A NEW TECHNICAL CRITERION FOR THE NOTE-COIN BOUNDARY

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1 A NEW TECHNICAL CRITERION FOR THE NOTE-COIN BOUNDARY Peter Koeze De Nederlandsche Bank N.V., Amsterdam March 1988 Digitised August 2006 Introduction Criteria for the note-coin boundary have traditionally invite study and research. Though never the subject of erce debate, it occasionally crops up, eg when a need is felt to replace a banknote by a coin. It is not only a subject of practical interest but also addresses political issues. In discussions among Central Bank, the Mint and the Ministry of Finance of a country di erences of opinion may sometimes surface about the desirability of replacing a banknote by a coin. A reasonably objective criterion might serve to settle such di erences. In the Netherlands, banknotes of the lowest denomination ( ve guilders) will be replaced shortly by coins of the same denomination. This appears to be an appropriate occasion to raise the subject again and to present a new technical criterion for the note-coin boundary based on the lives and cycle times of banknotes. Once accepted in abstracto by all parties concerned, it should prove a useful tool in establishing the note-coin boundary in practice. Existing criteria In 1981 Michael Knight, the then Secretary of the Statistics Committee of the (standing) Banknote Printers Conference BPC, compiled a diagram showing the denominations of coins and banknotes of all members [1]. In the diagram the two sequences of denominations are depicted as one continuum, the note-coin boundary separating the two. In 1983 Roberto Mori, one of the members on the Committee, set out in a systematic way which criteria might be feasible for the note-coin boundary Views expressed herein are the author s and do not necessarily re ect the o cial position of De Nederlandsche Bank. 1

2 [2]. He mentioned statistical, nancial and logistic criteria. However, he found none of them of any practical use and came to the conclusion that the note-coin boundary should be xed at the point where the Central bank is no longer able to cope with the issue of paper money with its existing technical and organizational structure. Finally, a paper by Payne and Morgan deserves to be mentioned [3]. They suggest a heuristic criterion involving the average day s pay D in a country. They ascertained that the note-coin boundary is usually found between D=50 and D=20. France and Germany, and Argentina proved to be exceptions with higher and lower note-coin boundaries, respectively. The new technical criterion Basically, the question when to substitute a coin for a banknote is technical. When the circulation of a denomination has grown to the extent that the usual banknote paper is no longer capable of withstanding the attendant stresses, it must be replaced by a stronger material. In principle, another kind of paper could serve, eg paper reinforced with plastic bres, but in practice such papers have other disadvantages which make them unattractive for use as banknote paper. The only realistic alternative has always been and still is metal. In choosing the note-coin boundary, two di erent considerations must be satis ed. On the one hand, the boundary should be as low as possible because banknotes are cheaper to produce than coins and the general public displays a strong preference for banknotes. On the other hand, it should not be so low that banknotes of the lower denominations deteriorate so rapidly during circulation that their average quality drops below the level still deemed acceptable. In more exact terms this may be phrased as follows. A minimum requirement for the average life of banknotes of a certain denomination is that it should exceed the mean time the banknotes remain in circulation, ie the mean time between issue and return. (Return of a banknote is not identical with withdrawal. A banknote may be returned several times before it is nally withdrawn.) When the average life is shorter than the mean time between issue and return, banknotes become worn before the Central Bank has had the opportunity to withdraw and exchange them for new notes. Such a situation is obviously undesirable, as it compels the public to handle un t notes. A stream of justi ed complaints will probably result. Now, the new technical criterion I would propose employs the ratio of the average life to the mean time between issue and return. The formula for the average life L is the one now in general use among BPC members: L = last year s circulation + this year s circulation this year s new notes + this year s withdrawals : 2

3 A similar formula for the mean time between issue and return or the mean cycle time C is C = last year s circulation + this year s circulation. this year s issues + this year s returns The new criterion N, being the ratio between the two, is then given by N = L C = this year s issues + this year s returns this year s new notes + this year s withdrawals. The theoretical asymptote of N is 1 because in a certain year and so that or new notes 6 issues withdrawals 6 returns new notes + withdrawals 6 issues + returns N > 1: In fact, N is the average number of times banknotes are reissued by the Central Bank before they are nally withdrawn, or, equivalently, the average number of loops or cycles traversed through the circulation. Thus, it is not surprising that N cannot drop below 1. Preferably, it should be signi - cantly larger than 1 for a particular denomination, in which case issuance of banknotes may be continued. However, if N tends to the asymptotic value of 1, banknotes ought to be replaced by coins in the near future. Empirical results The following table shows the gures for the Netherlands for the year denomination average life mean cycle time average number of cycles L C N NLG years years all denominations

4 According to the new criterion N, both the ve-guilder and the ten-guilder banknotes are about equally eligible for replacement by coins. Indeed, as from 2 May 1988 ve-guilder coins will be introduced and banknotes of the same denomination will cease to be issued. Although from a technical viewpoint the ten-guilder note should also be replaced, it would not be wise to introduce a second new coin too quickly after the rst. It seems inevitable to postpone the ten-guilder coin for a few years till the public has grown accustomed to the ve-guilder coin. The average life L in the above table forms part of the annual statistics gathered and published through the Statistics and Banknote Handling Committee. However, these statistics do not include the mean cycle time C as the member countries are not asked to report the cumulative numbers of banknotes issued and returned during the year. I would suggest to the members of this Committee that the cumulative numbers of banknotes issued and returned be included as part of the annual questionnaire sent out by our Secretary. In future, the mean cycle time and the average number of cycles, the new technical note-coin criterion, could then feature in our annual statistics in addition to the average life already reported. Summary and conclusion It is proposed that the ratio of the average life to the mean cycle time of banknotes be used as a technical criterion for the note-coin boundary. This ratio represents the average number of loops traversed through the circulation. When it tends to 1, replacement of banknotes of the denomination concerned by coins should be considered and taken in hand. References [1] Knight, M.; Notes and coin-ranges of denominational values in BPC member countries, BPC Statistics Committee, London, [2] Mori, R.; The boundary between banknotes and coin and the new Lit. 1,000 note, Banca d Italia, Rome, [3] Payne, L.C. and Morgan, H.M.; UK currency needs in the 1980s, The Banker, April 1981,

5 Note The original version of this paper was presented at the BPC Statistics and Banknote Handling Committee Meeting, Stockholm 1988, and the General Meeting of the Banknote Printers Conference BPC, Istanbul This digital version, composed in August 2006, follows the original with minor emendations. List of Publications: Curriculum vitae: De Nederlandsche Bank N.V. P.O. Box AB Amsterdam Netherlands Website: 5