Wealth inequality and asset pricing with durability and habit formation

In an exchange economy with identical agents, except for their initial endowment, we examine how wealth inequality affects the equilibrium level of the equity premium and the risk free rate when there is a single perishable good and the agents’ preferences are habit forming. We measure inequality by introducing a mean preserving transfer of endowment. This creates the departure from an egalitarian distribution of wealth. Preferences are modeled either as external or internal habits. For comparison purposes, we also allow for heterogeneity in habit strength and the coefficient of relative risk aversion. For our calibrations, we introduce two and three classes of wealth, in a simple two period model. We also explore the effects of the addition of a small uninsurable labor income risk. It seems that wealth inequality is important for both versions of the model. Wealth inequality raises the equity premium when agents exhibit habit persistence in their preferences, if and only if the absolute risk tolerance is concave. At the same time, a weak habit produces a higher equity premium than a strong habit. Moreover, when the absolute risk tolerance is convex, wealth inequality decreases the equity premium; however, the predicted equity premium is closer to its historically observed value in this case. If the absolute risk tolerance is linear (as in hyperbolic absolute risk aversion (HARA) preferences), wealth inequality has no effect on asset pricing, even after the introduction of habit persistence. Lastly, we extend our analysis to an infinite period with two goods, one perishable and one durable, and we report the effects of wealth inequality for each of our specifications.