A Rehabilitation of the Quantity Theory

0:00The motivation for this paper is that if you're anything like me, you look for a, you commonly look for a theory that describes the relationship between prices, quantities, inflation, the money supply, something like this, and we typically, at least if you're me and you probably are, you typically revert to the equation of exchange and the quantity theory of money to explain inflation, the relationship between inflation and money, and you know there's some problems with it and it doesn't fit into So starting from that foundation, what I wanted to do is say, what's wrong with the equation of exchange, what can we do to rehabilitate it and bring it more closely aligned with what we need it for, and then what would this rehabilitated theory actually look like?

0:52So just to briefly start, there's a couple of different ways you can look at it. The equation of exchange in general, and they're all tautologies, right? They're all true by definition. They're true by definition just by right of the way the definitions, the terms are actually defined and the way they interlock together. So the first one there, that's the Fisherian equation of exchange. PT on the right hand side is just an average price times the number of transactions in the economy. We've got Friedman's equation of exchange in the middle, where your right hand side is nominal income, prices times the real production of goods in the economy, or it's commonly proxied by real GDP. On the bottom we've got the Cambridge cash balance theory. This one's preferable in some circles because it actually looks like a money supply money demand equation, money supply on the right hand side, and then your money demand sorry money supply on the left hand side and then your demand on the right where some fraction K is what you demand to hold in your in your reserve balance or in your cash balance of your actual nominal income and they're all basically saying more or less the same thing or at least they can be made to be saying the same thing except in different terms and when I say they're all tautologies I mean that they're all true because of the way that we define the actual variables at hand and I don't think anybody would actually argue with that

2:14Now, what are some of the shortfalls of this? The first one that Austrians typically would look at is that we're dealing with one price level for the whole economy and it's a very ambiguous definition and it's one that we typically don't care about. Austrians like to talk about relative prices and not one price level in particular so this seems to be maybe not so useful. Money is ill-defined in these. What is the money supply? If you're dealing with the Cambridge cash Cash balance theory, the money supply you're using is typically M1 or something very narrow because we're looking at cash to be held for reserve balances. If you're looking at Friedman's equation of exchange, your money supply is typically a little bit more broad, M2 because you're looking at more credit-like instruments that would facilitate payments.

3:02Any way you talk, you slice it up. Money is a little bit different depending on which one you're actually using. The right hand side of these equations, we're looking at the gross level of transactions going on in the economy and that differs depending on what equation you're actually looking at. That's not a problem in and of itself, it just depends on how you want to actually define the equation, but I'd like to look at something that more is closely aligned with what Austrians would call a gross output or gross transactions taking place in the economy instead of something more narrowly defined like nominal GDP, which would be what the right hand side represents in Friedman's approach. Velocity comes under fire quite often. It's a little bit of an ambiguous contentless variable.

3:49In fact, if you actually look at the first two of these equations, velocity, it's really just the residual, right? It's the necessary equilibrating factor that you need to have and maybe the more correct Now, what's good about these equations? All of them are very easy explanations for price inflation. In fact, probably every single one of us, when we talk about inflation, price inflation in the economy, we resort to one of these explanations, right? Explanations for Price Inflation. In fact, probably every single one of us, when we talk about inflation, price inflation in the economy, we resort to one of these explanations, right? Austrian business cycles are fundamentally a theory of unsustainable inflationary-led booms, and here we have a very simple way that we can describe inflation in an economy.

4:40Hayek's policy norm for stabilizing nominal income through offsetting declines in the velocity of money with increases in the money supply. That's accepted in some circles, particularly free banking circles, and the equation of exchange seems fairly well suited for dealing with those kinds of prescriptions. So we've got some good things with it or some things that we want to keep, and we've got some bad things that we're trying to, or some shortfalls that we're trying to correct. So I want to take you through those four shortfalls I just showed you and rehabilitate it along So the first one was the price level that we use is really too broad to be useful for what we really want to use it for and what I, I should say it upfront, what I really want to use it for is integrating it into Austrian business cycle theory or having something that Austrians can actually deal with.

5:28Well, this is actually a fairly easy shortfall to correct. Austrians have a very good way that we can start categorizing goods depending on their nature or where they are in the process of production. So instead of just dealing with total transactions on the right hand side or total real output, why don't we break it up into output on capital goods or higher order goods and output which is devoted to consumer goods or lowest order goods. We end up with two different price levels, the price of consumer goods and the price of capital goods. They're still aggregate price levels, but notice that you now have a relative price in there, the relative price of capital with respect to consumer goods. Velocity, I call it V prime here because it's changed compared to how we would typically define it. Now it's not income velocity like it would be in Friedman's rendition of the equation of exchange. It's now total transactions or gross transactions velocity, if you want to call it that.

6:24Now, what about the second shortfall? The money supply is ill-defined and in particular what I have in mind when I say the money supply is ill-defined is the typical equation of exchange doesn't distinguish between base money or what we would call money proper and fiduciary media which is also used to enact transactions and payments. Quasi monies or close credit substitutes are are also something that we might want to keep in mind as something which facilitates transactions in the economy. And as Austrians, we have some pretty good tools or some pretty good theories to deal with this. The easiest one that I would start with is just to say, what kind of money do you actually want to define? Do that first and go from there. So the money supply that I want to define is base money and fiduciary media, which is fairly straightforward.

7:13This is Econ 101, M-naught or the total supply of base money in fiduciary media is just equal to your supply of base money divided by your reserve ratio, reserve ratio goes down, a greater amount of fiduciary media is outstanding. For $100 worth of base money at a 10% reserve ratio you've got $1000 worth of total money supply under this definition. Now, if we've got a definition for what we're actually talking about with money, let's start looking at what the specific reasons why you would hold money are. And in looking at this, there's two economists that I want to focus on, Murray Rothbard and John Keynes. Now, Rothbard, I should start by saying I think both of these approaches have a pitfall and both of them have an advantage.

7:59Rothbard's is the one that I actually prefer here. Rothbard does a very novel application where he divides the demand to hold money into two separate demands, your reservation demand, which is M superscript R, that's the amount of money out of your cash balance that you desire to hold to mitigate perceived uncertainty in the future, you don't intend to spend this, you will if an emergency arises, but you really hold it for an unknown reason. for a reason that's not yet materialized anyway. And then Rothbard has the exchange demand for money, this is your cash balance that you hold to enact payments or to facilitate you with payments. Now Keynes uses some similar terminology, he has the precautionary demand to hold money which is roughly analogous in many ways to the reservation demand to hold money.

8:50Keynes has the transactions demand for money, that demand you hold of money to facilitate your transactions. Transactions. And then Keynes has the savings demand, sorry, the speculative demand for money. This is the money you desire to hold to help you or to facilitate you in speculating in the economy. Or later on, a year later after the General Theory in 1937, he refined this and he called it the finance demand to hold money. It's just your demand to hold money for financial purposes instead of consumptive purposes. Now, I don't want to get into the debate of liquidity preference or where that enters into Keynes' I don't want to talk about time preference and how it enters into Rothbard's money demand, but I want to integrate the two of these together.

9:36The three terms that I integrate together are the reservation demand to hold money. This is your cash balance that you just want to put in your bank account for an unforeseen emergency. The exchange demand for money, which is that sum of money that you want to hold on to facilitate transactions for goods and services in the economy. And then I want to throw in there, for good measure, Keynes' speculative demand for money, although speculative is not the word that I want to use. I'd rather use the savings demand for money. This is your money that you hold in your cash balance to facilitate savings in the form of financial investment activities, loans typically. Now, the total money supply then has to be divided between all three of these money demands. They sum to unity. And the money demand which comes from your reserve is not going to be used for facilitating transactions in the economy.

10:27So we can factor that out if you're completely, which is what I've done over here on the extreme left-hand side, one minus your reserve demand for money, basically that is just factoring out for your reserve demand for money. And what you're left with is all of your cash balances that you hold to either facilitate transactions for good and services, Mises which is your money demand for exchange or financial transactions or savings transactions which is what I call M superscript S. Now each one of those dollars or currency unit that you hold in your cash balance does circulate throughout the economy at a certain velocity. Now in this case we're going to end up with two velocities. You get the velocity that your exchange money is going to circulate at and you get the velocity that your savings Now, in reality, we can't really disentangle these two effects, and everybody's well aware of that. In fact, your total money supply, you can't really disentangle this easily. It's just one big cash balance, correct?

11:26But theoretically, we can definitely distinguish between the two, and it's useful to do so as I'll show you here in a couple minutes. Now, focus on this term right here. This is basically the gross amount of lending that's taking place in an economy in any given time period. Period. It's your cash balance which you have held for saving or for finance purposes, times the velocity that it's circulating at, and it becomes the gross amount of loans which are being issued in the economy. If you're issuing loans in the economy at any given moment in time, it means that they have to be paid at some moment in time as well. So we need to add a term to the right hand side, and the term I add to the right hand side is just D for gross debt repayment. On the left-hand side, this term basically represents gross loans issued and the right-hand side offsets it with gross debt repayment.

12:17Just to simplify things, I've cleaned up this term here and called it M'. M' just represents that amount of your cash balance that you're holding to actually enact payments for exchanges or savings. Now, what are some things that we can talk about with this equation of exchange? One of the things that we might want to talk about is how the repayment of debt factors into the determination of price levels in the economy. Conceptually it's maybe a little bit more straightforward if we just regroup all of our debt terms or our loan terms over here on the right hand side. D is the total amount of debt which we're paying back in any time period. This term here is the total amount of loans which are being issued in any given time period. So the difference between them is just your net debt repayment.

13:05And from there, it's fairly straightforward to see that when it's positive, that is, more debts are being repaid in any time period than new loans are being issued. Chater as Paribus, the effect on your individual price levels of capital and consumer goods has to be negative or disinflationary. And the corollary holds true, if you're issuing more loans or more credit in any given time period than you are repaying debt, price pressures on capital and consumption have to be on net positive. Now you might think at this moment, why is it that you would include credit in this equation? Because one person, if they loan money to somebody, they've given up the purchasing power of that money and somebody else is using it to facilitate a transaction. So really there's no net change, right?

13:51One person's loss is another person's gain and then they're going to reverse it at some time in the future. So there really shouldn't be any effect. Joe, you take this approach in your paper, a simple theory of money prices, called something like that. Friedman is actually very clear on this when he formulates his own equation of exchange. I'll tell you why it's important to factor this out. If you are dealing with a monetary system that did not have fractional reserves, it's true that all credit that's issued in the economy would have to represent a renunciation of money by somebody else, but in the fractional reserve banking system things don't work this way, right? You have fractional reserves or fiduciary media which banks use to facilitate loans which do not represent a renunciation of consumption or investment by the person who's deposited that money in the bank.

14:36There's a disconnect here, which is why I've added it or felt the need to add this credit portion to the actual equation. Now I'll show you, we can make this look like the more conventional equation of exchange very easily. What would happen if there was no maturity transformation in the economy? If there's no maturity transformation, every single loan which gets issued is paid back in the exact same time period that it's issued. In our equation, that would just mean that debt repayments have to be the exact same as loans in any given time period. And if they're the same, that final term falls off. In fact, because this looks more like our conventional equation of exchange or is roughly analogous to it, we find that it's actually a specific case where there's no maturity transformation in the economy.

15:22If all loans are being repaid in the exact same period of time at which they are issued, then you don't have to worry about this. Well, so much for defining the money supply. What about the other two shortfalls? They're now taken care of as well, fairly well, or I feel fairly well. What is the, on the right-hand side of the equation of exchange, how do we actually define transactions? Transactions. The way that I've defined it is total money spent on capital goods plus total money spent on consumption goods plus all debt repayments. This is really the gross amount of money that you could spend in a given time period, right? You buy your goods, your consumption goods, you invest some of your money in capital goods and you pay off some of your debts that facilitated purchase of goods in the past. So we've got now a gross and the gross amount of transactions that are taking place instead of a much narrower definiment of it like would be used, defining of it like would be used in Friedman's case

16:21with nominal income. How about velocity being a contentless residual? We haven't really corrected that at all. In fact, if anything, we've made it worse because we introduced a whole new velocity term into the mix. But actually, there's some hope. On the exchange side of things, and this isn't specific to my rehabilitation, it applies to the more typical equations of exchange. The velocity of exchange is roughly analogous to the inverse of your demand to hold real cash balances, right? Celgen and free bankers are very clear on this. Reductions in velocity represent increases in your demand to hold cash in the form of your reservation demand. Now, the velocity of savings in here, it's really just the inverse of the average maturity of loans that you're issuing in any given time period.

17:12If your equation of exchange is dealing with a base period of one year and you've lent money for six months and then rolled it over to loan it again for six months, the average maturity of that six month loan was one half of the time period, which means the velocity of your loans or the velocity of your credit issued was two, right? You have issued your credit two times over or it circulated twice in that time period. Now I want to finish here because Joe is going to cut me off with one really big advantage of this. Actually it will coincide mostly with what Justin was just saying, why can't the Fed generate inflation? Now if you are to rely on the old equation of exchange, money supply increased by a lot, Prices didn't really do all that much.

18:02Real income didn't really do all that much. So velocity by definition had to just decline to offset it. You don't really say much in that statement. In fact, you could even go one step further. If you look back to one of the motivations for Keynes to write the general theory, it was a discontent with determining short-term income through the classical equation of exchange and the fact that if prices are sticky and if income doesn't really adjust to the money supply in the short term that increases in money have to just be offset by Declines in the Velocity of Money. There's not much you can really say about that. Now, this is just the long form of my rehabilitated equation of exchange. What has the Fed done? It's increased base money supply by a lot. That's always only been a small portion of the total increase in money supply because banks have increased the amount that they're holding onto.

18:52Their reserve ratio has increased. Individuals have increased the reservation demand for money and there is more debt repayment going on in the economy right now than there is gross loans being issued. I'll leave it at that. Thanks for the time.