between random variables. The measures are based on nonparametric quantile regressions and defined as logarithmic functions of restricted and unrestricted expectations of quantile check loss functions. They can consistently be estimated by replacing the unknown expectations of check loss functions by their nonparametric kernel estimates. We derive a…

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Do Environmental Markets Improve on Open Access? Evidence from California Groundwater Rights

环境市场能否优于开放取用?来自加州地下水权的证据

Environmental markets are widely prescribed as an alternative to open access regimes for natural resources. We develop a model of dynamic groundwater extraction to demonstrate how a spatial regression discontinuity design that exploits a spatially incomplete market for groundwater rights recovers a lower bound on the market’s net benefit. We apply this estimator to a major aquifer in water-scarce southern California and find that a groundwater market generated substantial…

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Inference for a two-stage enrichment design

两阶段富集试验设计的统计推断

Two-stage enrichment designs can be used to target the benefiting population in clinical trials based on patients’ biomarkers. In the case of continuous biomarkers, we show that using a bivariate model that treats biomarkers as random variables more accurately identifies a treatment-benefiting enriched population than assuming biomarkers are fixed. Additionally, we show that under the bivariate model, the maximum likelihood estimators (MLEs) follow a randomly scaled mixture…

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And the children shall lead: Gender diversity and performance in venture capital

孩子引领改变:风险投资中的性别多样性与业绩

Given overall lack of gender diversity in the venture capital and entrepreneurship industry shown in Calder-Wang and Gompers (2017) we ask: What promotes greater gender diversity in hiring? Does diversity lead to better firm performance and higher investment returns? In this paper, using a unique dataset of the gender of venture capital partners’ children, we find strong evidence that when partners have more daughters, the propensity to hire female partners increases.…

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Targeted monetary policy and bank lending behavior

定向货币政策与银行贷款行为

We exploit an allocation rule set by the ECB for the first series of TLTROs to study the effects of targeted monetary policy on banks’ credit supply to firms. Combining transaction-level data from the Italian credit register and an instrumental variable identification strategy, we find that targeted longer-term central bank liquidity decreased rates and increased loan amounts, also avoiding some unintended consequences of untargeted measures, such as carry-trade strategies…

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Instrument-based estimation with binarised treatments: issues and tests for the exclusion restriction

处理变量二值化后的工具变量估计:排除限制问题与检验

Summary When estimating local average and marginal treatment effects using instrumental variables (IVs), multivalued endogenous treatments are frequently converted to binary measures, supposedly to improve interpretability or policy relevance. Such binarisation introduces a violation of the IV exclusion if (a) the IV affects the multivalued treatment within support areas below and/or above the threshold and (b) such IV-induced changes in the multivalued treatment affect the…

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The Confidence Interval Method for Selecting Valid Instrumental Variables

选择有效工具变量的置信区间方法

Abstract We propose a new method, the confidence interval (CI) method, to select valid instruments from a larger set of potential instruments for instrumental variable (IV) estimation of the causal effect of an exposure on an outcome. Invalid instruments are such that they fail the exclusion conditions and enter the model as explanatory variables. The CI method is based on the CIs of the per instrument causal effects estimates and selects the largest group with all CIs…

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Leveraging the Fisher Randomization Test using Confidence Distributions: Inference, Combination and Fusion Learning

借助置信分布拓展Fisher随机化检验:推断、组合与融合学习

Abstract The flexibility and wide applicability of the Fisher randomization test (FRT) make it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions. Such a connection leads to development’s of (i) an unambiguous procedure for inversion of FRTs to generate…

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Optimal Statistical Inference for Individualized Treatment Effects in High-Dimensional Models

高维模型中个体化处理效应的最优统计推断

Abstract The ability to predict individualized treatment effects (ITEs) based on a given patient's profile is essential for personalized medicine. We propose a hypothesis testing approach to choosing between two potential treatments for a given individual in the framework of high-dimensional linear models. The methodological novelty lies in the construction of a debiased estimator of the ITE and establishment of its asymptotic normality uniformly for an arbitrary future…

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Sieve estimation of option-implied state price density

期权隐含状态价格密度的筛估计

This paper proposes a nonparametric estimator for the state price density implied by a single cross-section of European options with different strikes and the same maturity. The proposed estimator has two distinctive features. First, it extracts information from both call and put options, as opposed to only call options. Second, it does not require estimating any second-order derivative; instead, it solves a constrained and penalized linear regression. The asymptotic…

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Did Protestantism promote prosperity via higher human capital? Replicating the Becker–Woessmann (2009) results

新教是否通过提高人力资本促进繁荣?复现Becker–Woessmann结果

Summary This paper shows that the Becker–Woessmann reformulation of the Weber thesis—Protestants were more prosperous in 19th‐century Prussia because they had higher human capital—is untenable. Regional variations in the Prussian institutional framework influenced economic outcomes, but Becker and Woessmann's econometric analysis takes no account of these variables, which suggests that their instrumental variable—distance to Wittenberg, a spatial variable—is invalid. When…

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