This paper presents a novel Bayesian method for estimating dynamic stochastic general equilibrium (DSGE) models subject to a constrained posterior distribution for the implied Sharpe ratio. We apply our methodology to a DSGE model with habit formation in consumption and leisure, and show that the constrained estimation produces both reasonable asset‐pricing and business‐cycle implications. Next, we estimate the Smets–Wouters model subject to the same Sharpe ratio constraint. The results move the model closer to reproducing observed risk premia, but at increasing cost to its macroeconomic performance.

Bayesian estimation stochastic steady state prior choice Sharpe ratio C11 E32 E44 G12