By Yulei Luo, Jun Nie and Eric Young
This paper develops a tractable continuous-time recursive utility (RU) version of the Huggett (1993) model to explore how the preference for robustness (RB) interacts with intertemporal substitution and risk aversion and then affects the interest rate, the dynamics of consumption and income, and the welfare costs of model uncertainty in general equilibrium. We show that RB reduces the equilibrium interest rate and the relative volatility of consumption growth to income growth when the income process is stationary, but our benchmark model cannot match the observed relative volatility. An extension to an RU-RB model with a risky asset is successful at matching this ratio. The model implies that the welfare costs of uncertainty are very large.
I was not aware of a continuous-time version of the Huggett model, and it looks like a pretty powerful tool. It may be useful in addressing questions that are too difficult for the discrete-time version, like in this paper.
We started this project partially because we thought concerns about model misspecifcation have contributed to the low equilibrium interest rate observed in the U.S. For instance, after the Great Recession, businesses and consumers may have larger concerns whether they really understand how the macroeconomy is working. We want to construct a model to explicitly show the mechanism through such concerns may have influenced the agent’s decision and the equilibrium interest rate.
Then we realized when moving out of the linear-quadratic-Gaussian (LQG) framework, it is difficult to have analytical solutions and the most RB models (those we mentioned in the paper) did not separate risk aversion and intertemporal substitution which we thought may interact with RB in different ways.
So, toward the end, in the latest version we just finished, we are able to construct a tractable continuous-time dynamic stochastic general equilibrium (DSGE) model with robustness preference and recursive utility to achieve this goal. Of course, in addition to the low interest rate, we have used this framework to explore other dimensions.
Thank for your time reading our paper.