Here are two macroeconomic identities:
1. Y=C+I+G+NX
2. MV=PY
Both are true by definition.
1. If you start with Y=C+I+G+NX you can immediately see why fiscal policy works. An increase in G works directly to increase Y. "Look, there's G, right there in the equation!". It's only a little bit less obvious to see how tax policy works, and it's only a little bit less direct. "A cut in T increases C, and look, there's C right there in the equation!".
It's hard to see how monetary policy works. I can't see M anywhere in that Y=C+I+G+NX equation. If M does work, it can only work indirectly, which means whether or not it does work is uncertain and unreliable. "So, what exactly is this monetary policy transmission mechanism supposed to be?"
Of course, if you aren't stupid, you recognise the logical possibility that fiscal policy might not work. "Sure, I suppose an increase in G might cause an equal decrease in C+I+NX, but why exactly would we expect that to happen?" The burden of proof is on those who say that an increase in G would cause an equal decrease in C+I+NX, and that transmission mechanism is not at all obvious. And after all, when we talk about fiscal policy, aren't we assuming "other things equal"?
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!"
It's hard to see how fiscal policy works. I can't see G or T anywhere in that MV=PY equation. If G does work, it can only work indirectly, which means whether or not it does work is uncertain and unreliable. "So, what exactly is this fiscal policy transmission mechanism supposed to be?" If fiscal policy does work, it must work either by increasing M or increasing V, which means it's really just backdoor monetary policy.
Of course, if you aren't stupid, you recognise the logical possibility that monetary policy might not work. "Sure, I suppose an increase in M might cause an equal decrease in V, but why exactly would we expect that to happen?" The burden of proof is on those who say that an increase in M would cause an equal decrease in V, and that transmission mechanism is not at all obvious. And after all, when we talk about monetary policy, aren't we assuming "other things equal"?
3. So far my argument has been symmetric. But there's an obvious asymmetry between the two identities. P appears in the second, but not in the first. "How do we know that an increase in M won't just cause an equal increase in P, with no change in Y?". That's an obvious question when you see MV=PY, because "Look, there's P, right there in the equation!". If I re-wrote the first identity in nominal terms, as PY=PC+PI+PG+PNX, it might invite the same question. Or if I re-wrote the second identity in real terms, as Y=Vm (where m is the real money stock), I could hide that question.
Scott Sumner has written about the very common fallacy that sees fiscal policy as affecting real aggregate demand while monetary policy only affects nominal aggregate demand.
There are three different types of quantities: quantities demanded; quantities supplied; and quantities actually bought-and-sold. Which one of these three types of quantities does Y, C, I, G, and NX refer to? It's very easy to forget the supply side, if you leave P out.
4. 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. Plus, you can do neat things with Y=C+I+G+NX, like re-write it as S-I+T-G=NX, which looks different from Y=C+I+G+NX, because it has a whole new letter, S (defined as Y-T-C, so it's not really new at all).
5. I was born and bred (as an economist) using Y=C+I+G+NX. That identity is part of my identity. "You can take the boy out of the Y=C+I+G+NX, but you can't take the Y=C+I+G+NX out of the boy". I learned about MV=PY, of course, but it has always felt foreign to me. A couple of years back I decided that MV=PY is a more useful identity (though it should really be MV=PT), but it still feels, well, like wearing someone else's clothes.
6. I think MV=PT is more useful a way of organising our thoughts for business cycle theory because:
Recessions are always and everywhere a monetary (medium of exchange) phenomena, and Y=C+I+G+NX refers equally to a monetary exchange or barter economy.
Recessions are not about Y; they are about T. Production of newly-produced goods Y for home use and for barter with friends and neighbours seems to do very well in recessions; while monetary transactions T of all kinds, whether for newly-produced goods or not, seem to do badly.
7. For the macroeconomics of long run growth I would use a very different identity: Y=C+I+NX. I have left out G altogether. G is divided into government consumption and government investment, and C includes both private and government consumption, while I includes both private and government investment. What matters for long run growth is the division of output between consumption and investment, not between households, firms, and governments.
8. It is common to see amateur "internet economists" placing too great a reliance on identities. But maybe the only real difference is that they are not as good at hiding it as professional economists. (I did see one very very good professional economist recently resort to the purely gratuitous use of Y=C+I+G+NX in the middle of an otherwise respectable argument for why fiscal policy works. It was on Brad Delong's blog a few months back, but now I can't find it. It wasn't Brad himself.) It is easier to see the disease on others' faces.
9. The parallel with "Identity Politics" is deliberate, but I'm not sure how far I can push that parallel. And I can't quite figure out the relationship between this post and my old "Celestial Emporium of Benevolent Knowledge" post.
Worthwhile Canadian Initiative 
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.
Frances:
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”?
C+I+G+NX = MV/P
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.
??
Steve,
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).
@Saturos:
Thank you! Very helpful.
I’ve replied over at my place:
http://www.asymptosis.com/why-does-y-equal-real-gdp.html
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.)
GDP = Y
MV is, ineluctably, nominal dollars.
So:
Y = GDP = nominal dollars spent = MV = PY
So:
Y = PY
??