That is actually very simple to answer. One must simply note if the monetary and fiscal objectives of the finance ministry for the banking and finance sectors are being met or not and if over capacity has anything to do with it. I am assuming that the objectives and monitoring of the financial sector is very deep, thorough and forward looking.
Apart from that, one way would be to note profit margins of bank in an unregulated economy and the competitive pressures they are facing. Bad loans or low quality loans can also point to competitive/growth pressures that might need to be curtailed.
Another way to note over capacity of the banking sector can be to look at how customer accounts, and their usage. Too much customer debt or extra accounts, might simple be of no use...although not entirely a bad thing.
I am not an expert at Banking and finance, but these were just my thoughts.
A signal of overbanked banking system could be high competitiveness, i.e. low interest rates for debts and high interest rates for deposits ceteris paribus. Another symptom could be that a commercial bank exits the market. I am not also an expert at Banking as I studied economics and managament of nonfinancial companies
One method followed in India about the adequacy of banking system is to find out the ratio of bank branch per 1000 people. (now they say that we have one bank branch for every 10000 people in India). Over banking and under banking can be known based on the areas they serve for eg. it is overcrowding of banks in urban and metro centres whereas in upcountry and villages bank branches are few and far between. Thirdly, if competition is intense (as already indicated above) by quoting lower loan interest rate and higher deposit rates, and reduced spread or margin on any type of business, we can know more than required no. of banks/branches operate. Again this is centre-specific. Another way now being looked into is financial exlusion - that how much of the population do not have banking facilities - like a bank a/c., a loan, a credit card, and other banking services. Banking spread is also a function of level of literacy of the country. This is coming from an expert central banker.
In some ways this is a very odd question. First, what is the definition of "need" in the case of the "system" (financial system? the economy as a whole?) I presume you mean banks rather than bank branches (which unfortunately makes Dr Rajan's proposed measure problematic). The number of banks in relation to anything may be difficult to interpret. The US has almost 7000 institutions that report to the FDIC and these banks have some 90,000 offices. However, the concentration of deposits is high with three banks accounting for over 30% of all bank deposits. Is that too many banks? or too few? or both? One could argue that concentration of banks is a problem (too big to fail) and more banks might reduce that risk. Large concentrated banks might focus on capital market activities of large firms or governments and neglect small firms The availability of credit might have little to do with the number of banks at all but the overall stance of monetary policy or regulatory policy. To me, this is a highly complex issue that needs to be refined before it can be usefully answered.
https://www.researchgate.net/publication/286256177_Global_Financial_Crisis_Exploring_the_Special_Role_of_US_Banks_and_Regulations
Article Global Financial Crisis: Exploring the Special Role of U.S. ...
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