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COMBINING ESTIMATES OF CONDITIONAL TREATMENT EFFECTS

条件处理效应估计的组合

Estimating a treatment’s effect on an outcome conditional on covariates is a primary goal of many empirical investigations. Accurate estimation of the treatment effect given covariates can enable the optimal treatment to be applied to each unit or guide the deployment of limited treatment resources for maximum program benefit. Applications of conditional treatment effect estimation are found in direct marketing, economic policy, and personalized medicine. When estimating…

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On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confounding

存在中介—结局混杂时路径特定效应的半参数估计

Summary Path-specific effects constitute a broad class of mediated effects from an exposure to an outcome via one or more causal pathways along a set of intermediate variables. Most of the literature concerning estimation of mediated effects has focused on parametric models, with stringent assumptions regarding unmeasured confounding. We consider semiparametric inference of a path-specific effect when these assumptions are relaxed. In particular, we develop a suite of…

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International Shocks, Variable Markups, and Domestic Prices

国际冲击、可变加成与国内价格

Abstract How strong are strategic complementarities in price setting across firms? In this article, we provide a direct empirical estimate of firms’ price responses to changes in competitor prices. We develop a general theoretical framework and an empirical identification strategy, taking advantage of a new micro-level dataset for the Belgian manufacturing sector. We find strong evidence of strategic complementarities, with a typical firm adjusting its price with an…

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Partial identification of the treatment effect distribution and its functionals

处理效应分布及其泛函的部分识别

In the treatment effect problem, the available information is on the marginal distributions of potential outcomes, but not on their joint distribution. The only point identified functional of the treatment effect distribution is its average, the average treatment effect (ATE). Quantiles and other functionals of the distribution of treatment effect are only partially identified. Bounds on a single quantile and on the cumulative distribution function (c.d.f.) in a single point…

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Panel data quantile regression with grouped fixed effects

含分组固定效应的面板分位数回归

This paper introduces estimation methods for grouped latent heterogeneity in panel data quantile regression. We assume that the observed individuals come from a heterogeneous population with a finite number of types. The number of types and group membership is not assumed to be known in advance and is estimated by means of a convex optimization problem. We provide conditions under which group membership is estimated consistently and establish asymptotic normality of the…

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Penalized sieve GEL for weighted average derivatives of nonparametric quantile IV regressions

非参数分位数工具变量回归加权平均导数的惩罚筛广义经验似然

This paper considers estimation and inference for a weighted average derivative (WAD) of a nonparametric quantile instrumental variables regression (NPQIV). NPQIV is a non-separable and nonlinear ill-posed inverse problem, which might be why there is no published work on the asymptotic properties of any estimator of its WAD. We first characterize the semiparametric efficiency bound for a WAD of a NPQIV, which, unfortunately, depends on an unknown conditional derivative…

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Conditional quantile processes based on series or many regressors

基于级数或大量回归变量的条件分位数过程

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric QR-series framework, covering many regressors as a special case, for performing inference on the entire conditional quantile function and its linear functionals. In this framework, we approximate the entire conditional quantile function by a…

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On the predictive risk in misspecified quantile regression

模型误设下分位数回归的预测风险

In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple (asymptotic) characterizations of the associated bias, also called expected optimism. We propose estimates for the expected optimism and the predictive risk, and establish their uniform consistency under mild conditions. Our results hold…

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What do mean impacts miss? Distributional effects of corporate diversification

平均效应遗漏了什么?企业多元化的分布效应

Corporate diversification is one of the most debated topics in finance over the past two decades. While it is widely believed that there exists a discount in the stock market valuation of conglomerate firms, the extant research based on least squares methods points to different directions. We argue that the existing empirical analyses ignore some important data features, especially cross sectional heterogeneity, predicted by both theories and casual observations on corporate…

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Asymptotic inference for the constrained quantile regression process

受约束分位数回归过程的渐近推断

I investigate the asymptotic distribution of linear quantile regression coefficient estimates when the parameter lies on the boundary of the parameter space. In order to allow for inferences made across many conditional quantiles, I provide a uniform characterization of constrained quantile regression estimates as a stochastic process over an interval of quantile levels. To do this I pose the process of estimates as solutions to a parameterized family of constrained…

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Quantiles via moments

通过矩估计分位数

We study the conditions under which it is possible to estimate regression quantiles by estimating conditional means. The advantage of this approach is that it allows the use of methods that are only valid in the estimation of conditional means, while still providing information on how the regressors affect the entire conditional distribution. The methods we propose are not meant to replace the well-established quantile regression estimator, but provide an additional tool…

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Placebo inference on treatment effects when the number of clusters is small

聚类数量较少时处理效应的安慰剂推断

I introduce a general, Fisher-style randomization testing framework to conduct nearly exact inference about the lack of effect of a binary treatment in the presence of very few, large clusters when the treatment effect is identified across clusters. The proposed randomization test formalizes and extends the intuitive notion of generating null distributions by assigning placebo treatments to untreated clusters. I show that under simple and easily verifiable conditions, the…

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Predictive quantile regressions under persistence and conditional heteroskedasticity

持久性与条件异方差下的预测分位数回归

This paper provides an improved inference for predictive quantile regressions with persistent predictors and conditionally heteroskedastic errors. The confidence intervals based on conventional quantile regression techniques are not valid when predictors are highly persistent. Moreover, the conditional heteroskedasticity introduces rather complicated nuisance parameters in the limit theory, whose estimation errors can be another source of distortion. We propose a…

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Smoothed GMM for quantile models

分位数模型的平滑广义矩估计

We consider estimation of finite-dimensional parameters identified by general conditional quantile restrictions, including instrumental variables quantile regression. Within a generalized method of moments framework, moment functions are smoothed to aid both computation and precision. Consistency and asymptotic normality are established under weaker assumptions than previously seen in the literature, allowing dependent data and nonlinear structural models. Simulations…

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Quantile-regression-based clustering for panel data

基于分位数回归的面板数据聚类

In panel data analysis, it is important to identify subgroups of units with heterogeneous parameters. This can not only increase the model flexibility but also produce more efficient estimation by pooling information across units within the same group. In this paper, we propose a new quantile-regression-based clustering method for panel data. We develop an iterative algorithm using a similar idea of k-means clustering to identify subgroups with heterogeneous slopes at a…

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Measurement error in discrete health facility choice models: An example from urban Senegal

离散医疗设施选择模型中的测量误差:塞内加尔城市案例

Summary We use individual‐level health facility choice data from urban Senegal to estimate consumer preferences for facility characteristics related to maternal health services. We find that consumers consider a large number of quality‐related facility characteristics, as well as travel costs, when making their health facility choice. In contrast to the typical assumption in the literature, our findings indicate that individuals frequently bypass the facility nearest their…

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Endogenous censoring in the mixed proportional hazard model with an application to optimal unemployment insurance

混合比例风险模型中的内生删失及其在最优失业保险中的应用

Summary We examine the sensitivity of estimates of the MPH model with respect to assumptions on the censoring mechanism in the context of an economic model of optimal unemployment insurance. We assume a parametric model for the duration of interest and leave the distribution of censoring unrestricted, allowing it to be correlated with observed and unobserved characteristics. We provide a practical characterization of the identified set with moment inequalities and suggest…

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Semiparametric estimation of structural failure time models in continuous-time processes

连续时间过程中的结构失效时间模型半参数估计

Summary Structural failure time models are causal models for estimating the effect of time-varying treatments on a survival outcome. G-estimation and artificial censoring have been proposed for estimating the model parameters in the presence of time-dependent confounding and administrative censoring. However, most existing methods require manually pre-processing data into regularly spaced data, which may invalidate the subsequent causal analysis. Moreover, the computation…

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High-dimensional causal discovery under non-Gaussianity

非高斯条件下的高维因果发现

Summary We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable-specific error term and the other observed variables $Y_u$ with $\sigma(u) < \sigma (v)$. The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has previously been…

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Minimal dispersion approximately balancing weights: asymptotic properties and practical considerations

最小离散度近似平衡权重:渐近性质与实践问题

Summary Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods, which find the weights of minimum dispersion that approximately balance the covariates. We call these weights ‘minimal weights’ and study them under a common optimization framework. Our key observation is that finding weights which achieve approximate covariate balance is…

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Comment: The Challenges of Multiple Causes

评论:多重原因的挑战

We begin by congratulating Yixin Wang and David Blei for their thought-provoking article that opens up a new research frontier in the field of causal inference. The authors directly tackle the challenging question of how to infer causal effects of many treatments in the presence of unmeasured confounding. We expect their article to have a major impact by further advancing our understanding of this important methodological problem. This commentary has two goals. We first…

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The Blessings of Multiple Causes

多重原因的益处

Causal inference from observational data is a vital problem, but it comes with strong assumptions. Most methods assume that we observe all confounders, variables that affect both the causal variables and the outcome variables. This assumption is standard but it is also untestable. In this article, we develop the deconfounder, a way to do causal inference with weaker assumptions than the traditional methods require. The deconfounder is designed for problems of multiple causal…

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Design, Identification, and Sensitivity Analysis for Patient Preference Trials

患者偏好试验的设计、识别与敏感性分析

Social and medical scientists are often concerned that the external validity of experimental results may be compromised because of heterogeneous treatment effects. If a treatment has different effects on those who would choose to take it and those who would not, the average treatment effect estimated in a standard randomized controlled trial (RCT) may give a misleading picture of its impact outside of the study sample. Patient preference trials (PPTs), where participants’…

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Tuning-Free Heterogeneous Inference in Massive Networks

大规模网络中的免调参异质性推断

Heterogeneity is often natural in many contemporary applications involving massive data. While posing new challenges to effective learning, it can play a crucial role in powering meaningful scientific discoveries through the integration of information among subpopulations of interest. In this article, we exploit multiple networks with Gaussian graphs to encode the connectivity patterns of a large number of features on the subpopulations. To uncover the underlying sparsity…

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