At the zero lower bound, the New Keynesian model predicts that output and inflation collapse to implausibly low levels and that government spending and forward guidance have implausibly large effects. To resolve these anomalies, we introduce wealth into the utility function; the justification is that wealth is a marker of social status, and people value status. Since people partly save to accrue social status, the Euler equation is modified. As a result, when the marginal utility of wealth is sufficiently large, the dynamical system representing the zero-lower-bound equilibrium transforms from a saddle to a source, which resolves all the anomalies.
Figure 1: Phase diagrams of the New Keynesian (NK) and wealth-in-the-utility New Keynesian (WUNK) models
Michaillat, Pascal, and Emmanuel Saez. 2021. “Resolving New Keynesian Anomalies with Wealth in the Utility Function.” Review of Economics and Statistics 103 (2): 197–215. https://doi.org/10.1162/rest_a_00893 .