From May through October 2012 Gottfried Leibbrandt posted a regular blog to accompany the chapters in his book, The Statistics of Payments. Below you will find each of his blog postings, with the 15 October 2012 blog containing a link to download his book in its entirety.

Gottfried Leibbrandt – CEO, SWIFT and Member of the SWIFT Institute Advisory Council

Succeeded Lázaro Campos as CEO of SWIFT in July 2012. Gottfried Leibbrandt joined SWIFT in 2005 to focus on the development of the SWIFT2010 strategy. Upon completion of the strategy, he was appointed as Head of Standards and then in 2007, was promoted to Head of Marketing. Prior to joining SWIFT, Gottfried worked for McKinsey & Company for 18 years where he was a partner in the Amsterdam office and a co-leader of the European payments practice. He holds a Masters degree in Econometrics and Statistics from the Vrije Universteit Amsterdam and a MBA from the Stanford Graduate School of Business. Gottfried also holds a PhD in Economics from Maastricht University. His thesis was “Payment instruments and network effects: Adoption, harmonization and succession of network technologies across countries”.

15 October 2012

This is my concluding blog on the statistics of payments. These blogs applied statistical techniques to payments: how is their value distributed, how does the use of payment instruments grow or decline, what is the geographical spread of bank notes, etc. The enclosed pdf bundles these blogs in a single booklet. It can be downloaded and read on an iPad or in paper form. It could provide plane reading for those of us going to Sibos Osaka later this month. That would close the circle since I started writing the first chapter on my way back from Sibos Toronto last year. There is no hiding the fact that payments fascinate me, and obviously I’d like to hear any reactions, suggestions for further research, etc.

Download The Statistics of Payments, here.

24 September 2012

This is the final chapter, but not quite my final blog. In chapter 12 we found that bigger banks are more likely to have a lot of interbank connections than smaller banks. The question is, how are banks distributed by size? I use data on total assets for 28,000 banks, and find that the largest bank had 1.5 trillion EUR, the smallest had 100,000 EUR while the average was 9 billion EUR. Most banks are small to medium, with a few very large ones. What we’ve found in these last few chapters is that payment size, the number of links of banks and the size of banks all follow statistical distributions with ‘fat tails’. One consequence of this is concentration: 5% of all SWIFT payments account for 95% of the value, 20% of banks account for 80% of all counterparty links and 5% of banks account for 95% of all assets. Next week in my final blog, you can download The Statistics of Payments in its entirety.

Download chapter 13, How big is your bank? here.

24 September 2012

Whether you’re actor Kevin Bacon, a page on the world wide web, or a bank, we are all connected…and connected in very similar ways. A Power-law is a type of relationship between the size of events and their frequency. Several studies of payments networks have found the node-degree distribution to follow power laws. The sizes of human settlements, the intensity of wars, the size of meteorites, income and wealth, the size of files sent over the Internet and natural phenomena such as rainfall, hurricanes and earthquakes all appear to follow a Power-law. In the interbank market we take the banks to be the nodes of a network, and if two banks exchange payments they share a link. Interbank networks have the same topology as other networks: most banks have few links, while a few banks have a large number of links. Links do not form randomly, but instead a new node is much more likely to link itself to an existing node that already has a high number of links. Such networks are efficient but vulnerable to failure of a single highly connected node. Can you say “systemically important”?

Download chapter 12, What is the topology of your payment network?, here.

16 September 2012

As we near the end of my book, I thought it might be time for a little pop quiz. Question: When is 1 the most popular number and 9 the least popular? Answer: Whenever numbers are more or less evenly spread over multiple orders of magnitude. In these situations, Benford’s law, or the first-digit law, applies: the first digit of the amount is much more likely to be 1 than 9. Benford law’s predicts that for 30% of all payments the first digit of the amount is a 1, while it is a 9 for only 5% of payments. This applies to any set of numbers that span several orders of magnitude such as incomes on tax returns, annual sales of firms, and the population of cities. It even applies to SWIFT transfers.

Download chapter 11, Does your amount start with a 1? Benford’s law, here.

10 September 2012

So far we’ve looked primarily at cash payments. Now let’s talk about transactions over interbank payment systems such as TARGET, Fedwire, CHAPS and of course SWIFT. Interbank payments are several orders of magnitude larger than cash transactions: the average SWIFT payment is the equivalent of EUR 400,000 while the average Fedwire payment is even larger at USD 1,200,000. Interestingly, however, their size follows the same type of statistical distribution as cash payments, namely the Log-normal distribution. The obvious question is: why? What process would generate this apparently pervasive distribution of payment size? The honest answer is…we don’t know. But I bet you a dollar it would be fun to find out.

Download chapter 10, How big is that payment?, here.

3 September 2012

Back in chapter 5 I asked where you spend your money? Is it close to home, further away, abroad? We found that money itself does not travel very far. But what about transaction patterns in general? In today’s globalised economy surely money travels between countries much more so than within countries? If the world were flat transactions patterns would be global. In such a world the majority of transactions would be cross-border. The reality, however, is very different. At most 5% of all payments in the world are cross-border, the rest are domestic. Clearly transactions patterns are heavily domestically biased. We really do prefer to stay close to home.

Download chapter 9, The payment world isn’t flat, here.

27 August 2012

We’re all the same, but everyone is different. While all countries are adopting electronic instruments, there are significant differences in the use of payment instruments. BRIC countries like Brazil and Russia use cash for more than 90% of all transactions; while developed countries like Japan and Italy for more than 85%; and Germany and Switzerland for 70-75%. Most of the other developed countries use cash for only 55-60% of their transactions. Non-cash payment instruments across the G-10 countries show three broad categories: cash-countries like Italy and Japan with low usage of non-cash instruments, the four check countries mentioned in chapter 7 (Canada, France, the UK and the US), and “ACH-countries” that rely on transfer payments and direct debits (including many Central and Northern European countries). Much research has been done into the causes of these differences. For example it has been argued that high cash usage may be related to high taxes and low crime rates. A better explanation could be that payment mechanisms are subject to network effects: the more people are using a certain instrument, the more valuable the instrument becomes to all users. Usage patterns differ by country and these differences are persistent: once an instrument has critical mass in a country, why would it change to a standard from another country, especially since cross-border transactions are such a low fraction of total?

Download chapter 8, Sprechen Sie cash?, here.

20 August 2012

In Canada, France, the UK and the US the use of checks is in constant decline, although still used for a significant number of payments. In Germany and Belgium checks continued to be used at low levels, whereas in the Netherlands checks were actively phased out altogether in 2001. It is, however, difficult to completely retire a payment instrument as the UK found in 2011 when they attempted to withdraw the check altogether. They were met with fierce consumer and political resistance and were forced to scrap their plans. Checks can be compared to the telex as an intermediate technology; better than what they replaced (phone / mail / cash), but eventually driven out by more efficient electronic networks. The telex gained adoption in the 1960s, and continued to grow through the early 80s. With the rise of electronic networks like SITA (airline industry) and SWIFT (banks), the number of telex subscribers began to decline as of 1987. In the case of SWIFT, it wasn’t until the network gained critical mass before the banks began to decommission the telex. What will it take for checks to be decommissioned?

Download chapter 7, Rumors of the death of checks are greatly exaggerated, here.

13 August 2012

So far we’ve looked at cash. As with any aspect of life, there is always competition. For cash competition comes in many forms such as checks, credit / debit cards, ACH transfers, etc. The use of payment instruments has undeniably changed over the past 20 years, and in chapter 6 we look at the growth of electronic instruments. Today checks are disappearing (and have virtually disappeared in some countries) and cards are used for a significant portion of purchases. Debit card transactions in G10 countries has a fitted ‘S-curve’, with a steepness parameter of a=0.28. Fitting a curve to debit card growth in BRIC countries yields a remarkably similar steepness parameter of a=0.29. Growth in BRIC countries appears to follow almost exactly the same path as it did in G-10 countries some 13 years earlier. However, cash is still king, at least in terms of the number of transactions (although since cash transactions tend to be relatively small, their share in the overall value is lower). In the Netherlands for example, per capita cash transactions are more than three times the number of debit card transactions. On the other hand, unless the pace of POS-debit adoption increases dramatically, it will take another 20 years before it surpasses cash as the dominant medium at the Point of Sale.

Download chapter 6, Cash or Card?, here.

6 August 2012

Where do you spend your money? Is it close to home, further away, abroad? In this chapter we literally follow the money. Less than 5% of all non-cash transactions are cross-border. It appears that when travelling abroad, consumers tend to use cash more frequently than at home. Typically, however, it seems that money itself does not travel very far. When the Euro was first introduced it was expected that over half the coins in Germany would be ‘foreign’ in six years. The reality is that as of 2008 75% of EUR1 coins in Germany were of German origin. Denomination rears its head again, as we find that EUR1 and EUR2 coins spread about twice as fast as 5 and 10 cent coins, and almost three times as fast as 1 and 2 cent coins. A US based project called Where’s George supports the view that money does not travel far. When tracking individual bank notes it seems that more than 50% of notes travel less than 10 km between reporting points. Money, like humans, it appears, prefer to stay close to home.

Download chapter 5, Where’s George?, here.

23 July 2012

In this chapter we ask a simple question; How often does a dollar bill change hands? This quantity, known as the velocity of money, is relevant because it influences inflation: higher velocity of money has the same effect as an increase in the quantity of money; if money works harder, you need less of it. The Federal Reserve estimates that physical currency turns over 55 times per year, i.e. about once a week. The denomination of cash, however, plays a role here with $1 and $5 notes changing hands much more frequently than higher denomination notes. Referring back to chapter 3, this is not the case for the underground economy, where money changes hands much less frequently.

Download chapter 4, How fast is that buck?, here.

17 July 2012

In Chapter 2 we looked at the optimal set of coins and notes in your wallet. We also found that the most frequent payment size is close to $2. You would therefore expect to see more low denomination notes in circulation. Expectations, however, often differ from reality. 75% of US currency by value is in $100 notes and a third of Euro currency is in EUR500 notes. The average consumer holds about 50-100 in cash in their wallet. And yet there is some $3,000 in circulation for every American and EUR2,450 for every euro zone inhabitant. Even if we account for cash held by businesses (about half of what consumers are holding) there is a huge gap, with most of the missing currency in the higher denominations. In chapter 3 we look at where all this cash is. The answers may surprise you.

Download chapter 3, What Happened to all the $100 bills?, here.

18 June 2012

In any given currency one question always arises: What is the optimal set of coins and notes? The denominations should allow for paying all varieties of amounts in a convenient way. As we saw in chapter 1 of my blog, cash payments span multiple orders of magnitude: from 0.01 cent to hundreds of dollars. So as a central banker, what denominations should you select? In chapter 2 we look at how this problem has been solved…over and over again going back to the Romans.

Download chapter 2, As Phony as a $3 Bill, here.

21 May 2012

Payments are part of everyday life as well as a crucial element of the financial fabric of society. Over the next three months or so I will post chapters of my book, The Statistics of Payments, which focuses on the statistical aspects of payments in two different ways. It looks at payment statistics: the number and size of transactions as well as the type of instruments we use. But it also applies tools from mathematical branch known as statistics to these figures: frequency distributions, growth curves and relationships between variables. The focus of this work is on patterns and trends in the data, taking a view across countries and payment industries. This area can be thought of as a middle layer between raw data and economic analysis of causes and effects in payments. The aim is to provide a better basis for deeper analysis into underlying drivers, but also to point out gaps in the data and suggest interesting areas for further analysis. We will begin by looking at the most basic of payment instruments: cash; by far the most common payment instrument.

Download chapter 1, The Size of Cash Payments, here.