"More decisions need to be decentralised from the government to the PSB boards, once they have been fully professionalised," he said while delivering C D Deshmukh Lecture here.
"For instance, should boards not determine strategy as well as the appointment or renewal of their chief executive? What about their executive directors? Can bank boards have more freedom in choosing these?
"Can boards be given the freedom to set compensation structures and performance measures for their senior executives, including long term stock options?," he said.
"If we want to address the concern that many public sector banks have identical strategies and are competing for the same pie, we have to allow the boards more freedom to differentiate their banks," he said.
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Rajan also stressed that PSBs will require more professional boards that can chart a differentiated strategy for them.
"The Bank Board Bureau, which will select board members, will come into operation soon. We have to pay board members of PSBs a market compensation if we are to attract decent talent - otherwise we risk attracting an unwieldy mix of the truly patriotic and the truly unscrupulous, with the latter intending to profit by their board position," he said.
"When thousands of crores can be diverted by a bad board decision, should we not ensure we have adequate integrity and talent on bank boards?," he said.
Rajan said that competition will help in sustained growth and foster financial inclusion.
"In order to get sustained growth, we need more competition, especially from new entrants who are in a better position to reach hitherto excluded parts of our economy," he said.
"We will put licensing for universal banks on tap soon," he said.
Incumbents have expressed fears about unfair competition. Competition is only unfair if it is not on the same playing field, he said.