During the last twenty years, beginning with the provocative paper by Goldfeld [5] that revealed the case of the missing the question of whether money demand (the relationship between money, income, and an interest rate) is stable has been intensively investigated using a variety of econometric techniques. Currently, the most popular framework for examining the behavior of money demand is the cointegration framework. In this framework, the stationarity of money demand instead of the stability of money demand is evaluated. Earlier tests of the stability of money demand typically centered on whether the coefficient estimates were stable, i.e. not subject to a structural break. These tests did not consider the underlying time series aspects of the variables in money demand or the time series properties of their joint relationship prior to estimation as is now common given the seminal work of Engle and Granger [1]. Since then, newer tests have focussed on the time series properties of the money demand variables and whether the joint relationship between the variables is stationary, i.e., whether the variables are cointegrated. Engle and Granger [1] and Johansen and Juselius [10] offer cointegration estimation procedures that have been applied by numerous researchers to the money-incomeinterest rate relationship. The pervasive finding is that money demand is non-stationary (see section II, below). Structural stability has not typically been a facet of investigation. However, the issues of stationarity and stability should not necessarily be treated independently. Failure to take account of structural change may bias the results in favor of non-stationarity, as shown in Perron [16].1 History suggests that the economic environment and monetary institutions, regulations, and operating procedures have changed over time. In the early 1970s, the fixed exchange rate system collapsed when the gold exchange standard was abandoned and the U.S. dollar became a fiat currency. During that same time, the U.S. suffered an oil price shock that produced accelerating inflation and stagnant GDP growth-an outcome that had never before been experienced in