The Band Pass Filter*

We develop optimal finite‐sample approximations for the band pass filter. These approximations include one‐sided filters that can be used in real time. Optimal approximations depend upon the details of the time series representation that generates the data. Fortunately, for U.S. macroeconomic data, getting the details exactly right is not crucial. A simple approach, based on the generally false assumption that the data are generated by a random walk, is nearly optimal. We use the tools discussed here to document a new fact: There has been a significant shift in the money–inflation relationship before and after 1960.     

Inflation And Efficiency In A Search Economy*

We present a model in which purely monetary inflation systematically affects efficiency, welfare, and relative prices. The model focuses on the microeconomics of trade in search markets under inflation. Inflation, by increasing the cost of holding money, undermines the market's ability to sustain long‐term customer relationships. Because those relationships generate the most efficient transactions patterns, overall welfare unambiguously declines.     

Consumer inertia, firm growth and industry dynamics

We develop a model of firm size, based on the hypothesis that consumers are “locked in,” because of search costs, with firms they have patronized in the past. As a consequence, older firms have a larger clientele and are able to extract higher profits. The equilibrium of this model yields: (i) A downward sloping density of firm sizes. (ii) Older firms are less likely to exit than younger firms. (iii) Larger firms spend more on R&D.