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Spatio-temporal Event Studies for Air Quality Assessment under Cross-sectional Dependence

横截面依赖下空气质量评估的时空事件研究

Event Studies (ES) are statistical tools that assess whether a particular event of interest has caused changes in the level of one or more relevant time series. We are interested in ES applied to multivariate time series characterized by high spatial (cross-sectional) and temporal dependence. We pursue two goals. First, we propose to extend the existing taxonomy on ES, mainly deriving from the financial field, by generalizing the underlying statistical concepts and then…

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Policy Evaluation during a Pandemic

疫情期间的政策评估

National and local governments have implemented a large number of policies in response to the Covid-19 pandemic. Evaluating the effects of these policies, both on the number of Covid-19 cases as well as on other economic outcomes is a key ingredient for policymakers to be able to determine which policies are most effective as well as the relative costs and benefits of particular policies. In this paper, we consider the relative merits of common identification strategies that…

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Structural mean models for instrumented difference-in-differences

工具变量双重差分的结构均值模型

In the standard difference-in-differences research design, the parallel trends assumption may be violated when the relationship between the exposure trend and the outcome trend is confounded by unmeasured confounders. Progress can be made if there is an exogenous variable that (i) does not directly influence the change in outcome means (i.e. the outcome trend) except through influencing the change in exposure means (i.e. the exposure trend), and (ii) is not related to the…

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When Is Parallel Trends Sensitive to Functional Form?

平行趋势何时对函数形式敏感?

This paper assesses when the validity of difference-in-differences depends on functional form. We provide a novel characterization: the parallel trends assumption holds under all strictly monotonic transformations of the outcome if and only if a stronger ``parallel trends''-type condition holds for the cumulative distribution function of untreated potential outcomes. This condition for parallel trends to be insensitive to functional form is satisfied if and essentially only…

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Difference-in-Differences with a Misclassified Treatment

处理状态误分类下的双重差分

This paper studies identification and estimation of the average treatment effect on the treated (ATT) in difference-in-difference (DID) designs when the variable that classifies individuals into treatment and control groups (treatment status, D) is endogenously misclassified. We show that misclassification in D hampers consistent estimation of ATT because 1) it restricts us from identifying the truly treated from those misclassified as being treated and 2) differential…

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Triangulating Instrumental Variable, confounder adjustment and Difference-in-Difference methods for comparative effectiveness research in observational data

观察性比较效果研究中的工具变量、混杂调整与双重差分三角验证

Observational studies can play a useful role in assessing the comparative effectiveness of competing treatments. In a clinical trial the randomization of participants to treatment and control groups generally results in well-balanced groups with respect to possible confounders, which makes the analysis straightforward. However, when analysing observational data, the potential for unmeasured confounding makes comparing treatment effects much more challenging. Causal inference…

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Alternative approaches for analysing repeated measures data that are missing not at random

非随机缺失重复测量数据的替代分析方法

We consider studies where multiple measures on an outcome variable are collected over time, but some subjects drop out before the end of follow up. Analyses of such data often proceed under either a 'last observation carried forward' or 'missing at random' assumption. We consider two alternative strategies for identification; the first is closely related to the difference-in-differences methodology in the causal inference literature. The second enables correction for…

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Two-stage differences in differences

两阶段双重差分

A recent literature has shown that when adoption of a treatment is staggered and average treatment effects vary across groups and over time, difference-in-differences regression does not identify an easily interpretable measure of the typical effect of the treatment. In this paper, I extend this literature in two ways. First, I provide some simple underlying intuition for why difference-in-differences regression does not identify a group$\times$period average treatment…

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Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey

异质处理效应下的双向固定效应与双重差分:文献综述

Linear regressions with period and group fixed effects are widely used to estimate policies' effects: 26 of the 100 most cited papers published by the American Economic Review from 2015 to 2019 estimate such regressions. It has recently been shown that those regressions may produce misleading estimates, if the policy's effect is heterogeneous between groups or over time, as is often the case. This survey reviews a fast-growing literature that documents this issue, and that…

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The Effect of Increased Access to IVF on Women's Careers

扩大试管婴儿服务可及性对女性职业发展的影响

Motherhood is the main contributor to gender gaps in the labor market. IVF is a method of assisted reproduction that can delay fertility, which results in decreased motherhood income penalty. In this research, I estimate the effects of expanded access to in vitro fertilization (IVF) arising from state insurance mandates. I use a difference-in-differences model to estimate the effect of increased IVF accessibility for delaying childbirth and decreasing the motherhood income…

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Nonparametric Difference-in-Differences in Repeated Cross-Sections with Continuous Treatments

重复截面中连续处理的非参数双重差分

This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an exogenous change over time which affects the treatment in a heterogeneous way, stationarity of the distribution of unobservables and a rank invariance condition on the time trend. On the other hand, we do not impose any functional form…

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{did2s}: Two-Stage Difference-in-Differences

did2s:两阶段双重差分方法与 R 软件包

Recent work has highlighted the difficulties of estimating difference-in-differences models when treatment timing occurs at different times for different units. This article introduces the R package did2s which implements the estimator introduced in Gardner (2021). The article provides an approachable review of the underlying econometric theory and introduces the syntax for the function did2s. Further, the package introduces a function, event_study, that provides a common…

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Difference-in-Differences for Policy Evaluation

用于政策评估的双重差分法

Difference-in-differences is one of the most used identification strategies in empirical work in economics. This chapter reviews a number of important, recent developments related to difference-in-differences. First, this chapter reviews recent work pointing out limitations of two way fixed effects regressions (these are panel data regressions that have been the dominant approach to implementing difference-in-differences identification strategies) that arise in empirically…

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Treatment Effects in Interactive Fixed Effects Models with a Small Number of Time Periods

少量时期下交互固定效应模型的处理效应

This paper considers identifying and estimating the Average Treatment Effect on the Treated (ATT) when untreated potential outcomes are generated by an interactive fixed effects model. That is, in addition to time-period and individual fixed effects, we consider the case where there is an unobserved time invariant variable whose effect on untreated potential outcomes may change over time and which can therefore cause outcomes (in the absence of participating in the…

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Do We Exploit all Information for Counterfactual Analysis? Benefits of Factor Models and Idiosyncratic Correction

反事实分析是否充分利用信息?因子模型与特异成分修正的作用

Optimal pricing, i.e., determining the price level that maximizes profit or revenue of a given product, is a vital task for the retail industry. To select such a quantity, one needs first to estimate the price elasticity from the product demand. Regression methods usually fail to recover such elasticities due to confounding effects and price endogeneity. Therefore, randomized experiments are typically required. However, elasticities can be highly heterogeneous depending on…

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Difference-in-Differences with Geocoded Microdata

使用地理编码微观数据的双重差分

This paper formalizes a common approach for estimating effects of treatment at a specific location using geocoded microdata. This estimator compares units immediately next to treatment (an inner-ring) to units just slightly further away (an outer-ring). I introduce intuitive assumptions needed to identify the average treatment effect among the affected units and illustrates pitfalls that occur when these assumptions fail. Since one of these assumptions requires knowledge of…

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Statistical Power for Estimating Treatment Effects Using Difference-in-Differences and Comparative Interrupted Time Series Designs with Variation in Treatment Timing

处理时点变化下双重差分与比较中断时间序列设计的统计功效

This article develops new closed-form variance expressions for power analyses for commonly used difference-in-differences (DID) and comparative interrupted time series (CITS) panel data estimators. The main contribution is to incorporate variation in treatment timing into the analysis. The power formulas also account for other key design features that arise in practice: autocorrelated errors, unequal measurement intervals, and clustering due to the unit of treatment…

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Geographic Difference-in-Discontinuities

地理断点差分方法

A recent econometric literature has critiqued the use of regression discontinuities where administrative borders serves as the 'cutoff'. Identification in this context is difficult since multiple treatments can change at the cutoff and individuals can easily sort on either side of the border. This note extends the difference-in-discontinuities framework discussed in Grembi et. al. (2016) to a geographic setting. The paper formalizes the identifying assumptions in this…

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Nonparametric Heterogeneous Treatment Effect Estimation in Repeated Cross Sectional Designs

重复截面设计中的非参数异质性处理效应估计

Identifying heterogeneity in a population's response to a health or policy intervention is crucial for evaluating and informing policy decisions. We propose a novel heterogeneous treatment effect estimator in the difference-in-differences design with repeated cross sectional data, where we observe different samples of a population at two time periods separated by the onset of a policy intervention, as well as samples of a population that serves as the control. Our estimator…

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Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models

以最小桥函数控制面板数据中的未观测混杂:从双向固定效应到因子模型

We develop a new approach for identifying and estimating average causal effects in panel data under a linear factor model with unmeasured confounders. Compared to other methods tackling factor models such as synthetic controls and matrix completion, our method does not require the number of time periods to grow infinitely. Instead, we draw inspiration from the two-way fixed effect model as a special case of the linear factor model, where a simple difference-in-differences…

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Synthetic Difference in Differences

合成双重差分

We present a new estimator for causal effects with panel data that builds on insights behind the widely used difference in differences and synthetic control methods. Relative to these methods we find, both theoretically and empirically, that this "synthetic difference in differences" estimator has desirable robustness properties, and that it performs well in settings where the conventional estimators are commonly used in practice. We study the asymptotic behavior of the…

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Synthesized Difference in Differences

合成式双重差分

We consider estimating the conditional average treatment effect for everyone by eliminating confounding and selection bias. Unfortunately, randomized clinical trials (RCTs) eliminate confounding but impose strict exclusion criteria that prevent sampling of the entire clinical population. Observational datasets are more inclusive but suffer from confounding. We therefore analyze RCT and observational data simultaneously in order to extract the strengths of each. Our solution…

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Inference for multi-valued heterogeneous treatment effects when the number of treated units is small

处理组单位较少时多值异质性处理效应的推断

We propose a method for conducting asymptotically valid inference for treatment effects in a multi-valued treatment framework where the number of units in the treatment arms can be small and do not grow with the sample size. We accomplish this by casting the model as a semi-/non-parametric conditional quantile model and using known finite sample results about the law of the indicator function that defines the conditional quantile. Our framework allows for structural…

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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

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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