Redistributing Peer Effects (joint with Ezra Oberfield)

Abstract: 

We study how a planner should assign agents to clubs---schools, firms, neighborhoods---whose quality depends on the composition of their members, when agents privately invest in becoming qualified. Investments are risky, and both the planner and the agent observe only noisy signals of qualification. When forming clubs, the planner balances three objectives: rewarding strong signals to sustain investment, insuring agents against unsuccessful investments, and redistributing toward those who face higher cost of investment. The optimal assignment takes a simple shape. Agents with weak signals are grouped into low quality clubs that pool a wide range of posteriors, while those with strong signals are fully separated into homogeneous clubs with higher quality. Higher-ability agents receive more dispersed placements across clubs and steeper consumption schedules in the signal. A single type-specific subsidy, linear in the quality of the club one joins, implements the optimum---with direct implications for the design of college-aid formulas and related redistributive policies in settings with peer effects. We next study an environment with two observably distinct populations, one for which investment costs tend to be higher. For a given signal, the planner assigns peers of higher qualification to members of the disadvantaged population.