Multiple authorities, in fact. Microfinance Institutions are of different types. Bigger ones operate as NBFCs and smaller ones in the form of trusts, NGOs, co-operatives or self-help groups. RBI regulates NBFC-MFIs since creation of the category in 2012 in the wake of the 2010 Andhra Pradesh microfinance crisis. For the rest, regulation is not strict. These are governed by local or state-level authorities or, to an extent, by institutions like NABARD. But majority of assets in MFI industry is managed by big NBFC-MFIs. So RBI has direct control over systemic risks in the sector. MFIs play key role in making credit available to informal sector that's typically left untouched by big lending institutions.