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工具变量:IV、2SLS 与内生性识别。
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Inferences for a Partially Varying Coefficient Model With Endogenous Regressors

含内生解释变量的部分变系数模型的估计与推断

In this article, we propose a new class of semiparametric instrumental variable models with partially varying coefficients, in which the structural function has a partially linear form and the impact of endogenous structural variables can vary over different levels of some exogenous variables. We propose a three-step estimation procedure to estimate both functional and constant coefficients. The consistency and asymptotic normality of these proposed estimators are…

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Two-stage least squares as minimum distance

作为最小距离估计的两阶段最小二乘

SummaryThe two-stage least-squares (2SLS) instrumental-variables (IV) estimator for the parameters in linear models with a single endogenous variable is shown to be identical to an optimal minimum-distance (MD) estimator based on the individual instrument-specific IV estimators. The 2SLS estimator is a linear combination of the individual estimators, with the weights determined by their variances and covariances under conditional homoskedasticity. It is further shown that…

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Optimum thresholding using mean and conditional mean squared error

基于均方误差与条件均方误差的最优阈值选择

We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity. The nonparametric threshold estimator IV̂n of the integrated variance IV≔∫0Tσs2ds proposed in Mancini (2009) is constructed using observations on a discrete time grid, and precisely it sums up the squared increments of the process when they are below a threshold, which depends on the observation time step and, sometimes, model parameters or…

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Estimating within‐cluster spillover effects using a cluster randomization with application to knowledge diffusion in rural India

利用簇随机化估计簇内溢出效应:印度农村知识扩散应用

Summary Spillover effects within randomized clusters pose a challenge for identifying impacts of an individualized treatment. The paper proposes a solution. Longitudinal and intra‐household observations are combined in estimating the direct knowledge gain from watching an info‐movie in rural India, while randomized village assignment identifies knowledge sharing. Simulations on synthetic data and econometric tests provide support for the estimation method. We find evidence…

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On Heckits, LATE, and Numerical Equivalence

Heckit估计、局部平均处理效应与数值等价性

Structural econometric methods are often criticized for being sensitive to functional form assumptions. We study parametric estimators of the local average treatment effect (LATE) derived from a widely used class of latent threshold crossing models and show they yield LATE estimates algebraically equivalent to the instrumental variables (IV) estimator. Our leading example is Heckman's (1979) two‐step (“Heckit”) control function estimator which, with two‐sided non‐compliance,…

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Identification of average effects under magnitude and sign restrictions on confounding

混杂效应幅度与符号限制下的平均效应识别

This paper studies measuring various average effects of X on Y in general structural systems with unobserved confounders U , a potential instrument Z , and a proxy W for U . We do not require X or Z to be exogenous given the covariates or W to be a perfect one‐to‐one mapping of U . We study the identification of coefficients in linear structures as well as covariate‐conditioned average nonparametric discrete and marginal effects (e.g., average treatment effect on the…

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Identification‐ and singularity‐robust inference for moment condition models

矩条件模型中对识别强度与奇异性稳健的推断

This paper introduces a new identification‐ and singularity‐robust conditional quasi‐likelihood ratio (SR‐CQLR) test and a new identification‐ and singularity‐robust Anderson and Rubin (1949) (SR‐AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is…

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Improved inference on the rank of a matrix

矩阵秩的改进推断

This paper develops a general framework for conducting inference on the rank of an unknown matrix Π 0 . A defining feature of our setup is the null hypothesis of the form H 0 : rank ( Π 0 ) ≤ r . The problem is of first‐order importance because the previous literature focuses on H 0 ′ : rank ( Π 0 ) = r by implicitly assuming away rank ( Π 0 ) < r , which may lead to invalid rank tests due to overrejections. In particular, we show that limiting distributions of test…

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A more powerful subvector Anderson Rubin test in linear instrumental variables regression

线性工具变量回归中更有功效的子向量 Anderson–Rubin 检验

We study subvector inference in the linear instrumental variables model assuming homoskedasticity but allowing for weak instruments. The subvector Anderson and Rubin (1949) test that uses chi square critical values with degrees of freedom reduced by the number of parameters not under test, proposed by Guggenberger, Kleibergen, Mavroeidis, and Chen (2012), controls size but is generally conservative. We propose a conditional subvector Anderson and Rubin test that uses…

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Identification of a nonseparable model under endogeneity using binary proxies for unobserved heterogeneity

利用未观测异质性的二元代理识别内生非可分模型

In this paper, I study identification of a nonseparable model with endogeneity arising due to unobserved heterogeneity. Identification relies on the availability of binary proxies that can be used to control for the unobserved heterogeneity. I show that the model is identified in the limit as the number of proxies increases. The argument does not require an instrumental variable that is excluded from the outcome equation nor does it require the support of the unobserved…

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Time Use and Labor Productivity: The Returns to Sleep

时间利用与劳动生产率:睡眠的回报

Abstract We investigate how the largest use of time—sleep—affects productivity. Time use data from the United States allow us to test a model in which sleep improves productivity. Consistent with theory, we find sleep is more complementary to home production than to leisure for nonemployed individuals. We then show that later sunset time reduces worker sleep and earnings. After ruling out alternative hypotheses, we implement an instrumental variables specification that…

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Robots at Work

工作中的机器人

We analyze for the first time the economic contributions of modern industrial robots, which are flexible, versatile, and autonomous machines. We use novel panel data on robot adoption within industries in seventeen countries from 1993 to 2007 and new instrumental variables that rely on robots’ comparative advantage in specific tasks. Our findings suggest that increased robot use contributed approximately 0.36 percentage points to annual labor productivity growth, while at…

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NONPARAMETRIC INSTRUMENTAL REGRESSION WITH ERRORS IN VARIABLES

存在变量测量误差的非参数工具变量回归

This paper considers nonparametric instrumental variable regression when the endogenous variable is contaminated with classical measurement error. Existing methods are inconsistent in the presence of measurement error. We propose a wavelet deconvolution estimator for the structural function that modifies the generalized Fourier coefficients of the orthogonal series estimator to take into account the measurement error. We establish the convergence rates of our estimator for…

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Testing endogeneity with high dimensional covariates

高维协变量下的内生性检验

Modern, high dimensional data has renewed investigation on instrumental variables (IV) analysis, primarily focusing on estimation of effects of endogenous variables and putting little attention towards specification tests. This paper studies in high dimensions the Durbin–Wu–Hausman (DWH) test, a popular specification test for endogeneity in IV regression. We show, surprisingly, that the DWH test maintains its size in high dimensions, but at an expense of power. We propose a…

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On Bootstrap inconsistency and Bonferroni-based size-correction for the subset Anderson–Rubin test under conditional homoskedasticity

条件同方差下子集Anderson–Rubin检验的Bootstrap不一致与Bonferroni尺寸校正

We focus on the linear instrumental variable model with two endogenous regressors under conditional homoskedasticity, and study the subset Anderson and Rubin (1949, AR) test when the nuisance structural parameter, the unrestricted slope coefficient of endogenous regressor, may be weakly identified. Weak identification leads to nonstandard null limiting distributions, and alternative to the usual chi-squared critical value is needed. We first investigate the bootstrap…

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Sequential estimation of censored quantile regression models

删失分位数回归模型的序贯估计

In this paper we propose sequential censored quantile regression (SCQR) and sequential instrumental variables censored quantile regression estimators (SIVCQR). We effectively transform the difficult censored quantile regression and censored instrumental variables quantile regression problems into more standard QR and IVQR procedures, consequently, our approaches make the quantile regression techniques for censored data easily accessible to applied researchers. Simulation…

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Beyond plausibly exogenous

超越“近似外生”:工具变量排除限制的敏感性分析

We synthesize two recent advances in the literature on instrumental variable (IV) estimation that test and relax the exclusion restriction. Our approach first estimates the direct effect of the IV on the outcome in a subsample for which the IV does not affect the treatment variable. Subsequently, this estimate for the direct effect is used as input for the plausibly exogenous method developed by Conley, Hansen and Rossi. This two‐step procedure provides a novel and informed…

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Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model

矩阵指数空间模型的非正规 N2SLS 与 LASSO 估计

In this paper, we consider estimation of the matrix exponential spatial specification model with the Durbin and endogenous regressors. We find that the nonlinear two-stage least squares (N2SLS) estimator is in general consistent and asymptotically normal. However, when the Durbin and endogenous regressors are irrelevant, the gradient vector of the N2SLS criterion function has a singular covariance matrix with probability approaching one (w.p.a.1.). Some components of the…

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SIMPLE, ROBUST, AND ACCURATE F AND t TESTS IN COINTEGRATED SYSTEMS

协整系统中简易、稳健且精确的 F 与 t 检验

This paper proposes new, simple, and more accurate statistical tests in a cointegrated system that allows for endogenous regressors and serially dependent errors. The approach involves first transforming the time series using orthonormal basis functions in L 2 [0, 1], which have energy concentrated at low frequencies, and then running an augmented regression based on the transformed data and constructing the test statistics in the usual way. The approach is essentially the…

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IV AND GMM INFERENCE IN ENDOGENOUS STOCHASTIC UNIT ROOT MODELS

内生随机单位根模型中的 IV 与 GMM 推断

Lieberman and Phillips (2017; LP) introduced a multivariate stochastic unit root (STUR) model, which allows for random, time varying local departures from a unit root (UR) model, where nonlinear least squares (NLLS) may be used for estimation and inference on the STUR coefficient. In a structural version of this model where the driver variables of the STUR coefficient are endogenous, the NLLS estimate of the STUR parameter is inconsistent, as are the corresponding estimates…

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STRUCTURAL CHANGE IN NONSTATIONARY AR(1) MODELS

非平稳 AR(1) 模型中的结构变化

This article revisits the asymptotic inference for nonstationary AR(1) models of Phillips and Magdalinos (2007a) by incorporating a structural change in the AR parameter at an unknown time k 0 . Consider the model ${y_t} = {\beta _1}{y_{t - 1}}I\{ t \le {k_0}\} + {\beta _2}{y_{t - 1}}I\{ t > {k_0}\} + {\varepsilon _t},t = 1,2, \ldots ,T$ , where I {·} denotes the indicator function, one of ${\beta _1}$ and ${\beta _2}$ depends on the sample size T , and the other is equal to…

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Confidence Intervals for Causal Effects with Invalid Instruments by Using Two-Stage Hard Thresholding with Voting

存在无效工具变量时的因果效应置信区间:两阶段硬阈值与投票

Summary A major challenge in instrumental variable (IV) analysis is to find instruments that are valid, or have no direct effect on the outcome and are ignorable. Typically one is unsure whether all of the putative IVs are in fact valid. We propose a general inference procedure in the presence of invalid IVs, called two-stage hard thresholding with voting. The procedure uses two hard thresholding steps to select strong instruments and to generate candidate sets of valid IVs.…

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A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs

工具变量识别不同局部平均处理效应时的 2SLS 一致方差估计量

Under treatment effect heterogeneity, an instrument identifies the instrument-specific local average treatment effect (LATE). With multiple instruments, two-stage least squares (2SLS) estimand is a weighted average of different LATEs. What is often overlooked in the literature is that the postulated moment condition evaluated at the 2SLS estimand does not hold unless those LATEs are the same. If so, the conventional heteroscedasticity-robust variance estimator would be…

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Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective

非参数加性工具变量估计:组收缩估计视角

In this article, we study a nonparametric approach regarding a general nonlinear reduced form equation to achieve a better approximation of the optimal instrument. Accordingly, we propose the nonparametric additive instrumental variable estimator (NAIVE) with the adaptive group Lasso. We theoretically demonstrate that the proposed estimator is root-n consistent and asymptotically normal. The adaptive group Lasso helps us select the valid instruments while the dimensionality…

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