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Some properties of the LIML estimator in a dynamic panel structural equation

动态面板结构方程中 LIML 估计量的若干性质

We investigate the finite sample and asymptotic properties of the within-groups (WG), the random-effects quasi-maximum likelihood (RQML), the generalized method of moment (GMM) and the limited information maximum likelihood (LIML) estimators for a panel autoregressive structural equation model with random effects when both T (time-dimension) and N (cross-section dimension) are large. When we use the forward-filtering due to Alvarez and Arellano (2003), the WG, the RQML and…

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Moment Restriction-Based Econometric Methods: An overview

基于矩限制的计量经济学方法:概览

Moment restriction-based econometric modelling is a broad class which includes the parametric, semiparametric and nonparametric approaches. Moments and conditional moments themselves are nonparametric quantities. If a model is specified in part up to some finite dimensional parameters, this will provide semiparametric estimates or tests. If we use the score to construct moment restrictions to estimate finite dimensional parameters, this yields maximum likelihood (ML)…

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On finite sample properties of alternative estimators of coefficients in a structural equation with many instruments

多工具变量结构方程系数估计量的有限样本比较

We compare four different estimation methods for the coefficients of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum empirical likelihood (MEL) estimator and the generalized method of moments (GMM) (or the estimating equation) estimator. Tables and…

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On the asymptotic optimality of the LIML estimator with possibly many instruments

工具变量可能众多时 LIML 估计量的渐近最优性

We consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables. We derive some asymptotic properties of the limited information maximum likelihood (LIML) estimator when the number of instruments is large; some of these results are new as well as old, and we relate them to results in some recent studies. We have found that the variance of the limiting distribution of the LIML…

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Tests of overidentification and predeterminedness in simultaneous equation models

联立方程模型的过度识别与预定性检验

A set of simultaneous equations that is a part of a larger complete system is considered. One hypothesis concerning this set of equations is that it is overidentified as a block by a block of zero restrictions. Another hypothesis is that a subset of the current endogenous variables is uncorrelated with the disturbances in the set of simultaneous equations (‘econometric predeterminedness’). Likelihood ratio, Lagrange multiplier, and Wald tests are derived for the…

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Approximate Distributions and Power of Test Statistics for Overidentifying Restrictions in a System of Simultaneous Equations

联立方程系统中过度识别约束检验的近似分布与功效

We derive asymptotic expansions of the distributions of test statistics for over-identifying restrictions in a system of simultaneous equations under the null and the non-null hypotheses. We investigate the effects of the normality assumption for disturbances on the test statistics based on their asymptotic expansions. We also study the power functions of test statistics based on their asymptotic expansions. After modifying their critical regions to the same significance…

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Comparing Single-Equation Estimators in a Simultaneous Equation System

联立方程系统中单方程估计量的比较

Comparisons of estimators are made on the basis of their mean squared errors and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely. The estimators include k -class estimators (limited information maximum likelihood, two-stage least squares, and ordinary least squares) and linear combinations of them as well as…

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Properties of Predictors in Misspecified Autoregressive Time Series Models

误设自回归时间序列模型中预测量的性质

This article investigates major effects of misspecification in stationary linear time series models when we fit a pth-order autoregressive model. The true model can be an autoregressive moving average model. We derive the formulas of bias and mean squared error (MSE) of the least squares estimator and the hth period ahead prediction MSE in the time domain. Contrary to previous studies, the process in estimation is not necessarily independent of the process in prediction, and…

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Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator

有限信息极大似然估计量分布函数的计算

T. W. Anderson, Naoto Kunitomo, Takamitsu Sawa, Evaluation of the Distribution Function of the Limited Information Maximum Likelihood Estimator, Econometrica, Vol. 50, No. 4 (Jul., 1982), pp. 1009-1027

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Asymptotic Expansions of the Distributions of Estimators in a Linear Functional Relationship and Simultaneous Equations

线性函数关系与联立方程中估计量分布的渐近展开

We derive asymptotic expansions of the distributions of the maximum likelihood (ML) estimator and the ordinary least squares (OLS) estimator in a linear functional relationship model as the sample size increases infinitely. These expansions are equivalent to the asymptotic expansions of the distributions of the limited information maximum likelihood (LIML) estimator when the covariance is known to within a proportionality constant and the two-stage least squares (TSLS)…

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Improving the Maximum Likelihood Estimate in Linear Functional Relationships for Alternative Parameter Sequences

不同参数序列下线性函数关系最大似然估计的改进

We propose an improvement of the maximum likelihood (ML) estimate in linear functional relationships. The improved estimate is a linear combination of the ML and the least squares estimate so as to remove the bias of the former. Approximations to the distribution of the estimate are derived for two alternative parameter sequences: a sequence in which the noncentrality parameter (the spread of the true values) increases while the number of observations stays fixed, and that…

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Improving the Maximum Likelihood Estimate in Linear Functional Relationships for Alternative Parameter Sequences

不同参数序列下线性函数关系最大似然估计的改进

We propose an improvement of the maximum likelihood (ML) estimate in linear functional relationships. The improved estimate is a linear combination of the ML and the least squares estimate so as to remove the bias of the former. Approximations to the distribution of the estimate are derived for two alternative parameter sequences: a sequence in which the noncentrality parameter (the spread of the true values) increases while the number of observations stays fixed, and that…

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