On the integrability of money-demand functions by the Sidrauski and the shopping-time models

This paper investigates which properties money-demand functions must satisfy so that they are consistent with Lucas's [Lucas Jr., R.E., 2000. Inflation and welfare. Econometrica 68, 247-274] versions of the Sidrauski and the shopping-time models. We conclude that shopping-time-integrable money-demand functions are necessarily also Sidrauski-integrable, but that the converse is not necessarily true, unless a boundedness assumption on the nominal interest rate is made. Both the log-log with an interest-rate elasticity greater than or equal to one and the semi-log money demands may serve as counterexamples. All the models and results are also extended to the case in which there are several assets in the economy performing monetary functions. (C) 2009 Published by Elsevier B.V.