The behavior of velocity and nominal interest rates in a cash-in-advance model

A prominent feature of U.S. monetary data is the nonstationarity of M1 velocity. One aspect of the empirical failure of the dynamic general equilibrium monetary models of money demand is the inability of these models to reproduce a nonstationary income velocity. The Euler's equations of these models reflect that equilibrium income velocity and nominal interest rates are both stationary, which is inconsistent with the stylized facts, Using a specific parametric form of a cash-in-advance model a la Lucas and Stokey (1987) we argue that the failure to reproduce a nonstationary income velocity may be due to the assumption of a homogeneous utility function involving cash and credit goods. Once this homogeneity restriction is relaxed, the equilibrium income velocity becomes nonstationary. A long-run nonlinear relationship between velocity, nominal interest rates and real output then emerges, which is consistent overall with the data.