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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 would find it really useful to have a simple concrete mathematical model that demonstrates monetary disequilibrium. I could use it to troubleshoot my intuitions about monetary matters, develop new and better intuitions, and better explain the logic of monetary disequilibrium better. Unfortunately, I haven’t run across such a model and it looks like my current math and modeling skills are insufficient to produce one myself.  Does anyone have a paper, book or post that presents mathematical model of monetary disequilibrium suited for at least one of these purposes?

Here’s an example of what I would expect such a model to look like:

An economy with a large number of two types of agents each producing a different good and an infinite number of periods. Both agents have the same type of utility function which has a term for how much of each good they consume in each period, how much of their production good they produce, and a term for the utility of money which is proportional to the amount they spend in each period. There should be some set of prices that characterize total equilibrium. We can investigate the effects of monetary disequilibrium by seeing how different price paths influence different agent’s utility, production and consumption over time.

Karl Smith claims

Money does not create anything. Value stored as money is value lost; lost because it represents resources not directed towards capital.

There is some truth to what he says, but this claim is false. It’s not that investing in money doesn’t actually cause an increase in capital available, it’s that it happens to invest in not very productive way.
As I’ve said before, I think it’s useful to think of central banks as private “producers of money” (who happen to have a monopoly and aren’t motivated primarily by profit). Think of the dollars as a product built and sold by the Fed. What does the Fed use to produce dollars? They use government bonds. They take them and use them to make their promise that dollars will maintain their value credible. This isn’t the only way money can be produced, other financial assets could be used, such as a basket of stocks. Because of this, investing in money is effectively the same as investing in whatever asset the central bank uses to produce its money (albeit at a worse interest rate).
Assuming the Fed approximately expands the dollar supply when demand to hold dollars goes up (and vice versa), an increase in demand to hold money means the Fed buys whatever asset they use to produce money. This causes an increase in the demand for that asset. You might not think that an increase in demand for government bonds causes good investment on the margin, but it’s also not wasted completely. How much waste depends on: 1) the government bond supply curve 2) the elasticity of demand between government bonds and other assets 3)  how good the government is at doing productive investments relative to private investment.

That said, it’s conceptually easy to make money a poor store of value: give it a large negative interest rate. This is necessary when the asset used to produce money (normally government bonds) have a low or negative interest rate in order to avoid having the central bank subsidize people’s holding of money.

Economists frequently mention the idea of an Optimal Currency Area. Krugman does it. Barry Eichengreen does it. Even monetary equilibriumist Nick Rowe does it.

As I understand it, the idea is that monetary policy helps alleviate recessions. Because different one area can be in a boom and another in a bust at the same time, it is useful to have small currency areas because then you can have more finely tuned monetary policy. This pushes the currency area that maximizes benefits (the optimal currency area) smaller. The fact that arranging trade with different currencies can be more expensive and that areas can have correlated business cycles pushes the optimal currency area bigger.

If you understand monetary economics from a monetary-equilibrium perspective, this should strike you as exceedingly odd.

First, lets make some important distinctions. Lets say a “recession” is a temporary decline in the production of market goods, without specifying it’s cause. The monetary equilibrium theorists note that an a decrease in the quantity of money relative to the demand for money can cause such a temporary decline in production and has a negative effect on welfare (explanation). Any given recession might be due to monetary disequilibrium  and/or other effects.

Monetary equilibrium theory implies that relieving monetary disequilibrium by adjusting the quantity of money to reflect changes in the demand for money is welfare enhancing because it avoids price adjustment costs as well as the costs of non-equilibrium production.

However, monetary equilibrium theory does not suggest that adjusting the quantity of money to respond to (temporary or non-temporary) changes in production for reasons other that monetary disequilibrium is welfare enhancing. If production of market goods falls because of a real productivity shock, increasing the quantity to compensate increases market good production but is welfare reducing because it adds adjustment costs and moves market good production away from it’s equilibrium level.

Thus, if Optimal Currency Areas are to make sense from a monetary disequilibrium perspective, it must be that different areas in the same currency zone can have monetary disequilibrium in the opposite directions.

The major purpose of the financial system is to move money (and other assets) from those who want them relatively less to those who want them relatively more. People who want to hold money relatively more than others borrow or sell assets and vice versa.

If the financial system is not doing this, then we already have two different currencies. Monetary policy conducted in the first area doesn’t have much of an effect on the second area and vice versa. The same bills in the first area may have a totally different price than in the second area. Making these two kinds currencies more readily distinguishable (by changing the “currency area”) would only make it harder for the whole economy to come to equilibrium.

I often see people express the idea that the production or destruction of money must necessarily cause problems for the economy because that money does not “represent new real wealth”. There are many variants of this notion, such as that “good money” must “represent” some real asset (like gold).

However, this notion is fundamentally confused.

First, notice that as method of economic reasoning “representation” not great; there is no deep economic notion of “representation”. At best it could be a heuristic, you notice that money is not connected to particular real projects and think “huh, that’s weird” and decide to investigate further.

Next, notice that financial assets in general do not derive their value from “representing” some project or another. A financial asset derives its value from another party’s credible promise that the holder of the financial asset may receive something of value at some point in the future. For example, a corporation may issue bonds to undertake a new project and these bonds will have value, but the value is not derived from the project, the value is derived from the promise the corporation gives that the bonds will be honored. Such corporate bonds would have the same value whether the corporation issued them for a new profitable project or an unprofitable project or because of a clerical error, and they would cease to have value if the corporation’s promise went away.

Financial assets are useful because they are useful to either the issuer or the holder. Bonds allow businesses to undertake projects or smooth out cash flows; stocks allow businesses to get initial capital and allow investors to store resources;  money helps lower transactions costs for people.

Finally, note that a financial asset is an asset to one party (the holder) and a liability to another party (the issuer). The subjective value of the asset to the holder may be larger or smaller than the subjective value of the liability to the issuer.

The US dollar has value because there are implicit (but credible) promises that it can be exchanged for something of value. These promises come from two sources: 1) the general public because they currently accept money as payment for other things of value 2) the Federal Reserve because they implicitly promise that they will trade dollars for something else of value in order to make sure that dollars continue to be valuable. Like other financial assets, its value has nothing to do with whether it represents real assets or not, and whether the economy would be better off with more or less of it has nothing to do with whether it “represents” real projects.

This was an attempt to address a popular confusion. I’m not totally satisfied with it, so if you have suggestions on how to improve it or know an article that does it better, let me know.

Silas Barta and I have a long ongoing debate (part 1, 2,3 part 2 actually comes before part 1) about monetary economics, 2008 recession policy and the views of mainstream macro-economists. This post summarizes the progress of the debate:

Theoretical issues

I think I’ve convinced Silas of a couple of things: I’ve clarified the mechanism by which monetary disequilibrium works. I’ve convinced Silas that the non-monetary impacts of conducting monetary policy, meaning buying and selling financial assets with newly created money, are not large. I have convinced Silas that having the Fed try to adjust the quantity of money to accommodate changes in the demand for money is not a terrible policy, though I don’t think I’ve convinced him it’s a good policy.

Silas has convinced me that the possibility of a decrease in the demand for money due to a decrease in market activity (for example, a shift towards consuming leisure instead of consumer goods) should be taken seriously. I think the evidence strongly indicates that’s not what’s going on right now, but a good monetary system should be able to handle such a change. I am not sure what kind of rule would deal well with this case as well as more conventional cases.

2008 recession policy

Silas and I still disagree about whether the evidence suggests that a high demand for money relative to the quantity of money has been a major problem over the last ~2 years. I haven’t convinced Silas that TARP and similar policies are basically independent of monetary policy, meaning not recommended (or disrecommended) by standard macro as well as implementable independently of monetary policy. Silas and I also disagree about how bad TARP and similar policies were. I claim that they were not terrible but not great. Silas seems to think they were terrible, but I am not clear on why.

Mainstream macro-economist’s view of the world

Silas and I still disagree about whether mainstream macro-economists see surface level economic statistics (inflation, GDP, spending, loans, interest rates, unemployment etc.) as ends in themselves, rather than being indicative of the state of the economy. I say it is obvious that mainstream macro-economists understand this distinction, while Silas maintains he doesn’t see any evidence they do. Silas and I do agree that many mainstream macro-economists have a poor understanding of monetary economics, so that even if they do understand the surface level statistics/ actual welfare distinction much of their advice will be bad.

Previously, I discussed the features which distinguish money from other goods (Money as a good), why you should view most money as a branded product, and how that affects the perspective you should take on central bank actions (Money as a product). I showed that it makes sense to talk about the best quantity of a particular money in the economy. Now I want to discuss one important process that affects what the best quantity of money is.

This process is called “monetary disequilibrium”, “excess cash balances mechanism” and probably some other things as well. The Keynesian concept of the “Paradox Of Thrift” is related, though less well developed. I will first describe the process informally. In later posts I will describe it more formally. My intent here is to give an intuitive explanation of the basics of monetary disequilibrium.

The real quantity of money that people would like to hold in equilibrium can change over time. Because prices are sticky this can have real effects in the economy. To see how, consider an economy initially at equilibrium with a fixed quantity of money and prices that adjust to changes only after some time (sticky prices). Some people in the economy decide they want to hold higher money balances than they had in the past:

When people hold less money than they would like, they try to increase their holdings of money in two ways: 1) try to reduce their spending 2) try to increase their income. The quantity of money is fixed, so if one person holds a higher nominal quantity of money than before, all others must hold a lower quantity of money than before in aggregate. Prices are fixed, so this is also true for the real quantity of money. When one person reduces their spending, they reduce the income of all others in aggregate. Unless those others desire to hold less money than before, they now hold less money than they would like. Now those others also try to increase their money holdings by the same means. This is a vicious circle and aggregate spending and incomes decline. The circle ends when people no longer want to cut their their spending to achieve higher money balances.

There are two effects which determine how far this process proceeds. 1) The quantity that people want to hold is positively related to the quantity people expect to spend, so as people expect to spend less they will need to hold somewhat less money. 2) As people reduce their spending, those reductions become more painful, so will be more reluctant to trade off consumption for increased money balances.

This process reduces the real quantity of market transactions below it’s equilibrium level. The real quantity of market transactions can only return to normal when prices have adjusted to the new equilibrium, so that people can hold higher real money balances given the fixed nominal quantity of money.

This is the foundational insight of money-based macroeconomics. For some reason this process is not explained in introductory macroeconomics classes, nor commonly discussed by mainstream macro-economists. I believe understanding this logic is critical for understanding the effect of money in the economy and for understanding macroeconomic fluctuations.

Arnold Kling constantly says things that give me the impression that he does not really grok the money-based macro theories he criticizes. For example, he once stated

Pretty much everything in AS/AD is riding on the hypothesis that labor supply is highly elastic at the nominal wage and labor demand is reasonably elastic at the real wage.

Depending on what exactly he meant, this is either false or very misleading.  There are certainly people who think it works this way, macro-economists even, but as Nick Rowe as explained, explanations that rely on the first order effects of real prices do not make sense. The only foundations for AS/AD-like models that make any sense is some kind of monetary-disequilibrium theory. In a monetary disequilibrium theory (Sumner calls it excess cash balances mechanism), if people hold lower real money balances than they would like, they try to accumulate higher money balances by reducing their spending or trying to increase their sales. Since one person’s spending is another’s income, an overall increase in the demand for money without an increase in the supply of money will lead to a decrease in overall spending (you can also call this a decrease in AD, though I don’t see the use).

The latest example is here (#2) (I was a tad too rude in the comments, and I apologize for that)

Yesterday in my high school econ class, I found myself trying to explain why having a separate currency that could depreciate would enable the PIIGS to live happily ever after. I made the textbook argument, but I found myself not so convinced. OK, so maybe you can tell a story where one country that has a recession and a large fiscal deficit would be better off with devaluation. But there are so many countries in that position right now, and they cannot all devalue.

Speaking of “cannot all devalue,” doesn’t the impact of the PIIGS crisis completely nullify QE2? If the dollar appreciates 10 percent and the foreign sector is 10 percent of the economy, then that represents 1 percent disinflation, which probably more than wipes out any inflationary impact of the Fed’s new bond buying program.

To me this just screams “missing the point”. Exchange rate effects are not how coherent money-based macro. Neither are the traditional income/substitution effects (unless you mean substitution towards holding money). It’s monetary disequilibrium.

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.

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.