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工具变量:IV、2SLS 与内生性识别。
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A Robust Test for Weak Instruments

弱工具变量的稳健检验

We develop a test for weak instruments in linear instrumental variables regression that is robust to heteroscedasticity, autocorrelation, and clustering. Our test statistic is a scaled nonrobust first-stage F statistic. Instruments are considered weak when the two-stage least squares or the limited information maximum likelihood Nagar bias is large relative to a benchmark. We apply our procedures to the estimation of the elasticity of intertemporal substitution, where our…

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Unconditional Quantile Treatment Effects Under Endogeneity

内生性下的无条件分位数处理效应

This article develops estimators for unconditional quantile treatment effects when the treatment selection is endogenous. We use an instrumental variable (IV) to solve for the endogeneity of the binary treatment variable. Identification is based on a monotonicity assumption in the treatment choice equation and is achieved without any functional form restriction. We propose a weighting estimator that is extremely simple to implement. This estimator is root n consistent,…

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An instrumental variable model of multiple discrete choice

多项离散选择的工具变量模型

This paper studies identification of latent utility functions in multiple discrete choice models in which there may be endogenous explanatory variables, that is explanatory variables that are not restricted to be distributed independently of the unobserved determinants of latent utilities. The model does not employ large support, special regressor or control function restrictions, indeed it is silent about the process delivering values of endogenous explanatory variables and…

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Regressions with Berkson errors in covariates—A nonparametric approach

协变量含 Berkson 型误差的回归:非参数方法

This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via Monte Carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health. These…

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Local Linear GMM Estimation of Functional Coefficient IV Models With an Application to Estimating the Rate of Return to Schooling

函数系数工具变量模型的局部线性 GMM 估计及教育回报应用

We consider the local linear generalized method of moment (GMM) estimation of functional coefficient models with a mix of discrete and continuous data and in the presence of endogenous regressors. We establish the asymptotic normality of the estimator and derive the optimal instrumental variable that minimizes the asymptotic variance-covariance matrix among the class of all local linear GMM estimators. Data-dependent bandwidth sequences are also allowed for. We propose a…

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Modeling structural equations with endogenous regressors and heterogeneity through derivative constraints

通过导数约束建模内生解释变量与异质性结构方程

In this paper, I present a general modeling framework for nonparametric models with endogenous regressors and heterogeneity. I show that many existing models in the literature can be derived from a structural equation with unobserved heterogeneity by imposing constancy assumptions on the first and second derivatives. I consider a less restrictive model that imposes constancy assumptions on the second partial derivative of the structural equation. Assuming the existence of…

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Estimation of spatial autoregressive models with randomly missing data in the dependent variable

因变量随机缺失时空间自回归模型的估计

We suggest and compare different methods for estimating spatial autoregressive models with randomly missing data in the dependent variable. Aside from the traditional expectation-maximization (EM) algorithm, a nonlinear least squares method is suggested and a generalized method of moments estimation is developed for the model. A two-stage least squares estimation with imputation is proposed as well. We analytically compare these estimation methods and find that generalized…

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Identification and inference in a simultaneous equation under alternative information sets and sampling schemes

不同信息集与抽样方案下联立方程的识别和推断

In simple static linear simultaneous equation models the empirical distributions of IV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. We demonstrate that the limiting distribution of consistent IV is not affected by conditioning on exogenous regressors, whereas that of inconsistent OLS is. The OLS asymptotic and simulated actual variances are shown to diminish by extending the set of exogenous variables…

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Instrumental variables estimation and inference in the presence of many exogenous regressors

存在大量外生回归变量时的工具变量估计与推断

We consider a standard instrumental variables model contaminated by the presence of a large number of exogenous regressors. In an asymptotic framework where this number is proportional to the sample size, we study the impact of their ratio on the validity of existing estimators and tests. When the instruments are few, the inference using the conventional 2SLS estimator and associated t and J statistics, as well as the Anderson–Rubin and Kleibergen tests, is still valid. When…

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Estimation of dynamic panel data models with sample selection

存在样本选择的动态面板数据模型估计

SUMMARY We propose a new method for estimating dynamic panel data models with selection. The method uses backward substitution for the lagged dependent variable, which leads to an estimating equation that requires correcting for contemporaneous selection only. The estimator is valid under relatively weak assumptions about errors and permits avoiding the weak instruments problem associated with differencing. We also propose a simple test for selection bias that is based on…

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On the simultaneity problem in the aid and growth debate

援助与增长争论中的联立性问题

SUMMARY This paper shows that foreign aid has a significant positive average effect on real per capita gross domestic product (GDP) growth if, and only if, the quantitatively large negative reverse causal effect of per capita GDP growth on foreign aid is adjusted for in the growth regression. Instrumental variables estimates show that a 1 percentage point increase in GDP per capita growth decreased foreign aid by over 4%. Adjusting for this quantitatively large, negative…

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Inference Based on Conditional Moment Inequalities

基于条件矩不等式的推断

In this paper, we propose an instrumental variable approach to constructing confidence sets (CS's) for the true parameter in models defined by conditional moment inequalities/equalities. We show that by properly choosing instrument functions, one can transform conditional moment inequalities/equalities into unconditional ones without losing identification power. Based on the unconditional moment inequalities/equalities, we construct CS's by inverting Cramér–von Mises-type or…

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Bayesian model averaging in the instrumental variable regression model

工具变量回归中的贝叶斯模型平均

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The…

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A class of adaptive importance sampling weighted EM algorithms for efficient and robust posterior and predictive simulation

用于后验与预测模拟的自适应重要性加权 EM 算法

A class of adaptive sampling methods is introduced for efficient posterior and predictive simulation. The proposed methods are robust in the sense that they can handle target distributions that exhibit non-elliptical shapes such as multimodality and skewness. The basic method makes use of sequences of importance weighted Expectation Maximization steps in order to efficiently construct a mixture of Student-t densities that approximates accurately the target…

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Instrumental Variable Estimators for Binary Outcomes

二元结局的工具变量估计量

Instrumental variables (IVs) can be used to construct estimators of exposure effects on the outcomes of studies affected by nonignorable selection of the exposure. Estimators that fail to adjust for the effects of nonignorable selection will be biased and inconsistent. Such situations commonly arise in observational studies, but are also a problem for randomized experiments affected by nonignorable noncompliance. In this article, we review IV estimators for studies in which…

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Functional Causal Mediation Analysis With an Application to Brain Connectivity

函数型因果中介分析及脑连接应用

Mediation analysis is often used in the behavioral sciences to investigate the role of intermediate variables that lie on the causal path between a randomized treatment and an outcome variable. Typically, mediation is assessed using structural equation models (SEMs), with model coefficients interpreted as causal effects. In this article, we present an extension of SEMs to the functional data analysis (FDA) setting that allows the mediating variable to be a continuous…

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Profitability and capital structure: Evidence from import penetration

盈利能力与资本结构:来自进口渗透的证据

Firms experiencing increases in import competition significantly reduce their leverage ratios by issuing equity and selling assets to repay debt. Using import tariffs and foreign exchange rates as instrumental variables for import penetration, I show that these results are not manifestations of endogenous relations between import competition and leverage. The results are consistent with traditional trade-off models of capital structure that predict a positive relation…

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On the size distortion of tests after an overidentifying restrictions pretest

过度识别限制预检验之后的检验尺寸扭曲

SUMMARY In the linear instrumental variables model, we provide theoretical and Monte Carlo evidence for the size distortion of a two‐stage hypothesis test that uses a test of overidentifying restrictions (OR) in the first stage. We derive a lower bound for the asymptotic size of the two‐stage test. The lower bound is given by the asymptotic size of a test that rejects the null hypothesis when two conditions are met: the test of OR used in the first stage does not reject and…

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Weak instrument inference in the presence of parameter instability

参数不稳定下的弱工具变量推断

This paper addresses the question of how to conduct inference on weakly identified coefficients in unstable econometric models. The weak correlations between the instruments and the relevant first‐order condition are modelled as local to zero, and we focus on moderate parameter instabilities. We show that, in the presence of weak identification, asymptotic distributions on the estimators and tests remain robust to moderate instability. Therefore, inference on the subset of…

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Testing a parametric function against a non‐parametric alternative in IV and GMM settings

IV与GMM框架下参数函数对非参数备择的检验

This paper develops a specification test for functional form for models identified by a conditional moment restriction, including IV and GMM settings. The framework is one where the moment restriction is specified as a function of data, a finite-dimensional parameter vector and a non-parametric function (an infinite-dimensional parameter vector). The null hypothesis is that the moment restriction does not depend on the non-parametric function. The test is relatively easy to…

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GEL statistics under weak identification

弱识别下的广义经验似然统计量

The central concern of this paper is the provision in a time series moment condition framework of practical recommendations of confidence regions for parameters whose coverage probabilities are robust to the strength or weakness of identification. To this end we develop Pearson-type test statistics based on GEL implied probabilities formed from general kernel smoothed versions of the moment indicators. We also modify the statistics suggested in Guggenberger and Smith (2008)…

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Inference regarding multiple structural changes in linear models with endogenous regressors

含内生解释变量的线性模型中多重结构变化的推断

This paper considers the linear model with endogenous regressors and multiple changes in the parameters at unknown times. It is shown that minimization of a Generalized Method of Moments criterion yields inconsistent estimators of the break fractions, but minimization of the Two Stage Least Squares (2SLS) criterion yields consistent estimators of these parameters. We develop a methodology for estimation and inference of the parameters of the model based on 2SLS. The analysis…

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A regularization approach to the many instruments problem

多工具变量问题的正则化方法

This paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite. In order to improve the small sample properties of standard instrumental variable (IV) estimators, we propose three modified IV estimators based on three different ways of inverting the covariance matrix of the instruments. These inverses involve a regularization or smoothing parameter. It should be stressed that no restriction…

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CUE with many weak instruments and nearly singular design

多弱工具变量与近奇异设计下的连续更新估计

This paper analyzes many weak moment asymptotics under the possibility of similar moments. The possibility of highly related moments arises when there are many of them. Knight and Fu (2000) designate the issue of similar regressors as the “nearly singular” design in the least squares case. In the nearly singular design, the sample variance converges to a singular limit term. However, Knight and Fu (2000) assume that on the nullspace of the limit term, the difference between…

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