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Identifiability Criteria in Nonlinear Systems

非线性系统的可识别性判据

This paper considers the problem of criteria for the identifiability of a structural equation which is one of a set of equations linear in the parameters but not in the variables. The criteria are developed in terms of parameter restrictions of the rank condition type. By expansion in Taylor's series and combination with the results of Fisher [2], these results can be easily extended to far more general nonlinear systems. THE USUAL treatment of identifiability criteria is…

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The Covariance Matrices of Reduced-Form Coefficients and of Forecasts for a Structural Econometric Model

结构计量经济模型的简化式系数与预测值的协方差矩阵

A. S. Goldberger, A. L. Nagar, H. S. Odeh, The Covariance Matrices of Reduced-Form Coefficients and of Forecasts for a Structural Econometric Model, Econometrica, Vol. 29, No. 4 (Oct., 1961), pp. 556-573

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Stable Paretian Random Functions and the Multiplicative Variation of Income

帕累托型稳定随机函数与收入的乘法变化

a new family of stable non-gaussian random functions, U(t), and it is intimately connected with random walks of log U(t). Its principal feature is, however, that no use is made of the principle of proportionate effect, the model being rather based upon the fact that there exist certain limits for sums of random functions, upon which the effect of chance in time is multiplicative. (Actually, the result is more general.) This feature provides a new type of motivation for the…

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The Estimation of Distributed Lags: A Comment

分布滞后的估计:评论

Considering first the case of a known autocorrelation coefficient $, Klein observes that (4) may be viewed as a structural linear relation between the latent variables yt' -et, xI and yt'-l -et-,. Even knowing $, two of those variables are not observable. But the y' and yt' may be computed; et and et-, may be considered as errors of observation of the corresponding latent variables. In comparison with the classical models containing errors in variables, (4) is somewhat…

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Efficient Allocation of a Multi-Purpose Sample

多用途样本的有效配置

SUMMARY WHEN LISTING addresses within sample blocks for surveys the field interviewer hastily assigns economic ratings of L, M, and H (for low, medium, and high) to dwellings. The means and the standard deviations differ greatly among these strata with regard to socioeconomic characteristics; hence they may be used for allocating different sampling rates to decrease the variance of sample means and totals. Disproportionate sampling rates bring gains in precision for the…

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Errors in Variables and Engel Curve Analysis

变量测量误差与恩格尔曲线分析

The traditional method of estimating Engel curve parameters uses either (recorded) income or total expenditure as an independent variable in least squares analysis. Neither of these is, however, a satisfactory index of the economic position of the family. This results in biased estimates of the income elasticities of the various consumption categories. The bias can, however, be eliminated in large samples by using both income and total expenditures in the estimation…

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The Place of Least Squares in Econometrics

最小二乘法在计量经济学中的地位

IN A RECENT paper,' Frederick V. Waugh argues strongly for the use of ordinary least squares in simultaneous systems. His argument is not that least squares gives unbiased estimates of structural parameters2 but that they do (as consistent structural estimators do not) give unbiased estimates of the dependent variable in the regression equation given the values of the other variables and that this is what is needed for forecasting purposes. This note argues that Waugh's…

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The Graduation of Income Distributions

收入分布的修匀

A FUNCTION representing the distribution of income in a society can serve a number of purposes. It may be used to smooth out irregularities in the observed income distribution caused by the misreporting of income. In this role it is similar to the graduation formulae used in demographic work to correct an age distribution distorted by mistatements of age. An income function may also form the basis of a model explaining how an income distribution is generated. Interest here…

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On a Method of Computing Engel Elasticities from Concentration Curves

从集中曲线计算恩格尔弹性的方法

THIS PAPER PRESENTS, on the assumption of lognormality, a simple graphical method of deriving the Engel elasticities for various items of consumer expenditure from what are known as concentration curves. Usually two types of such curves are distinguished: (a) the Lorenz curve which relates the proportion of total expenditure to the proportion of persons spending up to a given level of total expenditure per capita, and (b) the specific concentration curve which relates the…

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