Time Consistent Behaviour and Discount Rates

Abstract

Decisions such as saving, investing, policymaking, have consequences in multiple time periods and are called intertemporal. These choices require decision-makers to trade-off costs and benefits at different points in time. Time preference is the preference for immediate gratification or utility over delayed gratification. The discount rate is a tool used to measure this psychological phenomenon. This thesis considers the problem of an individual maximizing his utility from consumption and final wealth when his discount rate is not constant. The question we answer is the following: if we allow the individual to update his decisions, will he stick to his original strategy or will he switch? We show that there are cases in which the individual's strategy keeps changing thus his behaviour becomes time inconsistent. In Chapter 1, we introduce two notions to solve this inconsistency problem: The agent can pre commit i.e. he does not change his original optimal strategy. The agent can also plan for his future changes of strategy and adopt time consistent strategies also known as subgame perfect strategies. We also review the existing literature on time discounting and time consistency. Chapter 2 considers the time consistency in the expected utility maximization problem. The risk preference is of the Constant Relative Risk Aversion (CRRA) type, the time preference is specified by a non constant discount rate and we allow the volatility of the stock price to be stochastic. We show that the determination of one quantity: the utility weighted discount rate completely characterizes the individual's subgame perfect strategies. Chapter 3 is about equilibrium pricing in a model populated by several economic agents in a complete financial market. These agents are investing, saving and consuming and want to maximize their expected utility of consumption and final wealth. We allow the economic agents to differ in their risk preferences, beliefs about the future of the economy and in their time preferences (non constant discount rates). Since the optimal strategies are time inconsistent, the equilibrium is computed by using the time 0 optimal ( precommitment) strategies for the market clearing conditions. Chapter 4 considers the same model as chapter 2. We solve the equilibrium problem when time consistent strategies are used for the market clearing conditions. We limit the study to two economic agents. The subgame perfect equilibrium is compared to the optimal equilibrium of Chapter 3.