We develop a method to solve and simulate cash-in-advance models of money and asset prices. We calibrate the models to U.S. data spanning the period 1890-1987 and study some empirical regularities observed over this period. The phenomena of interest include the average level of stock returns and returns on nominal bonds, the covariation of realized real interest rates and real asset returns with inflation, and the ability of nominal interest rates to predict inflation and nominal stock returns.