The correct answer is option 2: Self-Government. Panchayati Raj Institutions (PRIs) are primarily institutions of self-government at the local level in India. These institutions play a crucial role in the decentralization of power and ensuring grassroots democracy.

Option 1: Popular Government - While PRIs involve popular participation and representation, they are not solely institutions of popular government. Popular government implies a form of governance where the people directly participate in decision-making processes, whereas PRIs are representative bodies elected by the people.

Option 3: Federal Government - PRIs are not institutions of federal government. Federal government refers to a system where power is divided between a central authority and regional governments. PRIs are local-level governing bodies and do not have the characteristics of a federal government.

Option 4: Quasi-Government - Quasi-government refers to organizations or entities that have some characteristics of government but are not fully government bodies. PRIs, on the other hand, are established and function as legitimate government institutions responsible for local governance.

In summary, PRIs are institutions of self-government at the local level, empowering local communities to make decisions and manage their own affairs.