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DID 与事件研究:双重差分、多期处理与事件研究。
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Revisiting Event-Study Designs: Robust and Efficient Estimation

Abstract We develop a framework for difference-in-differences designs with staggered treatment adoption and heterogeneous causal effects. We show that conventional regression-based estimators fail to provide unbiased estimates of relevant estimands absent strong restrictions on treatment-effect homogeneity. We then derive the efficient estimator addressing this challenge, which takes an intuitive “imputation” form when treatment-effect heterogeneity is unrestricted. We…

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Causal models for longitudinal and panel data: a survey

Summary In this survey we discuss the recent causal panel data literature. This recent literature has focused on credibly estimating causal effects of binary interventions in settings with longitudinal data, emphasising practical advice for empirical researchers. It pays particular attention to heterogeneity in the causal effects, often in situations where few units are treated and with particular structures on the assignment pattern. The literature has extended earlier work…

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On “Imputation of Counterfactual Outcomes When the Errors Are Predictable”: Viewing the PUP as the DID and the LDV

从双重差分与滞后因变量视角理解 PUP

I discuss the practical unbiased predictor (PUP; Gonçalves and Ng) from the viewpoint of the literature on identification in event studies. The PUP can be seen as the prediction based on a generalized estimand that encompasses both the difference-in-differences (DID) and the lagged dependent variable (LDV). This feature of the PUP allows for a doubly robust property that the identification is achieved when either the parallel trend assumption or the LDV assumption holds at…

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Testing for Equivalence of Pre-Trends in Difference-in-Differences Estimation

双重差分估计中处理前趋势的等价性检验

The plausibility of the “parallel trends assumption” in Difference-in-Differences estimation is usually assessed by a test of the null hypothesis that the difference between the average outcomes of both groups is constant over time before the treatment. However, failure to reject the null hypothesis does not imply the absence of differences in time trends between both groups. We provide equivalence tests that allow researchers to find evidence in favor of the parallel trends…

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Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models

非随机缺失下的矩阵补全及其在因果面板模型中的应用

This paper develops an inferential framework for matrix completion when missing is not at random and without the requirement of strong signals. Our development is based on the observation that if the number of missing entries is small enough compared to the panel size, then they can be estimated well even when missing is not at random. Taking advantage of this fact, we divide the missing entries into smaller groups and estimate each group via nuclear norm regularization. In…

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Part‐time subsidies and maternal reemployment: Evidence from a difference‐in‐differences analysis

兼职补贴与母亲再就业:双重差分分析的证据

Summary Employment interruptions of mothers are still one of the main causes for different labour market outcomes between women and men. Employment subsidies can incentivise mothers to shorten employment interruptions after childbirth. We examine a German parental leave reform incentivising an early return to part‐time work. Exploiting the exogenous variation defined by the child's birthday, we apply unconditional difference‐in‐differences (DiD) estimation using…

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Terrorism and education: Evidence from instrumental variables estimators

恐怖主义与教育:工具变量估计的证据

Summary This paper estimates the effect of exposure to terrorist violence on education. Since terrorists may choose targets endogenously, we construct a set of novel instruments. To that end, we leverage exogenous variation from a local terrorist group's revenues and its affiliation with al‐Qaeda. Across several Kenyan datasets, we find that attacks suppress school enrolment more than predicted by difference‐in‐differences‐type estimators. This indicates that terrorists…

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A Negative Correlation Strategy for Bracketing in Difference-in-Differences

双重差分中构造效应界限的负相关策略

The method of difference-in-differences (DID) is widely used to study the causal effect of policy interventions in observational studies. DID employs a before and after comparison of the treated and control units to remove bias due to time-invariant unmeasured confounders under the parallel trends assumption. Estimates from DID, however, will be biased if the outcomes for the treated and control units evolve differently in the absence of treatment, namely if the parallel…

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Human capital and migration: A cautionary tale

人力资本与迁移:一个警示性案例

We analyze the impact that the option of migration might have on human capital accumulation. We show that, when the return to education for migrants is lower in the destination than in the origin, the overall incentive to accumulate human capital is reduced as restrictions on migration are relaxed. We use panel data from the Chinese Household Income Project to document that the return to education for rural individuals is lower in urban areas than in rural areas. We then use…

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Warding off Development: Local Control, Housing Supply, and NIMBYs

Abstract Local control of land-use regulation creates a not-in-my-backyard (NIMBY) problem that can suppress housing construction, contributing to rising prices and potentially slowing economic growth. I study how increased local control affects housing production by exploiting a common electoral reform—changing from “at-large” to “ward” elections for town council. These reforms, which are not typically motivated by housing markets, shrink each representative’s constituency…

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Changes in Social Network Structure in Response to Exposure to Formal Credit Markets

Abstract We show that the entry of formal financial institutions can have far-reaching and long-lasting impacts on informal lending and social networks more generally. We first study the introduction of microfinance in 75 villages in Karnataka, India, 43 of which were exposed to microfinance. Using difference-in-differences, we show that networks shrank more in exposed villages. Moreover, links between households that were both unlikely to borrow from microfinance were at…

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Correcting attrition bias using changes-in-changes

利用变化中的变化方法修正样本流失偏差

Attrition is a common and potentially important threat to internal validity in treatment effect studies. We extend the changes-in-changes approach to identify the average treatment effect for respondents and the entire study population in the presence of attrition. Our method, which exploits baseline outcome data, can be applied to randomized experiments as well as quasi-experimental difference-in-difference designs. A formal comparison highlights that while widely used…

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Mandatory seatbelt laws and traffic fatalities: A reassessment

强制安全带法规与交通死亡:重新评估

Abstract Using data from the Fatality Analysis Reporting System for the period 1983–1997, Cohen and Einav ( Review of Economics and Statistics 2003; 85[4]: 828–843) found that mandatory seatbelt laws were associated with a 4–6% reduction in traffic fatalities among motor vehicle occupants. After successfully replicating their two‐way fixed effects estimates, we (1) add 22 years of data (1998–2019) to capture additional seatbelt policy variation and observe a longer…

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Spatial Correlation Robust Inference in Linear Regression and Panel Models

线性回归与面板模型中的空间相关稳健推断

We consider inference about a scalar coefficient in a linear regression with spatially correlated errors. Recent suggestions for more robust inference require stationarity of both regressors and dependent variables for their large sample validity. This rules out many empirically relevant applications, such as difference-in-difference designs. We develop a robustified version of the recently suggested SCPC method that addresses this challenge. We find that the method has good…

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Two-way fixed effects and differences-in-differences estimators with several treatments

多种处理下的双向固定效应与双重差分估计

We study two-way-fixed-effects regressions (TWFE) with several treatment variables. Under a parallel trends assumption, we show that the coefficient on each treatment identifies a weighted sum of that treatment’s effect, with possibly negative weights, plus a weighted sum of the effects of the other treatments. Thus, those estimators are not robust to heterogeneous effects and may be contaminated by other treatments’ effects. We further show that omitting a treatment from…

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Simple approaches to nonlinear difference-in-differences with panel data

Summary I derive simple, flexible strategies for difference-in-differences settings where the nature of the response variable may warrant a nonlinear model. I allow for general staggered interventions, with and without covariates. Under an index version of parallel trends, I show that average treatment effects on the treated (ATTs) are identified for each cohort and calendar time period in which a cohort was subjected to the intervention. The pooled quasi-maximum likelihood…

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Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey

Summary Linear regressions with period and group fixed effects are widely used to estimate policie’s 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…

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A More Credible Approach to Parallel Trends

Abstract This paper proposes tools for robust inference in difference-in-differences and event-study designs where the parallel trends assumption may be violated. Instead of requiring that parallel trends holds exactly, we impose restrictions on how different the post-treatment violations of parallel trends can be from the pre-treatment differences in trends (“pre-trends”). The causal parameter of interest is partially identified under these restrictions. We introduce two…

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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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What’s trending in difference-in-differences? A synthesis of the recent econometrics literature

双重差分的新进展:近期计量文献的综合梳理

This paper synthesizes recent advances in the econometrics of difference-in-differences (DiD) and provides concrete recommendations for practitioners. We begin by articulating a simple set of “canonical” assumptions under which the econometrics of DiD are well-understood. We then argue that recent advances in DiD methods can be broadly classified as relaxing some components of the canonical DiD setup, with a focus on (i) multiple periods and variation in treatment timing,…

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On event studies and distributed‐lags in two‐way fixed effects models: Identification, equivalence, and generalization

双向固定效应中的事件研究与分布滞后:识别、等价及推广

Summary We discuss three important properties of panel data event study designs. First, assuming constant treatment effects before and/or after some event time, also known as binning, is a natural restriction, which identifies dynamic treatment effects in the absence of never‐treated units. Second, event study designs with binned endpoints and distributed‐lag models are numerically identical. Third, classic dummy variable event study designs can be generalized to models that…

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Nonparametric difference-in-differences in repeated cross-sections with continuous treatments

重复截面与连续处理下的非参数双重差分

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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Common Ownership, Competition, and Top Management Incentives

We present a mechanism based on managerial incentives through which common ownership affects product market outcomes. Firm-level variation in common ownership causes variation in managerial incentives and productivity across firms, which leads to intraindustry and intrafirm cross-market variation in prices, output, markups, and market shares that is consistent with empirical evidence. The organizational structure of multiproduct firms and the passivity of common owners…

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Inference in difference‐in‐differences: How much should we trust in independent clusters?

双重差分推断:独立聚类假设有多可信?

Summary We analyze the challenges for inference in difference‐in‐differences (DID) when there is spatial correlation. We present novel theoretical insights and empirical evidence on the settings in which ignoring spatial correlation should lead to more or less distortions in DID applications. We show that details, such as the time frame used in the estimation, the choice of the treated and control groups, and the choice of the estimator, are key determinants of distortions…

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