The Variate Difference Method: A Reply
变量差分法：回应AI 解读 ↓
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变量差分法：回应
- 研究问题
- 变量差分法适用于何种随机扰动，为什么不能直接处理某些动态经济机制；相邻阶差分序列的方差相等应如何检验？
- 方法与思路
- 作者区分叠加随机扰动与影响经济动态的误差，讨论序列相关问题，并分析选择法检验的效率及方差相等检验的双尾处理。
- 材料陈述的贡献
- 摘要明确方法仅处理叠加的随机变化，承认选择法因只利用部分数据而效率不足，并主张方差相等检验同时考虑上下尾。
- 阅读关注点
- 核对叠加随机变化的假设、差分阶数增加时方差的变化，以及选择法的抽样机制、双尾检验依据和序列相关讨论。
- 阅读边界
- 这是一篇方法争论的回应；摘要未给出完整检验步骤，提及的序列相关精确检验来自此前著作，且被表述为试探性方案。
原文摘要
(1) MR. HAAVELMO' contends that the variate difference method is not applicable to certain dynamic economic schemes, as, e.g., the cobweb theorem. It never has been claimed that this is the case, and the author has pointed out very carefully in his monograph2 that the variate difference method deals only with superimposed random variation. A more extensive discussion of the general problem of the role of errors in economics is to be found in a short article published in the Quarterly Journal.3 The view is put forward there that some types of errors have a deep-rooted influence on economic developments, and this is in agreement with Mr. Haavelmo's statements. Dynamic schemes, like the one of Frisch and the ideas indicated in Haavelmo's article have to be dealt with by other methods. These problems are probably closely related to a study of serial correlation. The author has indicated some possible methods of analysis in an appendix of his monograph4 and even put forward tentatively an exact test of significance for serial correlation based upon the method of selection. (2) The author has indicated5 that he does not consider the method of selection an entirely satisfactory test of significance for the equality of the variances of two consecutive series of differences. It is of course very true that the test is not efficient since it utilizes only a certain percentage of the total data available. The fundamental hypothesis tested is the equality of the variances of two consecutive difference series. The case that the variance of the higher difference series is larger and not smaller than the variance of the lower difference series can arise (a) because they are really equal and appear different because of chance fluctuations, (b) because the variances form an increasing instead of a decreasing series and the whole method is not applicable. For this reason it seems that we have to consider not only the upper but also the lower tail of the distribution in testing the hypothesis that the variances of two consecutive difference series are equal and appear different only because of random fluctuations.