The effect of rounding on payment efficiency

Abstract

Theory predicts that dismissing the 1 and 2 euro cent coins from the denominational range of the euro facilitates payment efficiency. To examine whether this theory holds true in practice, data were collected for the Netherlands before and after September 2004, which marks the day that retail stores were allowed to round all amounts at 5 euro cents. The data consist of wallet contents for three cross sections of individuals. As the amounts of various coins in wallets are correlated, a multivariate Poisson-log Normal model is proposed to analyze these data. It is found that rounding leads to less 1 and 2 cent coins in wallets, but that still other coins are over or underrepresented, thereby suggesting that the euro range does not yet lead to fully efficient payment behavior.

Introduction

January 2002 marked the launch of the euro in 12 European countries. In the Netherlands the transition from the guilder to the euro involved a transition to a different denominational structure. The rather unique 1–2$\frac{1}{2}$–5 series for the guilder has been replaced by the more common 1–2–5 series, which is generally accepted as the optimal denominational series of banknotes and coins. Indeed, Boeschoten and Fase (1989) already concluded that the Dutch guilder range was efficient to some extent, but that a transition to the more common 1–2–5 range would be beneficial.

The euro coins have denominations €2, €1, €0.50, €0.20, €0.10, €0.05, €0.02 and €0.01, and this range involves two more coins than the guilder range used to have, which were 5, 2.50, 1, 0.25, 0.10 and 0.05 guilders. Apart from the different denominational structure, the introduction of the euro coins also implied the introduction of 1 and 2 cent coins. Ever since the launch of the euro, the paying public faced inconvenience dealing with these smaller denominations. The Dutch Central Bank commissioned a research agency to see if the public would support the notion that retailers would round at 5 euro cents, and it seemed that they did. Rounding implies that, say, €2.67 becomes €2.65 and that €2.68 becomes €2.70. As a result, from September 2004 onwards, retailers in The Netherlands are allowed to round, although the 1 and 2 cent coins are still legal tender and can be used everywhere.

An interesting question is whether such rounding really helps to facilitate payments. As we will show in Section 2 below, there is a simple theoretical result that supports the positive effects of rounding. Of course, the issue is whether this theory holds in practice. To examine this, we collected Dutch data before and after September 2004 on wallet contents for three cross sections. In Section 3 we describe the data collection method and we provide a few basic statistics of the data obtained through this natural experiment. As the amounts of various coins in wallets are correlated, we analyze these data using a multivariate Poisson-log Normal model, where we allow the intercept terms to vary across the cross sections. Details of this model are provided in Section 4, where we also compare it with other multivariate models for count data. The main reason to opt for our model is that the amounts of coins in individual wallets are likely to be correlated, whereas there is no reason to assume that this correlation should always be positive. Also, with our correlated count model we allow the number of different types of coins in a wallet to depend on the wallet size. In Section 5 we calibrate various models for our data, and we find that the log Normal gives the best fit. Based on the estimation results we conclude that rounding matters for the 1 and 2 cent coins, but that other coins are still over or underrepresented. Section 6 concludes and outlines a few topics for further research.