Short-horizon Duesenberry Equilibrium

TL;DR

This paper develops a continuous-time equilibrium model with heterogeneous agents optimizing over short horizons based on relative income, revealing endogenous market completeness, asset pricing implications, and a new perspective on the equity premium puzzle.

Contribution

It introduces a novel short-horizon Duesenberry equilibrium framework with endogenous market features and derives new asset pricing insights based on wealth volatility.

Findings

Market completeness and no arbitrage emerge endogenously from clearing.

Equilibrium asset prices are determined by wealth volatility, not just consumption.

The model explains the equity premium through total wealth volatility rather than consumption volatility.

Abstract

We develop a continuous-time general equilibrium framework for economies with a heterogeneous population -- modeled as a continuum -- that repeatedly optimizes over short horizons under relative-income (Duesenberry-type) criteria. The cross-section evolves through a Brownian flow on a type space, transporting an effective impatience field that captures time variation in preferences induced by demographic changes, aging, and broader social shifts. We establish three main results. First, we prove an optimal consumption--investment theorem for infinite heterogeneous populations in this Brownian-flow setting. Second, we define a \emph{short-horizon Duesenberry equilibrium} -- a sequential-trading (Radner-type) equilibrium in which agents repeatedly solve vanishing-horizon problems under a relative-income criterion -- and provide a complete characterization and existence proof under mild regularity conditions; notably, market completeness and absence of (state-tame) arbitrage emerge endogenously from the market clearing, rather than being imposed as hypotheses. Third, we derive sharp asset-pricing implications: in equilibrium, the market price of risk is pinned down by the volatility of aggregate \emph{total wealth} (financial plus human capital), implying that the equity premium is governed by the magnitudes and correlations of wealth and equity volatilities rather than by consumption volatility alone. This shifts the equity premium puzzle from an implausibly low consumption volatility to a question about the volatility of aggregate total wealth. The framework delivers explicit decompositions of the risk-free rate that are consistent with macro-finance stylized facts. All equilibrium quantities are expressed in terms of market primitives.