In my last post, I discussed my complaints with the standard approach to teaching aggregate demand in an intro class. I have been trying to come up with a better way of doing it and that has spilled over into IS/LM. I think I have a better model for that too. I will try to describe it here. For the record, I’m not saying IS/LM is “wrong” exactly, just that it is misleading and is not a very clear representation of the relationships it is meant to explain. My model can be turned into the standard IS/LM model with a few assumptions. But forcing you to make those assumptions, I think, helps greatly to understand what is going on.
The point of aggregate demand is to connect the real economy to the monetary economy. All short-run deviations from the long-run equilibrium are due to the monetary mechanism not functioning perfectly. This is what we are trying to model. The threads which connect these two things are the price level and the interest rate. Much like the traditional model, I will divide the demand side of the economy into two sectors: the real goods market and the money market. For the sake of simplicity, I am assuming a closed economy with no taxes or government spending. These other things can be added but it is a little more complicated than just adding a G onto aggregate demand (which, remember, is the whole point). I will leave that for another time. We will start with real goods.
The RG Curve
Assume that people have some preferences over consumption now and future real wealth (you can say future consumption if you prefer, but I like this way of saying it better). They also have a budget constraint. The budget constraint depends on income and the real interest rate. Solving the maximization problem is a simple microeconomic exercise. You will get a function for consumption and one for investment, which depend on income Y and the real rate r.
Now, at this point, you can recognize that these functions could have a lot of different properties, but let’s assume that they have the following.
The response of consumption to changes in either variable is not of fundamental importance. Note that you may assume that the consumption function is linear in Y and independent of r, but this is a restriction on consumer preferences and not necessary. (This eliminates one of my pet peeves about IS/LM.)
Now let this function I(Y,r) be the supply of loanable goods and let the demand for loanable goods be determined by the investment opportunities faced by firms such that the marginal product of investment is always equal to 1+r. Equilibrium in the market for loanable goods, then requires the quantity supplied to be equal to the quantity demanded.
This will determine an equilibrium real interest rate for any level of income. Note that expenditure (C(Y,r)+I(Y,r))is always equal to income. This is just the budget constraint from the consumer maximization problem. So equilibrium in the real goods market (which is made up of equilibrium in the loanable goods market as well as the consumption goods market since, from the consumer maximization we always have I(Y,r)+C(Y,r)=Y) implies a relationship between income and real rates.
Now if we assume that income equals output (Y), then we have a relationship between output and real rates. Note that this assumption, along with the consumer budget constraint, essentially represent the “Keynesian cross” from IS/LM. When income is higher, the supply of loanable goods will increase and the real interest rate will be lower. We can then write a function representing all combinations of income (Y) and real rates (r) which are an equilibrium in the real goods market. Let’s call this the “RG curve” for “real goods.” This will be downward sloping and essentially equivalent to the IS curve.
The MV Curve
Now consider the role that money plays. Notice that we did not include the price level or the nominal interest rate in the real goods markets. Also, remember that aggregate demand can be written as PY=MV. Let M be exogenous. Then our goal is to explain V.
Let L(i) be the fraction of total expenditure that people are willing to hold as money. This will depend on the interest rate. The higher the rate, the less cash they will be willing to hold, since the nominal rate is the price of holding money. If people are holding more money than desired, they will try to spend it, either on additional consumption or investment (probably by lending it) and this will have to increase either the price level or total output and therefore reduce velocity (and vice-versa if they are holding less than desired).
Equilibrium in the money market requires velocity to be 1/L(i) and this must, by definition, be equal to PY/M. This can be seen on a graph of V and Y for a given P and i.
This gives us a level of output which is consistent with the demand for money for any given price level and nominal interest rate. This will be increasing in i (since Li<0), decreasing in P and increasing in M. Call this function the “MV curve.”
At this point we have to deal with inflation expectations. One key feature of this model is that it is very explicit about which interest rates it is talking about where and so you have to deal with inflation expectations explicitly as well. This eliminates another one of my pet peeves about IS/LM (the more important one). The simplest way to do this is to assume that they are exogenous, and don’t depend on any of the other exogenous variables. Then, in equilibrium, the Fisher equation must hold.
Then we can rewrite the RG curve as RG(i-π^e). Then we have a nice downward-sloping RG curve and upward-sloping MV curve in i/Y space. Equilibrium in both the real goods market and the money market will determine a quantity of total output demanded and a nominal interest rate for any given price level. (Consumption, investment, velocity, and the real rate can all be easily recovered from this.)
The aggregate demand curve is then a function giving all combinations of output and price which make up an equilibrium in both the real goods market and the money market. It can easily be seen that this is downward-sloping in price. If the price is higher, PY/M will shift to the left in figure 2 which will cause the MV curve to shift to the left and imply a lower aggregate quantity demanded. Furthermore, we can deduce how the curve will shift when the following exogenous variables change.
If the money supply increases, this will shift PY/M to the right for any given P, which will cause the MV curve to also shift to the right and cause the aggregate quantity demanded for any given P to be higher. Note that for a given price level, and inflation expectation, this will lower the nominal rate, increase investment and decrease velocity. The degree to which the increase in money is absorbed by a decrease in velocity vs. an increase in aggregate quantity demanded depends on the slope of L(i).
If inflation expectations increase, this will cause RG(i-π^e) to shift to the right since any level of i will represent a lower level of r. This will cause the aggregate quantity demanded to be higher for any given P (an increase in aggregate demand). Note that this will cause an increase in i, but a decrease in r since the RG curve will shift up by exactly the amount of the increase in inflation expectations but it will move along the MV curve. This will mean an increase in output, investment and velocity.
If people become more impatient and want to consume more today, this will cause a decrease in investment supply and higher real rate for any given level of income which will cause the RG curve to shift to the right. This will cause the nominal rate, velocity and aggregate quantity demanded to increase for any given P.
If a new technology is discovered which increases the marginal product of investment, the demand for loanable goods will increase. This will cause the RG curve to shift to the right and the AD curve to do the same, which will increase investment, output and real and nominal interest rates. Note, that this may crowd out some consumption, depending on the shape of the indifference curves.
If people decide they want to hold less money—L(i) decreases—then 1/L(i) will be higher for any given i which means that the MV curve will shift to the right and the nominal and real rates will be lower, aggregate quantity demanded, velocity, and investment will be higher.
This model has two main benefits compared to IS/LM. One is that it has a bit more “micro foundations” in that it explicitly incorporates consumer preferences and demand for investment by firms. The other is that it carefully distinguishes between real rates and nominal rates which makes the transmission mechanism for monetary policy much more clear in my opinion. It also fits better with my framework of thinking about AD as Y=MV/P and dividing things into their effects on M and V rather than thinking in terms of C+I+G+NX and dividing things into their effects on those respectively (although note that you can still do that with this model). I see this as a sort of monetarist version of IS/LM, though I don’t know if people with monetarist street cred would agree with me or not.
So far I haven’t explicitly tried to incorporate fiscal policy. To do this would require you to make some assumptions about how it affects peoples’ preferences and where the money comes from. (Is it from taxes or borrowing? If the latter, is it borrowed from the private market or from the central bank increasing the money supply?) Note however, that these questions are central to determining the effect of such policy. You probably could just slap it onto AD if you wanted to assume that there were no effect on preferences (no crowding out) and you could change the household budget constraint to Y-T. If the government borrows, you could add their demand to the demand for loanable goods.
Sorry the figures look like crap. I need to figure out a better way to get them into wordpress
I took another step in my slow transformation into a macro guy this quarter by teaching introductory macroeconomics for the first time. I have taught intermediate once and a little bit of intro in a combined class at a school that was on semesters but frankly, I didn’t cover much macro in that one. So working through the introductory treatment of AS/AD was a little bit of a rough process and I suspect I learned the most out of everyone involved, which is not exactly ideal but has some redeeming value nonetheless.
This was only partly due to my lack of experience. It was also largely due to what I consider to be a severely flawed approach to teaching this stuff at an introductory level. I started out just following the textbook they gave me, but by the end I was sort of blazing my own trail. I am beginning to see what I think is a much better way of doing this. So I am writing this mostly for my own benefit, to help organize my thoughts for future classes. But I welcome feedback.
I have two main gripes with the standard treatment of AS/AD. The first is best illustrated by this question from my textbook.
Describe whether the following changes cause the aggregate demand curve to increase, decrease, or neither.
The price level increases.
Imports decrease and exports increase.
The price level decreases.
Government purchases decrease.
The reasoning behind this question is probably obvious. At the very beginning of the chapter they define aggregate demand as the following.
So obviously if investment increases, that must increase aggregate demand right? That makes sense if you implicitly assume that C, G and NX all stay constant. But that’s a silly thing to assume. Obviously, each of these things is endogenous. They must be or else there would be no P in that equation and then it wouldn’t make sense to call it aggregate demand. So they must mean:
So at the very least, I(P,…) is an exogenous demand for investment at different price levels. So just saying “investment increases” is reasoning from a quantity change. What you mean by “investment increases” must be “demand for investment increases.” But then you haven’t said anything other than “assume that aggregate demand increases, what is the effect on aggregate demand?” In which case, you haven’t really explained anything. In order to say anything interesting about how aggregate demand changes, you have to say what would cause an increase in demand for investment. And the things that change the demand for investment, sometimes also effect something else in there, and not always in the same way.
For example, you might say that a decrease in interest rates causes investment demand (as a function of the price level) to increase. But now you are reasoning from a price change. Why did interest rates fall? Did people become more patient? If they did, then you have an increase in the supply of loanable funds, a fall in the interest rate, an increase in investment demand and a decrease in consumption demand. Does that increase or decrease aggregate demand? Hmmmm……
On the other hand, what if you have a decrease in expected inflation. Does this change real interest rates? If not, what happens to demand for consumption and investment? If so, why? And then how does it change demand for investment and consumption? What if the central bank is setting a lower nominal rate and this is increasing inflation expectations and also lowering the real interest rate in the short run? This probably means investment demand is increased and consumption demand is also increased since people will want to consume more and save less at the same time that firms want to invest more. If this is the case, how is it that interest rates are lower again?
These are the difficult questions one has to grapple with in order to figure out macroeconomics. And to be sure, you can’t explain them all satisfactorily in an intro class. You have to make some assumptions that simplify things. But the problem with this C+I+G+NX approach is that it forces students to reason in a way that doesn’t really make sense without them realizing that it doesn’t make sense and it makes them less capable of grappling with these questions in the future instead of more capable because it trains them to think carelessly. It’s an intellectual dead-end street.
We should be teaching them to think carefully, organizing information in the way that is the most helpful for understanding the essence of the problem and keeping careful track of what assumptions go into that formulation. Instead, it seems like introductory macro is designed to give them as much random information to memorize as possible to keep them from thinking carefully enough about what is going on to realize that it doesn’t really make sense.
For instance, in their quest for more material to memorize, they give three reasons that the AD curve is downward sloping: the wealth effect, the interest rate effect and the international trade effect. These all amount to “when prices are higher, people can’t afford to buy as much” except the first one is this notion applied to consumption, the second is the same concept with respect to investment and the third is sort of the same concept with respect to net exports (I want to avoid going off on a tangent about international trade so I am going to glance over most of the stuff related to that). So why not just call this the “wealth affect” and say that it applies to both consumption and investment?
Next, we come to my other main gripe. When they are talking about things that shift the AD curve, the first thing they mention is changes in real wealth. Here is how they describe changes in real wealth.
“One determinant of people’s spending habits is their current wealth. If your great-aunt died and left you $1 million, you’d probably start spending more right away: you’d eat out tonight, upgrade your wardrobe, and maybe even shop for some bigger-ticket items. This observation also applies to entire nations. When national wealth increases, aggregate demand increases. If wealth falls, aggregate demand declines.
For example, many people own stocks or mutual funds that are tied to the stock market. So when the stock market fluctuates, the wealth of a large portion of the population is affected. When overall stock values rise, wealth increases, which increases aggregate demand However, if the stock market falls significantly, then wealth declines and aggregate demand decreases. Widespread changes in real estate values also affect wealth. Consider that for many people a house represents a large portion of their wealth. When real estate values rise and fall, individual wealth follows, and this outcome affects aggregate demand.
Before moving on, note that in this section we are talking about changes in individuals’ real wealth not caused by changes in the price level. When we discussed the slope of the aggregate demand curve, we distinguished the wealth effect, which is caused by changes in the economy’s price level (P).”
So when prices go up, you get poorer and move along the AD curve. Unless it is prices of stocks or houses, then you get richer and the AD curve shifts to the right. If this seems confusing, then you are probably thinking too clearly.
According to the book, the great depression was caused (partly) by the stock market crash of 1929 and the “great recession” was caused (partly) by the housing collapse of 2008. These are both wrong. The causality goes the other way. Financial markets react to changes in expectations about the future rapidly, so systemic problems with the economy tend to show up first in the markets.
If you are talking about the prices of all real estate or all stocks falling, are you talking about a change in relative prices or a change in the price level? If you are talking about the former, then a) why is that happening? And b) isn’t someone else’s real wealth increasing because they don’t own real estate and now they can buy more of it? How is it that some changes in relative prices make us poorer on aggregate and some make us richer? The book offers no clear explanation for this. If it is not a change in relative prices but a change in the price level, then isn’t it a movement along the demand curve, not a shift? And if that’s the case, does that mean the AD curve is upward sloping?
These are questions you might ask if you were trying to figure out this whole AD thing. It’s not exactly that they all can’t be answered, but the C+I+G+NX framework doesn’t help you answer them. It makes it more difficult to wrap you mind around. If you are trying to actually get to the heart of this thing, this is what you actually need to ask and answer
Q: Supply and demand for apples are measured in other goods that people are willing to trade/accept for apples. What is the demand for all goods measured in?
A: Money. AD represents people’s willingness to trade money for goods (consumption, investment, whatever). This means that it is all about the willingness of people to hold money. It’s all about money.
Now, why is AD downward sloping and what shifts it? To see this, instead of starting with Y=C+I+G+NX, ignore that because it doesn’t tell you anything worthwhile about what aggregate demand means or how it works, and instead start with this:
The equation of exchange. Like the first equation, this is also an identity. It must be true. Unlike the other equation, it highlights what actually matters. For starters, it has Y and P in it, so a student can easily derive an AD curve from it for a given V and M and see why it must be downward sloping. In short, this is because of the “wealth effect” described in the textbook, but now you can clearly see that it is just one effect which applies to money. If prices are higher, for a given amount of money and a given velocity, people can’t afford to buy as much stuff. This applies to both consumption and investment (and net exports as long as you assume they have to be purchased with domestic currency). So the downward-sloping part is pretty straightforward (again, assuming, for now, that velocity is constant).
Why does it shift? Well we can see easily that (for a given V) if you increase M, it will shift to the right. You don’t have to try to explain that increasing M lowers the interest rate and lowering the interest rate increases investment and deal with all of the implicit assumptions that are hidden in there. All of those assumptions are replaced by the assumption “V is constant.”
Similarly, if you hold M constant, then anything that shifts the AD curve must do so by changing velocity. This is the type of fundamental insight which is completely absent from the C+I+G approach. So take the things that the book says shift AD:
Real wealth: as we have already established, this is dumb.
Expected future prices: If people expect future prices to be higher, they will want to hold less money, they will want to buy more stuff today, velocity will increase and AD will shift to the right.
Expected future income: It’s actually not entirely clear that this should increase AD but here is what must happen if it does. Either it must make people want to hold less money at a given price level (and increase velocity) or it might increase the money supply. If banks are not reserve constrained, then people may borrow more and increase the broader measure of the money supply (or if you prefer, increase the velocity of M0). Or if the central bank is targeting an interest rate, it might increase the money base as demand (supply) for loanable funds increases (decreases).
Furthermore, you can take government spending. Instead of just saying “well it increases G so that’s an increase in AD right there” which is dumb. You have to ask yourself difficult but interesting questions. For instance, where does the money come from? Maybe you increase taxes. In which case shouldn’t that just crowd out private consumption? Yeah probably but how much does it decrease consumption? Well you can go through the whole spending multiplier thing and argue (notice I’m not saying “show”) that when the government takes your money and spends it, it causes more total spending than if they just let you spend it. Why? Because you will hold less money that way, or in other words, it will increase velocity.
Alternatively, they could borrow it. Who do they borrow it from? If they borrow it from the private economy then won’t this crowd out private investment? Yes. To what extent? Well, try to make some kind of argument that it will increase or decrease or not change velocity. What if they borrow it from the central bank? Then it’s an increase in M (and it’s really monetary policy) and it’s very clear how this will affect AD.
You wanna talk about “animal spirits?” That’s basically just a way of saying that velocity drops for some reason we don’t understand and can’t explain.
Now of course, it is equally true that V probably won’t remain constant when the money supply changes, but now you have focused attention clearly on the important thing. Remember AD is all about peoples’ willingness to hold money. And this is also the essence of Velocity. So we can start with the quantity theory (constant velocity) of money and then start asking what would cause velocity to change. And if you want, you can make velocity a function of the price level.
Let’s say that you think that velocity will be lower if prices are higher because when the price level is higher, it will take more dollars to equal the same amount of real money balances. You can explain that the AD curve will still be downward-sloping as long as the price elasticity of velocity is inelastic. At this point your intro class will probably look at you with glazed-over eyes but the point is that everything about AD depends on the quantity of money and velocity. All of the things that textbooks talk about shifting the curve by increasing investment or something like that are either wrong or they affect velocity. Instead of teaching them to think about C+I+G+NX, we should teach them to think about PY=MV. You can make velocity a function of whatever you want. But then you are concentrating on what matters. The fundamental forces which drive aggregate demand.
C, I, G, and NX are not the fundamental forces driving aggregate demand, they are just categories that you can divide it into. The fundamental force driving aggregate demand is the willingness to spend money on goods. It doesn’t matter if those goods are consumption or investment. The only thing that matters is how much money there is and how willing people are to hold that money instead of spending it on something. If you can grasp this concept, you get aggregate demand. If not, you don’t. If something affects AD, it must affect one or both of these. If you can see how it does that, you get it. If not, you are probably confused.
Now, this is all consistent with the model of aggregate demand taught in introductory macro, it’s just a better way of teaching it, in my opinion. When you get to intermediate, I have a similar set of gripes. So I am coming up with a better way of doing IS/LM. Coming soon.
Nick Rowe has (tongue-in-cheek) post about the land theory of value. I know he isn’t pushing that theory but as an exercise, let me try to address his ultimate question:
Plus, the Land Theory of Value is worth considering in its own right, or simply as an exercise in studying value theory. Why is it wrong? What are we looking for in a theory of value? What counts as success?
Bound up in this question is the question “what is value anyway?” I think what most classical, and modern mainstream economists are looking for in a theory of value is a way to explain (relative) prices. In other words, when they say “theory of value” they mean “theory of relative prices.” They take for granted that prices are a measurement of “value” and try to construct a theory that explains how this is true. This seems to be what Nick is after.
On the other hand, in my opinion–and internet Marxists will probably argue with this– the Marxist version of the labor theory of value is an attempt to define “value” independently of prices and then construct a theory which says that market prices are not representative of “value.” If this is the case, then you have a way of claiming that mutually voluntary (or, in other words, free) trade can be exploitative (someone wins and someone loses) and this is a foundational assumption underlying most Marxist rhetoric.
So if you take the latter approach and assume that all value comes from labor, then nobody can prove you wrong. If they say “okay, but what about this diamond, it is highly valuable but it takes very little labor to produce it,” you just respond “no, it isn’t highly valuable, because it didn’t take very much labor to produce it.” And if that makes you uneasy, then maybe you make up alternate definitions of value like “use value” and “exchange value” so that you can avoid reconciling your definition of value with the actual prices of things.
So I think most economists find the latter approach unappealing. The standard (subjective) theory of value also defines value independently of prices. Value means the quantity of other goods (somehow measured) which someone is willing to give up for something. This value is subjective and there is no attempt to explain where it comes from. We merely assume that people have some willingness to trade goods for other goods. A nice feature of this definition of value though is that, once you use it to explain prices, you find that prices are, in fact, a measure of value (specifically marginal value). So if, when you say “a theory of value,” you really mean “a theory of prices,” then this theory works for you, because it does explain prices.
Now what Nick seems to be describing is a theory of prices. He (or technically, his Dutch ancestor) is basically arguing that you can explain the prices of things in reference to land. It is not an independent theory of “value” (meaning independent of prices). It takes for granted that price is a measure of “value” and seeks to explain these measurements. But the theory described here does not explain these at all, it only shows that prices can be measured by a standard unit of land. This should not be surprising if you believe in the standard (subjective value) theory. In that model, you can measure the value of any good in terms of any other good.
Take this part.
You have to consider the marginal land, that is exactly on the margin between producing wheat and producing barley. If that marginal land could produce two tons of wheat or four tons of barley per acre, then the value of one ton of barley must be half the value of one ton of wheat. That way we can compare the value of land that only grows wheat to land that only grows barley. And the market prices will themselves tell us the relative values of all different sorts of land, so we can convert them all to standard land.
So you can observe the marginal rate of transformation between wheat and barley and that will be equal to the price. That’s fine. But that does nothing to determine why the margin is where it is. If there is a concave PPF, then the marginal rate of transformation between wheat and barley depends on how much of each the society chooses to produce. How do they determine how much wheat and how much barley to produce? Well if you believe in subjective value, then they buy whatever they value more until, on the margin, they are indifferent between $1 worth of wheat and $1 worth of barley (or if you prefer, you can measure the market price in any other good). This subjective value, along with the various production possibilities, determines a price.
If you wanted to, you could take some wheat land and use it to raise cockroaches. Assuming that no land is being used for this and the market price of cockroaches is negative (you pay to get rid of them). Do we conclude that the true “value” of cockroaches is determined by the amount of cockroaches you could raise on a “standard” unit of land? If so, is the price wrong? The lack of an existing margin also presents other problems but it’s not necessary to go into them. The point is that chickens are more valuable than cockroaches not because they take more land to produce but because we subjectively are willing to give up other goods for one and not the other.
Now, of course, if things work the way the standard theory says, then the relative price of wheat and barley will be equal to the marginal rate of transformation between the two. So if you can observe the marginal rate of transformation, you can observe the price. But this is different from explaining the price. In order to do that, you have to explain why the margin is where it is. And in order to do that, you need subjective value. Of course, Nick pointed this out to his ancestor and his ancestor made a meaningless reply.
Preferences! We cannot observe preferences. Land is real and objective. And the margin of cultivation between wheat and barley is real and objective, and we can observe it. We don’t need no stinking preferences to determine value!
But, again, the only difference between preferences and the margin of cultivation is that the latter is observable and the former isn’t. So if all you want in your theory is a way of observing value, then this works fine. But if you want to explain value, then you need subjective preferences. And besides, if you just want to observe value, you can just look at prices. So what is the point of a supposedly deeper “theory” based on land which only amounts to a more difficult way of observing the same thing?
The same argument applies to Van Rowe’s argument about crop rotation.
If there are three different crops, and three different ways of rotating them that are not linearly dependent, and all three rotations produce the same rate of profit, as they must, it is trivial matrix algebra to solve for the values of each crop.
There is no sense, independent of market prices, in which all 3 rotations must have the same profit. They must have the same profit only if prices are such that the farmer is indifferent between them. In a large market like those that people like me imagine, this will always be the case somewhere for someone and therefore, in theory, if you could find all of the marginal farmers and observe their production matrixes, you could back out the market prices. But, again, you would not have explained why those margins are where they are. In order to do that, you need a market to determine prices and that requires a demand curve, and that requires preferences.
All of this is ultimately equivalent to saying: “Supply determines the price, you don’t need demand. See, we can always just look at the marginal cost of production and figure out the price.” That’s nonsense, and so is this theory.
Nick Rowe has another post about “red money.” I love these posts because they are very close to the concept that I am trying to advance regarding the relationship between money (which Nick sometimes calls “green money”) and debt (which he sometimes calls “red money.”) But I have two gripes with this one. One is his abuse of the concept of utility, which some people who have read me before may roll their eyes at, but since I have assumed the role of internet utility policeman, I can’t let it slide. However, I will save it for last. The other is his insistence that his red money is not a debt.
Now, what is this a theory of? It’s not simply debt, because debt is an asset of someone. Red money is an asset of no one.
This is purely semantic of course, but I kind of take it as a shot at folks like me who like to talk about debt, so I feel compelled to point out the fact that it is purely semantic and based entirely on an entirely unrealistic assumption of his.
This conclusion is based on the notion that the red money is not an asset of anyone. But red money is an obligation to pay real goods in the future to someone. It’s just that the obligation is to a group of people (future young people) rather than to a specific individual. Therefore, it is difficult to say that any particular individual holds an asset.
However, in order to make this work, he has to make the (unrealistic) assumption that people have to dispose of all of their red money before they die. In reality, if you had red money, in the sense it is described, people would just accumulate vast amounts of red money and then never pay it back (sell it back?). The reason for this is precisely the reason that Nick claims it is not a debt, namely that no particular person holds an “asset” on the other end of that debt which could require them to pay.
Nick, of course, is aware of this and he deals with it by assuming that there is some punishment in the afterlife for dying with red money. But this assumption only serves to take the asset out of this mortal coil and place it instead in another realm. So, if you want, you can imagine that God holds the asset on the other end of your liability and it will be him that extracts payment if you fail to transfer it to someone else before death, but that is not changing the fundamental nature of the debt.
Of course, in real life, this wouldn’t work because many people would not believe that God would punish them if they didn’t sell all of their red money. So if you wanted to actually make red money work in a way similar to what Nick describes, you would need to come up with some way to punish people on earth for accumulating too much red money.
One way of doing this would be to create some kind of entity, on earth, that would hold the asset on the other end of the liability which is red money. This entity could then take the goods from the old and transfer them to the young, along with the requisite amount of red money. Then you would have a specific contract with that entity which would require you to pay real goods in a given timeframe and if you didn’t, that entity could come after you for the goods. At this point, someone would hold an “asset” for each unit of red money, and I think it would be difficult to argue that it was not a debt.
Of course, if that entity didn’t want to deal with collecting and distributing real goods, they could also issue another kind of notes, let’s call them “green money” to the young, along with their red money, and they could allow the old to use this green money to cancel out their red money. Then the young would trade the green money for goods from the old and the old would use the green money to repay their debt to the entity which issues red and green money and keeps track of who owes what (which is another way of saying that they hold the assets backing the red-money debts). Then they wouldn’t have to bother with real goods except in the event that some old person failed to come up with the requisite quantity of green money in the allotted time period.
Now I have no problem with making unrealistic assumptions in order to make a point, but if the point you make is driven entirely by an unrealistic assumption and when you replace it with a more realistic assumption that point is no longer valid, then you have a bad assumption (or a bad point depending on how you want to look at it).
So whose model seems more realistic, Nicks, in which red money is “not a debt” but people always resell it out of fear of punishment in the afterlife, or mine, in which red money is a debt and people resell it out of fear of having their stuff taken by the issuer of that debt? If it’s mine, then maybe we should think about the role that debt plays in all of this and not dismiss it as an unimportant detail.
Now, regarding utility, it is becoming apparent to me that it is macro people who are driving this particular regression in economic understanding. And the reason is somewhat understandable. Put simply, it’s easier to just assume diminishing marginal utility in each period than to assume the correct thing which is that people have diminishing marginal rates of substitution between consumption in each period. If Nick had proposed the same model, with the same equations and said that, I would have no beef.
Notice that his utility function, also exhibits the latter property, and it is that property which drives the results, not diminishing marginal utility. To see this, you can simply plug in a utility function which has increasing marginal utility and also diminishing MRS (for instance (cy^2)(co^2)). So Nick probably thinks it doesn’t matter whether you say it his way or my way, and I would have rolled my eyes and held my tongue if he hadn’t gone on to say this [emphasis added]:
“Diminishing Marginal Utility. If U=log(C), then dU/dC=1/C, which is a decreasing function of C. Every extra apple you eat per day gives you less and less extra utility. So you would rather eat 10 apples every day, than 9 apples on even days and 11 apples on odd days. And 0 apples on even days and 20 apples on odd days, would be even worse. We want to smooth our consumption across time periods (and across states of the world, because insurance is motivated by the same thing).”
So it’s not just a convenient mathematical assumption he is making, he is justifying that assumption with a defunct philosophy, with no theoretical or empirical justification, which the profession discarded a century ago. (Please note that I am talking about DMU not consumption smoothing, which I have no problem with, but which can be generated by diminishing MRS without resulting to making conjectures about purely hypothetical things like “satisfaction” or “happiness.”)
This corrupts peoples’ understanding of a concept that is at the heart of much of economics and it is frustrating to those of us who have to try to teach people intermediate micro in the proper way (at least those of us who care about getting this right which, much to my consternation, seems to be a dying breed, …..). I wish smart, reputable, economists, whom I know are capable of comprehending the distinction, could refrain from falling back on this type of logic.
So I’m writing Nick a citation from the internet utility police department. If he fails to correct the violation, there will be no consequences, since it’s a department I made up and I have no real power or sway with anyone. Except, of course, that a bunch of people may read your stuff and become confused about what utility means, or heaven forbid, become utilitarians. May their intellectual blood be on your hands. (Maybe there will be some penalty in the afterlife…)
P.S. Just for the record, I’m being smug here, I love Nick Rowe and I hope his afterlife is filled with nothing but happiness and satisfaction. But if it is, I hope he doesn’t describe it as a high level of utility.
Mike Sproul has a post on J.P. Koning’s site explaining the “backing theory” of the value of money. I think that there is a certain insight about the nature of money in this, but it goes horribly wrong when it starts talking about backing. I will divide my critique into two sections. The second one is more important. I. Criticism of the existing theory I happen to be a fellow critic of the standard monetary model, so I’m not saying it is perfect but there is some carelessness apparent in the way Mike characterizes it. Take this paragraph.
It’s reasonable to think that short selling of money is governed by the same principles that govern short selling of stocks. Specifically, the fact that short selling of stocks does not affect stock price makes us expect that short selling of money will not affect the value of money. I think this view is correct, but it puts me at odds with every economics textbook I have ever seen. The textbook view is that as borrowers (and their banks) create new money, they reduce the demand for base money, and this causes inflation. This is where things get weird, because the borrowers, being short in dollars, would gain from the very inflation that they caused! Nobody thinks this happens with GM stock, but just about everyone thinks that it happens with money.
First of all, he calls a movement along the demand curve a decrease in demand. (He does it a second time later on as well.) That may seem nitpicky but it is kind of a serious error in this context. Changes in demand for money play an important role in all mainstream theories and none of them would say that such a thing is caused by an increase in the money supply. Second, there is nothing weird about borrowers “gain(ing) from the very inflation they caused.” Things like the price level, and interest rates are market prices. They are determined by the individual actions of many people interacting with each other. The idea that “borrowers” can somehow act collectively to borrow, cause inflation and then benefit from that inflation is deeply confused. No theory claims that individuals try to create inflation by borrowing. If the central bank does something that causes people to expect higher inflation, then the cost of borrowing and lending will adjust to take that into account. To quote Scott Sumner, quoting Paul Krugman: “it’s a simultaneous system.” Then there is this.
If the textbooks are right, then the value of the dollar is determined by money supply and money demand, and not by the amount of backing the Fed holds against the dollars it has issued.
But that is not an either/or proposition. Every market price is determined by supply and demand in some sense. The question is what determines the supply and demand for money. And this brings us to the biggest problem (except for part II). Unlike a stock, the whole point of money is that it provides liquidity. (There is a sense in which a stock exists because it is more liquid than other ownership arrangements but it is not created from nothing for the sole purpose of making it easier to buy other things.) Mike Sproul seems to understand this in his characterization of money in the beginning.
Alternatively, you might buy that house by handing your IOU directly to the house seller. This would put you in a “forward style” short position in dollars (figure 2). If you are well known and trusted, then your IOU can actually circulate as money. But normally a bank would act as a broker between borrower and lender, and the bank would issue its own IOU (a checking account) in exchange for your IOU. The bank’s IOU will circulate more easily than your IOU, so we commonly talk as if the bank has created money
And he recognizes that there is a liquidity premium in the comments.
But once silver has lost all its monetary premium, additional creation of paper dollars (through short selling) can’t cause silver to fall any further. At that point the backing theory would be fully correct. The creation of new paper dollars will not cause either kind of inflation.
So there must be some supply and demand for liquidity and these must determine the “monetary premium” on silver in his example and an increase in the quantity of silver credit decreases the level of the monetary premium by moving along the demand curve for liquidity. (His last sentence doesn’t seem to make sense since it is the creation of new paper dollars which he is talking about causing “silver inflation” in the first place, but that’s probably not worth dwelling on.) So I think it is misguided to argue that the price of money is not determined by the supply and demand for money. Any attempt at explaining the value of money is really an attempt to explain the supply and demand for the same. Declaring that these don’t matter is not a productive first step. II. What is backing the money? The issues above aside, the real problem here is that Sproul is mischaracterizing the contract involved in the creation of money through credit. When a company issues stock, the stock represents ownership of a portion of the company. We can call this an IOU for the real assets and future earnings of the company. So money goes from the buyer to the issuer and the IOU goes the other way. Simple. When a bank issues money, the IOU goes from the borrower to the bank. The bank creates the money “out of thin air” and lends it and the borrower promises to pay back the same thing–namely money. So the money goes from the bank to the borrower and the IOU goes the other way. The money is not an IOU from the bank for any kind of real good. Mike Sproul is going astray by calling both things IOUs.
But normally a bank would act as a broker between borrower and lender, and the bank would issue its own IOU (a checking account) in exchange for your IOU.
But the role of money is the opposite of an IOU. It is the means with which the borrower’s IOU must be paid. There is no silver in this contract. There is no promise to deliver a stock, there is no ownership in the bank. The bank does not promise to redeem the money for anything except for wiping out the debt of the borrower(s). So there is no underlying asset forming the basis for the value of the dollar (there is actually, but it’s not what Mike Sproul says. I will come to that in a bit). In a short sale of a stock, the stock is the underlying asset. In the issuance of stock, the company is the underlying asset. If we had a gold or silver standard, in which dollars were redeemable for gold or silver, then those things would be the underlying asset and everything Mike Sproul says would be right (except for the part about decreasing demand in part I). However we don’t have that! So take this claim.
For example, if the Fed has issued $100 of paper currency, and its assets are worth 30 ounces of silver, then the backing value of each paper dollar is 0.30 oz/$.
And ask yourself what exactly he means by “assets.” No matter what you answer, the above makes no sense. For instance consider the following scenario. A bank is formed which has 30 oz. of silver. It then invents a unit of measurement called a dollar and prints 100 of them. Then it trades those 100 dollars for a promise to repay 100 dollars in one year (in other words, it lends them). Now what are the bank’s assets? Mike Sproul might say that their assets are 30 oz. of silver and therefore, you simply divide those assets by the number of dollars in circulation to arrive at the value of a dollar. But this can’t be right because didn’t he say that they are like a short seller and if they create more money, it doesn’t diminish the value of the money? Of course, if you are an accountant, you might say that their assets are 30 oz. of silver and an account receivable for 100 dollars, and of course this would be correct. But now how do you determine the value of a dollar? You divide 100 dollars and 30 oz. of silver by 100 dollars? Obviously that’s not mathematically possible. Maybe you need to find the net assets by subtracting the liabilities of the bank. In this case you get $100-$100+30 oz. of silver. So their net assets are 30 oz. of silver because, as Mike says, they have a neutral dollar position. They didn’t get any richer or poorer by this transaction. But then what do we divide these 30 oz. of silver by, now that we cancelled out the liability? If you answer that you divide them by the number of dollars outstanding, then you are back doing the same thing we established was wrong in the first place. Furthermore, what happens if the bank is laying some pipe in the back and they discover another 30 oz. of silver? Does the value of a dollar double? Does the bank now owe you twice as much silver for your dollar? After all, that would be the case if GM found some silver and you owned the stock. But money is not a stock! It does not represent ownership in the bank. The bank doesn’t owe you anything more than before, because they didn’t owe you anything in the first place except to extinguish your debt. Whatever other assets the bank happens to have, have no bearing on the contract between themselves and borrowers because they are not part of the contract. The bank does not need to have any other assets to create money like this. The bank can have no silver, make up the unit dollar, create 100 of them and lend them in return for a promise to pay them back in the future. Then what is the value of those dollars? How many of those dollars will it take to buy a TV? Or an oz. of silver for that matter? That’s a serious question and mainstream monetary theory has a crappy answer. But Mike Sproul is not answering it either, although, in a way he is getting close. If you are selling TVs and somebody comes to you with those newly created dollars, assuming you know that their contract with the bank is binding and therefore, they will want to get them back in the future by trading you some real assets in order to repay the bank, how would you go about trying to determine how many of them you should demand for a TV? Seriously think about it for a minute before I tell you. If I know anything about teaching (a big if) it’s that you gotta get them to consider the question before you answer it. I’ll wait. . . . OK, ready? You would want to know what will happen to the guy if he doesn’t repay! Does he get his head chopped off? If so, those dollars are worth a lot of TVs cause he will do almost anything to get them back. You will be able to demand everything he owns. If nothing happens to him, then you probably shouldn’t take them for any quantity of TVs. But what if the contract says that if he doesn’t repay the $100 in one year that he loses his car? Well then, in one year, you would able to demand anything up to the value of his car so you would probably be willing to sell him several TVs (depending on the car of course). If it is his house, then you would probably sell him a great many TVs. Now imagine millions of people with debts like this all competing to sell real goods and services for dollars which they can all use to retire their debts to the banks and keep their stuff and you have a modern fiat-money economy. The quantity of gold and silver in the central bank’s vault has nothing to do with it. If the Fed opened Fort Knox and there were no gold there, everyone would act outraged for a week and nothing would change. It is the value of the collateral securing all of those debts which is the underlying asset in the contract that creates money and it is the thread connecting nominal money values to real good values. And this is the reason that this value can change over time, because the value of that collateral changes (both in the sense that the original collateral for a particular loan changes in value and that the value of collateral required for new loans changes). So in some sense, of course, it is a relationship between the bank’s assets and liabilities that determines the value of the money, but I think that Mike Sproul is missing the relevant assets. Money is not an IOU it is a YOM (“you owe me”). If you have a loan, you owe money. If you don’t pay, then you owe some goods which you pledge as collateral. That is the asset that matters.
There is a bit of a paradox underlying much of monetary economics. If real rates are independent of monetary factors, then a reduction in the nominal rate should be accompanied by a reduction in the expected rate of inflation (or vice-versa). Yet we typically observe, at least in the short run, that if the central bank lowers its interest rate target, it causes a higher rate of inflation. Of course, both old monetarists and market monetarists reconcile this by saying “never reason from a price change” (always good advice) and instead, reason from a change in the money supply (and expected future money supply), assuming sticky prices in the short run and then separate the effects on interest rates into the well-known liquidity, income and Fisher effects which allows for the real rate to change in the short run and for the nominal rate to go either way.
That’s all perfectly reasonable but lately there has been a school of thought emerging known as “neo Fisherites” who are bringing this issue back into the discussion. Nick Rowe (for one) has recently been taking them to task(here, here and here).
Now let me say for starters that I suspect everything Nick says about these papers is correct, and I’m not trying to defend them. I agree that denying that lowering rates raises inflation is contrary to all observations, and I suspect (though I haven’t read them yet) that his analysis of the specific papers as lacking in economic intuition and relying on strange assumptions to “rig” the results in favor of their prior beliefs is most likely spot on. That is how I feel about most modern economic papers I read, sadly. However, I think beneath the snow job and the tiny pebble of wrongness, there is actually a kernel of insight (or at least the pebble started out as a kernel before it got all mangled and turned to the dark side) and it is closely related to the stuff I have been trying to say. So I will try to flesh it out a little bit in a way that does not contradict everything we know about how monetary policy actually works.
Note that this actually began as a discussion of monetary and “fiscal” policy, which I intend to get to but I will put that off for a future post since just dealing with this Fisher paradox will be enough to fill a lengthy post by itself, but keep in mind that adding that piece in will be important for making this model look like the real world. (And also keep in mind that I don’t mean what other people mean when I say “fiscal policy.” Frankly, it’s almost tongue-in-cheek. All macro is monetary.) Read more…
This is a reply to Nick Rowe’s post on the fragility/robustness of equilibria. For the record, I agree entirely with his overarching, macroeconomic point. I’m just nit-picking the technical details here (which I believe is what he’s looking for).
Here are Nick’s definitions.
Let G be a game, let S be a set of strategies in that game (one for each player), and let S* be a Nash equilibrium in that game. Assume a large number of players, and a continuous strategy space, if it helps (because that’s what I have in my mind).
Suppose that a small fraction n of the players deviate by a small amount e from S* (their hands tremble slightly), and that the remaining players know this. Let S*’ (if it exists) be a Nash equilibrium in the modified game.
If S*’ does not exist, then S* is a fragile Nash equilibrium.
If S*’ does not approach S* in the limit as n approaches zero, then S* is a fragile Nash equilibrium.
If S*’ does not approach S* in the limit as e approaches zero, then S* is a fragile Nash equilibrium.
But if S*’ does exist, and S*’ approaches S* in the limit as n or e approaches zero, then S* is a robust Nash equilibrium.
[This began as a comment on the original post so I will proceed in the second person]
I think the wheel you are reinventing is basically the idea of trembling hand perfection. I’m not quite an expert on that but I think I know enough game theory to go out on a limb here. So taking the definition from Wikipedia.
First we define a perturbed game. A perturbed game is a copy of a base game, with the restriction that only totally mixed strategies are allowed to be played. A totally mixed strategy is a mixed strategy where every pure strategy is played with non-zero probability. This is the “trembling hands” of the players; they sometimes play a different strategy than the one they intended to play. Then we define a strategy set S (in a base game) as being trembling hand perfect if there is a sequence of perturbed games that converge to the base game in which there is a series of Nash equilibria that converge to S.
I think the main difference between what you are doing and the TH concept is that you are limiting the errors to a “small fraction” of the players whereas the TH definition above assumes that all players have some probability of making a mistake.(also it assumes that all players know this not only the “non-trembling” players, which is only natural since there aren’t any such players.)
Now, I believe your game will pass both the traditional trembling-hand perfect criteria and your modified “robustnest/fragility” criteria for the same reasons, but let’s work with the standard modification since we don’t have to deal with two types. So let us assume that everyone chooses a “target” speed St and let each individual’s actual speed be Sti+ei where ei is an error with some distribution and assume that everyone’s errors are identically distributed and everyone knows the distribution.
Now there are two issues here. First, there is the issue of the number of players. If it is finite, I believe (though I haven’t done the math) that the game will break down even in its original form because when everyone is going the speed limit, any individual driver will be able to change the average slightly by changing their own speed and therefore be able to get paid by doing so and so everyone will want to do this. (Although, there might (in fact I bet there would) be an equilibrium where half of them drive over the speed limit and half drive under and the average speed is S*.)
However, if we assume an infinite number of players, then this won’t be a problem and the equilibrium (the one in question that is) to the base game will be as you say. However, now we have another issue to deal with.
First of all, let me say that the thing which makes TH difficult to deal with is the bit “there is a sequence of perturbed games that converge to the base game” which could mean a lot of different things. But let us assume that the sequence we are interested in is e converging to zero. But the problem here is that the thing that matters to each individual’s payoff is the average speed. And if the mean of e is zero, and everyone is choosing St=S* and there are an infinite number of them, then the average speed Sbar will always be S* and the equilibrium will work no matter what the distribution of e (so long as it is mean zero). This is because the distribution of sample means converges to the population mean as the sample size approaches infinity. (And note that if the mean of e is not zero, I’m pretty sure they can all just adjust their target to account for it and you will still have an equilibrium.)
I believe this will be the case in your formulation as well since a fraction of the infinite number of players will still be an infinite number and the distribution of the mean of their errors will still be degenerate. So essentially we have an equilibrium that doesn’t work under any circumstances with a finite number of drivers and is not ruled out under any circumstances with our proposed refinements.
What we need in order to rule this out is some way of saying that the average speed Sbar might vary for some reason. For instance if there were some error e which were random but applied to every driver (like weather or traffic or something, or “real” shocks in the case of the macroeconomy), that would probably blow it up in a way that would prevent it from converging, although I think you might be able to find one, like I said above, where some people choose a target a bit over and some a bit lower than S* and the amount over/under decreases as the distribution of e collapses to zero, which could be said to be “converging to S.”
This is interesting stuff though, I’m glad you got me thinking about it. There is a sort of fundamental dilemma underlying this I think, which is that much of game theory (and economics) is built around finding conditions under which everyone is indifferent and calling it an equilibrium. For instance, any mixed-strategy equilibrium basically requires the payout function to be flat over some range of strategies. But that ends up looking a lot like the kind of thing you want to rule out when you start looking for some kind of “stability” criteria.
So what we kind of want to do is have a way of determining whether the nature of an equilibrium is such that if you “unflattened” it a little bit, each individual would have a maximum in the general neighborhood of that equilibrium that is somehow qualitatively similar as opposed to “unflattening” it a little and finding a minimum there which is sort of the case we have here. However, this is a highly untechnical way of putting things.
In this case, we only get an equilibrium to the base game there because we made the payoff function flat in that equilibrium by assuming an infinite number of players. But doing that makes other things “flat” in a sense (makes the distribution of the average speed collapse to the target speed) which makes it hard to rule out. What I think you and I would both like to say is something like “let’s assume a ‘large’ number of players such that the effect each of their speeds has on the average is functionally zero but that there is still some random variation in the average.” Then we could say that even a slight variation in the average would torpedo the equilibrium and we would be happy. But man it’s hard to do that rigorously! (I had a similar problem in my dissertation which I never really solved.)
Another thing you could probably do for this particular case is put it in the context of a dynamic game and put some restriction on peoples’ beliefs like: everyone observes the average speed of the previous day and chooses their target speed based on the assumption that it will be the same today. Then ask what would happen if you had one day where the speed were slightly above or below the speed limit. Would it work back toward the equilibrium or would it shoot off to someplace else. Here, I think obviously, it would do the latter. It’s just that with an infinite number of players and an error with mean zero, we can’t get it to depart from the equilibrium in the first place.
Incidentally, I have been working on a bit of an apology for the neo-Fisherites. I agree about the “90 percent snow job with a tiny pebble of wrongness” analysis (great line by the way) but I think there is a kernel of solid intuition in there, it’s just being applied carelessly. I’ll have that soon.