Rajan, who briefed Parliament's Standing Committee of Finance on various aspects of economy and nonperforming asset (NPA) in banks, was asked by members on what should be the tenure of the RBI Governor, sources said.
He told the members that a three-year term is "short".
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In the US Fed, in addition to serving as members of the Board, the Chairman and Vice-Chairman serve terms of four years and may be reappointed to those roles who in turn serve until their terms as Governors expire.
Rajan, whose current three-year tenure ends on September 4, has already said no to a second term.
Sources further said that during the meeting that lasted for over three hours, the Governor briefed the panel, headed by senior Congress leader M Veerappa Moily, on state of the economy, reforms and restructuring of RBI, challenges in the banking sector in India and the way forward.
The committee was apprised by Rajan of the various steps taken to deal with the bad loan problem, said the sources.
The Reserve Bank has said the gross non-performing assets of the banks can rise to as high as 9.3% in 2016-17 after hitting 7.6% in March 2016.
Rajan, the sources added, also briefed MPs about the credit scenario of the banks. He is believed to have told the MPs that private lenders are more active on the lending front, but PSU banks are found to be reluctant even when there is no shortage of funds.
The Governor also explained to MPs the impact of Brexit on India and the global economy.
Earlier in the day, Rajan called on Finance Minister Arun Jaitley as the central bank and the government seek to quickly put in place a new interest rate-setting mechanism.
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