On Poverty Traps, Rational Bubbles, and Wealth Inequality

This paper develops a dynamic general equilibrium (DGE) model with heterogeneous agents to connect three macroeconomic phenomena: persistent poverty traps, sluggish real growth, and rising wealth inequality. The model achieves this by allowing agents, who differ in patience and face a subsistence consumption constraint, to choose portfolios between productive capital and a fixed-supply, unproductive asset susceptible to rational speculative bubbles. The analysis reveals that these bubbles, while rational, induce a positive wealth effect for asset-holders, which, through optimal consumption-smoothing (via agents’ Euler equations), reduces the aggregate savings rate, permanently "crowding out" productive capital that crowds out productive investment, leading to lower real wages and output, which in turn exacerbates wealth inequality by pushing constrained agents closer to the poverty trap. A calibration exercise, disciplined by real-world stylized facts, illustrates the model’s path-dependence and highlights the particular vulnerability of middle-income economies to such collapses