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两阶段最小二乘估计量的偏差AI 解读

This article derives the bias of the two-stage least squares estimator to the order of T-2, T being the number of observations. It is found that when the degree of overidentification in the equation concerned is unity, the 2SLS bias is zero to this order of approximation.

自相关误差下结构方程的小样本估计AI 解读

Many time series models have autocorrelated errors. A further problem may be that some of the right-hand variables are correlated with the error. Using Monte Carlo methods we investigated several estimators of such a model. We found that a transformation to correct the autocorrelation often improved matters, but that techniques to correct the other problems such as instrumental variables were usually ineffective. In many cases ordinary least squares had the smallest mean…

两阶段最小二乘估计量的偏误AI 解读

This article derives the bias of the two-stage least squares estimator to the order of T-2, T being the number of observations. It is found that when the degree of overidentification in the equation concerned is unity, the 2SLS bias is zero to this order of approximation.

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IN THEIR ARTICLE [5], Liu and Breen propose a new estimator of the large-sample asymptotic covariance matrix for the limited information maximum likelihood estimator in simultaneous equations, and express surprise that their estimator is different from the estimator proposed by Chernoff and Divinsky [1]. Additionally, they question the interpretation of a statistic used in the past to test over-identifying restrictions.

Haitovsky, Y., Multicollinearity in Regression Analysis: Comment, this REVIEW, LI (Nov. 1969), 486-489. Hocking, R. R., and R. N. Leslie, Selection of the Best Subset in Regression Analysis, Technometrics, Vol. 9, No. 4 (Nov. 1967), 531-540. Kendall, M. G., A Course in Multivariate Analysis (London: Charles Griffin and Company Ltd., 1957). Kendall, M. G., and A. Stuart, The Advanced Theory of Statistics, 3 (London: Charles Griffin and Company Ltd., 1966). Lancaster, K.,…

非正态备择下若干两样本位置检验的比较AI 解读

Summary Small to moderate sample size performance of the two-sample χ2, Kolmogorov–Smirnov, Wilcoxon and F-tests of location is investigated in a class of non-normal distributions through Monte Carlo sampling. The class of distributions is that of mixtures of two normal distributions with different means and/or variances. The cases of mixtures considered represent part of the regions for types I, II, IV, VI and VII of the Pearson system of continuous distributions. The…

非线性函数关系的广义最小二乘与最大似然估计AI 解读

Summary A non-linear functional relationship between two mathematical variables is postulated. Departures of observed random variates from the mathematical variable values are assumed to have zero mean and general but known covariance matrix. Assuming normality we obtain by maximum likelihood an expression for the asymptotic covariance matrix of the structural parameter estimates. The expression involves a certain matrix Ψ. A generalized least squares method is proposed…

计量经济学：统计基础与应用AI 解读

1. Elementary Aspects of Multivariate Analysis.- 1.1 Preliminaries.- 1.2 Joint, Marginal, and Conditional Distributions.- 1.3 A Mathematical Digression.- 1.4 The Multivariate Normal Distribution.- 1.5 Correlation Coefficients and Related Topics.- 1.6 Estimators of the Mean Vector and Covariance Matrix and their Distribution.- 1.7 Tests of Significance.- 2. Applications of Multivariate Analysis.- 2.1 Canonical Correlations and Canonical Variables.- 2.2 Principal Components.-…

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两阶段最小二乘估计量一次迭代的渐近性质AI 解读

In this article we obtain the asymptotic distribution of the first iterate of iterated two stage least squares; we demonstrate that this distribution is different from that of the usual two stage least squares estimator. Moreover, we show that the difference in the covariance matrices of their respective asymptotic distributions is, generally, neither positive nor negative semidefinite. In particular, we produce examples in which for some parametric configurations this…

交叉分类的关联度量（四）：渐近方差的简化AI 解读

The asymptotic sampling theory discussed in our 1963 article [3] for measures of association presented in earlier articles [1, 2] turns on the derivation of asymptotic variances that may be complex and tedious in specific cases. In the present article, we simplify and unify these derivations by exploiting the expression of measures of association as ratios. Comments on the use of asymptotic variances, and on a trap in their calculation, are also given.

两阶段最小二乘首次迭代估计量的渐近性质AI 解读

In this article we obtain the asymptotic distribution of the first iterate of iterated two stage least squares; we demonstrate that this distribution is different from that of the usual two stage least squares estimator. Moreover, we show that the difference in the covariance matrices of their respective asymptotic distributions is, generally, neither positive nor negative semidefinite. In particular, we produce examples in which for some parametric configurations this…

含两个内生变量时有限信息最大似然估计量的精确有限样本分布AI 解读

This article is concerned with the exact finite-sample distribution of the limited-information maximum likelihood estimator when the structural equation being estimated contains two endogenous variables and is identifiable in a complete system of linear stochastic equations. The density function derived, which is represented as a doubly infinite series of a complicated form, reveals the important fact that for arbitrary values of the parameters in the model, the LIML…

对《国防订单库存影响估计的一致性评论》的回应AI 解读

Gramlich and Galper (hereafter referred to as GG) indeed have performed a useful service by pointing out that an erroneous equation was included in my paper [3]. The corrected inventory change equation, the equation with all lagged orders included, was almost identical with the results obtained by applying GG's method (ii) to the order-inventory stock equation presented in Column (2), Table IV of my paper [3, p. 161]. The results are consistent when GG's methods (ii) and…

构造经济预测经验置信限的简便方法AI 解读

A simple method for the construction of empirical confidence intervals for time series forecasts is described. The procedure is to go through the series making a forecast from each point in time. The comparison of these forecasts with the known actual observations will yield an empirical distribution of forecasting errors. This distribution can then be used to set confidence intervals for subsequent forecasts. The technique appears to be particularly useful when the…

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含移动平均误差的多方程系统的识别问题AI 解读

where y(t) and x(t) are vectors of G components, z(t) has K components, B is a G x G matrix, and F is a G x K matrix.' The components of z(t) are predetermined at time t and the vector x(t) is not serially correlated, so that (among other requirements) we have

扰动较小时 k 类估计量的比较AI 解读

A new approach to the choice of econometric estimators, called small-sigma asymptotics, is introduced and applied to the choice of k-class estimators of the parameters of a single equation in a system of linear simultaneous stochastic equations. I find that when the degree of overidentification is no more than six, the two stage least squares estimator uniformly dominates the limited information maximum likelihood estimator in a certain sense. The small sigma method can be…

参数线性但内生变量非线性的计量系统与两阶段最小二乘AI 解读

It is demonstrated that a variant of the two-stage least squares technique can be used to estimate the parameters of a nonlinear model. To do this, the reduced form equations of such models are derived and discussed; then certain problems particular to the estimation of nonlinear models are considered.

A theory of identification is developed for general stochastic model whose probability law is determined by finite number of parameters. It is shown under weak regularity conditions that local identifiability of the unknown parameter vector is equivalent to nonsingularity of the information matrix. The use of reduced-form parameters to establish identifiability is also analyzed. The general results are applied to the familiar problem of determining whether the coefficients…

In two stage least squares estimation, when the matrix Z of predetermined variables has less than full column rank, Z'Z is singular. It is shown that in this situation 2SLS still can be used and that Y-the result of the first stage-is still uniquely determined; also shown is that 2SLS will often be equivalent to OLS. IN A LARGE SYSTEM containing many equations and many predetermined variables, it is a common occurrence to find that the second moment matrix involving all of…