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Yes. But just a side note, MV=PT is in a sense more intuitive than Y=C+I+G+NX. You can explain recessions to a laymen in a few sentences

1. Total sum money paid in transactions in an economy during a given year must equal to a total number of real goods and services times the price of these goods and services sold in an economy. It holds, it is an identity.

2. Imagine that sum of money transactions is fixed or decreasing - we are on a gold standard and people start to sew their money in mattresses. Now imagine that prices cannot change for whatever reason (like government regulation). Since the identity must hold, decrease in the sum of transactions MUST show as decrease of number of real goods and services sold in economy. There is no possible outcome.

Now if we look at the crises vie these lenses then at the core fiscal stimulus is about increasing V and monetary stimulus is about increasing M. Now the bonus of monetary stimulus (as I see Market Monetarist to say it) is that presumably only government (central bank) can manipulate M. So any threat by CB about M is automatically credible. There is nothing that participants may do about M. They may try to push V, but it is all they can do. Manipulating M is clear and transparent. M is always there - even if temporarily suppressed by V - silently waiting for the day when it WILL fall upon the defenceless nominal economy.

And just as a bonus - MMTers keep talking that this is not how the banking "really" operates. For them M=Credit and credit is determined by "creditworthiness" of private sector. "Creditworthiness" is endogenously given and is manipulated by sometimes benevolent and sometimes evil, but always chaotic "animal spirits". Therefore V (fiscal policy) is the only game in town. Ever.

i had been meaning to ask you this since i read your series of posts on how recessions are monetary phenomena (all outstanding, by the way). and now that you posted on 'living on a demand side world' and this post i am reminded once again

could you please do a post with key bibliography to understand the concept of a monetary exchange economy, the debunking of say's and walras' law, disequilibrium macro etc. in some posts you`ve mentioned barro, grossman, benassy, malinvaud, leijonhufvud and others, but it's a bit difficult to determine the actual papers (books?) you're referring too

a post like that would be really really great

Great post.

I used to read historical British economic papers from the post-war period and they would talk about "demand", which I took to be something like NGDP or PT. However, what they meant was RGDP/Y. So "demand recovered in the UK after 1980 and the 1981 budget" was confusing, because annual NGDP growth has been lower in the UK than 1980 ever since, but what the paper meant was that RGDP grew almost continuously in the years after the 1981 budget.

I.e. Y = etc. is a useful definition of real output, but a lousy definition of demand in the sense of "people buying things", because it doesn't include P.

Any thoughts on this analysis http://www.cargocultist.com/?p=1586 ?

JV: that's basically how I see it too. But it helps to be able to see it through the other person's eyes as well.

JCE: A post like that could be really really great.

Unfortunately, if it were written by me, it might be not so great at all. You see, we all have our weak spots, and you have put your finger right on one of mine. I can't remember stuff. Names, faces, economics articles, it's all a big blurr, mixed together in a big Irish Stew.

Let's see, there were 2 papers by Clower, both I think in that whitish or was it greenish Penguin paperback I think he edited, called...let me see, that book was here just last week, was it on my office desk or is it somewhere in my living room? And one paper was the one where he draws a matrix/table thingy showing a barter vs a monetary exchange economy; and the second was where he writes down a budget constraint and....

Half a dozen people commenting here could do a better job writing that post than I could.

Yes, I really ought to do that. But as I get older I have learned to recognise my own limitations, and stop trying to do things I'm not good at doing and that stress me. Like math, downloading data onto spreadsheets, and writing bibliographies.

Sorry JCE. I wish I could give you a better response.

W Peden: Yep, when people talk about "aggregate demand", it's hard to tell whether they are talking about a real quantity, a nominal quantity, or a curve.

Dave: Yep. Q is a flow. If Q is apples, it would have the units kg/year, and P would have the units $/kg, so PQ has the units $/year, which is the same as MV.

I don't see how you can, on the one hand, call those equations identities, and on the other hand act as if there are any causal relations anywhere in either equation. For example, a government with a gold standard peg might devalue its currency 3% against gold. People will react by holding 3% more money, which the government will issue passively. A change in P just caused a change in M. Or the government might issue 10% more money, and that money will be spent on goods that were previously bought with something not considered "money" (e.g., credit cards, gift certificated, savings account, etc). The change in M just caused a change in T, but no change in Y (or P).

Using these equations is like observing that your shadow is always beneath you, and concluding that you walked down the street because your shadow made you do it.

Nick Rowe,

As well as either a flow or a rate-of-change in a flow, though that's a more common problem.

Sorry, I am stupid and studies physics. And I am fine with Y=C+I+G+NX. The left part follows from the right part and that is the most basic convention in mathematics. But can please someone for once explain me why MV=PY is written as MV=PT given the absolute obsession of economists with P?

There should be a reason for that.

(sorry for the offtopic)

The identities are fine, but they aren't causal models. They are just constraints on causal models.

The famous curves are also not causal models, although they get closer. Economists turn the curves into seat-of-the-pant causal models by adding intuitive judgments about the way in which changes in factors exogenous to the curves themselves result in movements of the curves. But that involves ad hoc insertions that are not represented in the models themselves.

That's why these debates seem so endless.

Economists seem to have a lot of resistance to building temporal and causal-mechanical components explicitly into their models themselves. If you have a causal system in which the state of X depends causally on on the state of Y, but Y does not depend causally on the state of X, then X = kY might be and approximately true identity and a very useful approximation, but the causation goes in one specific direction, not the other.

Looks like Mike Sproul already said more or less the same thing I was trying to say.


Y=total quantity of goods produced
T=total quantity of goods bought with whatever kind of money is represented by M

Note that T might be 2% as big as Y. If M rises by 20%, then the central bank gets 20% more assets as the money is issued. So previously, we had $100 backed by assets worth 100 oz., and now we have $120 backed by assets worth 120 oz. Thus each dollar is still worth 1 oz, and there is no change in P. So the 20% rise in M causes (I'm mis-using the word) T to rise from 2% as big as Y to 2.4% as big as Y. (Either that or V falls 20%). But there is no change in Y.

Nick, your post also reminds me of this one:


"There's a second asymmetry. Y=C+I+G+NX is used in National Income Accounting. MV=PY isn't. It's administratively easier to collect the data using Y=C+I+G+NX, because you can divide the questions up between households, firms, governments, and foreigners. Even if those categories don't match at all exactly, and the same new car counts as I if a firm buys it and C if a household buys it. And so Y=C+I+G+NX has a hold on our thinking that MV=PY doesn't, even if that hold is based merely on administrative convenience of data collection. "

I'm not so sure if this asymmetry is as hard as you describe it. There are voluminous amounts of money supply data: M1, M2 etc. So MV=PY surely gets a grip in our thinking due to the money supply data collection apparatus.

Plus, if I am correct, PT is the description of the hot potato effect: P gives you the defined space for the 'bouncing back and forth' that is T. The measurement of the space and the times you get a 'ping' is the GDP which unfortunately I don't understand the first identity enough to figure out that particular quantity. One apparently needs T rather than Y for that to be clear.

Mike, in the way MV=PY is written the mathematical logic is from P to MV, i.e. if P increases then M and/or V have to increase. Since mainstream economics is crazy about inflation, i.e. changes of P, then the monetarism in the form of MV=PY is logically very poor to explain changes in P. PY=MV would be a correct way to write the identity but I have never seen it this way.

But then there must be a reason why it is always MV=PY and not the other way around.


The reason is that us economists aren't too bright. We can't even put the independent variable on the horizontal axis when we draw supply and demand curves.

The mathematical inabilities of economists never cease to amaze me. Try giving them a differential equation, you'll see heads exploding.

@Mike Sproul,
Although I joke about supply and demand graphs myself in my principles classes, there is actually a reason why we draw them the way that we do (i.e. backwards). Graphical analysis in economics was popularized by Alfred Marshall, in whose theory price was the dependent variable. Marshall was very much focused on explaining the market for bread, the most important commodity in the average person's life (next to beer) in England even in the late 1800s. For that market, quantity as driven by weather, is the more exogenous factor, with price responding. (Marshall was also very interested in calculating consumer and producer surplus, and intuitively, when calculating surplus, I think it makes more sense to graph the gap between price and MB and MC oriented vertically.) However, with the relative decline of agriculture our understanding has reversed the role of the variables. However, in most other graphs in economics the axes are labelled conventionally, with the dependent variable on the vertical axis.

That's a prejudice without much merit. Many economists have dual degree backgrounds in math and economics (e.g. Kocherlakota, Steve Williamson etc.) and of course many famous economists were actually mathematicians (e.g. Keynes, Nash etc.) And it's hard to conceive of someone succeeding in graduate economics these days without some kind of quantitative background. I can't honestly say I use differential equations much myself these days, but I studied both ODEs and PDEs at the graduate math level before I was exposed to them again in graduate economics.

P.S. If I recall correctly, outside of some engineering fields, economists rank only behind mathematicians and physicists in their average quantitative GRE subscore.

"2. If you start with MV=PY you can immediately see why monetary policy works. An increase in M works directly to increase Y. "Look, there's M, right there in the equation!"

I can see many internet economists making the mistake that the monetary policy controls M, when it doesn't. If the private sector doesn't want to take on debt, you cannot increase M. You can change the private sector asset portfolio *composition*, but this doesn't do a thing.

Arguments on why fiscal policy is much more powerful than monetary policy are more nuanced than you present here.

This is my take on MV = PY.

Start with Y, a total of spending (it doesn't matter which one, as long as you're consistent). Define R = dY/dT. Now say Y is an aggregate of Xi. So Y = Sum Xi, then R = d (sum Xi)/dt = sum dXi/dt. If Y is in dollars, and T is in years, the R is in $/yr.

Suppose we have a theory concerning the money supply and want to express R in terms of it. Then

M *($/M)*R =dY/dT.

and if we call the integral of ($/M)*R V we get, surprise

MV= Y = integral dy/dt dt.

Not a P in sight. If we want P, we need another change of variable U = Y/P. Now


where P is the price of a notional aggregate good U, which is a sum of Wi* Xi normalized to make PoUo = Yo at time period o. The Wi are weights which define how aggregation is to be done.

You can say MV=PY if you specify that Y is in notional good units. I don't see this as an improvement, but as a non-economist, I lack respect for economic tradition. I tend to look at things from the viewpoint of physics.

You can also say MV =PQ to avoid any confusion as to units.

If Y is GDP, then you have to allow for GDP measuring only transactions fitting a peculiar definition of added value. Personally, I'd rather work with total expenditure, but even then, you have to deal with multiple kinds of money and you'll get a different V for M1, M2, M3...

As to the meanings layered over this therein the economist "must minister to himself".

You wrote:
"If the private sector doesn't want to take on debt, you cannot increase M. You can change the private sector asset portfolio *composition*, but this doesn't do a thing."

I'm sorry but my initial reaction was "huh?"

Currently households are maintaining unusually high shares of liquid assets in their portfolios, indicating there has been the mother of all positive money demand shocks (and no, you don't need to increase debt to increase money):


Household have adjusted their portfolios toward highly liquid, safe assets. This is something the Fed can control through proper expectations management. Here's a paper by David Beckworth and Joshua Hendrickson that provides evidence on the link between household portfolio rebalancing and aggregate nominal spending:


MV=PY; M, P & Y can be measured. V cannot be measured, so it becomes a fill-in-the-blank number.

Sergei: these are identities. They have zero causal implications. You could rearrange them any way round and it makes no difference whatsoever. It's only when you add some bahavioural assumptions that it makes sense to write them one way round rather than another.

For example, in a classical model of a small open economy we should write the first identity as NX=Y-C-I-G, because the stuff on the RHS is all exogenous and determines NX Roughly, Net eXports are determined as the residual of Y minus domestic absorption. We export whatever goods we produce but choose not to buy ourselves. A (temporary) increase in G will cause an equal decrease in NX, and no change in C, I, or Y.

For a second example, in a classical model with fixed exchange rates and Purchasing Power Parity we should write the second identity as M=PY/V, because everything on the RHS becomes exogenous, and determines the stock of money.

Peter N: I did not follow you there at all.

First, think of P and Y (and C and I and G) as vectors. So Y is {2 apples per year, 3 bananas per year}, and P is {$1 per apple, $2 per banana}. Then P.Y is $2+$4=$6 per year.

Second, if you want to take the scalar P.Y and decompose it into two scalars P and Y, then you use something called "index number theory", which lets you "add" together apples and bananas, and "add" together the price of apples and the price of bananas, so you get a weighted average of the level of output and the level of prices. Yes, economists *can* "add" apples and bananas (well, up to a point, because we know there's more than one way to do this, and it doesn't really work). We teach students very basic index number theory in ECON1000, but I want to avoid it here. Here's the wiki.

All of Y,C,I,G,NX,P,T are either vectors or index numbers. M and V may be too.

BigEd: that's not quite right.

In principle V can be measured directly. Just put a tracking device on each dollar bill, and count cheques etc. And some economists actually try to do this in practice, IIRC, by looking at wear and tear on notes, to try to measure illegal transactions that won't be measured any other way.

In practice, Y is *mostly* measured just by adding up C+I+G+NX (expenditure method). So Y is also a "fill-in-the-blank number". (There's also a separate income measure, but the two measures never agree.)


I was hoping to avoid index number theory too (I had to learn enough about index numbers to fight my way through Barnett.), since it wasn't what I was interested in saying, which is that there's a way to proceed that makes V not be magic and makes the dimensional analysis come out right. For this all you need is a transformation from summing dollars to summing components of an aggregate. index numbers are definitely the right way, but they're beyond what's reasonable in a post (and your reference is better than I could do anyway).

I tried to roll the whole business into the weights, which were undefined and depended on how you were going to aggregate. Using explicit vector arithmetic is cleaner, but you need scalar P and Y to talk as we casually do about price indices and aggregate demand. The dot product of the 2 vectors must, by definition, be the same as the scalar product of quantity of the aggregate and its price.

The advantage of the vectors is that Pi*Yi is always a dollar amount, but you have to use index numbers to apply the correct weights. Then you calculate P from the aggregates. If the aggregation was done in dollars, P will be a dimensionless price index, and using Y as the symbol for the aggregate is appropriate.

What I was trying to show was that the derivation of the MV side of the equation is effectively independent of that of the right hand side. V is a real velocity provided Y includes all transactions involving M, and M is something like Divisia M4.

If Y = GDP, then there's considerable distortion from so large an omission, and it's not clear V is very useful, but make Y be all expenditure and M be Divisia M4, then V may very well be quite a useful number.

MV=PY seems a bit pointless if only the product MV is meaningful, and M and V are individually nebulous even if they're well defined in the abstract.

Peter N. Sorry. I underestimated your knowledge, as well as not understanding you.

OK, I *think* I maybe (partly) follow you now. Would it be correct to say (for your bottom line) that income velocity in MV=PY cannot in principle be defined and measured except as derived from PY/M, but that transactions velocity in MV=PT can in principle be independently defined and measured??

Nick, I understand perfectly well that they are identities. Y=C+I+G+NX can also be written as C+I+G+NX=Y and yet I have never seen it this way. And that is fine because most people including economists are interested in the former mathematical representation for economic matters. There is nothing wrong with the latter representation. And these days I come across many economic writings about China in which economists imply the latter form even though they do not write any math symbols. That is when economists talk about over-investment and under-consumption. But the former mathematical form of the GDP identity is perfectly fine because that is what most people are interested in.

But then, when I get to MV=PY, I suddenly stumble upon a clear contradiction between mathematical logic and economic logic. The, without doubt, dominant economic theory revolves around prices and inflation starting from independent inflation targeting central banks and finishing :) with you talking about "always and everywhere" and market monetarism. Your economic logic clearly implies PY=MV. But then you write something completely the opposite.

It is not about being or not being identities but communication. What do you want to communicate with MV=PY? I personally read such mathematical language like price level is exogenous and influences monetary behavior represented by M and V. And then I read the words of a regular language (ok, foreign for me) of your post and the message I get from the words is ... the opposite. Or it seems so to me.

So why is MV=PY written as MV=PY while the message you are sending is the opposite?

This is the reason of my confusion. I am sure I am not the first one confused by the monetarist logic and their presentation style esp in the MV=PY. But since I have *never*ever* seen that identity as PY=MV I wonder why is it the case. Ok, I might not have read enough on economics. I did not spend my life studying it and instead spent a couple of years studying physics. But in physics mathematics is just a tool which has a clear goal to help understand. Well, it seems not to be the case in economics. Why is that?

This post has got me thinking about why I regard the national income identity (and its financial balances version) as centrally important, while MV=PT strikes me as near-meaningless. Here is the reason:

There are four variables in the equation of exchange; three are actively chosen by agents. People choose M, either because they are central bankers or because they are establishing or altering a credit relationship with a fractional reserve financial intermediary. They choose nominal prices through the offers they make or accept. They choose a volume of T based on the quantities of goods entailed in those offers. V, however, is chosen by no one. It is a residual, whatever it needs to be in order for the identity to hold. I don’t write more or fewer checks because I care about check-writing, but only to transact, to act on the right-hand side of the identity. (Living in Germany for the time being, I hardly write checks at all, but that’s another story.)

Every item in the national income identity, however, is chosen. People choose to receive incomes in return for services, and all the expenditure items are chosen as well. This identity therefore embodies a genuine constraint; it adds new information that corresponds to the systemic logic of an economy whose incomes and expenditures have to add up. I don’t see any such new information in the equation of exchange.

Put ten economists in a room and they will likely agree to what Y,C,I,G,NX and P is.

Put ten economists in a room and no one will agree to what M is, and V is simply a residual.

If you choose a rather strict definition of M and consistently stick to that one, MV=PY might have a meaning (but it is not clear due to the complete lack of accepted theories about V). Not that I see how anyone could create an analytically meaningful definition of M either.

Nick Thanks.


"Put ten economists in a room and they will likely agree to what Y,C,I,G,NX and P is."

I doubt it. Y, G and NX: yes. C & I: are purchases of residential housing C or I? P: REALLY?!

MV = PY may be vague, but it is true (in the boring way that identities are true) for every sort of M. Once we get into theories about values of V for particular Ms, then we're away from identities and into the realm of susbtantial theories.

Equally, Y = etc. tells us nothing in itself. It's once we start making assumptions about the values on the right hand side of the equation that we can get some empirical content.

And if Keynesians can get a pass on "animal spirits", then monetarists can definitely get a pass on "M". Something doesn't have to be precisely definable to be meaningful.

You seem to be in a bit of a rut lately, Nick. Perhaps this BIS paper will set your mind working in a fresh direction: http://www.bis.org/publ/work379.pdf.

It's called "When capital adequacy and interest rate policy are substitutes (and when they are not)". As you can see, the authors (Cechetti & Kohler) do not distinguish between "interest rate policy" and central bank policy generally. If you can get past that, though, they make an interesting comparison. So to avoid further offending your sensibilities, I am going to censor "interest rate language" from the following teaser:

... commercial banks are the central bank’s point of contact with the financial system. It is by changing banks’ ability and willingness to issue deposits and make loans that monetary policy has any impact at all. [...] Policymakers can do this directly, by announcing the level of remuneration for reserve balances, by controlling the supply of reserves so that the market price is at or near its target, or by some other means. Regardless, adjustments [...] will influence banks’ cost of doing business, changing all [...] asset values in the economy. Particularly relevant here is that policy [...] changes influence the value of banks’ own assets and liabilities, affecting the level of banks’ capital and risk-taking capacity.

Now consider the impact of changes in capital adequacy requirements. By changing the amount of capital a bank is required to hold, regulators are again influencing banks’ cost of doing business.

Once you start to think about the correspondence between [central bank] policy and capital adequacy policy, it is clear that there are a variety of ways to explain it. With this in mind, we introduce an alternative policy tool into a simple macroeconomic model with a stylised banking system.

Peter Dorman: "There are four variables in the equation of exchange; three are actively chosen by agents. People choose M, either because they are central bankers or because they are establishing or altering a credit relationship with a fractional reserve financial intermediary. They choose nominal prices through the offers they make or accept. They choose a volume of T based on the quantities of goods entailed in those offers. V, however, is chosen by no one."

Lovely comment. I came to exactly the opposite conclusion when I realised that in a recession, V is precisely what individuals *can* choose. See my post I linked to above.

Think of a really simple model of a recession, like Paul Krugman's babysitter model, where people buy and sell babysitter services for money. (Y=T in this simple model).

Prices are sticky, and won't adjust quickly. (P is fixed).

Total M is fixed too low (relative to P). Each individual can get more M, by buying fewer babysitters, but in aggregate they can't.

Each individual's Y (income from selling babysitter services) is fixed too low. He wants to sell more, but can't. It's a recession.

The only thing an individual can choose, and all individuals can choose, is V. They can choose, both individually and in aggregate, how quickly they spend their money. Do they hold it for 1 day, 1 week, or 1 month, before spending it?

So Y is determined by: Y=(fixed M x desired V)/(fixed P)

Phil: that looks interesting, from the bit you quoted. But do you notice the parallel (OK, not an exact parallel) to using changes in reserve requirements as an instrument of monetary policy? (China still does that, from what I read.)

Yep, I've been in a little bit of a rut recently. "People keep saying things wrong on the internet", and I need to correct them! (I doubt I am changing many minds, but I hope they may at least see there's another way of looking at things.) "Ours the task eternal"!

But I'm about to take a 2 week break anyway starting this evening. I may have a head full of a load of new thoughts when I return.

Another crucial difference between Y=C+I+G+NX and MV=PY is that in the former all quantities are *independently measurable*. MV=PY is a *definition* of v, nothing more. The only thing you could use it for is to measure v, which is useless because v doesn't plug into any other equation. If v was stable, you could maybe use it in the very same equation for a different point of time, different economy etc., but since it is not, you just stop. That is, unless you are an economist.

This is largely beside the point, but:

“Animal spirit” usually refers to a change in the marginal propensity to consume/save or/and to changes in expectations about the future – it is usually clear from the context.

Residential investments (new houses) is of course an investment – is there anyone disagreeing with that?

Different economists might prefer different price indexes but at least 9 out of ten will be able to agree about a rather narrow range for the price development (significantly more narrow range than different money measures).

Anyway, my point:

Y = etc. is a decomposition of Y into arbitrary (but rather analytically useful and rather well-defined) parts that allows us to communicate stuff about subsets of Y. Of course you could slice and dice it in a hundred other ways, maybe better ones, but “I increased while G and C decreased” is a pretty clear statement.

MV=PY is not a decomposition. It states that if people bye stuff with “money” to a value of X, you need M “money” used at an average V times. It is an analytical, but trivially true, statement given that “money” is the same thing in both instances. I.e. that “Y” is only those things (old or new) that is bought with paper money if “money” is paper money. However, without any kind of (at least loose) constraint on V, it cannot ever be used on anything , even if M were defined. In actual usage, M is usually undefined, and Y is usually something like newly produced goods, which mean that no actual M aggregate combined with its actual velocity will be equal to that Y. I.e. people use paper money to buy old stuff to, so the amount of paper money times the actual velocity of paper money certainly will not be equal to whatever Y that is used in the practical application.

You might argue that the total (old and new) stuff that is bought for paper money is proportional to the new goods, and that stuff bought for paper money is proportional to the total amount bought for “money”, but that is a awful lot of assumptions for something that claim to be an “identity” – and the proportionality would hardly stay constant if e.g. the amount of paper money increased while all other stuff that goes into the undefined “money” aggregate stayed the same.

So, actual applications of MV=PY are usually trivially false, M is usually undefined and without some theory of V it is an utterly meaningless statement.

OhMy: compare Y=C+I+G+NX to "the # of my kids = the # of my sons + the # of my daughters. Are those 3 things independently measurable? Nope. We count my kids, and divide them up into boys and girls.

Here's how to measure V: I follow you around, and watch every dollar that goes into your pocket, and see how long it stays there. (And people who try to measure the size of the underground economy, where you can't measure P or T, actually do try to estimate V independently (from wear and tear of banknotes, I think, anyone know for sure?)

Nick, I've read the earlier post in praise of MV≡PT (can we agree to keep identities distinct from equations?), and I still don't understand. Suppose we live in a world in which money is the only asset, so we abstract from portfolio choice. If I want more money (more wealth), and I can't earn more, then, yes, I can spend less. But wouldn't it be correct to say I have chosen a lower PT? I look at my budget and say, hmmmm, too many nights on the town -- I'll have to cut back. So I stay at home and mess around with econ blogs. The V that results is simply a statistical residual. To put it differently, I have made a single choice, to spend less and save more. Which item should I imagine myself as having chosen, PT or Y? (Note: PT is a single item for me if I am a price-taker.)

Nick, maybe slightly off topic. But why can't I find any macroeconomic identity that uses the language of stocks and not flows? Y=C+I+G is purely flows, and MV=PY is stocks and flows.

The System of National Accounts structures not only the collection of national income data, but also national balance sheet data. This is stock data. Is this data in search of an identity? It seems that monetarists' language is built around the MV=PY identity, Keynsians around Y=C+I+G. Which group of macroeconomists try to work off a balance sheet identity?


"Residential investments (new houses) is of course an investment – is there anyone disagreeing with that?"

Say someone buys a house and lives in it. It depreciates in value unless it is maintained. Why is that not consumption?

"Different economists might prefer different price indexes but at least 9 out of ten will be able to agree about a rather narrow range for the price development (significantly more narrow range than different money measures)."

Not only will they prefer different price indexes, but they will prefer different indexes for different purposes. It is simply false to say that they will probably agree on what P is, especially since there's a fundamental difference between price indexes and overall P (the price level of all things that can be bought).

In MV = PY, V is the income velocity of M. Only in MV = PT is V the same as the rate at which M is used.

BOTH identities are trivially true. NEITHER is "meaningful" (in the sense of having any testable content) until constraints are put on the variables. BOTH perform a function: Y = etc. gives us a decomposition of Y; MV = PY gives us a definition of the (income) demand to hold money. By constraining values of the variables (e.g. "if we exogenously increase G, then Y increases" "V is more stable than M" etc.) we can get some hypotheses going.

So M is just as definable and often defined as P; MV = PY is as meaningful as Y = etc.; and because V in the MV = PY equation is income velocity, it is always trivially true.

JP Koning: "Which group of macroeconomists try to work off a balance sheet identity?"

*Post*-Keynsians :) esp Marc Lavoie and Wynne Godley. I am reading them currently and they really tried hard

Peter: (How did you do that identity symbol??)

In a recession, I can only choose half of my T's, not the other half. I can buy as much as I want to buy (that's half my T's), but I cannot choose to sell as much as I want to sell (that's the other half of my T's). The amount I am able to sell is determined by how much others choose to buy from me.

But I can choose my V (in a recession), regardless of what anyone else chooses. We all choose our individual V's, and the aggregate V is just the sum (OK, the average) of the individual V's. There is no risk of any fallacy of composition when we are talking about V. There is a risk of fallacy of composition when we are talking about T (or Y) and M.

Sergei: No, they are using *both* stocks and flows, which is what nearly all of us do.

JP: in continuous time, you get two budget constraints: the flow budget constraint (with flow equilibrium conditions) and the stock budget constraint (with stock equilibrium conditions). Any sort of Tobinesque analysis of portfolio choice has some sort of Md+Bd+Kd=Wealth=M+B+K sort of stock identity/budget constraint built in.

Nick, I compose in a word processor (WordPerfect, in fact), then cut and paste. I would do this even without special characters, since it gives me a chance to reflect a little bit more before firing away on the send button. (Not that this always helps....) Anyway, it's funny that at this late stage we are still disputing what a word like "choose" means. I think of it in what I always thought was the normal economic way: people express offers and accept or reject the offers of others. If you reject an offer, like a job because it pays lousy, that's a choice. (I'm not freighting this with any moral baggage. If you reject an offer to sell one of your kidneys, that's a choice too, one I'd like everyone to be in a position to make.) So PT is your choice, no? And whatever you don't spend you save and retain in your wealth account. So is there a degree of freedom, so to speak, for V? Are you making two choices, one for PT and another for V?

@Mike, Dan:

"The identities are fine, but they aren't causal models. They are just constraints on causal models."

Yes, but it's really useful to know about those constraints. I'm an ecologist and evolutionary biologist, and there's a broadly-analogous identity in evolution: the Price equation, which I will take this opportunity to briefly gloss in case anyone's interested (I've mentioned it in comments on other posts too). For details see:


If you're not interested in evolutionary analogies, just skip what follows! ;-)

Basically, what the Price equation tells you is that total evolutionary change (say, in the mean body size of a population from the parental generation to the offspring generation) necessarily comprises two additive components. One is attributable to evolution by natural selection, meaning it's due to covariation between the body size of parental individuals and the number of offspring they leave in the next generation. For instance, if larger individuals are more successful at leaving offspring, then all else being equal, mean body size of the offspring population will exceed that of the parents. The other is attributable to transmission bias, which just means anything that causes the body sizes of offspring individuals to deviate systematically from the sizes of their parents. For instance, if for whatever reason every offspring individual is larger than its parent(s), mean body size of the offspring population will exceed that of the parent population, all else being equal.

What's the use of this? Well, one use in evolution is to allow generalization. If you don't have the Price equation, and the corresponding generally-applicable concepts like "natural selection", you can't recognize that, say, bacterial populations changing over time in response to antibiotics have anything to do with, say, changes over time in the beak size of Darwin's finches. It's *really* useful to be able to recognize both of those as specific instances of the general phenomenon of evolution by natural selection. It allows you to do things like compare the strength of selection across different populations or on different traits or etc. It also serves as a starting point for lower-level mechanistic studies. It's only once you've measured, say, the strength of selection imposed by some antibiotic that you can start asking about the underlying biochemical mechanisms that cause that antibiotic to generate the selection it does. This sort of use of the Price equation, and the associated general concepts, is so taken for granted that we mostly fail to notice it. It's not easy to imagine what it would be like to try to do evolutionary biology without these general concepts. I guess it would be impossible, and the field wouldn't exist. So if you're the sort of person who's inclined to dismiss these sorts of identities as trivial and uninteresting, you should recognize that you're implying that evolutionary biology is trivial and uninteresting (maybe you want to imply that!)

Is the Price equation "causal"? Well, depends what you mean by "cause". An evolutionary biologist would ordinarily describe natural selection as a "cause" of evolution. Even though one could, for any particular instance of natural selection, redescribe it in lower-level, system-specific mechanistic terms. I could talk, for instance, about the biochemical mechanisms that cause antibiotics to lead to interruption of the cell cycle in most bacteria, except those that have a mutation in the right effluent pump gene. And if I want to talk about finch beaks, I could talk in terms of the biomechanics of seed crushing, the physiology of digestion and metabolism and post-assimilation energy and nutrient allocation to different biological functions... But surely you miss a lot if you only talk about causality at that level, and not at any other higher (or lower!) level. It's *really* useful to know that low-level mechanisms (biochemical, physiological, or whatever) are *only* relevant to evolution when they generate trait-fitness covariation, and/or bias parent-offspring transmission. Those are the only "causal routes" by which low-level mechanisms can have "percolate up" and have high-level consequences. If you don't want to use the word "cause" to describe what's going on at the higher level, that's fine--so long as that refusal doesn't blind you to what's going on at the higher level.

The Price equation, the "high level" identity, isn't sufficient on its own for understanding evolution, either in any specific instance or in general. Yes, you can absolutely be misled if all you think about is the Price equation, without ever thinking about lower-level mechanisms. But neither can we do without the Price equation, or at least the general concepts that the Price equation makes precise. I suspect something similar is true in economics.

And by the way, there are also alternative versions of the Price equation, different ways of carving up total evolutionary change, which seem roughly analogous to alternative macroeconomic identities. Which also seems useful to me from my evolutionary perspective. Different partitionings give you complementary insights. Most folks in my field share that view, though unfortunately there are a few prominent people (Nowak at Harvard is one) who insist on arguing that one partitioning is "right" and the other "wrong".

Jeremy: "Different partitionings give you complementary insights. Most folks in my field share that view, though unfortunately there are a few prominent people (Nowak at Harvard is one) who insist on arguing that one partitioning is "right" and the other "wrong"."

That's how I see it too. And it depends on what the question is too (long run growth? short run recessions?).

Peter Dorman: OK, now I see where you are coming from. I'm much more "Keynesian" than you. As a first approximation, in a recession I see people being able to choose what they buy but not choose what they sell. Of course, that's an oversimplification. More generally it takes less effort to buy and more effort to sell, compared to a booming economy.


"OhMy: compare Y=C+I+G+NX to "the # of my kids = the # of my sons + the # of my daughters. Are those 3 things independently measurable? Nope. We count my kids, and divide them up into boys and girls.

Here's how to measure V: I follow you around, and watch every dollar that goes into your pocket, and see how long it stays there"

Yes, Y is not independently measurable, it is the sum of the rest of the terms, which are independently measurable. You care about Y, add them, done.

MV=PY on the other hand does not let you say anything about Y. For that you need v. You say yourself that "you follow me around and count", which is *precisely* what Y=C+I+G+NX is, it is the count of the transactions. So to make MV=PY useful you need to know Y in the first place, it means it is useless, because it needs the first identity, and the first doesn't need the MV=PY.

Nick, we should stop writing the same posts;-)

See here: http://marketmonetarist.com/2012/02/26/most-people-do-national-accounting-economics-including-most-austrians/

Nick, thanks for the tip. Enjoy your holiday.

Honestly, I see this discussion as a little bit surreal. I propose a new topic, let's discuss this: Natural numbers are composed from odd numbers and even numbers. "No,no. Natural numbers consist of prime numbers and non-prime numbers. This composition is far superior to yours. Because if you check if some number is a prime number, you have to check if it is divisible by 2 and then you know if it is odd or even. So your identity is only subset of my identity". "No, no. Decomposing natural numbers into odd and even ones enables you to construct some very important mathematical proofs that you cannot do if you think about natural numbers in your way. Therefore my version of identity is more practical and vastly better then yours." "Hey guys, did you know that in Austria they consider zero as a natural number? [blank stare...]"

W. Peden: Say someone buys a house and lives in it. It depreciates in value unless it is maintained. Why is that not consumption?

As far as I know, "consumption" is defined arbitrary and is a residuum of how of how economists think about savings. The key concept here is time. As you go into direction of smaller and smaller timeframe, everything is savings. The the second after you receive your salary on your account you saved all your income you received last month. The second after your utilities bill was automatically subtracted from your account, consumption comes into being. And on the other side everything is consumption given enough time. Everything decays and falls into ruins, even knowledge can be lost. Supposedly our universe will die one way or another. Or humanity may extinct. At that point everything humanity did during its history will have been consumed.

J.V. Dubois (first post)
"Now imagine that prices cannot change for whatever reason (like government regulation)."

You mean government regulation like contract law. Long term contracts (including debt contracts) are a large part of inflexible prices (but other things like information costs and uncertainty and menu costs are important also).

Reason: I actually meant price controls. I generally use this example for people who were too long exposed to libertarian-austrian way of thinking - that is most laymen. It just illustrates that there exists a real possibility that money matters and that money can be instrumental in a very real way. Using government regulation in any example increases likelihood that these people will digest it. Once they are on board, you may start having a real discussion like if the prices can be sticky even without any form of government regulation.

"Once they are on board, you may start having a real discussion like if the prices can be sticky even without any form of government regulation."

Shouldn't that be something like - "you may start having a real discussion about why prices might be sticky even without any form of government regulation" - since it is generally observed that they are.

Why can't we all just get along:

MV = PC + PI + PG + PNX

On a more serious note, I can't figure out why you like MV=PT. I may be incorrect, but I recall reading that 99% plus of T is transactions in markets like forex. So you are basically measuring financial market transactions. Now those may be correlated with real transactions, but it seems to me that we should measure what we are interested in. If the two ever diverged, i.e. if T soared and Y plummeted, surely that would count as a recession.

I prefer M*(1/k) = PY

In that equation k is exactly what it claims to be, the preferred ratio of base money to income. Obviously V isn't really "velocity".

Scott: It might be so that Nick would argue with your definition of recession: http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/12/why-y.html

On some deeper level I think that Nick is right. It is probably because new output is perfect substitute for used goods that enables us to measure just the former to spot that there is a recession going on. If they would not be perfect substitutes, we may not be able to spot usual signs of recessions (such as unemployment) but we could definitely be poorer due to less gains from trade (of old stuff). So using monetary policy to promote more trade in old stuff could make us richer. I think the same could be said for bonds and other transactions if we assume that people undertake these transactions for a reason. If there would be something like sticky bond prices that cause bond markets not to clear, I can imagine government intervention. I think it is our luck that the usual behavioral constrains we put on the MV=PT identity cause that transactions of bonds or other financial instruments don't bother us as much.

Juts an additional note: so I think that you are perfectly right that MV=PT does not help us much in solving the current recessio and that your version may be better for tracking NGDP that you are obviously so interested in. However MV=PT enables us to look at what the recession is in a new eyes. Maybe it makes sens to decompose PT into different components, like prices (and velocities) tied to bond transactions, land transactions, used stuff transactions and such. And maybe some future policy makers will find new ways of how to use these alternative views on the identity to reach different objectives. And I think that this is what Nicks talks about - being able to look at things in a different way (via different identity) may give you fresh ideas of how to think about issues.

One advantage of MV = PT is that it might set things up for explaining the transmission mechanism between monetary policy and economic activity, which I find is a black-box in a lot of monetary theory.

"What matters for long run growth is the division of output between consumption and investment, not between households, firms, and governments."

Really, Nick? Government's share of GDP doesn't really matter for long run growth? Of course I agree that C + I + G + NX isn't very useful for that, in fact neither is any such identity, you should be using a production function of some sort...

Saturos - perhaps you saw this earlier, but in case you didn't, Nick is away from the internet for a couple of weeks.


How about a present for him when he gets back? Paul Krugman has published a new book "End this Depression Now!" which mentions the esteemed Dr. Sumner above (in an academics disagreeing sort of way). You could post a general thread about the book, let the macro crowd post on it and have a nice pleasant macro thread for Nick when he comes back.

You don't even have to post any macro, I know that not your thing.

Determinant, We could start by mentioning how Krugman recently anointed Scott "the heir to Milton Friedman"...


... although coming from him I guess that was more like "the Heir of Slytherin".

As to Scott's comment above, I think Nick's focus on T is because he wants to look at the flow of the medium of exchange as the link binding the sale of all commodities together. Supply and demand makes money look too much like just another asset. Whereas it's only excess demand for money that can cause a general glut. Also supply and demand for money makes it look too much like other commodities, with a single annual output which clears in a single annual consolidated market exchange. Whereas the annual "output" of money in the annual set of all monetary exchanges is the quantity of money times its velocity. And an increase in the "demand" for money in terms of hoarding larger balances is really a reduction in this extended supply on the overall market for exchange of money against goods-in-general.

It really depends on how you look at the supply and demand for money. If you look at it as the general exchange of goods for money, you can use your "intuitive" supply and demand model to determine the price level. And this is very much in line with MV=PY. If on the other hand you want to view the supply and demand for stocks of money balances that people wish to hold in the aggregate, then excess cash balances, instead of clearing the market by undercutting as in the standard econ101 story, actually drive up the price level by hot-potatoing for as long as necessary until the price level rises enough to equate demand and supply. Output is only in that story indirectly, we don't specifically know how much prices rise for a given dump of excess balances. And in fact this story is more about transactions than output purchases. Now you can transform M/P = kY into the exchange equation by taking k as the inverse of desired velocity, but that's a highly unclear and indirect representation of the underlying picture.

Remember that the desire to hold less money is only an indirect statement about the velocity one requires to sustain one's level of nominal income, and that too in the aggregate - it's the total stock of money being held that has to circulate often enough to create the total level of nominal income, and not one's individual piece of that stock. Now if the actual M is not equal to the collectively desired M, then the resulting surplus/shortage of spending must continue until nominal income adjusts by enough to make desires match reality. But notice how the price level here becomes merely something that "needs to adjust" in order to equate the desired and actual stocks of an asset, money. It doesn't clearly show you why money is special. Whereas MV = PY explicitly models money's role as the medium of exchange, which also tells you why disruptions to that process causes general gluts, and why Nick Rowe prefers it. MV = PY explicitly shows you the determination of the price level through the trade of money for all other goods - and you immediately know that it's special.

I like MV = PC + PI + PG + PNX, though. Although it's ultimately a bad model, for reasons that Nick and Scott (http://www.themoneyillusion.com/?p=274; http://www.themoneyillusion.com/?p=14072) have both pointed out.

Scott sees it my way too, sometimes: http://www.themoneyillusion.com/?p=3173
And sometimes he combines both: http://www.themoneyillusion.com/?p=461

Y = C + I + G + NX is only an identity if Y is demand for output. If Y is GDP (supply of output), then Y = C + I + G + NX is NOT true by definition, but is a market-clearing condition that will hold in equilibrium.

It is not at all obvious that an exogenous increase in one component of demand will cause an increase in equilibrium output. In the simplest model I can think of (1-period, households choose consumption and labor, government budget constraint holds with equality), an increase in G will raise Y if taxes are lump-sum (due to the income effect of higher taxes), but generally will NOT raise output if there is an income tax. And in either case the multiplier is less than 1 and consumption falls.

Sorry to be late to this party, because my essential confusion seems to be scattered through the discussion. Undoubtedly displaying my ignorance, but I do read about this a lot, and seem to see the same confusion or at least disagreement/failure to communicate in others.

In Y=C+I+G+NX, Y is designated in (nominal) dollars -- because that's how we measure it, by adding up all the dollar transactions.

But in MV=PY it isn't. It seems to be a quantity of (unspecified) units of output.

If it is there designated in dollars, we have:

P$ x Y$ = PY$^2 . What is "dollars squared"?


M and V here are clearly "quantity of dollars" and "number of turnovers per period." Yielding a product (nominal gdp) designated in dollars.

P here must mean "dollars per unit of output." (That's what a price *is* -- dollars per unit.) Yielding a result designated in units of output.

Is Y designated in units, or in dollars? It doesn't seem like it can be both. Or if it is, then the two Ys are different things -- by construction -- and the two identities share no common terms.


Talk to any Keynesian and you'll find that they're far more inclined to interpret Y = C + I + G + NX as referring to real (CPI or GDP deflator adjusted) quantities. Of course P is here assumed to equal 1, because "prices don't matter in the short run". But I agree that it makes far more sense, and is far more consistent with the Keynesian approach, to talk about nominal spending flows. (Really, you should use lowercase for real variables, and uppercase for nominal - and the identity is true in either case, as it's just a listing of the different categories that any spending or output must fall into.) Matt Yglesias (http://www.slate.com/blogs/moneybox/2012/05/13/fun_with_accounting_identities.html) has a new post in which he takes Scott Sumner's version: MV = C + I + G + NX. That might be the best approach of all - it shows you that all the changes in "income accounting" variables that get reported on the news must all be manifestations of fluctuations in the overall volume of spending, MV. If we're talking about fiscal policy or "exogenous shocks" to NGDP, then this must be a fluctuation in V (base velocity).


Thank you! Very helpful.

I've replied over at my place:


I'd love to hear your further thoughts.

Let me express my confusion more succinctly:

GDP is counted in nominal dollars -- total expenditures on final goods and services. (Expenditure approach.)


MV is, ineluctably, nominal dollars.


Y = GDP = nominal dollars spent = MV = PY


Y = PY


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