Bounded Rationality and the Elasticity Puzzle: What Can We Learn from the Agent-Based Computational Consumption Capital Asset Pricing Model?

In this paper, an agent-based computational capital asset pricing model is applied to address an issue, known as the elasticity puzzle, originating from a famous reciprocal relation between the elasticity of intertemporal substitution (EIS) and the relative risk aversion (RRA) coefficient. By the reciprocal relation, the implied RRA coefficient can be unexpectedly, and possibly unacceptably, high when the estimated elasticity of EIS is so low and even closer to zero. Existing studies, be they theoretical or empirical, to deal with the elasticity puzzle are largely confined to the conventional framework built upon the devices of rational expectations and representative agents. A number of recent empirical studies, however, have documented heterogeneity in the elasticity. It is found that the intertemporal elasticity is different between the poor and the rich, and between stockholders and non-stockholders. Two questions immediately arise. The first one concerns the aggregation problem. If the intertemporal elasticity is heterogeneous among agents, then what is the relation between the aggregate elasticity and its individual counterparts. The second one is why the rich and the stockholders tend to have to high intertemporal elasticities, and their opposites tend to have low ones. Why is such a behavioral parameter so critical in determining the wealth share of individuals? Empirical studies also find that the Euler consumption equation applies well only to the stock market participants, and not to all individuals. It is certainly plausible that not all individuals can do optimization well. So, here comes the third question. Is it possible that some agents who happen to do optimization well and hence behave closer to what the Euler equation predicts eventually become wealthier, and for those who do not and hence fail the Euler equation eventually become poor? Do the rich really have higher intertemporal elasticities, or are they just smarter or with a better luck? Is that possible the observed heterogeneity in intertemporal ealsticity is just spurious? Using agent-based computational model, we study a consumption CAPM model composed of boundedly-rational heterogeneous agents. They are heterogeneous in their forecasts, saving and investment decisions, driven by an adaptive scheme, such as GAs. Simulating the model can generate a sequence of time-series observations of individuals' profiles, including beliefs, consumption, savings, and portfolios. Unlike most theoretical or empirical studies of the consumption CAPM model, the agent-based computational model do not assume an exogenously given stochastic process of returns and consumption. Instead, aggregate consumption, asset prices, and returns are also endogenously generated with agents under specified RRA and EIS. With this endogenously generated aggregate and individual data, we are better equipped to answer the three questions posed above in a fashion of survival dynamics