We study dynamic general equilibrium in one-tree and two-trees Lucas economies with one consumption good and two CRRA investors with heterogeneous risk aversions and portfolio constraints. We provide a tractable characterization of equilibrium without relying on the assumption of logarithmic constrained investors, popular in the literature, under which wealth-consumption ratios of these investors are unaffected by constraints. In one-tree economy we focus on the impact of limited stock market participation and margin constraints on market prices of risk, interest rates, stock return volatilities and price-dividend ratios. We demonstrate conditions under which constraints increase or decrease these equilibrium processes, and generate dynamic patterns consistent with empirical findings. In a two-trees economy we demonstrate that investor heterogeneity gives rise to large countercyclical excess stock return correlations, but margin constraints significantly reduce them by restricting the leverage in the economy, and give rise to rich saddle-type patterns. We also derive a new closed-form consumption CAPM that captures the impact of constraints on stock risk premia.
This discussion paper won a Paul Woolley Centre discussion paper prize.
