Inequality and the zero lower bound

BIS Working Papers  |  No 1160  | 
11 January 2024



Recent decades have been characterised by a surge in wealth inequality and a persistent decline in real rates. This has partially reversed in the current inflationary spike although it is expected to return once price pressures abate. These two observations suggest that: (i) the zero lower bound (ZLB) on nominal interest rates may have highly heterogeneous effects across households with different levels of ; and (ii) changes in wealth inequality could be driving real rates closer to the ZLB.


We build and globally solve a heterogeneous agent New Keynesian (HANK) model with a ZLB to demonstrate how household inequality intensifies the probability of hitting the ZLB. Crucially, we explicitly account for the risk of hitting the ZLB in households' expectations. We do so by solving our model non-linearly through a novel neural network algorithm that allows us to compute the stochastic equilibrium dynamics of the economy. We then calibrate the model to replicate key cross-sectional and aggregate moments of the US economy and consider a wide array of exercises that study the distributional implications of contractionary shocks at the ZLB, as well as the effects of different inflation targets on long-run interest rates.


We find two main results. First, negative effects of a contractionary shock at the ZLB fall disproportionately on wealth-poor households, exacerbating inequality. Second, inequality makes monetary policy non-neutral in the long run to a significant extent. A lower inflation target makes spells of ZLB more likely, raises households' precautionary savings and thus leads to a reduction in long-run real interest rates. We show that a drop in the inflation target resembling the drop in average inflation between 1980 and 2015, tied to a rise in wealth inequality resembling the increase in the Gini index in the early 2000s, implies a substantial drop in long-run real rates. According to our new theory, the natural rate of interest depends on the central bank's inflation target.


This paper studies how household inequality shapes the effects of the zero lower bound (ZLB) on nominal interest rates on aggregate dynamics. To do so, we consider a heterogeneous agent New Keynesian (HANK) model with an occasionally binding ZLB and solve for its fully non-linear stochastic equilibrium using a novel neural network algorithm. In this setting, changes in the monetary policy stance influence households' precautionary savings by altering the frequency of ZLB events. As a result, the model features monetary policy non-neutrality in the long run. The degree of long-run non-neutrality, i.e., by how much monetary policy shifts real rates in the ergodic distribution of the model, can be substantial when we combine low inflation targets and high levels of wealth inequality.

JEL classification: D31, E12, E21, E31, E43, E52, E58

Keywords: heterogeneous agents, HANK models, neural networks, non-linear dynamics