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What do we get from two-way fixed effects regressions? Implications from numerical equivalence

双向固定效应回归估计了什么?数值等价关系的启示

Summary This paper develops numerical and causal interpretations of two-way fixed effects (TWFE) regressions in settings with nonbinary, nonstaggered treatments and time-varying covariates. Using the equivalence between TWFE and pooled first-difference (FD) regressions, I express the TWFE coefficient as a weighted average of FD coefficients across all horizons, clarifying how short- and long-run changes contribute to the estimate. Causal interpretation of the TWFE…

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Quantile treatment effects in difference-in-discontinuities designs

断点差分设计中的分位数处理效应

Summary This paper studies identification and doubly robust (DR) estimation of quantile treatment effects (QTEs) in difference-in-discontinuities (diff-in-disc) designs when a new treatment is introduced in the post period and a confounding discontinuous policy is present in both periods. We show that QTEs are point identified under a conditional stable-distributional-effect assumption for the confounding treatment, a restriction that is analogous to the distributional…

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The Value of Piped Water and Sewers: Evidence from 19th Century Chicago

自来水与下水道的价值:19世纪芝加哥的证据

Abstract We estimate the impact of piped water and sewers on property values in late 19th century Chicago. The cost of sewer construction depends sensitively on imperceptible variation in elevation, and such variation delays water and sewer service to part of the city. This delay provides quasirandom variation for causal estimates. We extrapolate ate estimates from our natural experiment to the area treated with water and sewer service during 1874–1880 using a new estimator.…

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On Recoding Ordered Treatments as Binary Indicators

将有序处理重新编码为二元指标的含义

Abstract Researchers using instrumental variables to investigate ordered treatments often recode treatment into an indicator for any exposure. We investigate this estimand under the assumption that the instruments shift compliers from no treatment to some but not from some treatment to more. We show that when extensive margin compliers only (EMCO) exist, this estimand captures a weighted average of treatment effects that can be partially unbundled into each complier group’s…

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Debiasing and t -Tests for Synthetic Control Inference on Average Causal Effects

合成控制平均因果效应推断的去偏与 t 检验

We propose a practical and robust method for making inference on average treatment effects estimated by synthetic controls. We develop a K-fold cross-fitting procedure for bias correction. To avoid the difficult estimation of the long-run variance, inference is based on a self-normalized t-statistic, which has an asymptotically pivotal t-distribution. Our t-test is easy to implement, provably robust against misspecification, and valid with stationary and nonstationary data.…

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Optimal Tests Following Sequential Experiments

序贯实验后的最优检验

We develop methods for inference following sequential experiments by studying the asymptotic properties of tests. We find that the large-sample power of any test can be matched by a test in a suitable limit experiment involving Gaussian diffusions. This establishes that a fixed set of statistics are asymptotically sufficient for testing; these are the number of times each treatment has been sampled and the final value of the score/efficient influence function process for…

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Testing for underpowered literatures

检验文献集合中的统计功效不足

How many experimental studies would have come to different conclusions had they been run on larger samples? I show how to estimate the expected number of statistically significant results that a set of experiments would have reported had their sample sizes all been counterfactually increased. The proposed deconvolution estimator is asymptotically normal and adjusts for publication bias. Unlike related methods, this approach requires no assumptions of any kind about the…

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Instrumental variable regression with varying-intensity repeated treatments

强度变化的重复处理下的工具变量回归

Instrumental variable models with repeated endogenous treatments are popular in empirical research using pooled cross-sectional or short panel datasets. This paper proposes a novel semi-parametric approach that explicitly considers 1) path dependency in the contemporaneous treatment effect and 2) a direct carryover effect from past treatments. We demonstrate that when either of these new features is present, the standard two-stage least squares estimator is generally…

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Regression adjustment in completely randomized experiments with many covariates

多协变量完全随机实验中的回归调整

This paper investigates estimation and inference for average treatment effects in completely randomized experiments when researchers observe potentially many covariates. Within Neyman’s (1923) design-based framework, allowing the number of covariates to grow more slowly than the sample size, we demonstrate that a cross-fitted regression adjustment estimator–adapted from Aronow and Middleton (2013)–exhibits more favorable asymptotic properties than existing alternatives, such…

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Difference-in-differences with interference

存在干扰时的双重差分

In many scenarios, such as the evaluation of place-based policies, potential outcomes depend not only on the unit’s own treatment but also on its neighbors’ treatments. Despite this, “difference-in-differences” (DID) type estimators typically ignore such interference among neighbors. I show in this paper that the canonical DID estimators generally fail to identify interesting causal effects in the presence of neighborhood interference. To incorporate interference structure…

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Estimation and inference on average treatment effect in percentage points under heterogeneity

异质性下百分点平均处理效应的估计与推断

In semi-logarithmic regressions, treatment coefficients are often interpreted as approximations of an average treatment effect (ATE) in percentage points. This paper highlights the overlooked bias of this approximation under treatment effect heterogeneity, arising from Jensen’s inequality. The issue is particularly relevant for difference-in-differences designs with log-transformed outcomes and staggered treatment adoption, where treatment effects may vary across groups and…

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Flexible covariate adjustments in regression discontinuity designs

断点回归设计中的灵活协变量调整

Empirical regression discontinuity (RD) studies often include covariates in their specifications to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more efficiently than existing methods and can accommodate many covariates. Our estimators are simple to implement and involve running a standard RD analysis after subtracting a function of the covariates from the original outcome variable. We…

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Identification-robust inference for the LATE with high-dimensional covariates

高维协变量下局部平均处理效应的识别稳健推断

This paper presents an inference method for the local average treatment effect (LATE) in the presence of high-dimensional covariates, regardless of the strength of identification. We propose an orthogonalized Anderson-Rubin test statistic that maintains uniformly valid asymptotic size. We provide an easy-to-implement algorithm for inferring the high-dimensional LATE by inverting our test statistic and employing the double/debiased machine learning method. Simulation results…

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Estimating individual responses when tomorrow matters

未来预期重要时的个体反应估计

We propose an approach to estimate how individuals’ expectations influence their responses to a counterfactual change. The approach relies on average partial effects, which recover counterfactual impacts under conditions that we specify. We propose a three-step estimation method that relies on panel data on subjective expectations. We illustrate our approach in a model of consumption and saving, focusing on the impact of an income tax that not only changes current income but…

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A goodness-of-fit test for sparse networks

稀疏网络的拟合优度检验

The stochastic block model (SBM) has been widely used to analyze network data. Various goodness-of-fit tests have been proposed to assess the adequacy of model structures. To the best of our knowledge, however, none of the existing approaches are applicable for sparse networks in which the connection probability of any two communities is of order n−1logn, and the number of communities is divergent. To fill this gap, we propose a novel goodness-of-fit test for the stochastic…

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Censored partial linear quantile regression with endogeneity

含内生性的删失部分线性分位数回归

This paper considers the estimation of a censored partial linear quantile regression model with endogeneity. Our method extends those for partial linear quantile regression (Lee, 2003, Qu et al. 2024), nonparametric quantile regression (Qu and Yoon, 2015, Belloni et al., 2019), and censored linear quantile regression with endogeneity (Chen, 2018). Our estimation method involves a tractable sequential-multiple-step procedure. We establish the uniform consistency, the uniform…

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Threshold spatial panel regression with fixed effects

含固定效应的门槛空间面板回归

We introduce general estimation and inference methods for threshold spatial panel regression with two-way fixed effects in a diminishing-threshold-effects framework. A valid objective function is obtained through a simple adjustment on the concentrated quasi loglikelihood with fixed effects being concentrated out, which leads to a consistent estimation of all common parameters. We show that the estimation of threshold parameter has a negligible effect on the asymptotic…

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Incorporating Micro Data into Differentiated Products Demand Estimation with PyBLP

使用 PyBLP 将微观数据纳入差异化产品需求估计

We delineate a general framework for incorporating many types of micro data from summary statistics to full surveys of selected consumers into Berry, Levinsohn, and Pakes (1995)-style estimates of differentiated products demand systems. We extend recommended practices for BLP estimation in Conlon and Gortmaker (2020) to the case with micro data and implement them in our open-source package PyBLP. Monte Carlo experiments and empirical examples suggest that incorporating micro…

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A User’s guide for inference in models defined by moment inequalities

矩不等式模型推断的实用指南

Models defined by moment inequalities have become a standard modeling framework for empirical economists, spreading over a wide range of fields within economics. From the point of view of an empirical researcher, the literature on inference in moment inequality models is large and complex, including multiple survey papers that document the non-standard features these models possess, the main novel concepts behind inference in these models, and the most recent developments…

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Gambling away stability: Sports betting’s impact on vulnerable households

赌掉稳定:体育博彩对脆弱家庭的影响

We estimate the causal effect of online sports betting on households’ investment, spending, and debt management decisions using household transaction data and a staggered difference-in-differences framework. Following legalization, sports betting spreads quickly, with both the number of participants and frequency of bets increasing over time. This increase does not displace other gambling or consumption but significantly reduces savings, as risky bets crowd out positive…

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A Smooth Specification Test for the Propensity Score

倾向得分的平滑设定检验

ABSTRACT This paper proposes a simple smooth specification test for the propensity score in the spirit of Neyman (1937). We derive a particular restriction on the propensity score and construct the specification test based on it. Using the density‐weighting method, we transform the original specification testing problem into a test of the joint significance of the generalized Fourier coefficients. We propose a novel projection method to eliminate the parameter estimation…

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Conditional Randomization Tests for the Specification of Interference Structure

干扰结构设定的条件随机化检验

ABSTRACT This study proposes specification tests for interference structure in causal inference with spillovers. We focus on experimental settings in which the treatment assignment mechanism is known. To test whether a given exposure mapping adequately summarizes the true interference structure, we develop conditional randomization tests by utilizing the hierarchical relationship between the null and alternative exposure mappings. When there are multiple candidate exposure…

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Opportunistic Upskilling in European Labour Markets—Evidence From a Wide Replication

欧洲劳动力市场的机会性技能升级:广泛复现证据

ABSTRACT We build on Modestino et al., who analysed “opportunistic upskilling” during the 2007 recession in the US, by extending their approach to European labour markets following recent economic shocks. Using a comprehensive dataset of online job postings (2019–2023) and an instrumental variable approach leveraging Ukrainian refugee inflows, we find that increases in labour supply have a significant positive effect on both education and experience requirements. Our…

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Regularization of Synthetic Controls for Policy Evaluation

政策评估中合成控制的正则化

ABSTRACT We propose a unified framework for interpreting and comparing a broad class of synthetic control (SC) methods. Our framework is built on an analysis of a mean‐squared prediction error (MSPE) bound for the counterfactual predicted by a generic SC method, without imposing a specific outcome model. Using this framework, we develop a generalized SC method that provides a more comprehensive regularization of the MSPE bound than several existing SC methods. Through…

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