"It is important that governments around the world look beyond sometimes uninformed and motivated public criticism and protect the independence of their central bank to act. That is essential for stable sustainable growth," Rajan told the 10th Statistics Day Conference here.
Criticism of the central bank using arguments unsupported by evidence was widespread, he said.
The Bank of England was criticised for laying out the economic costs of Brexit - Britain's exit from European Union, the ECB (European Central Bank) has been attacked for doing too much to restore health to troubled peripheral financial sectors and the Federal Reserve System was under fire for departing from the Taylor Rule.
Taylor rule is a monetary policy rule which determines the change in interest rate in line with inflation and other macroeconomic factors.
The Governor said moderately high inflation had pernicious effect on the weaker sections of society and the fragilities accumulate, and eventually lead to crisis.
"The best way central banks can support growth over the medium term is by keeping inflation low and stable. It is necessary to build institutions to ensure macroeconomic stability. This is why successive governments, in their wisdom, have given the RBI a measure of independence," Rajan said.
He said the Narendra Modi government had shown commitment to low inflation through a formal inflation target and the creation of a monetary policy committee.
He said the slowdown in the growth of non-food credit by public sector banks was not because of lack of demand or capital, nor was it because of high interest rates but largely due to stress in public sector banks, stemming from past mistakes in lending.
"This will not be fixed just by a cut in policy rates. Instead, what is required is a clean-up of the balance sheets of public sector banks, which is underway and needs to be taken to its logical conclusion."
After initial reluctance, banks have entered the spirit of the clean-up. It was the duty of the central bank to press for bank clean-up earlier, he said.
The stock market, after reacting negatively initially early this year, was more supportive of public sector bank stock prices, probably reflecting the belief that the clean-up was good over the medium term.
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