On Money Growth and the Business Cycle

Abstract

Perfectly flexible price models of the business cycle in which money is introduced through a cash-in-advance (CIA) constraint are interpreted as models in which money neutrality and superneutrality hold. This conclusion is grounded on calibration and simulation of an approximated solution to a problem where the representative agent has a specific (log) utility function. Lacking an explicit solution and resting on special cases, these models produce an empirical evidence that is in fact strongly contingent on the chosen set of parameters and biased towards money neutrality and/or superneutrality and may miss qualitatively important interactions between money and the real business cycle. In a fairly general continuous time framework, we derive the equilibrium paths of real economic variables without approximation. When the stochastic nature of the inflation tax is properly accounted for, money non-neutrality and non-superneutrality are in fact inherent in CIA monetary versions of the real business cycle. In the special case of a log utility function, we solve completely and explicitly the representative agent's problem, again without approximation. In addition to easing and enriching the analysis as compared to the discrete time approach, our methodology permits to show that the introduction of price rigidities and/or limited participation is not necessary to make the CIA models exhibit significant money non-neutrality.