Solving for a Cash-in-Advance economy using a Finite Element Method, and a Note on Velocity

A solution methodology employing finite elements and a parameterized expectations algorithm is proposed for computing the equilibrium of a CIA model economy. The stochastic growth model considered introduces money via a CIA constraint, and takes consumption as the cash good and leisure and capital investment as credit goods. The ability of the methodology to approximate the solution of the model while allowing for the cash-in-advance constraint to occasionally bind permits to perform an analysis on the variability of velocity of money; for which a note in the matter is included in the paper. Different calibrations of the model economy, various sources of exogenous perturbations, and the inclusion of frictions on the information structure of the model, in a way similar to that of Svensson (1985), are considered. Velocity volatility, measured using the coefficient of variation, arises in the model due to uncertainty on the realization of the state of the economy, and information frictions increases it. JEL Classification: C63; C68; O42