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Identifiability of Gaussian structural equation models with equal error variances

等误差方差高斯结构方程模型的可识别性

We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model is a directed acyclic graph describing the relationships between the variables. In Gaussian structural equation models with linear functions, the graph can be identified from the joint distribution only up to Markov equivalence classes, assuming faithfulness. In…

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crs: A PACKAGE FOR NONPARAMETRIC SPLINE ESTIMATION IN R

SUMMARY crs is a library for R written by Jeffrey S. Racine (Maintainer) and Zhenghua Nie. This add‐on package provides a collection of functions for spline‐based nonparametric estimation of regression functions with both continuous and categorical regressors. Currently, the crs package integrates data‐driven methods for selecting the spline degree, the number of knots and the necessary bandwidths for nonparametric conditional mean, IV and quantile regression. A function for…

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Partial identification of finite mixtures in econometric models

计量经济模型中有限混合分布的部分识别

We consider partial identification of finite mixture models in the presence of an observable source of variation in the mixture weights that leaves component distributions unchanged, as is the case in large classes of econometric models. We first show that when the number J of component distributions is known a priori, the family of mixture models compatible with the data is a subset of a J(J−1)-dimensional space. When the outcome variable is continuous, this subset is…

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Complementarity and aggregate implications of assortative matching: A nonparametric analysis

互补性与同类匹配的总体影响:非参数分析

This paper presents econometric methods for measuring the average output effect of reallocating an indivisible input across production units. A distinctive feature of reallocations is that, by definition, they involve no augmentation of resources and, as such, leave the marginal distribution of the reallocated input unchanged. Nevertheless, if the production technology is nonseparable, they may alter average output. An example is the reallocation of teachers across…

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Concave-monotone treatment response and monotone treatment selection: With an application to the returns to schooling

凹单调处理反应与单调处理选择:教育回报的应用

This paper identifies sharp bounds on the mean treatment response and average treatment effect under the assumptions of both the concave-monotone treatment response (concave-MTR) and the monotone treatment selection (MTS).We use our bounds and the U.S. National Longitudinal Survey of Youth 1979 to estimate mean returns to schooling.Our upper-bound estimates are substantially smaller than (i) estimates using only the concave-MTR assumption of Manski (1997), and (ii) estimates…

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Identification of income-leisure preferences and evaluation of income tax policy

收入—闲暇偏好的识别与所得税政策评估

The merits of alternative income tax policies depend on the population distribution of preferences for income and leisure. Standard theory, which supposes that persons want more income and more leisure, does not predict how they resolve the tension between these desires. Empirical studies of labor supply have imposed strong preference assumptions that lack foundation. This paper examines anew the problem of inference on income–leisure preferences and considers the…

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Identification theory for high dimensional static and dynamic factor models

高维静态与动态因子模型的识别理论

High dimensional factor models can involve thousands of parameters. The Jacobian matrix for identification is of a large dimension. It can be difficult and numerically inaccurate to evaluate the rank of such a Jacobian matrix. We reduce the identification problem to a small rank problem, which is easy to check. The identification conditions allow both linear and nonlinear restrictions. Under reasonable assumptions for high dimensional factor models, the small rank conditions…

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Treatment effect estimation with covariate measurement error

协变量测量误差下的处理效应估计

This paper investigates the effect that covariate measurement error has on a treatment effect analysis built on an unconfoundedness restriction in which there is conditioning on error free covariates. The approach uses small parameter asymptotic methods to obtain the approximate effects of measurement error for estimators of average treatment effects. The approximations can be estimated using data on observed outcomes, the treatment indicator and error contaminated…

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ESTIMATING THE PERSISTENCE AND THE AUTOCORRELATION FUNCTION OF A TIME SERIES THAT IS MEASURED WITH ERROR

含测量误差时间序列的持续性与自相关函数估计

An economic time series can often be viewed as a noisy proxy for an underlying economic variable. Measurement errors will influence the dynamic properties of the observed process and may conceal the persistence of the underlying time series. In this paper we develop instrumental variable (IV) methods for extracting information about the latent process. Our framework can be used to estimate the autocorrelation function of the latent volatility process and a key persistence…

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MEASUREMENT ERRORS IN DYNAMIC MODELS

动态模型中的测量误差

Static models that are not identifiable in the presence of white noise measurement errors are known to be potentially identifiable when the model has dynamics. However, few results are available for the plausible case of serially correlated measurement errors. This paper provides order and rank conditions for “limited information” identification of parameters in dynamic models with measurement errors where some aspects of the probability model are not fully specified or…

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Identification-robust inference for endogeneity parameters in linear structural models

线性结构模型中内生性参数的识别稳健推断

We provide a generalization of the Anderson–Rubin (AR) procedure for inference on parameters that represent the dependence between possibly endogenous explanatory variables and disturbances in a linear structural equation (endogeneity parameters). We stress the distinction between regression and covariance endogeneity parameters. Such parameters have intrinsic interest (because they measure the effect of latent variables, which induce simultaneity) and play a central role in…

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Probit Transformation for Kernel Density Estimation on the Unit Interval

单位区间核密度估计的Probit变换方法

Kernel estimation of a probability density function supported on the unit interval has proved difficult, because of the well-known boundary bias issues a conventional kernel density estimator would necessarily face in this situation. Transforming the variable of interest into a variable whose density has unconstrained support, estimating that density, and obtaining an estimate of the density of the original variable through back-transformation, seems a natural idea to easily…

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A Model-Averaging Approach for High-Dimensional Regression

高维回归的模型平均方法

This article considers high-dimensional regression problems in which the number of predictors p exceeds the sample size n. We develop a model-averaging procedure for high-dimensional regression problems. Unlike most variable selection studies featuring the identification of true predictors, our focus here is on the prediction accuracy for the true conditional mean of y given the p predictors. Our method consists of two steps. The first step is to construct a class of…

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Non-Parametric Identification and Estimation of the Number of Components in Multivariate Mixtures

多元混合模型成分数的非参数识别与估计

Summary We analyse the identifiability of the number of components in k-variate, M-component finite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components from the distribution function of the observed data. When k⩾2, a lower bound on the number of components (M) is…

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Estimating turning points using large data sets

利用大型数据集估计经济周期转折点

Dating business cycles entails ascertaining economy-wide turning points. Broadly speaking, there are two approaches in the literature. The first approach, which dates to Burns and Mitchell (1946), is to identify turning points individually in a large number of series, then to look for a common date that could be called an aggregate turning point. The second approach, which has been the focus of more recent academic and applied work, is to look for turning points in a few, or…

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Optimal estimation of cointegrated systems with irrelevant instruments

利用无关工具变量最优估计协整系统

It has been known since Phillips and Hansen (1990) that cointegrated systems can be consistently estimated using stochastic trend instruments that are independent of the system variables. A similar phenomenon occurs with deterministically trending instruments. The present work shows that such “irrelevant” deterministic trend instruments may be systematically used to produce asymptotically efficient estimates of a cointegrated system. The approach is convenient in practice,…

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Aggregation in large dynamic panels

大型动态面板中的聚合

This paper investigates the problem of aggregation in the case of large linear dynamic panels, where each micro unit is potentially related to all other micro units, and where micro innovations are allowed to be cross sectionally dependent. Following Pesaran (2003), an optimal aggregate function is derived and used (i) to establish conditions under which Granger’s (1980) conjecture regarding the long memory properties of aggregate variables from ‘a very large scale dynamic,…

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Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators

GMM 估计中误设稳健自助法的渐近精化

I propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals based on GMM estimators even when the model is misspecified. In addition, my bootstrap does not require recentering the moment function, which has been considered as critical for GMM. Regardless of model misspecification, the proposed bootstrap achieves the same sharp magnitude of refinements as the conventional bootstrap methods which establish asymptotic…

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Nonparametric inference for counterfactual means: Bias-correction, confidence sets, and weak IV

反事实均值的非参数推断:偏差修正、置信集与弱工具变量

This paper supplements Manski (1990) and Manski and Pepper (2000) and contributes to the literature by introducing the concept of weak IV for the partially identified mean counterfactual outcomes when an instrumental variable (IV) or a monotone instrumental variable (MIV) is available (IV or MIV assumption respectively); developing asymptotically uniformly valid confidence sets for the counterfactual mean outcomes and average treatment effects under the assumptions;…

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Semiparametric models with single-index nuisance parameters

含单指标干扰参数的半参数模型

In many semiparametric models, the parameter of interest is identified through conditional expectations, where the conditioning variable involves a single-index that is estimated in the first step. Among the examples are sample selection models and propensity score matching estimators. When the first-step estimator follows cube-root asymptotics, no method of analyzing the asymptotic variance of the second step estimator exists in the literature. This paper provides…

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Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression

非参数工具变量回归中含噪非线性算子方程的迭代估计

This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach…

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DO PEERS AFFECT STUDENT ACHIEVEMENT? EVIDENCE FROM CANADA USING GROUP SIZE VARIATION

SUMMARY We provide the first empirical application of a new approach proposed by Lee ( Journal of Econometrics 2007; 140 (2), 333–374) to estimate peer effects in a linear‐in‐means model when individuals interact in groups. Assumingsufficient group size variation, this approach allows to control for correlated effects at the group level and to solve the simultaneity (reflection) problem. We clarify the intuition behind identification of peer effects in the model. We…

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Identification Using Stability Restrictions

利用稳定性限制进行识别

This paper studies inference in models that are identified by moment restrictions. We show how instability of the moments can be used constructively to improve the identification of structural parameters that are stable over time. A leading example is macroeconomic models that are immune to the well‐known (Lucas (1976)) critique in the face of policy regime shifts. This insight is used to develop novel econometric methods that extend the widely used generalized method of…

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A Practical Two-Step Method for Testing Moment Inequalities

检验矩不等式的实用两步法

This paper considers the problem of testing a finite number of moment inequalities. We propose a two‐step approach. In the first step, a confidence region for the moments is constructed. In the second step, this set is used to provide information about which moments are “negative.” A Bonferonni‐type correction is used to account for the fact that, with some probability, the moments may not lie in the confidence region. It is shown that the test controls size uniformly over a…

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