Essays on the economics of information
Keywords: Economics.

This thesis consists of three essays on the economics of information. We study economic situations that involve information asymmetry. For example in an informal insurance market the borrower has private information about her income that the lender cannot observe. In a social learning context different agents possess different signals about the state of the world. In a principal-agent problem the agent could privately observe a productivity shock that is unknown to the principal. We study these situations using tools from mechanism design. In Chapter 1 we study repeated communication between a long-run sender and a long-run receiver. In each period the sender observes the state of the world -- which is i.i.d. across time -- and reports the state to the receiver. The receiver takes an action based on the history of the sender's reports and public randomization signals. The receiver fully commits to her action at each point in history, and the sender commits to nothing. We allow arbitrary state space, action space, and preferences. We characterize the set of possible payoffs for the sender and the receiver when both are infinitely patient -- i.e., as the discount factor goes to one. We also study the payoff set when the discount factor is less than (but close to) one. In particular we bound the rate of convergence to points on the frontier of the limit payoff set; the rate of convergence differs radically for discrete and continuous models, and we provide a unified view of the rate of convergence results based on the shape of the frontier of the limit payoff set. We discuss three applications of our results. First for dynamic CEO compensation we characterize the firm's revenue from the optimal contract as the interest rate goes to zero. Second we show that dynamic delegation -- a common problem in agencies -- is equivalent to our model. Third we study a reputation problem where the sender's preference is unknown, and we give a lower bound for the receiver's expected payoff as the discount factor goes to one. In Chapter 2 we study a social learning model in which people choose who to talk to and strategically exchange information. Agents start with heterogeneous priors about an unknown state of the world. First each agent chooses a partner. Then everyone observes a private i.i.d. signal and sends a message to her partner. Finally everyone takes an action based on her prior, her private signal, and her partner's message. Our main finding is that when the signal space and action space are binary, assortative matching arises in equilibrium, but it is generally inefficient for social welfare and information aggregation. In addition we construct counter-examples (non-assortative matching) in the case of multiple signals or multiple actions. In Chapter 3 (joint with Gabriel Carroll) we study a principal-agent problem where the agent has private information about her productivity shock. Our goal is to investigate the idea that linear contracts are reliable because they give the same incentives for effort at every point along the contract. We ask whether this reliability leads to a microfoundation for linear contracts, when the principal is profit-maximizing. We consider a principal-agent model with risk neutrality and limited liability, in which the agent observes the realization of a mean-zero shock to output before choosing how much effort to exert. We show that such a model can indeed provide a foundation for reliable contracts, and illustrate what elements are required. In particular, we must assume that the principal knows a lower bound, but not an upper bound, on the shocks.