Velocity Volatility Assessment of Monetary Shocks on Cash-in-Advance Economies

A projection method employing finite elements and a parameterized expectations algorithm is proposed for the global approximation of the equilibrium of a cash-in-advance model economy. The algorithm is shown to be accurate and efficient approximating highly nonlinear regions of the policy functions, specifically along the space of state variables where the slackness multiplier of the cash-in-advance constraint alternates between zero and strictly positive values. This favorable trait allows for a rigorous analysis on the variability of velocity of money. Velocity volatility, measured by its coefficient of variation, arises in the model on a consumption smoothing purpose by the agent at instances where the variation of expected marginal utility of consumption is relatively high due to the realization of a sufficiently low serially correlated monetary shock. In a simulation of the stochastic economic environment responding to a Markovian series of monetary growth rates and no frictions present, the equilibrium approximated via the proposed numerical solution method explains 80.3% of the velocity variability recently observed in the data; a significant improvement over previous attempts found in the literature.