I need an analytical framework in sense of already presented indicators for the supranational institutions efficiency (or failure), within the liberal theories discourse.
Nenad, What is the definition of 'supranational institutional efficiency' that you are working from? Secondly what is your definition (or what are the definitional limits) of the institutions whose efficiency you wish to assess? Thirdly (sorry about this..) what is the teleological fromaework within which yu are intending to conduct this research?
Your question, as you can see, begs many other much more fundamental ones.
In the event that you confine yourself to those institutions which have offices and staff and are generally recognised as 'supranational organisations' then one's starting point must be their own annual reports and self-assessments of their effectiveness. What you do with them then rather depends upon your definition of efficiency? Which in turn rather depends upon the 'human developmental' framework within which you view the purpose of that set of international behaviours which you are researching.
Perhaps then our colleagues will immediately identify what it is you need and bless you with a tsunami of links!! :-)
Nenad, It may be useful to look at at the following:
Terence C. Halliday and Gregory Shaffer (eds)m Transnational Legal Orders (Cambridge University Press, 2015)
Sabino Cassese (ed) Research Handbook on Global Administrative Law (Edward Elgar Publishing, 2016)
Thomas Hale and David Held (eds), Handbook of Transnational Governance: Institutions and Innovations (Polity Press, 2011).
Maybe it is useful to look also at the literature on effectiveness (of law), in addition to or instead of efficiency. My article 'The Effectiveness of European Community Law: Institutions, Processes, Tools and Techniques', Modern Law Review, 1993 (!) might be helpful, also for the footnotes. Since then, there is of course a lot of other published work.
There are some existing indicators for comparing national governance world wide. I do not know if they are already familiar to you or if they are useful for you. But still I include some links to further information.
As others have noted, will depend heavily on your understanding of institutional efficiency - in principle hard to measure, since both sides of the means/goal achivement relation that effeiciency implies are conceptually hard toc apture for supranational institutions. For a recent, somewhat more modest proposal to assess IO performance you might want to look at this: https://www.researchgate.net/publication/294088126_The_Performance_of_International_Organizations_A_Policy_Output_Approach
Article The Performance of International Organizations: A Policy Out...