Household Savings and Monetary Policy under Individual and Aggregate Stochastic Volatility

We study a heterogeneous-agent model with sticky-prices in which total factor productivity and individual productivity are subject to stochastic volatility shocks. Agents save through liquid bonds and illiquid capital and shares. To construct equilibrium, we use a deep learning algorithm. Our method preserves non-linearities, which is essential for understanding portfolio choices. With rich heterogeneity at the household level, we are able to quantify the impact of uncertainty across the income and wealth distribution. We find that persistent high levels of uncertainty increase wealth inequality, and that in response to a contractionary monetary policy shock, illiquid wealth inequality decreases and liquid wealth inequality increases