Sample Design and Estimation of the Lifetimes of Federal Reserve Notes

• Activity Number: 466
• Type: Contributed
• Date/Time: Thursday, August 7, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Darrel W. Parke*+ and Xuemei Liu
• Companies: Federal Reserve Board and Federal Reserve Board
• Keywords: sample size ; cluster sampling ; inventory models

Abstract

The Federal Reserve (FR) maintains several time series pertaining to FR notes, including number paid out, number in circulation, and the numbers inspected and destroyed at each of the 37 FR offices. In a steady state, the average lifetime of notes is a rather straightforward calculation based on these series. However, recently the series have been unstable, and a survey of notes about to be destroyed at the FR offices was conducted to provide a direct estimate of the average lifetime of notes. Outside data on the ages of a cross-section of notes were used to postulate a lifetime distribution and estimate a required sample size for this survey, and the destruction rates were used to estimate the number of offices (clusters) that should be included. The serial number of each sample note was recorded in order to match with existing data to determine when the note was shipped to the FR office, thus the note's gross lifetime. Several methods were used to impute shipment date in cases where the match failed. Finally, inventory models were used to estimate the time spent in FR vaults. We concluded that the average lifetime of notes has increased substantially over the last decade.