Regarding the Index
I want to further understand how they compute this index. Unfortunately, they give very few details on this, probably because this index is a proprietary tool and they want to protect their IP
Their index is actually open access, you can access the data here and the index is based on evolution of insolvencies with base year being 2000.
They also provide data on the evolution of insolvencies but I can't see anywhere any methodology of how the evolution of insolvencies was itself created (which is a red flag if you ask me). Based on the way how data look it seems it is the percentage change in in how many insolvencies occurred. So that would imply they have access to data on number of insolvencies which is also corroborated by the their references to number of filled insolvencies within the report.
However, the report includes author will full contact information, so I would hope that if you would reach out they would share their methodology with you.
Regarding Factors affecting Insolvency:
I am not completely sure what you mean by explaining insolvency at a macro level. Any macroeconomic aggregate of insolvencies will be based on individual insolvencies driven primarily by microeconomic factors - but they would still affect any aggregate of insolvency, so I suppose they would affect insolvency on 'macro level', but I assume you wanted only macroeconomic variables.
According to Sang et al. 2013 examining impact of macroeconomic variables affecting insolvencies in construction industry in South Korea the authors show that insolvencies can be affected by:
- changes in GDP (especially negative changes; recessions)
- interest rates
- consumer price index
- corporate bond yields
- exchange rate (this is most likely due to S. Korea being small open economy)
In addition other studies (e.g. Bonfim, 2009; Bhattacharjee, et al. 2009 and sources cited therein) generally find that what is driving firm insolvency from macroeconomic is general macroeconomic instability (in fact many of the above listed variables can be considered proxies for macroeconomic stability e.g. change in GDP, inflation etc.) and also to non-trivial degree country specific institutional framework (which is not surprising since true economic insolvency is difficult to observe so often firm is considered insolvent when it is declared insolvent by law). However, the above answer is quite general the drivers can actually differ by industry as studies also show competition is important factor. Furthermore, the insolvencies in financial sector and real economy are not necessary affected by the same factors, but to go further in depth within a single answer on these issues is beyond the scope of SE.