**5. Conclusions**

Let us recall the research questions: can one find an empirical law for describing the economic freedom (EF) of nations through the main measure indices, i.e., the Economic Freedom of the World (EFW) index [38] and the Index of Economic Freedom (IEF) [39]? What simple empirical laws can be found through a simple analysis of rank-size laws? Are such laws of interest for discussing the main determinant, according to the literature, i.e., each country's GDP?

We have taken some data pertaining to the 1997–2007 period, that is before 2008, thus before a recent "financial crisis", in order not to involve "multiple exaggerated develop-

ments" [43], but nevertheless in order to include a drastic turning point, 11 September 2001, following another geo-economico-political event, the fall of the Berlin wall. We have pointed out that the study of EF should develop over two distinct periods, at this time, mainly because the index's 2008 definition of economic freedom has been modified. In so doing we have selected data, leading to 138 countries examined over a period extending from 2000 to 2006, thus 2 sets of 862 data points.

We have found that the rank distributions obey either an exponential or a power law or a mixed behaviour. The EFW rank relationship is exponential for countries of high rank ( ≥20), but log-log plots point to a behaviour close to a power law when considering the whole sample. In contrast, the IEF overall ranking has an exponential behaviour. Interestingly, IEF rank-size rule log-log plots point to the existence of a transitional point between two different power laws, i.e., near rank 10.

Besides, the IEF appears to be "more conservative" than the EFW index.

Moreover, when searching for (analytical law) correlations between the country GDP and either EF indices (we have not looked for regressions between these macroeconomic variables and the various "pillars" of the indices, the literature is already abundant), we have distinguished regional aspects, i.e., defining six continents. We find that the EFW index relationship to country GDP is characterised by a power law, with a rather stable exponent ( *γ* 0.674) as a function of time. In contrast, the IEF relationship with the country's gross domestic product points to a downward evolutive power law parameter as a function of time. Markedly the two studied indices provide different aspects of EF.

In so doing, we add numerical considerations to the literature, as should be somewhat expected by econophysics research, for this special issue, but presenting to others a different perspective. The rank-size law approach seems original for the present topics. It brings some information on the "statistical universality" of EF during the considered time interval. Thus we expect to open gates for rigorous approaches, i.e., stressing objectiveness in the modelling, rather than ideological bases.

Thereafter, suggestions for further research can be listed: among others, one could consider other time intervals; for example including the 2008 financial crisis, and nowadays considering the COVID-19 pandemic. This is left for our expected paper II. On the other hand, It would be nice to have more "economic considerations" and "historical considerations", looking at each pillar separately in more detail. For example, one could consider some renormalisation of the indices, taking into account, size (and type) of governments, size of country populations, inflation rates, foreign direct investments, health burden, etc., on one hand, and on the other hand, migration factors, religious factors, education levels, trade union strengths, pandemic constraints, local climate, etc., all of which presents quite a numerical challenge to econophysicists.

**Author Contributions:** All authors have contributed equally. All authors have read and agreed to submitting this version of the manuscript.

**Funding:** M.A. has been partially supported by a gran<sup>t</sup> of the Romanian National Authority for Scientific Research and Innovation, CNDS-UEFISCDI, project number PN-III-P4-IDPCCF-2016-0084.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sources are mentioned in the text and references; they are freely accessible.

**Conflicts of Interest:** The authors declare no conflict of interest.
