PCA on Capelle-Blancard et al. (2019)

[superlianer]

请问下，PCA那个文章里面，Table A.1.6里面的系数是怎么得到的？比如corruption的系数为0.19？

[JiaxiangBU]

@superlianer

处理方法为

1. 先PCA得到每个变量和 PCs 的 loading

2. 取行最大 rowMax，每个 PC 中的 loading 只保留行最大的，其他设为0

   Three principal components extract most of the variance from the original dataset. Control corruption (0.90), rule of law (0.91), voice (0.83), effectiveness (0.90), political stability (0.60) and security and regulatory quality (0.86) have the highest factor loading on the first compo nent. This component is labeled “governance quality index” (GOVI). This GOVI dimension explains most of the variance from the dataset: 46.69% (Capelle-Blancard et al. 2019)

   Specifically, the first component, which represents the first composite index: “governance quality index” (GOVI) is computed as follows: GOVI = 0.19∗corruption + 0.20∗rule + 0.16∗voice + 0.19∗effectiveness + 0.08∗stability + 0.18∗regulatory. (Capelle-Blancard et al. 2019)

3. 处理后，对 PCs 再进行标准化。

   normalized sum of squared loading (Capelle-Blancard et al. 2019)

   library(magrittr)

   ## Warning: package 'magrittr' was built under R version 3.6.1

   c(.9,.91,.83,.9,.6,.86) %>% 
       magrittr::raise_to_power(2) %>% 
       {./sum(.)}

   ## [1] 0.1911910 0.1954633 0.1626068 0.1911910 0.0849738 0.1745740

   取平方和做分母。

4. 最后对PCs对方差的解释占比作为PCs的权重，构建 ESGGI

   For example, the weighting of the first intermediate composite index is 0.45 (45%), calculated as follows: 5.65/(5.65 + 3.52 + 3.27) (Capelle-Blancard et al. 2019)

   ESGGI = 0.45∗GOVI + 0.30∗SODI + 0.25∗ENVI (Capelle-Blancard et al. 2019)

这种处理方法可以这么认为。

1. 首先不是所有权重都使用，类似于 OLS 和 Lasso 的区别，把小的权重设为0，做了正则化的处理，保证指数更泛化。
2. 其次最后取平方和做分母，相当于做标准化。

Capelle-Blancard, Gunther, Patricia Crifo, Marc-Arthur Diaye, Rim Oueghlissi, and Bert Scholtens. 2019. “Sovereign Bond Yield Spreads and Sustainability: An Empirical Analysis of Oecd Countries.” *Journal of Banking & Finance* 98: 156–69. .

[JiaxiangBU]

补充，

是的，你可以看下这样处理后是不是新的loadings 平方和后等于1？ 是不是就是一个长度为1的单位向量了。