Optimal recursive utility maximization with debt-to-income limits

We study a continuous-time optimal consumption and portfolio selection problem when an economic agent with recursive utility faces stochastic income and debt-to-income (DTI) borrowing limits. The recursive utility setup with time-varying borrowing constraints yields novel implications for optimal investment and marginal propensity to consume (MPC). We find that the optimal portfolio's dependency on the elasticity of intertemporal substitution (EIS) arises specifically due to borrowing constraints, regardless of constant investment opportunities. Our model generates the result consistent with the MPC heterogeneity reported by recent empirical literature. We also provide a novel testable implication that, particularly when constrained, active stock traders exhibit fairly higher MPCs compared to individuals not engaged in stock trading. Additionally, we make a technical contribution by developing a new transform to address problems associated with recursive utility.