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Distance Metrics for Measuring Joint Dependence with Application to Causal Inference

衡量联合依赖的距离度量及其在因果推断中的应用

Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d≥2 random vectors. We introduce the high-order distance covariance to measure the so-called Lancaster interaction dependence. The joint distance covariance is then defined as a linear combination of pairwise distance covariances and their higher-order counterparts…

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Including Covariates in the Regression Discontinuity Design

在断点回归设计中纳入协变量

This article proposes a fully nonparametric kernel method to account for observed covariates in regression discontinuity designs (RDD), which may increase precision of treatment effect estimation. It is shown that conditioning on covariates reduces the asymptotic variance and allows estimating the treatment effect at the rate of one-dimensional nonparametric regression, irrespective of the dimension of the continuously distributed elements in the conditioning set.…

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Direct and Indirect Effects Based on Difference-in-Differences With an Application to Political Preferences Following the Vietnam Draft Lottery

基于双重差分的直接与间接效应:越战征兵抽签后的政治偏好

We propose a difference-in-differences approach for disentangling a total treatment effect within specific subpopulations into a direct effect and an indirect effect operating through a binary mediating variable. Random treatment assignment along with specific common trend and effect homogeneity assumptions identify the direct effects on the always and never takers, whose mediator is not affected by the treatment, as well as the direct and indirect effects on the compliers,…

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Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs

尖锐断点回归设计下分位数效应的一致推断

This study develops methods for conducting uniform inference on quantile treatment effects for sharp regression discontinuity designs. We develop a score test for the treatment significance hypothesis and Wald-type tests for the hypotheses related to treatment significance, homogeneity, and unambiguity. The bias from the nonparametric estimation is studied in detail. In particular, we show that under some conditions, the asymptotic distribution of the score test is…

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Regional Transfer Multipliers

区域转移支付乘数

Abstract A series of discontinuities in the allocation mechanism of federal transfers to municipal governments in Brazil allow us to identify the causal effect of public spending on local labour markets, using a “fuzzy” Regression Discontinuity Design (RDD). Our estimates imply a cost per job of about 8,000 US dollars per year and a local income multiplier around two. The effect comes mostly from employment in services and is more pronounced among less financially developed…

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Inference on Causal and Structural Parameters using Many Moment Inequalities

利用大量矩不等式对因果参数与结构参数进行推断

Abstract This article considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this problem allows to carry out inference on causal and structural parameters; a notable example is the market structure model of Ciliberto and Tamer (2009) where $p=2^{m+1}$ with $m$ being the number of firms that could possibly…

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Non-separable models with high-dimensional data

高维数据下的非可分模型

This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and numerical…

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Instrumental variables and the sign of the average treatment effect

工具变量与平均处理效应的符号

This paper considers identification and inference about the sign of the average effect of a binary endogenous regressor (or treatment) on a binary outcome of interest when a binary instrument is available. In this setting, the average effect of the endogenous regressor on the outcome is sometimes referred to as the average treatment effect (ATE). We consider four different sets of assumptions: instrument exogeneity, instrument exogeneity and monotonicity on the outcome…

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Identification and wavelet estimation of weighted ATE under discontinuous and kink incentive assignment mechanisms

不连续与折点激励分配机制下加权平均处理效应的识别及小波估计

This paper studies identification, estimation, and inference of a weighted average treatment effect (W-ATE) parameter in a class of switching regime models, where the agent’s selection of treatment is affected by either a discontinuous or kink incentive assignment mechanism and some unobservable characteristic. For each assignment mechanism, we (i) establish identification and propose a local wavelet estimator of the W-ATE; (ii) establish asymptotic properties of the local…

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Nearly random designs with greatly improved balance

大幅改善协变量平衡的近随机实验设计

Summary We present a procedure that divides a set of experimental units into two groups that are similar on a prespecified set of covariates and are almost as random as with a complete randomization. Under complete randomization, the difference in the standardized average between treatment and control is $O_{\rm p}(n^{-1/2})$, which may be material in small samples. We present an algorithm that reduces imbalance to $O_{\rm p}(n^{-3})$ for one covariate and $O_{\rm p}\{n^{-(1 + 2/p)}\}$…

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On marginal and conditional parameters in logistic regression models

逻辑回归模型中的边际参数与条件参数

Summary We derive the exact formula linking the parameters of marginal and conditional logistic regression models with binary mediators when no conditional independence assumptions can be made. The formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish, thereby recovering well-known results as particular cases. It also permits the disentangling of direct and indirect effects as well as quantifying the…

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Sensitivity Analysis for Inverse Probability Weighting Estimators via the Percentile Bootstrap

通过百分位自助法对逆概率加权估计进行敏感性分析

Summary To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the ‘missingness at random’ and ‘no unmeasured confounder’ assumptions. However, these assumptions are unverifiable by using empirical data and pose serious threats to the validity of the qualitative conclusions of statistical inference. A sensitivity analysis asks how the conclusions may change if the unverifiable assumptions are violated…

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Bayesian nonparametric sparse VAR models

贝叶斯非参数稀疏向量自回归模型

High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR models that can improve estimation efficiency and prediction accuracy. Our hierarchical prior overcomes overparametrization and overfitting issues by clustering the VAR coefficients into groups and by shrinking the coefficients of each…

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Exogenous uncertainty and the identification of structural vector autoregressions with external instruments

外生不确定性与使用外部工具变量的结构向量自回归识别

Summary We provide necessary and sufficient conditions for the identification (point‐identification) of structural vector autoregressions (SVARs) with external instruments considering the case in which r instruments are used to identify g structural shocks of interest, r ≥ g ≥ 1. Novel frequentist estimation methods are discussed by considering both a “partial shocks” identification strategy, where only g structural shocks are of interest and are instrumented, and a “full…

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Mostly harmless simulations? Using Monte Carlo studies for estimator selection

大多无害的模拟?用蒙特卡洛研究选择估计量

Summary We consider two recent suggestions for how to perform an empirically motivated Monte Carlo study to help select a treatment effect estimator under unconfoundedness. We show theoretically that neither is likely to be informative except under restrictive conditions that are unlikely to be satisfied in many contexts. To test empirical relevance, we also apply the approaches to a real‐world setting where estimator performance is known. Both approaches are worse than…

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Estimation in a generalization of bivariate probit models with dummy endogenous regressors

含内生虚拟解释变量的广义双变量Probit模型估计

Summary The purpose of this paper is to provide guidelines for empirical researchers who use a class of bivariate threshold crossing models with dummy endogenous variables. A common practice employed by the researchers is the specification of the joint distribution of unobservables as a bivariate normal distribution, which results in a bivariate probit model . To address the problem of misspecification in this practice, we propose an easy‐to‐implement semiparametric…

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Two applications of wild bootstrap methods to improve inference in cluster‐IV models

用野生自助法改善聚类工具变量模型推断的两个应用

Summary Microeconomic data often have within‐cluster dependence, which affects standard error estimation and inference. When the number of clusters is small, asymptotic tests can be severely oversized. In the instrumental variables (IV) model, the potential presence of weak instruments further complicates hypothesis testing. We use wild bootstrap methods to improve inference in two empirical applications with these characteristics. Building from estimating equations and…

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On testing conditional qualitative treatment effects

条件定性处理效应的检验

Precision medicine is an emerging medical paradigm that focuses on finding the most effective treatment strategy tailored for individual patients. In the literature, most of the existing works focused on estimating the optimal treatment regime. However, there has been less attention devoted to hypothesis testing regarding the optimal treatment regime. In this paper, we first introduce the notion of conditional qualitative treatment effects (CQTE) of a set of variables given…

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Robust uniform inference for quantile treatment effects in regression discontinuity designs

回归不连续设计中分位数处理效应的稳健一致推断

The practical importance of inference with robustness against large bandwidths for causal effects in regression discontinuity and kink designs is widely recognized. Existing robust methods cover many cases, but do not handle uniform inference for CDF and quantile processes in fuzzy designs. In this light, this paper extends the literature by developing a unified framework of inference with robustness against large bandwidths that applies to uniform inference for quantile…

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Inference on Difference-in-Differences average treatment effects: A fixed- b approach

双重差分平均处理效应推断:固定 b 方法

This paper provides an analysis of the standard errors proposed by Driscoll and Kraay (1998) (DK) in linear Difference-in-Differences (DD) models with fixed effects and individual-specific time trends. The analysis is accomplished within the fixed-b asymptotic framework developed by Kiefer and Vogelsang (2005) for heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimator based tests. For both the fixed-N, large-T, and large-N, large-T cases, it is…

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Government debt and corporate leverage: International evidence

政府债务与企业杠杆:国际证据

We empirically investigate the impact of government debt on corporate financing decisions in an international setting. We show a negative relation between government debt and corporate leverage using data on 40 countries between 1990–2014. This negative relation is stronger for government debt that is financed domestically, for firms that are larger and more profitable, and in countries with more developed equity markets. To address potential endogeneity concerns, we use an…

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Estimating and Testing Vaccine Sieve Effects Using Machine Learning

利用机器学习估计和检验疫苗筛效应

When available, vaccines are an effective means of disease prevention. Unfortunately, efficacious vaccines have not yet been developed for several major infectious diseases, including HIV and malaria. Vaccine sieve analysis studies whether and how the efficacy of a vaccine varies with the genetics of the pathogen of interest, which can guide subsequent vaccine development and deployment. In sieve analyses, the effect of the vaccine on the cumulative incidence corresponding…

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Invariant Causal Prediction for Sequential Data

序贯数据的不变因果预测

We investigate the problem of inferring the causal predictors of a response Y from a set of d explanatory variables (X1, …, Xd). Classical ordinary least-square regression includes all predictors that reduce the variance of Y. Using only the causal predictors instead leads to models that have the advantage of remaining invariant under interventions; loosely speaking they lead to invariance across different “environments” or “heterogeneity patterns.” More precisely, the…

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On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments

存在部分无效工具变量时Lasso在工具变量估计中的使用

We investigate the behavior of the Lasso for selecting invalid instruments in linear instrumental variables models for estimating causal effects of exposures on outcomes, as proposed recently by Kang et al. Invalid instruments are such that they fail the exclusion restriction and enter the model as explanatory variables. We show that for this setup, the Lasso may not consistently select the invalid instruments if these are relatively strong. We propose a median estimator…

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