Monetary models based on cash-in-advance constraints make strong predictions about the stochastic properties of endogeneous variables such as the velocity of circulation of money, the rate of inflation, and real and nominal interest rates. We develop numerical methods to understand these predictions because the models cannot be characterized analytically. We calibrate some cash-in-advance models using driving processes estimated from U. S. time-series data to generate model predictions that are compared to sample statistics. Formulations of the models that generate variability in velocity corresponding to the U.S. data typically fail along other dimensions.

We compare the empirical performance of a standard incomplete markets asset pricing model with that of a novel model with constrained Pareto‐optimal allocations. We represent the models’ stochastic discount factors in terms of the cross‐sectional distribution of consumption and use these representations to evaluate the models’ empirical implications. The first model is inconsistent with the equity premium in the United States, United Kingdom, and Italy. The second model is consistent with the equity premium and the risk‐free rate in all three countries if the coefficient of relative risk aversion is roughly 5 and the quarterly discount factor is less than 0.5.

Monetary models based on cash-in-advance constraints make strong predictions about the stochastic properties of endogeneous variables such as the velocity of circulation of money, the rate of inflation, and real and nominal interest rates. We develop numerical methods to understand these predictions because the models cannot be characterized analytically. We calibrate some cash-in-advance models using driving processes estimated from U. S. time-series data to generate model predictions that are compared to sample statistics. Formulations of the models that generate variability in velocity corresponding to the U.S. data typically fail along other dimensions.