UC San Diego

Chapter I of this dissertation addresses the problem of optimally forecasting a binary variable based on a vector of covariates in the context of two different decision making environments. First we consider a single decision maker with given preferences, who has to choose between two actions on the basis of an unobserved binary outcome. Previous research has shown that traditional prediction methods, such as a logit regression estimated by maximum likelihood and combined with a cutoff, may produce suboptimal decisions in this context. We point out, however, that often a prediction is made to assist in the decisions of a whole population of individuals with heterogeneous preferences who face various (binary) decision problems which are only tied together by a common unobserved binary outcome. A typical example is a public weather forecaster who needs to predict whether it will rain tomorrow. We show that a logit or probit regression estimated by maximum likelihood may well be "socially" optimal in this context in that it will lead certain populations of decision makers to social welfare maximizing decisions even when the underlying conditional probability model is grossly misspecified. Chapter II analyzes the situation of a loan officer that makes sequential decisions on whether to grant loans or not to applicants. Before making each decision, the loan officer can observe some characteristic of the applicant, and in the case that a loan is granted, he can observe if whether it is paid back or not. On the other hand, when a loan is denied the officer cannot observe the applicant's behavior. This selection problem will have an effect on the lender's ability to learn about the population of borrowers. We find that in some cases the lender will be able to make correct decisions in the long run, but in other cases not, i.e. he can make mistakes forever. The crucial factor that determines whether full learning will occur is the nature of the information that the lender observes from the applicant before making each loan. A Network Externality arises when the satisfaction that a consumer gets from the consumption of a given good depends (usually positively) on the number of consumers that consume the same good. A common feature of markets where NE are present is the phenomenon called "tipping", which is the tendency of one of the competing goods or protocols to win a substantial share of the market. In Chapter III it is argued that for tipping to occur there must be some underlying indivisibility in the consumption space. In addition to the problems posed by externalities for existence of equilibrium, indivisibilities create discontinuous demand behavior (not merely nonconvexity). In the paper we provide sufficient conditions for existence of competitive equilibrium with NE and indivisibilities. The key conditions are a large number of consumers and dispersion in their income distribution