Persistence Dependence in Empirical Relations: The Velocity of Money

Standard theory predicts persistence dependence in numerous economic relationships. (For example, persistence dependence is precisely the kind of nonlinear relationship posited in the Permanent Income Hypothesis; persistence dependence is the inverse of "frequency dependence" in a relationship.) Until recently, however, it was challenging to achieve credible inference about persistence dependence in an economic relationship using available methods. However, recently developed econometric tools (Ashley and Verbrugge, 2009a) allow one to elegantly quantify the variation in a time-series relationship across persistence levels, even when the data must be first-differenced because they are I(1), or nearly so. We apply these tools to study the velocity of money. Standard theory predicts that velocity should be positively correlated with the nominal interest rate: A high nominal interest rate raises the opportunity cost of holding wealth in liquid form, prompting agents to economize on money holdings. But as Cochrane (2012) pointed out, the velocity-interest rate linkage appears to be weak upon first-differencing. We argue that the root cause of this phenomenon is a particularly intuitive form of nonlinear dependence in the relationship: The strength of the relationship depends on the persistence level of a particular interest rate fluctuation. In particular, this relationship is substantially (and statistically significantly) stronger at low frequencies—i.e., at high interest rate fluctuation persistence levels. Because we allow for persistence dependence in the estimated relationship, this strong association is apparent despite the first-difference transformation applied to these data.