Advantages of an Ellipse when Modeling Leisure Utility

Utility functions that are additively-separable in goods consumption and leisure are often used in dynamic stochastic general equilibrium (DSGE) models. This paper illustrates how the use of an elliptical functional form for the utility of leisure can be substituted for the more common constant relative risk aversion (CRRA) or constant Frisch elasticity (CFE) utility functions. The advantage of this is that it rules out the possibility of households demanding leisure or labor that exceeds their time endowment. A non-negatively constraint on leisure or labor can be incorporated into a model, of course. However, in very large heterogeneous agent models, it is often advantageous to avoid the computational burden associated with such occasionally-binding constraints. Using two simple models, we show that behavior with elliptical utility closely matches that CFE disutility. The match with CRRA utility is not as close, but still good.