What are the determinants of the natural rate of interest and how market rate converges to it? I'd like to know how is determined the natural/neutral rate of interest. Moreover, how the market rate can converge to it ? If you have some references it would be great !
What determines interest rates?
Let's try to understand the emergence of interest rates from first principles. We'll imagine an island inhabited only by Robinson Crusoe and Friday. For sustenance, they pick coconuts - the only food source available to them. Each coconut can either be consumed immediately or saved up for future use.
One day, Crusoe does not manage to pick any coconuts and having none saved up asks frugal Friday to loan him one from his stockpile. In return, Crusoe promises to give Friday more than one coconut at some later time. Let's consider what factors would affect how many future coconuts Crusoe must promise Friday in order to persuade him to issue the loan.

If Crusoe is hungry right now, he will have a high time preference (=low patience). Therefore he will be willing to promise a large number of future coconuts for one present coconut.
If Friday has a large number of coconuts saved up, say 100, he will be more willing to part with one of them for a modest fee. If he only has 10 saved up, he will demand more future coconuts if he is to loan out 10% of his savings. How many coconuts Friday has saved up determines the marginal utility of 1 coconut and thus how willing he is to loan it out.
If Friday thinks there is a high risk that Crusoe will struggle to pick enough coconuts in the future to pay back his loan, he will be less willing to issue a loan without being compensated for it.

If more inhabitants are added to the island, we can imagine a market for &quot;coconut loans&quot;. Lenders will compete to offer customers an interest rate that correctly balances time preference, risks, etc. Those who offer too high an interest rate will get few customers, while those who offer one that is too low risk going bust.
Note that there is no such thing as &quot;the interest rate&quot;. There are only particular interest rates on particular loans made between particular people. Like many other things, talking about the &quot;natural&quot; interest rate and how lenders converge to it can sometimes be a helpful abstraction, but the true, underlying mechanisms should always be kept in mind.
In reality, the picture is more complicated since it is possible for central banks to artificially affect it in a way that is not constricted by supply and demand. I can recommend this article for a discussion of the subject.