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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.

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联立方程模型的对应原理AI 解读

Simultaneity as a LimitA well-known and highly convincing position on the nature of simultaneity in econometric models is that such models are only approximations to the true state of affairs.In fact, causation takes time, and the reactions given by the equations of the model truly occur not instantaneously but with a very small time lag.Unfortunately, however, data do not come to us sufficiently finely divided in time to allow us to observe such fastmoving reactions, so we…

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We examine the question of whether Leontief's [15] conditions for separability and aggregation need be approximately satisfied if only approximate aggregates are to be constructed. It is found that they must be approximately satisfied unless the functions involved exhibit increasingly irregular behavior as the approximation involved in the aggregate gets better. The irregularities involved are related to the violation of Lipschitz Conditions. The stringency of the Leontief…

近似设定与 k 类估计量的选择AI 解读

This paper carries on work in [2] and [4] on the asymptotic effects of small specification error in simultaneous equation estimation. The specification errors considered are inherent in the approximate nature of econometric models. It is shown that for any parameter and small enough specification error, the probability limits of two-stage least squares and limited-information maximum-likelihood, while different, lie on the same side of the true parameter value, the…

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不同 k 类估计量对设定误差的相对敏感性AI 解读

The behavior of the probability limits of different k-class estimators under specification error is examined. Despite the fact that the probability limits are different when errors are not zero, it is shown that there exists no case in which either of the two leading estimators is uniformly more robust than the other if the criterion is any positive semi-definite quadratic form in the inconsistencies.

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近似可识别性与扰动项方差AI 解读

THE OBSERVATION that large disparity in the variances of the disturbances from different structural equations in a simultaneous system can aid identification is as old as the discovery of the identification problem itself. Thus, in the classic example of E. J. Working [10], it is observed that whereas in the Marshallian cross neither the supply nor the demand curve is identified, this is not the case if one of the curves shifts about a great deal relative to the other. If…

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柯西样本估计的一则札记AI 解读

A class of estimators is proposed for the estimation of the center of the Cauchy distribution. Each estimator in the class is the arithmetic average of a central subset of the sample order statistics. Although the sample median is a member of the proposed class, it is not the most efficient. The average of roughly the middle quarter of the ordered sample has the lowest asymptotic variance.

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非线性系统的可识别性判据AI 解读

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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