Apakah angka indeks boleh di-log ?

Question:

Can we take log of any index (i.e. HHI index, CR4 index or Lerner index)?

Answers:

1. No problem what matters is interpretation
2. Hi! You can do it. Good luck.
3. From an empirical experience taking natural log of an index improves results of the model's findings. 
4. It is very possible but you need to interpret the findings as percentage change.
5. I think we should not used log of a variable representing an index. infact, index by it self a ratio or percentage and when we take log(log by it self represent percentage or growth type phenomena). it may leads to a challenge in interpretation.
6. I think you have to go beyond the mathematical sense of taking a log of an index. Regardless of the mathematical feasibility and meaning of this log and the mathematical-econometrical relationship between variables... what about the economic meaning of those variables and relationships? So, I think you have to start with a deep reflexion about the economics (theoretical) meaning of variables and the relationships between them. Once you have undertaken this theoretical review, you will be able to correctly interpret variables and relationships, and then you will find the (economics) answer for your question. In other words, the purpose of transforming variables or build indexes is to help us to analyse and interpret economic theories, to evaluate economic policies, to make forecasting, etc. Obtaining better estimations results (p-values, r2,...) should not be a target by itself, but only if this improvement in estimation can help us to analyse, interpret, evaluate,... answering our research questions or contrasting our research hypothesis.

Sumber:

https://www.researchgate.net/post/Can-we-take-log-of-any-index-ie-HHI-index-CR4-index-or-Lerner-index