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Underidentification?

欠识别?

We develop methods for testing that an econometric model is underidentified and for estimating the nature of the failed identification. We adopt a generalized-method-of moments perspective in a possibly non-linear econometric specification. If, after attempting to replicate the structural relation, we find substantial evidence against the overidentifying restrictions of an augmented model, this is evidence against underidentification of the original model. To diagnose how…

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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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The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions

含未知函数的序贯矩限制模型的半参数效率界

This paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions. Our results extend those of Chamberlain (1992b) and Ai and Chen (2003) for semiparametric conditional moment restrictions with identical information sets to the case of nested information sets, and those of Chamberlain (1992a) and Brown and Newey (1998) for models of sequential moment restrictions…

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Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors

内生解释变量非参数回归模型中线性泛函估计的效率界

Let Y=μ∗(X)+ε, where μ∗ is unknown and E[ε|X]≠0 with positive probability but there exist instrumental variables W such that E[ε|W]=0 w.p.1. It is well known that such nonparametric regression models are generally “ill-posed” in the sense that the map from the data to μ∗ is not continuous. In this paper, we derive the efficiency bounds for estimating certain linear functionals of μ∗ without assuming μ∗ itself to be identified.

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Explaining and Forecasting Results of the Self-sufficiency Project

解释与预测自给自足项目的结果

This paper studies the self-sufficiency project (SSP), a controlled randomized experiment concerning welfare, by estimating a model of endogenous skill accumulation, multidimensional job opportunities, and time-varying opportunity costs of labour market time. Methods for estimating dynamic programming models with unobserved heterogeneity are extended to account for unexpected policy interventions and endogenous sample selection and initial conditions. Parameters are…

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Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments

强或弱工具变量下联立方程模型的近乎无偏估计

We propose two simple bias-reduction procedures that apply to estimators in a general static simultaneous equation model and that are valid under relatively weak distributional assumptions for the errors. Standard jackknife estimators, as applied to 2SLS, may not reduce the bias of the exogenous variable coefficient estimators since the estimator biases are not monotonically nonincreasing with sample size (a necessary condition for successful bias reduction) and they have…

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REGRESSOR DIMENSION REDUCTION WITH ECONOMIC CONSTRAINTS: THE EXAMPLE OF DEMAND SYSTEMS WITH MANY GOODS

经济约束下的回归变量降维:多商品需求系统

Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicolinear covariates. We show how statistical dimension reduction techniques can be applied in models with these features. In particular, we consider estimation of derivatives of average structural functions in large consumer demand systems, which depend nonlinearly on the prices of many goods. Utility…

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Determinacy, indeterminacy and dynamic misspecification in linear rational expectations models

线性理性预期模型中的确定性、不确定性与动态误设

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model may have a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). The testing problem is addressed by a misspecification-type approach in which the overidentifying restrictions test obtained from the estimation of the system of Euler equations of the LRE model through the generalized method of moments…

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Mode Identification of Volatility in Time-Varying Autoregression

时变自回归模型中波动方差函数的峰数识别

In many applications, time series exhibit nonstationary behavior that might reasonably be modeled as a time-varying autoregressive (AR) process. In the context of such a model, we discuss the problem of testing for modality of the variance function. We propose a test of modality that is local and, when used iteratively, can be used to identify the total number of modes in a given series. This problem is closely related to peak detection and identification, which has…

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Identifying the Effects of SNAP (Food Stamps) on Child Health Outcomes When Participation Is Endogenous and Misreported

参与内生且存在误报时 SNAP 对儿童健康的效应识别

The literature assessing the efficacy of the Supplemental Nutrition Assistance Program (SNAP), formerly known as the Food Stamp Program, has long puzzled over positive associations between SNAP receipt and various undesirable health outcomes such as food insecurity. Assessing the causal impacts of SNAP, however, is hampered by two key identification problems: endogenous selection into participation and extensive systematic underreporting of participation status. Using data…

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Discussion: Latent variable graphical model selection via convex optimization

讨论:通过凸优化选择潜变量图模型

I want to start by congratulating Professors Chandrasekaran, Parrilo and Willsky for this fine piece of work.Their paper, hereafter referred to as CPW, addresses one of the biggest practical challenges of Gaussian graphical models-how to make inferences for a graphical model in the presence of missing variables.The difficulty comes from the fact that the validity of conditional independence relationships implied by a graphical model relies critically on the assumption that…

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Rejoinder: Latent variable graphical model selection via convex optimization

作者答复:通过凸优化选择潜变量图模型

Introduction.We thank all the discussants for their careful reading of our paper, and for their insightful critiques.We would also like to thank the editors for organizing this discussion.Our paper contributes to the area of high-dimensional statistics which has received much attention over the past several years across the statistics, machine learning and signal processing communities.In this rejoinder we clarify and comment on some of the points raised in the…

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Latent variable graphical model selection via convex optimization

通过凸优化选择潜变量图模型

Suppose we observe samples of a subset of a collection of random variables. No additional information is provided about the number of latent variables, nor of the relationship between the latent and observed variables. Is it possible to discover the number of latent components, and to learn a statistical model over the entire collection of variables? We address this question in the setting in which the latent and observed variables are jointly Gaussian, with the conditional…

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Identification With Imperfect Instruments

不完美工具变量下的识别

Dealing with endogenous regressors is a central challenge of applied research. The standard solution is to use instrumental variables that are assumed to be uncorrelated with unobservables. We instead allow the instrumental variable to be correlated with the error term, but we assume the correlation between the instrumental variable and the error term has the same sign as the correlation between the endogenous regressor and the error term and that the instrumental variable…

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GLOBAL IDENTIFICATION IN NONLINEAR MODELS WITH MOMENT RESTRICTIONS

矩限制非线性模型的全局识别

This paper derives sufficient conditions for global identification in nonlinear models characterized by a finite number of unconditional moment restrictions. The main contribution of this paper is to provide a set of assumptions that are alternative to those of Gale-Nikaidô-Fisher-Rothenberg, and which when satisfied guarantee that the moment conditions globally identify the parameters of interest.

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INDIVIDUAL VERSUS AGGREGATE INCOME ELASTICITIES FOR HETEROGENEOUS POPULATIONS

异质人群的个体与总体需求收入弹性

SUMMARY This paper deals with different concepts of income elasticities of demand for a heterogeneous population and the relationship between individual and aggregate elasticities. In general, the aggregate elasticity is not equal to the mean of individual elasticities. The difference depends on the heterogeneity of the population and is quantified by a covariance term. Sign and magnitude of this term are determined by an empirical analysis based on the UK Family Expenditure…

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Identifying Distributional Characteristics in Random Coefficients Panel Data Models

随机系数面板模型中分布特征的识别

We study the identification of panel models with linear individual-specific coefficients when T is fixed. We show identification of the variance of the effects under conditional uncorrelatedness. Identification requires restricted dependence of errors, reflecting a trade-off between heterogeneity and error dynamics. We show identification of the probability distribution of individual effects when errors follow an Autoregressive Moving Average process under conditional…

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The Trace Restriction: An Alternative Identification Strategy for the Bayesian Multinomial Probit Model

迹约束:贝叶斯多项 Probit 模型的替代识别策略

Previous authors have made Bayesian multinomial probit models identifiable by fixing a parameter on the main diagonal of the covariance matrix. The choice of which element one fixes can influence posterior predictions. Thus, we propose restricting the trace of the covariance matrix, which we achieve without computational penalty. This permits a prior that is symmetric to permutations of the nonbase outcome categories. We find in real and simulated consumer choice datasets…

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Labor income profiles are not heterogeneous: Evidence from income growth rates

劳动收入轨迹并不异质:来自收入增长率的证据

Idiosyncratic labor incomes are typically modeled either by stochastic processes with heterogeneous income profiles (HIPs) or restricted income profiles (RIPs).The HIP assumes that individual labor income grows deterministically at an unobserved rate and contains a persistent but stationary component, while the RIP assumes that income contains a random walk, a stationary component, and no unobserved deterministic growth-rate component.I show that if idiosyncratic labor…

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Instrumental variable estimation with heteroskedasticity and many instruments

异方差与多工具变量下的工具变量估计

This paper gives a relatively simple, well behaved solution to the problem of many instruments in heteroskedastic data. Such settings are common in microeconometric applications where many instruments are used to improve efficiency and allowance for heteroskedasticity is generally important. The solution is a Fuller (1977) like estimator and standard errors that are robust to heteroskedasticity and many instruments. We show that the estimator has finite moments and high…

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Analysing bivariate survival data with interval sampling and application to cancer epidemiology

区间抽样下二元生存数据分析及癌症流行病学应用

In biomedical studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as outcomes to identify the progression of a disease. In cancer studies, interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme, termed interval sampling, in which the first failure event is identified within a calendar time interval, the…

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Likelihood-Based Procedures for Threshold Diagnostics and Uncertainty in Extreme Value Modelling

极值建模中阈值诊断与不确定性的似然方法

Summary For extreme value modelling based on threshold techniques, a well-documented issue is the sensitivity of inference from the model to the choice of threshold. The threshold above which we assume a non-homogeneous Poisson process, or equivalently generalized Pareto representation, to be a reasonable approximation to the distribution is traditionally selected before analysis and subsequently treated as fixed and known. In doing so, the analyst cannot account for the…

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