Occasionally Binding Constraints in DSGE Models with Heterogeneous Agents: a Generalised Nonlinear Framework and Applications to Inequality and Monetary Policy at the ZLB

The role of Occasionally Binding Constraints (OBCs) in transmitting and amplifying macroeconomic shocks in economies institutionally chracterised by market-incompleteness is of increasing interest to quantitative theory and policy. This paper presents a novel framework and iterative algorithm to efficiently formulate and solve for transitional dynamics in a wide class of heterogeneous agent DSGE (HA-DSGE) models with OBCs. The framework accommodates a wide range of constraints, such as policy bounds, without requiring any specific assumptions as to the form of the aggregate shocks must take at an equilibrium solution, and is modelunspecific, marking a departure from the methodological literture on the topic. More imporantly, it preserves key nonlinearities often lost in perturbation-based methods important to retain for a more granular analysis of the interaction between agent heterogeneity and OBCs and its implications for modelling policy transmission through the distribution. In particular, the nonlinearity arising from the interaction, in a rational expectations and forward-looking setting, between the endogenous regime sequence (whether the constraint binds) and the behaviour of heterogeneous agents. The proposed Double Shooting algorithm novelly integrates the Sequence- Space OccBin approach with an iterative and informationally efficient method for solving nonlinearly HA-DSGE models in the sequence space that exploits the availability of a Directed Acyclic Graph (DAG) to efficiently partition the system of equations holding at a sequence space equilibrium and generalising the solution procedure for deterministic transition paths familiar from KS modelling. The algorithm developed is then applied to a fully-fledged one-asset HANK model with a zero lower bound (ZLB) on interest rate. The analysis highlights how wealth distributional dynamics along the transition path can critically influence monetary policy effectiveness (and vice versa) both outside and especially at the ZLB. Thereby, we highlight through the potential role of unconventional redistributive fiscal measures and fiscal forward guidance in addressing recessionary-deflationary episodes, converging in a rich quantitative setting to intuitions familiar from the Keynesian and Post-Keynesian literatures.