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Estimating Treatment Effects Under Bounded Heterogeneity

有界异质性下的处理效应估计

Specifications that impose constant treatment effects are common and can be biased under heterogeneity, whereas fully flexible alternatives can be imprecise or infeasible. Under a bound on the target-weighted variance of treatment effects, this paper proposes a generalized ridge estimator, $\texttt{regulaTE}$, that yields heterogeneity-aware confidence intervals (CIs). The ridge penalty is chosen to minimize the heterogeneity-aware CI length in a homoskedastic Gaussian…

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A Practical Guide to Instrumental Variables Methods with Heterogeneous Treatment Effects

异质处理效应下工具变量方法的实用指南

Instrumental variables (IV) methods are central to applied microeconomics. While classical approaches assume linear models with constant effects, recent literature has shifted toward the local average treatment effect (LATE) framework to accommodate heterogeneous treatment effects. This paper provides a practical guide to aligning empirical practice with recent theory. We first examine how different specifications with covariates lead to distinct weighted averages of…

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Compound Selection Decisions: An Almost SURE Approach

复合选择决策:一种近乎 SURE 的方法

This paper proposes methods for producing compound selection decisions in a Gaussian sequence model. Given unknown, fixed parameters $μ_ {1:n}$ and known $σ_{1:n}$ with observations $Y_i \sim \textsf{N}(μ_i, σ_i^2)$, the decision maker would like to select a subset of indices $S$ so as to maximize utility $\frac{1}{n}\sum_{i\in S} (μ_i - K_i)$, for known costs $K_i$. Inspired by Stein's unbiased risk estimate (SURE), we introduce an almost unbiased estimator, called ASSURE,…

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Policy Learning with Confidence

兼顾置信保证的政策学习

This paper introduces a rule for policy selection in the presence of estimation uncertainty, explicitly accounting for estimation risk. The rule belongs to the class of risk-aware rules on the efficient decision frontier, characterized as policies offering maximal estimated welfare for a given level of estimation risk. Among this class, the proposed rule is chosen to provide a reporting guarantee, ensuring that the welfare delivered exceeds a threshold with a pre-specified…

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Empirical Welfare Maximization with Constraints

带约束的经验福利最大化

Empirical Welfare Maximization (EWM) is a framework that can be used to select welfare program eligibility policies based on data. This paper extends EWM by allowing for uncertainty in estimating the budget needed to implement the selected policy, in addition to its welfare. Due to the additional estimation error, I show there exist no rules that achieve the highest welfare possible while satisfying a budget constraint uniformly over a wide range of DGPs. This differs from…

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Adapting to Misspecification

适应模型误设

Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they can relax some of these assumptions to motivate a more robust, but variable, unrestricted estimator. When a bound on the bias of the restricted estimator is available, it is optimal to shrink the unrestricted estimator towards the…

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Using Multiple Outcomes to Improve the Synthetic Control Method

利用多个结果变量改进合成控制方法

When there are multiple outcome series of interest, Synthetic Control analyses typically proceed by estimating separate weights for each outcome. In this paper, we instead propose estimating a common set of weights across outcomes, by balancing either a vector of all outcomes or an index or average of them. Under a low-rank factor model, we show that these approaches lead to lower bias bounds than separate weights, and that averaging leads to further gains when the number of…

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Temporal Aggregation for the Synthetic Control Method

合成控制法中的时间聚合

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit with panel data. Two challenges arise with higher frequency data (e.g., monthly versus yearly): (1) achieving excellent pre-treatment fit is typically more challenging; and (2) overfitting to noise is more likely. Aggregating data over time can mitigate these problems but can also destroy important signal. In this paper, we bound the bias for SCM with…

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Weak Identification with Many Instruments

大量工具变量下的弱识别

Linear instrumental variable regressions are widely used to estimate causal effects. Many instruments arise from the use of ``technical'' instruments and more recently from the empirical strategy of ``judge design''. This paper surveys and summarizes ideas from recent literature on estimation and statistical inferences with many instruments for a single endogenous regressor. We discuss how to assess the strength of the instruments and how to conduct weak…

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Double Robustness for Complier Parameters and a Semiparametric Test for Complier Characteristics

服从者参数的双重稳健性与服从者特征的半参数检验

We propose a semiparametric test to evaluate (i) whether different instruments induce subpopulations of compliers with the same observable characteristics on average, and (ii) whether compliers have observable characteristics that are the same as the full population on average. The test is a flexible robustness check for the external validity of instruments. We use it to reinterpret the difference in LATE estimates that Angrist and Evans (1998) obtain when using different…

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Inference with Many Weak Instruments

大量弱工具变量下的统计推断

We develop a concept of weak identification in linear IV models in which the number of instruments can grow at the same rate or slower than the sample size. We propose a jackknifed version of the classical weak identification-robust Anderson-Rubin (AR) test statistic. Large-sample inference based on the jackknifed AR is valid under heteroscedasticity and weak identification. The feasible version of this statistic uses a novel variance estimator. The test has uniformly…

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Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects

异质处理效应下事件研究动态处理效应的估计

To estimate the dynamic effects of an absorbing treatment, researchers often use two-way fixed effects regressions that include leads and lags of the treatment. We show that in settings with variation in treatment timing across units, the coefficient on a given lead or lag can be contaminated by effects from other periods, and apparent pretrends can arise solely from treatment effects heterogeneity. We propose an alternative estimator that is free of contamination, and…

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