A Mean Field Model of Consumption Inertia and Keeping Up with the Joneses

Households compare their living standard with others' and dislike changing it. We study consumption and investment when felicity depends on consumption relative to a benchmark, the population's geometric average consumption, and cuts in felicity weigh more than increases. Asset returns are exogenous. For finitely many types and arbitrary initial wealth and inherited standards, a mean field equilibrium exists under a weak interaction condition, and for fixed budget multipliers the benchmark is the fixed point of a contraction. In a complete market with common risk, a mean field equilibrium at empirical type frequencies is an exact Nash equilibrium of the finite game, for any preferences over relative consumption. We bound the gain from deviating when plans computed at another composition are used. We compute equilibria in which groups with different wealth, inherited standards, and loss aversion revise spending at different dates. With identical households and common risk, the unique symmetric equilibrium is the policy of a single loss averse household with modified curvature. In a baseline example, ignoring the inherited standard costs up to 17% of wealth, while small errors about the composition of the reference group cost less than 0.5%.