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On Some Characterizations of Probability Distributions with Applications in Econometrics: A Centennial Tribute to CR Rao
Journal of Quantitative Economics Pub Date : 2021-04-27 , DOI: 10.1007/s40953-021-00234-2
B. L. S. Prakasa Rao , T. Krishna Kumar

CR Rao, the living legend in statistics, is celebrating his birth centenary year in 2020–21. One of the major areas in which Rao made significant contributions to statistics is characterization problems. The main objective of this paper is to connect the work of Rao and his followers on characterization to the underlying fundamental econometric problem. In doing so, the authors hope to draw the attention of the econometricians to the characterization method as a tool to further advance the less attempted problem of econometric modeling with errors in variables. The authors also hope that this paper would draw the attention of statisticians to the more interesting characterization problems arising in econometrics, there by providing fields of application to a class of characterization problems that otherwise remain mostly theoretical. Ragnar Frisch, the founder of econometrics, conceived the econometric model as a system of linear structural equations. Noting how one can use the reduced form equations to determine the joint distribution of the endogenous variables, given the distribution of the exogenous variables, Frisch asked the inverse question: under what distributional assumptions on the exogenous variables, does there exist a system of linear structural equations? Keeping this in the background, CR Rao answered that question in 1943 and 1947 using the characterization method and further advanced the characterization method in statistics. Rao and his followers, however, did not connect their work with the underlying econometric problem. The authors extend the econometric problem posed by Frisch to a two endogenous and two exogenous variables case and establish the existence of two linear structural equations and their identification, as an example of the potential benefits from this association between econometrics and statistics.



中文翻译:

关于概率分布的某些表征及其在计量经济学中的应用:百年纪念CR Rao

统计领域的鲜活传奇人物CR Rao正在庆祝他2020-21诞辰一百周年。饶对统计学做出重要贡献的主要领域之一是表征问题。本文的主要目的是将Rao及其追随者在表征方面的工作与潜在的基本计量经济学问题联系起来。在此过程中,作者希望引起计量经济学家对表征方法的关注,将其作为一种工具来进一步推进变量变量误差较小的计量经济学建模问题。作者还希望,本文可以通过提供一类适用于其他形式的特征描述问题的应用领域,来吸引统计学家对计量经济学中出现的更有趣的特征描述问题的关注。拉格纳·弗里施(Ragnar Frisch)计量经济学的创始人将计量经济学模型视为线性结构方程式的系统。考虑到给定外生变量的分布,弗里施注意到人们如何使用简化形式的方程式来确定内生变量的联合分布,弗里施问了一个反问:在外生变量的分布假设下,是否存在线性结构系统方程式?CR Rao将其作为背景,在1943年和1947年使用表征方法回答了这个问题,并进一步提高了统计学中的表征方法。但是,饶和他的追随者们并未将他们的工作与潜在的计量经济学问题联系起来。

更新日期:2021-04-28
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