## A New Keynesian Model with Wealth in the Utility Function

Pascal Michaillat, Emmanuel Saez

February 2018

February 2018

This paper extends the textbook New Keynesian model by introducing wealth in the utility function. As bonds are in zero net supply, the consumption Euler equation imposes that the real interest rate is decreasing in output; in the textbook model in contrast the real interest rate is constant, equal to the time discount factor. As a result, our simple extension eliminates many of the puzzling properties of the textbook model. Our equilibrium has a unique steady state, which may be at the zero lower bound or away from it; the equilibrium is always determinate, whether the economy is at the zero lower bound or not, and whether monetary policy is active or passive; inflation and real interest rate can be positive or negative, at the zero lower bound and away from it; contractionary monetary policy raises both real and nominal interest rates; there is no forward-guidance puzzle; the effect of technology and government spending depends in non-puzzling ways on the stance of monetary policy and slack.