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合成控制:合成控制及其扩展。
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Synthetic Survival Control: Extending Synthetic Controls for "When-If" Decision

合成生存控制:面向事件发生时间反事实的合成控制扩展

Estimating causal effects on time-to-event outcomes from observational data is particularly challenging due to censoring, limited sample sizes, and non-random treatment assignment. The need for answering such "when-if" questions--how the timing of an event would change under a specified intervention--commonly arises in real-world settings with heterogeneous treatment adoption and confounding. To address these challenges, we propose Synthetic Survival Control (SSC) to…

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Synthetic Parallel Trends

合成平行趋势

Popular empirical strategies for policy evaluation in the panel data literature -- including difference-in-differences (DID), synthetic control (SC) methods, and their variants -- rely on key identifying assumptions that can be expressed through a specific choice of weights $ω$ relating pre-treatment trends to the counterfactual outcome. While each choice of $ω$ may be defensible in empirical contexts that motivate a particular method, it relies on fundamentally untestable…

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Asymptotically Unbiased Synthetic Control Methods by Moment Matching

基于矩匹配的渐近无偏合成控制方法

Synthetic Control Methods (SCMs) have become a fundamental tool for comparative case studies. The core idea behind SCMs is to estimate treatment effects by predicting counterfactual outcomes for a treated unit using a weighted combination of observed outcomes from untreated units. The accuracy of these predictions is crucial for evaluating the treatment effect of a policy intervention. Subsequent research has therefore focused on estimating SC weights. In this study, we…

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Bayesian shrinkage priors for penalized synthetic control estimators in the presence of spillovers

存在溢出效应时惩罚合成控制估计的贝叶斯收缩先验

Synthetic control (SC) methods are widely used to estimate the effects of policy interventions, especially those targeting specific geographic regions, referred to as units. These methods construct a weighted combination of untreated units, forming a "synthetic" control that approximates the counterfactual outcomes of the treated unit had the intervention not occurred. Although neighboring areas are often selected as controls due to their similarity in observed and…

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Efficiently Learning Synthetic Control Models for High-dimensional Disaggregated Data

高维细分数据中合成控制模型的高效学习

The Synthetic Control method (SC) has become a valuable tool for estimating causal effects. Originally designed for single-treated unit scenarios, it has recently found applications in high-dimensional disaggregated settings with multiple treated units. However, challenges in practical implementation and computational efficiency arise in such scenarios. To tackle these challenges, we propose a novel approach that integrates the Multivariate Square-root Lasso method into the…

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Estimating the Impact of the Bitcoin Halving on Its Price Using Synthetic Control

利用合成控制估计比特币减半对价格的影响

The third Bitcoin halving that took place in May 2020 cut down the mining reward from 12.5 to 6.25 BTC per block and thus slowed down the rate of issuance of new Bitcoins, making it more scarce. The fourth and most recent halving happened in April 2024, cutting the block reward further to 3.125 BTC. If the demand did not decrease simultaneously after these halvings, then the neoclassical economic theory posits that the price of Bitcoin should have increased due to the…

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Choosing an analytic approach: Key study design considerations in state policy evaluation

如何选择分析方法:州级政策评估中的关键研究设计考量

This paper reviews and details methods for state policy evaluation to guide selection of a research approach based on evaluation setting and available data. We highlight key design considerations for an analysis, including treatment and control group selection, timing of policy adoption, expected effect heterogeneity, and data considerations. We then provide an overview of analytic approaches and differentiate between methods based on evaluation context, such as settings…

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Autoregressive models for panel data causal inference with application to state-level opioid policies

面板因果推断中的自回归模型:州级阿片类药物政策应用

Motivated by the study of state opioid policies, we propose a novel approach that uses autoregressive models for causal effect estimation in settings with panel data and staggered treatment adoption. Specifically, we seek to estimate the impact of key opioid-related policies by quantifying the effects of must access prescription drug monitoring programs (PDMPs), naloxone access laws (NALs), and medical marijuana laws on opioid prescribing. Existing methods, such as…

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Consistency of an Intercept-Shifted Synthetic-Control Estimator under Weighted Parallel Trends

加权平行趋势下截距平移合成控制估计量的一致性

The average treatment effect on the treated (ATT) in a staggered-adoption panel is estimated using an intercept-augmented synthetic-control (SCM) estimator. A weighted parallel trends plus an intercept shift, together with mild regularity on the weight vectors (non-degenerate dispersion) and expanding pre-treatment length, are sufficient for consistency allowing for heavy-tailed shocks. These conditions can be more interpretable than the autoregressive or low-rank factor…

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Correlated Synthetic Controls

相关合成控制

Synthetic Control methods have recently gained considerable attention in applications with only one treated unit. Their popularity is partly based on the key insight that we can predict good synthetic counterfactuals for our treated unit. However, this insight of predicting counterfactuals is generalisable to microeconometric settings where we often observe many treated units. We propose the Correlated Synthetic Controls (CSC) estimator for such situations: intuitively, it…

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Practical considerations for Gaussian Process modeling for causal inference quasi-experimental studies with panel data

面板数据准实验因果推断中高斯过程建模的实践考量

Estimating causal effects in quasi-experiments with spatio-temporal panel data often requires adjusting for unmeasured confounding that varies across space and time. Gaussian Processes (GPs) offer a flexible, nonparametric modeling approach that can account for such complex dependencies through carefully chosen covariance kernels. In this paper, we provide a practical and interpretable framework for applying GPs to causal inference in panel data settings. We demonstrate how…

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Quantile Treatment Effects in High Dimensional Panel Data

高维面板数据中的分位数处理效应

We introduce novel estimators for quantile causal effects with high dimensional panel data (large $N$ and $T$), where only one or a few units are affected by the intervention or policy. Our method extends the generalized synthetic control method \citep{xu_2017} from average treatment effects on the treated to quantile treatment effects on the treated, allowing the underlying factor structure to change across the quantile of the interested outcome distribution. Our method…

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A Synthetic Business Cycle Approach to Counterfactual Analysis with Nonstationary Macroeconomic Data

非平稳宏观数据反事实分析的合成经济周期方法

This paper investigates the use of synthetic control methods for causal inference in macroeconomic settings when dealing with possibly nonstationary data. While the synthetic control approach has gained popularity for estimating counterfactual outcomes, we caution researchers against assuming a common nonstationary trend factor across units for macroeconomic outcomes, as doing so may result in misleading causal estimation-a pitfall we refer to as the spurious synthetic…

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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 inferences 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…

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Real-time Program Evaluation using Anytime-valid Rank Tests

利用随时有效秩检验开展实时项目评估

Counterfactual mean estimators such as difference-in-differences and synthetic control have grown into workhorse tools for program evaluation. Inference for these estimators is well-developed in settings where all post-treatment data is available at the time of analysis. However, in settings where data arrives sequentially, these tests do not permit real-time inference, as they require a pre-specified sample size T. We introduce real-time inference for program evaluation…

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Synthetic Controls for Experimental Design

用于实验设计的合成控制

This article studies experimental design in settings where the experimental units are large aggregate entities (e.g., markets), and only one or a small number of units can be exposed to the treatment. In such settings, randomization of the treatment may result in treated and control groups with very different characteristics at baseline, inducing biases. We propose a variety of experimental non-randomized synthetic control designs (Abadie, Diamond and Hainmueller, 2010,…

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Inference for Synthetic Controls via Refined Placebo Tests

利用改进安慰剂检验进行合成控制推断

The synthetic control method is often applied to problems with one treated unit and a small number of control units. A common inferential task in this setting is to test null hypotheses regarding the average treatment effect on the treated. Inference procedures that are justified asymptotically are often unsatisfactory due to (1) small sample sizes that render large-sample approximation fragile and (2) simplification of the estimation procedure that is implemented in…

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Single Proxy Synthetic Control

单代理合成控制

Synthetic control methods are widely used to estimate the treatment effect on a single treated unit in time-series settings. A common approach to estimate synthetic control weights is to regress the treated unit's pre-treatment outcome and covariates' time series measurements on those of untreated units via ordinary least squares. However, this approach can perform poorly if the pre-treatment fit is not near perfect, whether the weights are normalized or not. In this paper,…

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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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Uncertainty Quantification in Synthetic Controls with Staggered Treatment Adoption

错位处理采用下合成控制的不确定性量化

We propose principled prediction intervals to quantify the uncertainty of a large class of synthetic control predictions (or estimators) in settings with staggered treatment adoption, offering precise non-asymptotic coverage probability guarantees. From a methodological perspective, we provide a detailed discussion of different causal quantities to be predicted, which we call causal predictands, allowing for multiple treated units with treatment adoption at possibly…

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Estimating the Cost of Informal Care with a Novel Two-Stage Approach to Individual Synthetic Control

利用新两阶段个体合成控制方法估计非正式照护成本

Informal carers provide the majority of care for people living with challenges related to older age, long-term illness, or disability. However, the care they provide often results in a significant income penalty for carers, a factor largely overlooked in the economics literature and policy discourse. Leveraging data from the UK Household Longitudinal Study, this paper provides the first robust causal estimates of the caring income penalty using a novel individual synthetic…

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The inclusive Synthetic Control Method

包容式合成控制法

We introduce the inclusive synthetic control method (iSCM), a modification of synthetic control methods that includes units in the donor pool potentially affected, directly or indirectly, by an intervention. This method is ideal for situations where including treated units in the donor pool is essential or where donor units may experience spillover effects. The iSCM is straightforward to implement with most synthetic control estimators. As an empirical illustration, we…

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Caliper Synthetic Matching: Generalized Radius Matching with Local Synthetic Controls

卡尺合成匹配:结合局部合成控制的广义半径匹配

Matching promises transparent causal inferences for observational data, making it an intuitive approach for many applications. In practice, however, standard matching methods often perform poorly compared to modern approaches such as response-surface modeling and optimizing balancing weights. We propose Caliper Synthetic Matching (CSM) to address these challenges while preserving simple and transparent matches and match diagnostics. CSM extends Coarsened Exact Matching by…

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A Short Note on Event-Study Synthetic Difference-in-Differences Estimators

事件研究型合成双重差分估计量简论

I propose an event study extension of Synthetic Difference-in-Differences (SDID) estimators. I show that, in simple and staggered adoption designs, estimators from Arkhangelsky et al. (2021) can be disaggregated into dynamic treatment effect estimators, comparing the lagged outcome differentials of treated and synthetic controls to their pre-treatment average. Estimators presented in this note can be computed using the sdid_event Stata package.

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