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The wild bootstrap for few (treated) clusters

处理簇很少时的野生自助法

Inference based on cluster‐robust standard errors in linear regression models, using either the Student's t‐distribution or the wild cluster bootstrap, is known to fail when the number of treated clusters is very small. We propose a family of new procedures called the subcluster wild bootstrap, which includes the ordinary wild bootstrap as a limiting case. In the case of pure treatment models, where all observations within clusters are either treated or not, the latter…

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Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics

利用 L 统计量对(条件)分位数差与分位距进行非参数推断

We provide novel, high‐order accurate methods for non‐parametric inference on quantile differences between two populations in both unconditional and conditional settings. These quantile differences correspond to (conditional) quantile treatment effects under (conditional) independence of a binary treatment and potential outcomes. Our methods use the probability integral transform and a Dirichlet (rather than Gaussian) reference distribution to pick appropriate L‐statistics…

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Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production

条件效率测度的中心极限定理与非参数两阶段生产模型的可分性检验

In this paper, we demonstrate that standard central limit theorem (CLT) results do not hold for means of non‐parametric, conditional efficiency estimators, and we provide new CLTs that permit applied researchers to make valid inference about mean conditional efficiency or to compare mean efficiency across groups of producers. The new CLTs are used to develop a test of the restrictive ‘separability’ condition that is necessary for second‐stage regressions of efficiency…

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Adaptive Wild Bootstrap Tests for a Unit Root With Non‐Stationary Volatility

非平稳波动下的自适应野生自助法单位根检验

Recent research has emphasized that permanent changes in the innovation variance (caused by structural shifts or an integrated volatility process) lead to size distortions in conventional unit root tests. It has been shown how these size distortions can be resolved using the wild bootstrap. In this paper, we first derive the asymptotic power envelope for the unit root testing problem when the non‐stationary volatility process is known. Next, we show that under suitable…

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Double/debiased machine learning for treatment and structural parameters

We revisit the classic semi‐parametric problem of inference on a low‐dimensional parameter θ0 in the presence of high‐dimensional nuisance parameters η0. We depart from the classical setting by allowing for η0 to be so high‐dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate η0, we consider the use of statistical or machine learning (ML) methods, which are particularly…

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Simpler bootstrap estimation of the asymptotic variance of U ‐statistic‐based estimators

基于U统计量的估计量:更简便的渐近方差自助法估计

The bootstrap is a popular and useful tool for estimating the asymptotic variance of complicated estimators. Ironically, the fact that the estimators are complicated can make the standard bootstrap computationally burdensome because it requires repeated recalculation of the estimator. In this paper, we propose a method that is specific to extremum estimators based on U‐statistics. The contribution here is that rather than repeated recalculation of the U‐statistic‐based…

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Oracle and adaptive false discovery rate controlling methods for one‐sided testing: theory and application in treatment effect evaluation

单侧检验中控制错误发现率的预知与自适应方法:理论及处理效应评价应用

Economists are often interested in identifying effective policies or treatments together with subpopulations of individuals who respond positively (or with a sign that is expected) to these treatment interventions. In this paper, we propose an optimal false discovery rate controlling method that is especially useful for such one‐sided testing problems. The proposed procedure is optimal in the sense of minimizing the false non‐discovery rate while controlling the false…

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Identification and estimation of semi‐parametric censored dynamic panel data models of short time periods

短期删失动态面板模型的半参数识别与估计

In this paper, we present a semi‐parametric identification and estimation method for censored dynamic panel data models of short time periods and their average partial effects with only two periods of data. The proposed method transforms the semi‐parametric specification of censored dynamic panel data models into a parametric family of distribution functions of observables without specifying the distribution of the initial condition. Then the censored dynamic panel data…

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A simple and robust estimator for linear regression models with strictly exogenous instruments

严格外生工具变量下线性回归的简便稳健估计

In this paper, I investigate the estimation of linear regression models with strictly exogenous instruments under minimal identifying assumptions. I introduce a uniformly (in the data‐generating process) consistent estimator under nearly minimal identifying assumptions. The proposed estimator, called the integrated instrumental variables (IIV) estimator, is a simple weighted least‐squares estimator. It does not require the choice of a bandwidth or tuning parameter, or the…

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Identification of peer effects through social networks using variance restrictions

利用方差限制识别社会网络中的同伴效应

This paper presents a novel method to identify peer effects through exploiting fluctuations in the variances and covariances of outcomes over a social network. Endogenous and contextual peer effects can be disentangled by contrasting the covariances of the outcomes of peers with the covariances of the outcomes of peers of peers. Correlated effects are incorporated by allowing for unrestricted network level heterogeneity. The method is applied to the Project STAR data to…

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Multiple fixed effects in binary response panel data models

二元响应面板数据模型中的多重固定效应

This paper considers the adaptability of estimation methods for binary response panel data models to multiple fixed effects. It is motivated by the gravity equation used in international trade, where important papers use binary response models with fixed effects for both importing and exporting countries. Econometric theory has mostly focused on the estimation of single fixed effects models. This paper investigates whether existing methods can be modified to eliminate…

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Sparse estimation of huge networks with a block‐wise structure

具有分块结构的超大网络稀疏估计

Networks with a very large number of nodes appear in many application areas and pose challenges for traditional Gaussian graphical modelling approaches. In this paper, we focus on the estimation of a Gaussian graphical model when the dependence between variables has a block‐wise structure. We propose a penalized likelihood estimation of the inverse covariance matrix, also called Graphical LASSO, applied to block averages of observations, and we derive its asymptotic…

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Peer effects in bedtime decisions among adolescents: a social network model with sampled data

青少年就寝决策中的同伴效应:基于抽样数据的社会网络模型

Using unique information on a representative sample of US teenagers, we investigate peer effects in adolescent bedtime decisions. We extend the nonlinear least‐squares estimator for spatial autoregressive models to estimate network models with network fixed effects and sampled observations on the dependent variable. We show the extent to which neglecting the sampling issue yields misleading inferential results. When accounting for sampling, we find that, besides the…

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Estimation of social-influence-dependent peer pressure in a large network game

大型网络博弈中依赖社会影响力的同伴压力估计

Research on peer effects in sociology has long been focused on social interactions and the associated social influence process. In this paper, we extend a large‐network‐based game model to a model that allows for the dependence of social interactions on social‐influence status. In particular, we use the Katz–Bonacich centrality to measure individuals' social influences, which are obtained directly from the observation of a social network. To solve the computational burden…

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Least‐squares estimation of GARCH(1,1) models with heavy‐tailed errors

重尾误差下 GARCH(1,1) 模型的最小二乘估计

GARCH(1,1) models are widely used for modelling processes with time‐varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log‐transform‐based least‐squares approach to the estimation of GARCH(1,1) models. Within this approach, the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data, we show that knowledge of…

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Indirect inference in spatial autoregression

空间自回归中的间接推断

Ordinary least‐squares (OLS) is well known to produce an inconsistent estimator of the spatial parameter in pure spatial autoregression (SAR). In this paper, we explore the potential of indirect inference to correct the inconsistency of OLS. Under broad conditions, it is shown that indirect inference (II) based on OLS produces consistent and asymptotically normal estimates in pure SAR regression. The II estimator used here is robust to departures from normal disturbances and…

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A note on sufficiency in binary panel models

二元面板模型中充分性条件的一则札记

Consider estimating the slope coefficients of a fixed‐effect binary‐choice model from two‐period panel data. Two approaches to semiparametric estimation at the regular parametric rate have been proposed: one is based on a sufficiency requirement, and the other is based on a conditional‐median restriction. We show that, under standard assumptions, both conditions are equivalent.

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Semi‐linear mode regression

半线性众数回归

In this paper, I estimate the slope coefficient parameter β of the regression model Y=X′β+φ(V)+e, where the error term e satisfies Mode(e&7CX,V)=0 almost surely and ϕ is an unknown function. It is possible to achieve n−2/7‐consistency for estimating β when ϕ is known up to a finite‐dimensional parameter. I present a consistent and asymptotically normal estimator for β, which does not require prescribing a functional form for ϕ, let alone a parametrization. Furthermore, the…

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A sequential test for the specification of predictive densities

预测密度设定的序贯检验

We develop a specification test of predictive densities, based on the fact that the generalized residuals of correctly specified predictive density models are independent and identically distributed uniform. The proposed sequential test examines the hypotheses of serial independence and uniformity in two stages, wherein the first‐stage test of serial independence is robust to violation of uniformity. The approach of the data‐driven smooth test is employed to construct the…

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Model-selection tests for conditional moment restriction models

条件矩约束模型的模型选择检验

We propose a Vuong‐type model‐selection test for models defined by conditional moment restrictions. The moment restrictions that define the models can be standard equality restrictions that point‐identify the model parameters, or moment equality or inequality restrictions that partially identify the model parameters. The test uses a new average generalized empirical likelihood criterion function designed to incorporate full restriction of the conditional model. We also…

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Second-order refinement of empirical likelihood ratio tests of nonlinear restrictions

非线性约束经验似然比检验的二阶改进

In this paper, we investigate the second‐order properties of empirical likelihood ratio (ELR) tests of general nonlinear parametric restrictions for over‐identified moment restriction models. We derive the stochastic expansion of the ELR statistic for this very large class of testing problems and its formal distributional expansion. We show that we can improve the size properties of the ELR tests via either Bartlett correction or pseudo observation adjustment. Monte Carlo…

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Consistent tests for conditional treatment effects

条件处理效应的一致检验

We construct tests for the null hypothesis that the conditional average treatment effect is non‐negative, conditional on every possible value of a subset of covariates. Testing such a null hypothesis can provide more information than the sign of the average treatment effects parameter. The null hypothesis can be characterized as infinitely many of unconditional moment inequalities. A Kolmogorov–Smirnov test is constructed based on these unconditional moment inequalities, and…

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Nonparametric regression with nearly integrated regressors under long-run dependence

长期依赖下含近单位根解释变量的非参数回归

We study the nonparametric estimation of a regression function with nonstationary (integrated or nearly integrated) covariates and the error series of the regressor process following a fractional integrated autoregressive moving average model. A local linear estimation method is developed to estimate the unknown regression function. The asymptotic results of the resulting estimator at both interior points and boundaries are obtained. The asymptotic distribution is mixed…

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Testing for changes in (extreme) VaR

极端风险价值的变化检验

In this paper, we develop tests for a change in an unconditional small quantile (Value‐at‐Risk, VaR, in financial time series analysis) based on an estimator motivated by extreme value theory. This so‐called Weissman estimator allows tests to be applied for extreme VaR, where extant tests mostly fail. In view of applications, we allow for weakly dependent observations. Our test statistics rely on self‐normalization, which obviates the need to estimate the complicated…

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