Essays on General Equilibrium
This dissertation develops new general equilibrium results on how markets react to risk and aggregate information. The first chapter extends a classical result in portfolio theory about the effect of risk on value functions to its effect more generally on policy functions. If odd moments of shocks are zero up to some order, then the odd order marginal effects on value and policy functions of introducing these shocks are zero as well. Mathematically, all coefficients of corresponding odd order in the perturbation parameter are zero. If shocks are symmetric, e.g. normally distributed, then this holds for all odd orders. The main theorem (1) generalizes past results on perturbations and unifies their economic intuition, (2) improves the computation of stochastic coefficients, and (3) illustrates how to derive properties of high order perturbations through simple induction. The second chapter tries to reconcile classical versions of the efficient market hypothesis with the surveyed level of technical analysis in practice. If past security prices are public information, then any patterns contained within should be approximately accounted for in current prices, and fundamental analysis would be relied on relatively more. While each past security price might individually be public information, the disconnect is that it should not imply their collective patterns and interactions are public information as well. Economics, unlike probability theory, must recognize costs and therefore distinguish between observing pieces of information and analyzing their many interactions. (1) We generalize sigma-fields to families of events and define information more broadly as knowledge about optimization solutions. (2) This provides a new framework for efficiency hypotheses and theorems. (3) We illustrate how complex patterns arise from "variably diffuse information" that only technical analysts can aggregate indirectly, changing the informational behavior of prices.
Lott, Sherwin, "Essays on General Equilibrium" (2022). Dissertations available from ProQuest. AAI29166658.