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The Princeton Economic History of the Western World #12
The Big Problem of Small Change
The Big Problem of Small Change offers the first credible and analytically sound explanation of how a problem that dogged monetary authorities for hundreds of years was finally solved. Two leading economists, Thomas Sargent and François Velde, examine the evolution of Western European economies through the lens of one of the classic problems of monetary history--the recurring scarcity and depreciation of small change. Through penetrating and clearly worded analysis, they tell the story of how monetary technologies, doctrines, and practices evolved from 1300 to 1850; of how the "standard formula" was devised to address an age-old dilemma without causing inflation.
One big problem had long plagued commodity money (that is, money literally worth its weight in gold): governments were hard-pressed to provide a steady supply of small change because of its high costs of production. The ensuing shortages hampered trade and, paradoxically, resulted in inflation and depreciation of small change. After centuries of technological progress that limited counterfeiting, in the nineteenth century governments replaced the small change in use until then with fiat money (money not literally equal to the value claimed for it)--ensuring a secure flow of small change. But this was not all. By solving this problem, suggest Sargent and Velde, modern European states laid the intellectual and practical basis for the diverse forms of money that make the world go round today.
This keenly argued, richly imaginative, and attractively illustrated study presents a comprehensive history and theory of small change. The authors skillfully convey the intuition that underlies their rigorous analysis. All those intrigued by monetary history will recognize this book for the standard that it is.
One big problem had long plagued commodity money (that is, money literally worth its weight in gold): governments were hard-pressed to provide a steady supply of small change because of its high costs of production. The ensuing shortages hampered trade and, paradoxically, resulted in inflation and depreciation of small change. After centuries of technological progress that limited counterfeiting, in the nineteenth century governments replaced the small change in use until then with fiat money (money not literally equal to the value claimed for it)--ensuring a secure flow of small change. But this was not all. By solving this problem, suggest Sargent and Velde, modern European states laid the intellectual and practical basis for the diverse forms of money that make the world go round today.
This keenly argued, richly imaginative, and attractively illustrated study presents a comprehensive history and theory of small change. The authors skillfully convey the intuition that underlies their rigorous analysis. All those intrigued by monetary history will recognize this book for the standard that it is.
432 pages, Hardcover
First published January 7, 2002
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July 23, 2021
The year 402 A.D. is important in the history of Roman Britain because it's the year that the size of Roman coin discoveries in Britain begins to dwindle. 401-402 were also the years that Italy was first invaded by the Gothic army of Alaric. The minting of coins in London had already ended in 388, after the execution of the Britannic-army-backed usurper Magnus Maximus by Theodosius I, and all new full-bodied coins must have arrived from the continent. What we see in the archeological record after 402 is the clipping and restamping of old coins to circulate a larger quantity of them. Without sufficient coin, you can't pay troops, you can't buy large amounts of foreign commodities to arm or feed your people, and typically there is a correlated period of economic and political distress. In Britain, specifically, we see a shrinking of its defensive forces, the increased use of Saxon mercenaries in exchange for settlement (akin to Foederati), and the revolt of its elite against Roman imperial rule in 409 and the subsequent chaos that beset the island.
The story of the final decades of Roman rule in Britain are from Marc Morris' The Anglo-Saxons , not from Sargent's and Velde's The Problem of Small Change, but it serves as an excellent example of how shortages of small change are associated with periods of economic and political distress. In the case of Britain, the coin shortage seems to have exogenous causes as a result of the cessation of Roman imperial and commercial patronage. But, even local attempts to fix the shortage by clipping and restamping fell short. Sargent and Velde show that the problem of supplying sufficient small denomination coins plagued states until the perfect confluence of technology and human capital allowed governments to adopt the "standard formula."
The standard formula in its most basic essence is a large commodity-money denomination coin, with all small change produces in the form tokens without intrinsic value. These tokens are fractional and convertible through an exchange rate with the large denomination coin. The quintessential example of the standard formula is the gold standard. It took Western Europe many millennia to reach this monetary system and The Problem of Small Change is an attempt to explain historically how different aspects of the standard formula were discovered through trial-and-error.
The Problem of Small Change is closest to a textbook in its organization and how it reads. Parts of it are highly technical and mathematical, specifically chapters dealing with the central model of the standard formula. The rest of the book is a superficial chronology of historical events and how they relate back to the model. The first part of the history is a short coverage of technological developments that allowed for more accurate, more difficult to counterfeit, small denomination coins. The second part is a history of different monetary policies, their failures and gaps with respect to the standard formula, and how they contributed to society's learnings. The authors cover a period roughly between the reintroduction of coinage by Charlemagne and the adoption of the gold standard by Western Europe and the United States.
I agree with Leland Yeager that the history is disjointed, oftentimes poorly written and superficial, and sometimes more confusing than helpful. In fact, the book was somewhat difficult to get through at first because you struggle to understand what exactly the authors are grasping at. Admittedly, and in all fairness, as you work through it everything starts to come together. In this sense, the book is a lot like a textbook in that individual pieces of the model are separated and studied, and so its hard to get global context until you experience the trajectory the authors are taking you on.
The book would have been far more compelling to a wider audience had the history had a little bit more depth to it. There is very little context on monetary history in each example outside the very strict realm of small change, which is normal for a textbook with a hyper-focus on the narrow argument the authors are making. The problem is that you don't get a very strong understanding of policy because there's no inclusion of factors like war, financing, and taxes, all things that would affect monetary policy and the supply of small change — especially because the earlier in history you move, the more important government is in the distribution of small coin to pay for wages and war commodities. There is also very little tangible, concrete context on how problems of small change affected people and states. This is part of the reason early history chapters are harder to follow; you don't really get a strong understanding of the problem and why it came about, rather you get a very superficial chronology of events that are then tied to the authors' model as a matter of fact. I am not one to take things on faith or on the authority of the authors, even a Nobel-winning one. The book would have profited from better analysis.
Taking the book's weakness in its historical exposition in mind, it nevertheless gives an interesting story that helps make sense of the bigger picture — I just think it will be up to someone else to take on that project.
What is interesting about the story, apart from the model that gives us a basis to better understand some of the economic problems that pre-modern states suffered from, is how our understanding of money shifted over time. Until recently, money in Western Europe has always come in the form of commodity money — gold, silver, copper, bronze, et cetera. For a long time, the value of money was ascribed to the value of the commodity. It was only after a period of time when jurists and thinkers started to realize that there was value to money beyond the commodity — i.e. value of money qua money (as a medium of exchange), or the value of money in terms of the goods you can buy. This disassociation of monetary value from the commodity its made of is important because it's what allows for small change to be tokens with no intrinsic value, but still have value as a medium of exchange.
Experiments with token money began early. As banking became more sophisticated, especially in late Medieval and Renaissance Italy, you begin to see commodity coins replaced by IOUs. You also see the introduction of token coins in extreme situations, like sieges, where minting was not an option so leaders had to pay mercenaries and soldiers in IOUs redeemable after the siege. These situations, as well as legal problems resulting from fluctuations in the value of different coins with respect to themselves and each other, force jurists and governments to re-think the nature of money in order to better arbitrate contract disputes. Thus, the focus of these early chapters is the distinction between the value of the commodity in money and the value of the money itself.
The book then takes you through Castille's experimentation with token fiat money without convertibility, over-issue, and the gradual discovery of the quantity theory of money. You go through similar experiments in Italy, how these affected local price levels and exchange rates between different coins, then through revolutionary France, until you get to England, the constant problem of the lack of small change, and how England slowly came to resolving the issue by adopting the gold standard.
There's a couple of analytical conclusions that the authors come to that are interesting:
1. Why was there a persistent problem of small coinage in sufficient quantities? Partly because the costs of minting are proportionally higher on smaller value coins. The rate of seignorage will be proportionally higher the lesser value the coin has, therefore small coinage is inherently under-valued. Reducing the cost of coinage, including the cost of counterfeits, was crucial to resolving the problem.
2. Early on, the problem of small change also had to do with fluctuations in the value of different commodities. As the price of goods in different commodities changed, these affected the margins at where each metal was worth either minting or melting. Let's say the value of goods in terms of gold increases, incentivizing the minting of gold and the melting of silver. Gold can only be used for exchange above a certain value threshold, so as the supply of silver coins disappears their availability for small transactions also disappears. In real life, these relative values fluctuated in different directions, and these fluctuations would create "structural" shortages as people had to respond to fundamentals by taking their coins or commodities to the mind for melting or minting.
3. Assume there is a positive income shock; that is, there is a rightward supply shock that makes everyone better off in terms of goods. The amount of small coinage at the same price level will need to increase for efficiency in exchange, otherwise some exchanges will not take place. The common counter-argument here is that the value of silver with respect to goods will change to make any given amount of silver coinage the right amount. See point (2). To increase the stock of small coin, governments and mints clip and restamp by decreasing the intrinsic content of commodity. The result is more coins trading at tale, thus inflation. This is an interesting case for income-shock inflation, i.e. the supply of money chasing real growth.
The implication is that the problem of small coinage did not have to do with purposeful government mismanagement. Governments were interested in supplying an optimal amount of small coinage. I think some people would disagree, but then again it was government that would benefit from an optimal amount of small coinage, especially the earlier in history you move. There is also an element of chicken or egg, because a lot of the clipping and restamping would have been done to provide governments with more small coins with which to pay wages and buy commodities. The alternative would have been to produce new full-bodied coins, but there are market forces (points 1-3 above) that precluded that.
This is where I think more historical context would have improved the narrative. Governments had to struggle with financing wars, building programs, and other expenses. They ran up against constraints on financing. Thus, a lot of the monetary experiments, like clipping, restamping, siege money, token money, etc., were incentivized by the need to be financed. They were constrained in their ability to do so by market forces. In a way, The Problem of Small Change is how governments struggled with this reality and slowly stumbled their way to market-friendlier solutions like the gold standard. This process was a complex one with multiple and individual factors, like technology and human capital. This is an interesting story, I just don't think this book really tells it.
To some extent, the book is too focused on the model. One pet peeve I have about the model is that throughout the book the authors give more concise descriptions of the Standard Formula provided by past economists. These are a few sentences long. We get a rational expectations model that takes chapters and a lot of math to understand. The model does give us insight in the sense of being able to visualize movements between variables and, from there, analyze cause and effect. This is important, otherwise understanding above points 1-3 would have been more difficult. However, the focus of the historical factors is too much on the movements between variables and too little on cause and effect. And what discussion there is on cause and effect is often marred by superficial analysis and a selective telling of the history (i.e. omitted variable bias).
I, therefore, come away from the book with mixed feelings. This is a good book with important learnings, but there is something lacking. Part of this may have to do with the fact that the mathematical model was already available: https://www.jstor.org/stable/2601227"https://www.jstor.org/stable/2601227. The purpose of the book was to expand the argument. I think the expansion was not as good as it could have been, although if you put enough work into it and connect the dots on your own, you'll likely end your experience having learned quite a bit.
The story of the final decades of Roman rule in Britain are from Marc Morris' The Anglo-Saxons , not from Sargent's and Velde's The Problem of Small Change, but it serves as an excellent example of how shortages of small change are associated with periods of economic and political distress. In the case of Britain, the coin shortage seems to have exogenous causes as a result of the cessation of Roman imperial and commercial patronage. But, even local attempts to fix the shortage by clipping and restamping fell short. Sargent and Velde show that the problem of supplying sufficient small denomination coins plagued states until the perfect confluence of technology and human capital allowed governments to adopt the "standard formula."
The standard formula in its most basic essence is a large commodity-money denomination coin, with all small change produces in the form tokens without intrinsic value. These tokens are fractional and convertible through an exchange rate with the large denomination coin. The quintessential example of the standard formula is the gold standard. It took Western Europe many millennia to reach this monetary system and The Problem of Small Change is an attempt to explain historically how different aspects of the standard formula were discovered through trial-and-error.
The Problem of Small Change is closest to a textbook in its organization and how it reads. Parts of it are highly technical and mathematical, specifically chapters dealing with the central model of the standard formula. The rest of the book is a superficial chronology of historical events and how they relate back to the model. The first part of the history is a short coverage of technological developments that allowed for more accurate, more difficult to counterfeit, small denomination coins. The second part is a history of different monetary policies, their failures and gaps with respect to the standard formula, and how they contributed to society's learnings. The authors cover a period roughly between the reintroduction of coinage by Charlemagne and the adoption of the gold standard by Western Europe and the United States.
I agree with Leland Yeager that the history is disjointed, oftentimes poorly written and superficial, and sometimes more confusing than helpful. In fact, the book was somewhat difficult to get through at first because you struggle to understand what exactly the authors are grasping at. Admittedly, and in all fairness, as you work through it everything starts to come together. In this sense, the book is a lot like a textbook in that individual pieces of the model are separated and studied, and so its hard to get global context until you experience the trajectory the authors are taking you on.
The book would have been far more compelling to a wider audience had the history had a little bit more depth to it. There is very little context on monetary history in each example outside the very strict realm of small change, which is normal for a textbook with a hyper-focus on the narrow argument the authors are making. The problem is that you don't get a very strong understanding of policy because there's no inclusion of factors like war, financing, and taxes, all things that would affect monetary policy and the supply of small change — especially because the earlier in history you move, the more important government is in the distribution of small coin to pay for wages and war commodities. There is also very little tangible, concrete context on how problems of small change affected people and states. This is part of the reason early history chapters are harder to follow; you don't really get a strong understanding of the problem and why it came about, rather you get a very superficial chronology of events that are then tied to the authors' model as a matter of fact. I am not one to take things on faith or on the authority of the authors, even a Nobel-winning one. The book would have profited from better analysis.
Taking the book's weakness in its historical exposition in mind, it nevertheless gives an interesting story that helps make sense of the bigger picture — I just think it will be up to someone else to take on that project.
What is interesting about the story, apart from the model that gives us a basis to better understand some of the economic problems that pre-modern states suffered from, is how our understanding of money shifted over time. Until recently, money in Western Europe has always come in the form of commodity money — gold, silver, copper, bronze, et cetera. For a long time, the value of money was ascribed to the value of the commodity. It was only after a period of time when jurists and thinkers started to realize that there was value to money beyond the commodity — i.e. value of money qua money (as a medium of exchange), or the value of money in terms of the goods you can buy. This disassociation of monetary value from the commodity its made of is important because it's what allows for small change to be tokens with no intrinsic value, but still have value as a medium of exchange.
Experiments with token money began early. As banking became more sophisticated, especially in late Medieval and Renaissance Italy, you begin to see commodity coins replaced by IOUs. You also see the introduction of token coins in extreme situations, like sieges, where minting was not an option so leaders had to pay mercenaries and soldiers in IOUs redeemable after the siege. These situations, as well as legal problems resulting from fluctuations in the value of different coins with respect to themselves and each other, force jurists and governments to re-think the nature of money in order to better arbitrate contract disputes. Thus, the focus of these early chapters is the distinction between the value of the commodity in money and the value of the money itself.
The book then takes you through Castille's experimentation with token fiat money without convertibility, over-issue, and the gradual discovery of the quantity theory of money. You go through similar experiments in Italy, how these affected local price levels and exchange rates between different coins, then through revolutionary France, until you get to England, the constant problem of the lack of small change, and how England slowly came to resolving the issue by adopting the gold standard.
There's a couple of analytical conclusions that the authors come to that are interesting:
1. Why was there a persistent problem of small coinage in sufficient quantities? Partly because the costs of minting are proportionally higher on smaller value coins. The rate of seignorage will be proportionally higher the lesser value the coin has, therefore small coinage is inherently under-valued. Reducing the cost of coinage, including the cost of counterfeits, was crucial to resolving the problem.
2. Early on, the problem of small change also had to do with fluctuations in the value of different commodities. As the price of goods in different commodities changed, these affected the margins at where each metal was worth either minting or melting. Let's say the value of goods in terms of gold increases, incentivizing the minting of gold and the melting of silver. Gold can only be used for exchange above a certain value threshold, so as the supply of silver coins disappears their availability for small transactions also disappears. In real life, these relative values fluctuated in different directions, and these fluctuations would create "structural" shortages as people had to respond to fundamentals by taking their coins or commodities to the mind for melting or minting.
3. Assume there is a positive income shock; that is, there is a rightward supply shock that makes everyone better off in terms of goods. The amount of small coinage at the same price level will need to increase for efficiency in exchange, otherwise some exchanges will not take place. The common counter-argument here is that the value of silver with respect to goods will change to make any given amount of silver coinage the right amount. See point (2). To increase the stock of small coin, governments and mints clip and restamp by decreasing the intrinsic content of commodity. The result is more coins trading at tale, thus inflation. This is an interesting case for income-shock inflation, i.e. the supply of money chasing real growth.
The implication is that the problem of small coinage did not have to do with purposeful government mismanagement. Governments were interested in supplying an optimal amount of small coinage. I think some people would disagree, but then again it was government that would benefit from an optimal amount of small coinage, especially the earlier in history you move. There is also an element of chicken or egg, because a lot of the clipping and restamping would have been done to provide governments with more small coins with which to pay wages and buy commodities. The alternative would have been to produce new full-bodied coins, but there are market forces (points 1-3 above) that precluded that.
This is where I think more historical context would have improved the narrative. Governments had to struggle with financing wars, building programs, and other expenses. They ran up against constraints on financing. Thus, a lot of the monetary experiments, like clipping, restamping, siege money, token money, etc., were incentivized by the need to be financed. They were constrained in their ability to do so by market forces. In a way, The Problem of Small Change is how governments struggled with this reality and slowly stumbled their way to market-friendlier solutions like the gold standard. This process was a complex one with multiple and individual factors, like technology and human capital. This is an interesting story, I just don't think this book really tells it.
To some extent, the book is too focused on the model. One pet peeve I have about the model is that throughout the book the authors give more concise descriptions of the Standard Formula provided by past economists. These are a few sentences long. We get a rational expectations model that takes chapters and a lot of math to understand. The model does give us insight in the sense of being able to visualize movements between variables and, from there, analyze cause and effect. This is important, otherwise understanding above points 1-3 would have been more difficult. However, the focus of the historical factors is too much on the movements between variables and too little on cause and effect. And what discussion there is on cause and effect is often marred by superficial analysis and a selective telling of the history (i.e. omitted variable bias).
I, therefore, come away from the book with mixed feelings. This is a good book with important learnings, but there is something lacking. Part of this may have to do with the fact that the mathematical model was already available: https://www.jstor.org/stable/2601227"https://www.jstor.org/stable/2601227. The purpose of the book was to expand the argument. I think the expansion was not as good as it could have been, although if you put enough work into it and connect the dots on your own, you'll likely end your experience having learned quite a bit.
December 10, 2015
This book opens up new vistas on the intellectual and economic history of Europe, all by paying close attention to the nature of small, rounded coins.
The "big problem of small change" was much bigger than one would expect. Originally, when there was only one coin in Western Europe, the Carolignian penny, manufactured beginning around 800, there was no problem. The old quantity theory of money applied, meaning more pennies in the economy meant higher prices, and fewer pennies, lower prices. Yet when the penny proved insufficient for larger trades, beginning in 1200 courts and counts introduced higher denomination coins, usually called "grosso" or some variation on such, which was some multiple of the small coin. Now, with two coins in the market, there was a tendency for small coins to be hoarded during shortages and (paradoxically) for the smaller coin to depreciate in value. This lead to chronic inflations, and often futile attempts to re-establish the relationship between the two coins, through forced legal tender laws. The higher minting cost of small coins per unit of silver made the shortages more severe and the inflations more devastating.
The solution to the big problem was the "standard formula," first articulated by Sir Henry Slingsby in the 1660s. Instead of counting everything in units of the small coin, countries counted from the larger coin (say, the pound or the dollar). They also made the small coin no longer worth its actual content of silver, but made it a mere "token" valued relative to the large coin at the discretion of the prince. By the 1700s, this standard formula was largely in place, thanks partially to new screw-presses and milling technology that made counterfeiting "tokens" more difficult. This represented a crucial and unappreciated step towards pure fiat money.
Sargent and Velde fill their book with algebraic equations describing the nature of their price and coin theories, but they also go into detail on the legal and intellectual underpinnings of this shift. They show how the old Roman law doctrine saw coins as mere metals, and said people could shift any prince's stamped metal for another, as long as the amount of metal was the same. But French jurist Charles Dumoulin in the 16th century said the real value of a coin was its "aestimatio," its value in exchange. This allowed a king to decide that a "franc was a franc," and allowed discretion of the king to prevail in setting coin rates. In the "Mixt Money Case" of 1604 in England, a court allowed James I to give any money any value, just as he could turn a "mean person" into an honorable one.
If one's scared of the math, there is still plenty of food for thought in this book through its economic and intellectual history. The book shows how seeming minor changes in the world of thought and mechanics have real influence on the economies and fates of nations.
The "big problem of small change" was much bigger than one would expect. Originally, when there was only one coin in Western Europe, the Carolignian penny, manufactured beginning around 800, there was no problem. The old quantity theory of money applied, meaning more pennies in the economy meant higher prices, and fewer pennies, lower prices. Yet when the penny proved insufficient for larger trades, beginning in 1200 courts and counts introduced higher denomination coins, usually called "grosso" or some variation on such, which was some multiple of the small coin. Now, with two coins in the market, there was a tendency for small coins to be hoarded during shortages and (paradoxically) for the smaller coin to depreciate in value. This lead to chronic inflations, and often futile attempts to re-establish the relationship between the two coins, through forced legal tender laws. The higher minting cost of small coins per unit of silver made the shortages more severe and the inflations more devastating.
The solution to the big problem was the "standard formula," first articulated by Sir Henry Slingsby in the 1660s. Instead of counting everything in units of the small coin, countries counted from the larger coin (say, the pound or the dollar). They also made the small coin no longer worth its actual content of silver, but made it a mere "token" valued relative to the large coin at the discretion of the prince. By the 1700s, this standard formula was largely in place, thanks partially to new screw-presses and milling technology that made counterfeiting "tokens" more difficult. This represented a crucial and unappreciated step towards pure fiat money.
Sargent and Velde fill their book with algebraic equations describing the nature of their price and coin theories, but they also go into detail on the legal and intellectual underpinnings of this shift. They show how the old Roman law doctrine saw coins as mere metals, and said people could shift any prince's stamped metal for another, as long as the amount of metal was the same. But French jurist Charles Dumoulin in the 16th century said the real value of a coin was its "aestimatio," its value in exchange. This allowed a king to decide that a "franc was a franc," and allowed discretion of the king to prevail in setting coin rates. In the "Mixt Money Case" of 1604 in England, a court allowed James I to give any money any value, just as he could turn a "mean person" into an honorable one.
If one's scared of the math, there is still plenty of food for thought in this book through its economic and intellectual history. The book shows how seeming minor changes in the world of thought and mechanics have real influence on the economies and fates of nations.
December 4, 2013
Yes, Virginia, "ducats" really existed! Although the economics math in this book was completely beyond me (who knew that three little horizontal lines mean "congruent"?), I enjoyed reading about the evolution of monetary theory from the 12th century to present day, especially stuff like "ghost money" and "siege money." Also, this is a wonderful book with which to disabuse your Tea Party uncle of the notion that returning to the gold standard is desirable or even possible.
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