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It’s probably hard moving his family to England from Canada to go work at the Bank of England, but the world is better for it.

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Since I have been unable to find a simple mathematical model of monetary disequilibrium, I’ve been interested in putting on together. Mathematical models help people narrow down exactly where disagreements lie and make help make sure that their thinking isn’t confused. Since there’s a lot of disagreement and confusion in macroeconomics, I think simple mathematical models should be especially helpful here.

The model I’ve built consists of a large number of identical agents (I believe this is called a “representative agent” model) in an economy with two goods, backrubs and money. You can’t consume your own backrubs, so they have to be traded in a market, but it still makes sense to have a market for them. In this model, money provides utility by fascilitating trade, the more money agents have relative to the amount they’re buying the more utility they get. The utility of money can vary over time. I’ve described the model more in depth in my write up.

Most macro models I’ve seen start at too high a level, taking aggregate demand/supply, interest rates, etc. as basic concepts instead of  utility functions and optimization. To be as clear as possible, I’ve tried to the model start from first principles as much as possible.

If you find an error or want to make a technical or non-technical suggestion, please let me know. Though the model is fairly simple (it uses only simple calculus), I haven’t done much economic modeling before, so I wouldn’t be very surprised to find errors.

I’ve written up the model here (LaTeX source). I also have an excel simulation of the model which I’m working on. I think it’s working right, but I haven’t checked it thoroughly yet (the draft is here). I’ll probably update these a bit in the future.


I want to make the case that thinking of money as a product specifically designed to be used as money and produced by a producer is often a useful perspective, and that this perspective remains useful for government created money. From this perspective, the Federal Reserve (a branch of the Federal government) is the producer of US dollars and the Chinese government is the producer of the yuán. This perspective grew out of my ongoing debate with Silas.

It is not difficult to imagine money which is not produced by anyone. An economy that uses pure gold in no particular shape uses money which is not anyone’s product. There might be gold miners, but they do not produce gold for use as money necessarily, and it could be the case that gold is simply found on the ground occasionally. It is also easy to see the drawbacks of such a money. If gold is in nonstandard lumps it must be weighed and purity tested for each transaction. It also means that people must keep a real resource that might otherwise be used for some productive purpose, so it may mean gold is not used in the optimal manner.

One can ameliorate some of these problems by using a similar but separate product specifically designed to be used as money. A sedan is serviceable for transporting lumber, but a product specifically designed for the task, such as a truck, is much better. Perhaps some bank or government will start minting standard weight and purity gold coins specifically to be used as money for a fee, and people will come to prefer using these coins to gold lumps, perhaps trading at a premium to gold lumps. Now these coins have become different product from gold lumps. The bank takes gold lumps and produces gold coins that have extra properties. These coins can meaningfully said to be the product of that bank or government and not the product of any other bank or government even if competitors produce very similar coins.

If such coins are to succeed it is important for it to bear the bank or government’s name or be otherwise branded. If the coins are not branded or brands are not respected, then it is easy for counterfeiters to ruin the product by producing similar but lower purity coins. However, it is important to distinguish between counterfeiting and merely competing products. A rival bank or government who mints their own coins with a different brand has produced a separate product, much as Gucci bags are not counterfeits of Chanel bags even if they look similar. If a competitor with a different brand produces lower quality coins, they will just ruin their product no one else’s.

This perspective applies very well to government monies. All government monies that I have seen bear a brand of that government (US dollars say “Federal reserve note”), and other people are not allowed to produce money with that brand. Some countries, including the US allow competitors, and some countries do not (link). Most central banks, including the Federal Reserve, turn a profit from their activities.

Most methods of improving a non-product money will involve making money into a product, for the same reason that most methods of improving wild tomatoes as a food source involve making tomatoes into a product. It is almost certainly optimal for most money to be product money.

One implication of this view is that it is meaningful to talk about the optimal level of money production by a bank or government, for the same reasons it is meaningful to talk about the optimal level of bread production by bread producers, there will be some level of production that maximizes welfare (and/or producer profits depending on your optimization criteria).

Another implication of this view is that government produced money is not necessarily special. It is possible that it is special because private producers can’t commit to appropriate production or because money production has some externality that private producers do not take into account, but this is something to be demonstrated rather than true a priori.


This is the first part of a planned introduction to monetary economics. I imagine it will develop slowly, but hopefully I will stick with it. I plan to first post sections here and then revise them and place them into a single document. Please leave a comment if you have a comment or criticism.

Monies have two major uses which distinguish them from all other goods:

  • Unit of Account – Prices are quoted in terms of money rather than other goods. For example, the price of a gallon of milk will be quoted as $1.59/gallon rather than .1 music lessons/gallon.
  • Medium of exchange – When people trade, they trade goods for money and then trade money for other goods. I usually cannot trade music lessons for groceries at the grocery store, but I can trade money for groceries at the grocery store.

These two uses are distinct and separable, but come together so often that we have a name for goods that have both uses. A good that is both a Unit of Account and a Medium of Exchange is called a Money.

A good can be a Medium of Exchange but not a Unit of Account. Postage stamps (not forever stamps) are a good example; you need stamps to give stamps to the post office to mail a letter, but the price is given in terms of money (you need 43 cents worth of stamps).

For another example, consider an economy where wool is very common and used as the Medium of Exchange. However wool is difficult to quantify, it has a mass which is nontrivial to weigh in large quantities but can be eyeballed effectively by experienced wool traders and a quality which is difficult to quantity but can also be discerned by wool traders. Since wool is difficult to quantify prices are not generally quoted but negotiated on the spot, so wool does not serve as a Unit of Account (there is none).

A good can also be a Unit of Account but not a Medium of Exchange. If prices in some market are quoted in terms of a good M (for example .1 music lessons/gallon) but with the understanding that the exchange will be conducted with gold (you will exchange .1 music lessons worth of gold (looking at other prices) for a gallon of milk) then M is a Unit of Account in that market but not a Medium of Exchange.

Properties of Units of Account

Units of Account require some properties to be workable as Units of Account. These properties can play an important role in the economics of money, but not necessarily unique to Units of Account. These are some but there are probably others as well:

  • Quantifiable – Units of Account must be quantifiable in some way in order to communicate prices. Many goods besides goods used as Units of Account are quantifiable.
  • Translatable – Units of Account must be able to be translated into meaningful terms of trade for an actual transaction. The preserved body of chairman Mao does not work well as a Unit of Account because it is difficult to translate “.1 bodies of Mao” into a meaningful quantity of any other goods.

Properties of Mediums of Exchange

Mediums of Exchange require some properties to be workable as Mediums of Exchange. These properties can play an important role in the economics of money, but not necessarily unique to Mediums of Exchange. These are some but there are probably others as well:

  • Store of Value – Since people hold a Medium of Exchange in order use them for future purchases, they must be worth something in the future so they must be able to effectively move resources through time. If you make $20 babysitting today, you can either spend it and consume  today, or you can spend it next week and consume then. No one will use a good as a medium of exchange if it does not store value to some degree. Mediums of Exchange are not special as a store of value; many other goods are also stores of value over time. Anything you would call an ‘asset’ is a store of value. All financial assets are stores of value, stocks, bonds options etc.. Assets vary in how they store value, some assets rise in value, some assets decline in value. Mediums of Exchange are also not necessarily special in how well it stores value over time; it can rise in value (deflation) or drop in value (inflation), it may even pay interest, like financial assets.
  • Transferable – If a good is not transferable to other agents, it cannot be used in exchange, so it cannot be a Medium of Exchange. Education is a Store of Value, but not transferable, so it can’t be used as a Medium of Exchange. Since there is a lower limit on transfer costs (zero) and many goods are near this limit, differences along this dimension are not usually important.
  • Measurable – The important qualities of a good (including quantity) must be measurable (not necessarily quantifiable) to be used as a Medium of Exchange. Since there is a lower limit on measurement errors and costs (zero) and many goods are near this limit, differences along this dimension are not usually important. Lots of other goods are measurable; water is measurable (gallons); cupcakes are measurable (mass, deliciousness (which may not be quantifiable, but is measurable)).

In the sections above, the only highlighted property is Store of Value because this is the one that can be significantly different across different monies and across time. It plays an important role in practical monetary economics, but the other properties do not.

Different monies

In monetary economics we frequently talk about “money” as if  there were only one kind of money because we are usually focusing on one particular money. In reality there are many kinds of money; there are different currencies, and goods like bus tokens. Bus tokens are goods that are used in the same way as money is: bus ride prices are often quoted in terms of bus tokens (though not exclusively) and the bus will trade you bus tokens for a bus ride. Monetary economists would regard bus tokens as money. The difference between these different kinds of monies is the set of markets where where they are used as a unit of account and a medium of exchange. The set of markets that accept US dollars is much larger than the set of markets that use the bus tokens of a given bus system. Most US stores do not accept bus tokens, but they do accept US dollars. Likewise, most US stores do not quote prices in terms of bus tokens, but they do quote them in terms of US dollars. One can think of bus tokens as “bus money” and US dollars as “US money” and Euros as “Europe money”. The economics of money still applies to goods like bus tokens in the set of markets where they are used as money.


A while back, Nick Rowe had a post about the option value of cash. Rowe asserts that cash gives a real option to do anything. At first, I didn’t see a problem with this, but as part of my ongoing debate with Silas Barta, I’ve thought a bit more about this. I think Rowe’s point is technically correct, but misleading because he neglects to mention that all reasonably liquid stores of value give this option value. Reasonably liquid stores of value, primarily financial assets, can give you the option to purchase whatever you like later on. Now cash is more liquid than any other asset, so on the time scale of hours or days only cash gives you the option value you want, but on reasonable time scales (enough time for your brokerage firm to wire you the money) many financial assets will do.

It can also be misleading for another reason; it can be tempting to think that it’s cash itself that creates that option value, that this option free in the sense that it is available regardless of the state of the world. However, money is just a kind of asset. If the option of saving in terms of money sends false signals about the profitability of actual short run saving (in the form of trading promises or of doing actual real investment), this can cause problems. In the usual case, where cash pays 0% interest and market rates for short run saving is positive, say 2%, this leads people to inefficiently avoid holding money. In the case where cash pays 0% interest and market rates for short run savings are negative, say -2%, this causes the opposite problem people try to hold too much cash.

If the option of waiting a short period of time is very valuable, so everyone wants to do it, this may cause short run rates to be very negative and the 0% cash option to be very distortionary.


Google has apparently been testing unmanned cars with some success (link).

I suspect biggest impact of unmanned cars would be taxi services replacing private ownership of  cars. I would guess that the biggest differential cost between private car ownership and taxi services is the need for a non-passenger driver; human labor is expensive. If you eliminate this cost for taxis, it would become much more practical to call up a car and have it come pick you up when you need to go somewhere instead of keeping your own car around. Unmanned taxis would also eliminate a big fraction of the need for street parking, since cars could be kept in central parking garages. This would increase space efficiency in medium sized cities quite a lot.


There’s central bank independence and then there’s central bank discretion. Contra some bloggers I do think central bank independence is a good thing. However, I think part of what the current recession has shown is that central bank *discretion* is bad. Sumner, Krugman ect. agree that a lot of pain could have been avoided if the central bank had tried harder to hit their historically implicit target (~2% inflation). The bank should be relatively free from interference from other parts of the government, but the actual policy it follows should be much more constrained.

I propose the following: congress passes a law that requires the central bank to meet a target, and if it fails to meet that target central bank officials would be summoned before congress to explain themselves. However, the actual target would be set by the central bank. The target would be set by vote say every 10 years by the reserve committee (and the vote would be mandatory, to reduce status quo bias, though perhaps allowing the vote to be postponed for less than say 2 years by vote) with the possibility of an emergency change if a super-majority of the committee desires it. The target itself could be anything, a monetary aggregate path, an inflation target, a price level path target, and NGDP path target etc., whatever rule the committee thinks does the best job of promoting a good economy, other than “doing whatever the committee members want”.

The other powers of the Fed could be left intact or not, but this would ensure that they are exercised in a way consistent with the Fed’s target.

The benefits of such a policy would be twofold. First, this policy is more consistent with the Rule Of Law than current policy; it reduces the uncertainty about what macroeconomic policy will be, allowing people and businesses to plan better. Second, it will force the central bank to take a much more theoretical approach to monetary policy than it has without requiring congress to be particularly informed on the subject. Hopefully this will avoid the apparent tendency to throw everything known about macroeconomics out the window during a serious crisis, when it is most valuable. It does both these things while still allowing for the possibility that if some problem with the current rule becomes widely appreciated, the central bank can take quick action to work around it.


Silas poses the following question in the comments (link)

Let’s say a few scientists have announced that they’ve discovered an effectively unlimited/costless energy source (like the cold fusion situation). A few of their friends have gotten it to “work” too, in that it appears they’re really on to something — perhaps energy problems are about to be solved forever.

On the other hand, most claims like these turn out to be fraudulent or mistaken. And even if they’re doing everything properly, it could be that they’re not tabulating the energy flows correctly (i.e. not realizing that something critical is consumed in the process, meaning it requires more resources and energy input to keep it going indefinitely, which they hadn’t accounted for on deeming it costless). But still, there is much evidence for and against, and the truth or falsity of the claims really matters.

In this situation, it would be very wise not to commit resources to narrow uses, as the eventual unveiling of the truth about the energy claim will obviate many kinds of economic activities. If it turns out to be true, huge sectors of the economy become worthless: the drilling equipment for oil, energy prospecting equipment, coal mines, natural gas pipelines, equipment for maintaining these pipelines, transportation networks that exist because all of this, and, of course, all of the specialized workers and knowledge sets so related. Investing *more* in these will mean you’re “caught with your pants down” when the claims are verified to be true.

On the other hand, investment in the *opposite* direction will be painfully obviated if the claims turn out to be false. So all investments and most purchases carry an additional risk-cost, and so holding off on doing so is a rational response to the economic realities involving high uncertainty about the usefulness of particular goods. In this situation, if you got people to spend and invest for the sake of propping up spending and investing, you’re causing a huge waste of resources: since people don’t yet know which course of action is right, many more goods than otherwise are going to be committed to wasteful production structures.

First let me say that I haven’t come up with any satisfying answers to Silas’ question. I don’t know how to think about it properly, so I will be more humble.

There are a few reasons why the idea that a general reduction in spending due to increased money demand is a desirable signal:

  • A strong signal to avoid investment in affected sectors is already present, people who invest before the uncertainty is resolved will make worse investment decisions than people who don’t.
  • There are lots of reasons why money demand can increase and many of them do not have to do much with uncertainty like this. For example, some new financial technology might require lots of transactions and people need money in order to conduct the transactions.
  • A general spending reduction sends a very blunt signal. A shortage of money is likely to cause people to reduce their spending on many different margins, most of which will not be relevant to the sector. For example in the example you gave, the uncertainty is around one sector (energy) which may have little effect on some other sectors, so it likely makes sense to shift resources that cannot be transferred into the future into those sectors (say entertainment and housing)
  • The signal is fleeting, as prices adjust, the signal will go away even though the need for transfering resources into the future may continue. In a world with no sticky prices this signal would not exist; nominal spending would fall, but real spending would be stable.

I think one of the key issues is the time frame over which this plays out. I am not sure what kind of time frame Silas had in mind: ~2 months or ~2 years.

Over a time period of ~2 months, I am especially unsure how to think about the issue, but keep in mind that most proposals for nominal income targets focus on income expectations ~2 years out, and would only try to stabilize short term expectations to the extent that they affected longer term expectations (and only by trying to stabilize longer term expectations). I am unsure about the desirability of stabilizing income over  short time scales, but in any case, I don’t think it is possible.

Over a time period of ~2 years, I think I understand the issue a little bit better. Over the course of 2 years the appropriate response for the economy is to shift production away from investment in affected sectors and toward resources that can be stored until the uncertainty is resolved investment in unaffected sectors, consumption and leisure. It is important to note that there are many kinds of resources that you cannot transfer into the future easily, for example lots of kinds of labor. The proper response in these cases, is generally to do something else with them rather than do nothing with them. Prices are probably mostly flexible over this time period, so allowing nominal income to rise or fall will not affect resource allocation a lot, but will affect the dynamics of the transition.


Up until a few days ago, I had very little interest in macroeconomics, primarily because I had the impression that there were not very many well established, useful truths in macroeconomics. Then I read some of Scott Sumner’s writings which convinced me I was wrong.

Sumner’s thesis is that macroeconomists have a useful and well established framework for understanding the aggregate economy, and that the current downturn has been so bad only because most economists, including those at the Fed, have misunderstood or forgotten how to apply the framework properly. Reading his writings over the last few days has been fascinating. Sumner argues so forcefully and without apparent ideological motivation that I am compelled to investigate this framework.

So, thanks Sumner! For opening up a whole new branch of economics to me.

One of Sumner’s novel (to me) suggestions is to target Nominal GDP (NGDP) instead of the price level or inflation. Since I don’t know much about macro-economics I don’t have much to say about the proposal. I do have one way to frame the choice between price level targeting and NGDP targeting that I haven’t heard Sumner use (perhaps for good reason): targeting a price level path makes money stable with respect to the absolute quantities of goods it can be traded for; targeting NGDP makes money stable with respect to the fraction of total output it can be traded for. The latter might be desirable because it more nearly holds constant everyone’s ability to fulfill their agreements.


This sounds like a quality idea:

So my new idea is this: Require that water monopolies (private and public) purchase insurance against outages, shortages, toxic spills, etc. Such a requirement would produce two good results:

1. Current practices would immediately improve with oversight — solving the free-rider/coordination problem (in principal-agent jargon) of monitoring utilities.
2. Insurance companies would pay for future problems, which reduces the problem with ex-post rate increases to fix them.

This approach would be difficult to apply when the types of events you want to prevents are unknown unknowns, so that it is hard to write regulation for it.