Money-driven general equilibrium models with great difficulty are capable to explain the variability on velocity observed in the data, due to the insufficient propagation mechanisms associated with monetary shocks. Alas, a proper assessment on the variability of consumption velocity of money is fundamental to understanding the role of money in the business cycle and bestows insight on the microfoundations of monetary policy.
Attempting to answer for a significant allotment of its variability, financial frictions are introduced in the information structure of a cash-in-advance (CIA) dynamic stochastic general equilibrium model with the interest of studying the impact on velocity of serially correlated monetary shocks. On the proposed modeling environment, at each period the agent is required to make its choice on real money holdings prior to the realization of a monetary shock. Uncertainty regarding the current period’s realization of the money growth rate incentives the agent to carry additional units of cash than those that would be chosen if instead the portfolio is to be formed ex-post the realization of the shock. Frictions on the information structure accentuate a precautionary demand for money balances, causing variability in velocity. On the model, velocity variability will occur more succinctly at low rates of money growth for consumption smoothing purposes, on these cases the agent chooses to hold money for the next period because of expectations of future low realizations of the growth rate.
Given that this particular dynamic environment posses no analytical solution, a projection method which parameterizes expectations and employs finite elements in its approximations of the policy functions is proposed, thoroughly developed and employed to solve for the equilibrium of the economy. The approximation of the model’s functional equations using finite elements is an advantage over other commonly used perturbation or projection methods, such as a parameterization using a Chebyshev polynomial or the linearization of the system around its steady state, because it allows for the fit of numerous low order polynomials over non intersecting subdomains of the state space, rather than high-order polynomials over the complete domain. McGrattan (1998), in [10], stresses that the fractioning of the space results in an improvement on the precision of the approximation of the policy functions near regions of the state space that are of higher order or highly nonlinear. Aruoba et. al (2006) in [1] concurs with this result, and finds that finite element approximations proved being the most accurate, stable and of fastest convergence from a considered wide range of projection and perturbation methods.
Following a procedure first introduced by den Haan and Marcet (1990), in [5], the algorithm is able to efficiently handle the CIA constraint on transactions by parameterizing the optimal choice rule on the expectations of future real money holdings. The procedure allows for the inequality constraint on the planner’s problem to selectively and occasionally bind, enabling an analysis on the variability of money velocity.
The next section contains a detailed description of the modeling environment and the functional forms of its equilibrium conditions. Section 3 discusses the proposed solution methodology and the implementation of its algorithm. Section 4 shows the business cycle properties of the economy for a benchmark calibration and the implications on velocity of information and financial frictions. Section 5 concludes.
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