Pascal Michaillat and Emmanuel Saez: A New Keynesian Model with Wealth in the Utility Function: "Wealth... [in] the utility function. The extension modifies the Euler equation: in steady state the real interest rate is negatively related to consumption instead of being constant... Thus, when the marginal utility of wealth is large enough, the dynamical system representing the equilibrium is a source not only in normal times but also at the zero lower bound. This property eliminates the zero-lower-bound anomalies of the New Keynesian model, such as explosive output and inflation, and forward-guidance puzzle...
...There is no explosive slump if the ZLB is long-lasting, no explosive boom if forward guidance is long-lasting, and no reversal from slump to boom when the duration of forward guidance crosses some threshold. Hence in our model, the ZLB is not necessarily short-lived—it might last forever as a steady state—and forward-guidance policies have plausible, limited effects. At the same time, our model retains other ZLB properties: paradox of thrift, paradox of toil, and paradox of flexibility...
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