Justifying S-shaped Consumption Utility Functions Using Consumption-Based Asset Pricing

Utilizing the asset pricing framework, we justify S-shaped consumption utility functions by reconciling realized consumption with asset returns. The S-shaped consumption utility predicts a possible negative correlation between asset returns and lower quantiles of consumption growth, for which we find evidence from micro-level data. This evidence refutes a concave-shaped consumption utility as it leads to a violation of the law of one price. Additionally, the quantile-specific negative correlation accounts for the low correlation between consumption growth and asset returns, which is the core of various pricing puzzles. With a qualitative model, we demonstrate that many pricing anomalies stem from traditional models' global concavity of the utility functions. Furthermore, by estimating a micro-consumption-based structural asset pricing model with an S-shape restriction on the utility function, we find that individuals lower their reference consumption levels when stock prices decline, providing a quantitative solution to the equity premium puzzle