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Approximating a Truncated Normal Regression with the Method of Moments

用矩方法近似截断正态回归

A NUMBER OF ARTICLES have been written in recent as well as more distant times on the subject of limited dependent variables. This broad classification includes two particular special cases. First, the dependent variable has finite probability mass concentrated at some limit point-the so called Tobit model. This case is referred to as the censored model in the statistical literature. The second case is when the dependent variable simply has a limited range and follows a…

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Finite Sample Analysis of Misspecification in Simultaneous Equation Models

联立方程模型设定错误的有限样本分析

This article examines the effects of misspecification on the exact sampling distributions of the k-class estimators of a single equation in a simultaneous equations model. The analysis focuses on the effects of excluding relevant exogenous variables. The misspecification may occur in either the estimated equation itself or in the other equations in the system. Exact expressions and large-concentration parameter asymptotic expansions are stated and analyzed for the bias and…

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Conditional Independence for Statistical Operations

统计操作的条件独立理论

A general calculus of conditional independence is developed, suitable for application to a wide range of statistical concepts such as sufficiency, parameter-identification, adequacy and ancillarity. A vehicle for this theory is the statistical operation, a structure-preserving map between statistical spaces. Concepts such as completeness and identifiability of mixtures arise naturally and play an important part. Some general theorems are exemplified by applications to…

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The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables

含 n+1 个内生变量方程中工具变量估计量的精确分布

IN THE LATE 1960's, Richardson [18] and Sawa [20] derived the exact distribution of the two-stage least squares (2SLS) estimator in a structural equation (of a simultaneous system) that contained two endogenous variables and an arbitrary number of degrees of overidentification. Their results refer to the 2SLS estimator of the coefficient of the endogenous variable included on the right hand side of the equation and were obtained under the classical assumptions (to use the…

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The Asymptotic Distribution of the Sample Inverse Autocorrelations of an Autoregressive-Moving Average Process

ARMA 过程样本逆自相关的渐近分布

The inverse autocorrelations of a time series are useful at the identification stage of model building. In practice these quantities must be estimated from the data and so the distributional properties of the estimators are of great importance. In this paper the asymptotic distribution of the sample inverse autocorrelations is derived, making use of the duality between the autocorrelations and inverse autocorrelations of two autoregressive-moving average processes.

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A Monte Carlo Study of Small-Sample Properties of Simultaneous Equation Estimators with Normal and Nonnormal Disturbances

正态与非正态扰动下联立方程估计量的小样本蒙特卡洛比较

In this paper we consider four alternative forms of two-parameter normal and nonnormal error distributions and report on a Monte Carlo study of the small-sample properties of least squares, two-stage least squares, three-stage least squares and full information maximum likelihood estimators. On the basis of 1,000 replications of sample size 20 in two experiments on an overidentified model, we found that the small-sample rankings of econometric estimators of both structural…

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The Estimation of the Prais-Houthakker Model of Equivalence Scales

Prais–Houthakker 家庭等价尺度模型的估计

Given a preference basis for the model, a household's general equivalence scale is seen to be a cost of living index relative to the reference household type defined at constant prices. A maximum likelihood estimation procedure which can be applied both to cross-section data and pooled time-series/cross-sections is derived. The lack of identification of the model is established theoretically and checked empirically on British family expenditure survey data. With prior…

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Econometric Implications of the Rational Expectations Hypothesis

理性预期假说的计量经济学含义

The implications for applied econometrics of the assumption that unobservable expectations formed rationally in Muth's sense examined. The statistical properties of the resulting models and their distributed lag and time series representations described. Purely extrapolative forecasts of endogenous variables can be constructed, as alternatives to rational expectations, but less efficient. Identification and estimation considered: an order condition is that no more…

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Macroeconomics and Reality

宏观经济学与现实

Existing strategies for econometric analysis related to macroeconomics are subject to a number of serious objections, some recently formulated, some old. These objections are summarized in this paper, and it is argued that taken together they make it unlikely that macroeconomic models are in fact over identified, as the existing statistical theory usually assumes. The implications of this conclusion are explored, and an example of econometric work in a non-standard style,…

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The asymptotic distribution of the sample inverse autocorrelations of an autoregressive-moving average process

ARMA 过程样本逆自相关的渐近分布

The inverse autocorrelations of a time series are useful at the identification stage of model building. In practice these quantities must be estimated from the data and so the distributional properties of the estimators are of great importance. In this paper the asymptotic distribution of the sample inverse autocorrelations is derived, making use of the duality between the autocorrelations and inverse autocorrelations of two autoregressive-moving average processes.

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Distribution of the Residual Cross-Correlation in Univariate ARMA Time Series Models

单变量 ARMA 时间序列模型残差互相关的分布

Cross-correlations between univariate autoregressive moving average (ARMA) time series residuals are useful in the examination of relationships between time series (Pierce 1977a) and in the identification of dynamic regression models (Haugh and Box 1977). In this article, the asymptotic distribution of these residual cross-correlations is derived, and its application to the problem of testing for lagged relationships in the presence of instantaneous causality is discussed.…

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A Note on the Distribution Functions of LIML and 2SLS Structural Coefficient in the Exactly Identified Case

恰好识别情形下 LIML 与 2SLS 结构系数分布函数的说明

Many alternative techniques of estimating coefficients appearing in the structural representation of econometric models have been developed. The techniques of two-stage least squares (2SLS) and limited information maximum likelihood (LIML) yield identical estimates in the exactly identified case. The derivations of the density functions of these estimators for overidentified structural equations do not formally include the exactly identified case. In this note we demonstrate…

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A Structural Probit Model with Latent Variables

含潜变量的结构 Probit 模型

A model with dichotomous indicators of latent variables is developed. The latent variables are related to each other and to a set of exogenous variables in a system of structural relations. Identification and maximum likelihood estimation of the model are treated. A sociological application is presented in which a theoretical construct (an attitude) is related to a set of background variables. The construct is not measured directly, but is indicated by the answers to a pair…

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A Note on the Distribution Functions of LIML and 2SLS Structural Coefficient in the Exactly Identified Case

恰好识别情形下 LIML 与 2SLS 结构系数分布函数札记

Many alternative techniques of estimating coefficients appearing in the structural representation of econometric models have been developed. The techniques of two-stage least squares (2SLS) and limited information maximum likelihood (LIML) yield identical estimates in the exactly identified case. The derivations of the density functions of these estimators for overidentified structural equations do not formally include the exactly identified case. In this note we demonstrate…

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Conditional Independence in Statistical Theory

统计理论中的条件独立

Summary Some simple heuristic properties of conditional independence are shown to form a conceptual framework for much of the theory of statistical inference. This framework is illustrated by an examination of the rôle of conditional independence in several diverse areas of the field of statistics. Topics covered include sufficiency and ancillarity, parameter identification, causal inference, prediction sufficiency, data selection mechanisms, invariant statistical models and…

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Identification and Estimation in Binary Choice Models with Limited (Censored) Dependent Variables

含受限(删失)因变量的二元选择模型:识别与估计

A class of statistical models which generate simultaneous equation models with both discrete and continuous endogenous variables is introduced. This class of models can also be regarded as a new class of switching simultaneous equation models which are of general interest. Identification and estimation problems are investigated. Several simple consistent two stage methods are proposed. The consistency of those estimators is proved. Two step maximum likelihood procedures are…

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Testing Disease Dependence in Survival Experiments with Serial Sacrifice

含分期处死设计的生存实验中疾病依赖性的检验

An age-dependent compartment model is applied in a novel way to survival data. Analysis is performed of data from an “improved survival experiment” which incorporates serial sacrifice, and tests of hypotheses of dependent diseases are obtained. Problems dealing with identifiability of models are emphasized and discussed. Finally, these ideas are illustrated in connection with experimental data from mice exposed to radiation.

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Testing Disease Dependence in Survival Experiments with Serial Sacrifice

分批处死生存实验中的疾病依赖性检验

An age-dependent compartment model is applied in a novel way to survival data. Analysis is performed of data from an “improved survival experiment” which incorporates serial sacrifice, and tests of hypotheses of dependent diseases are obtained. Problems dealing with identifiability of models are emphasized and discussed. Finally, these ideas are illustrated in connection with experimental data from mice exposed to radiation.

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