The reason that New Keynesians don't like talking about the supply of money and velocity has nothing to do with problems in defining the supply of money, the instability of velocity, or the instability of the money supply multiplier. As I argued in my last two posts, similar criticisms would apply equally to the New Keynesians' actual and natural rates of interest.
The real reason is the New Keynesian view of the monetary policy transmission mechanism. They see it as working through interest rates. Given sticky prices, an exogenous decrease in the supply of money causes interest rates to rise which causes aggregate demand to fall, which causes a recession. So why not just cut out the irrelevant cr*p about money, and just say the central bank raises interest rates which causes aggregate demand to fall? Money and velocity play no role in the story. You can talk about them if you like, but they don't help you understand what's going on, and are merely a distraction.
New Keynesians have this precisely backward. Interest rates are neither necessary nor sufficient for the monetary policy transmission mechanism. Money/velocity is both necessary and sufficient.
Assume sticky prices.
Lets break this into two parts.
1. To show that interest rates are not necessary in the transmission mechanism, imagine a world with no interest rates at all. The only asset is money, which pays 0% interest. It's a backscratching economy, where backscratches must be paid for with money. Or Paul Krugman's baby-sitting coop, if you like. [Don't want to search for the link and blow my monthly ration of NYT views. Update: thanks to Phil, here's a Slate link.] Start in equilibrium. Then part of the stock of money is destroyed. At the existing PY, actual velocity exceeds desired (actual M is less than desired). So individuals buy fewer backscratches to reduce their actual velocity (to try to rebuild their actual money stocks). There's a recession, even though there are no interest rates. We can explain the recession in terms of money and/or velocity. Money/velocity is sufficient to explain the recession, while interest rates are not necessary.
Or, imagine a world in which there are non-money assets, but the interest rates on those assets (or their prices) are fixed by law, so cannot change. Start in equilibrium. Then part of the stock of money is destroyed. So individuals try to sell bonds and land etc. to rebuild their money stocks. But they fail to sell bonds and land, because everyone is trying to do the same thing, and prices of bonds and land cannot fall, so there's an excess supply. So they buy fewer backscratches instead, and there's a recession, even though interest rates never changed.
2. To show that interest rates are not sufficient in the transmission mechanism, imagine a world with barter rather than monetary exchange. The central bank controls not the supply of money but the supply of bling. Bling is the medium of account (prices are measured in terms of bling), but there is no medium of exchange. Bling does not circulate. We can't meaningfully talk about the velocity of bling. Because wearing bling is a form of conspicuous consumption of a durable good, and a way of flaunting ones real wealth, there is a demand for real bling, M/P, which depends positively on real income Y and negatively on the nominal interest rate (the opportunity cost of wearing bling). M/P = L(Y,i).
Suppose the central bank reduces the supply of bling. Interest rates rise, as people try to sell bonds and land to buy more bling. Since prices are measured in terms of bling, and prices are sticky, the real stock of bling M/P cannot rise back to equilibrium.
Does the increase in interest rates cause a recession due to deficient aggregate demand? "What do you mean we are both involuntarily unemployed because of deficient aggregate demand? This is a barter economy. Here's the deal: I scratch your back and you scratch mine. That way we are both better off, and we both get back to full employment." No, there is no recession, despite the central bank's tight bling policy causing high interest rates.
OK. Interest rates may play a role in the monetary policy transmission mechanism. For one thing, the demand for money (desired velocity) depends on interest rates. But the interest rate channel is just one way of telling the story of the transmission mechanism. It is not essential. It is neither necessary nor sufficient.
Worthwhile Canadian Initiative 
Joe, I think you are confusing the term ‘demand’ with the terms ‘purchases’ or ‘transactions’. A demand curve is an abstraction, a willingness to pay at different prices. Here’s an example. Microsoft does a stock split, one share becomes two. It’s announced overnight. It’s understood that the $80 shares will fall to roughly $40. How does the fall occur? When trading starts, the price could gradually be bid down . . .$70. $60, $50, etc. Or it could immediately fall to $40, from the very first trade. I say the latter. The theoretical S&D curves will shift down by 50% overnight on the news, and the change in S&D will result in the first transaction occurring at about $40. I hope this makes sense.
If prices change, then ipso facto S&D has changed. You wrongly assumed that meant transactions had occurred. Not so.
Thanks Professor! Understood!
Also, Krugman had an interesting post on Woodford, fiscal policy, and tinkerbell. Naturally, I am hoping that at some point you respond on your blog. However, you can hold off longer than July 4th, enjoy your vacation. Visit the cape.
http://krugman.blogs.nytimes.com/2011/06/20/woodford-on-monetary-and-fiscal-policy
Best.
Scott: ” In microeconomics the only price of apples that matters is the real price, the price relative to all other goods.”
I was talking about real prices. The real price of money has fallen relative to the real price of bonds. If the slump is due to a shortfall of money supply relative to what’s demanded then the opposite should be true.
Scott, it’s true that if the central bank holds the interest rate constant than the price level becomes indeterminate in the NK model. (This is a feature which NK inherits from RBC models, so it’s not a particularly Keynesian thing.) The indeterminacy goes away if the central bank controls the money supply or follows a sensible Taylor rule. So a fixed interest rate is not an optimal policy. But we can still assume that policy for theoretical purposes, to show that the NK transmission mechanism (for output and inflation) does not require variable interest rates.
Still, it’s clear that NK can’t give you all you want in the way of hot-potato properties. You might like to take a look at that Bénassy paper I linked to early in the thread. His OLG model gives you a determinate price level in all circumstances.
Kevin: “it’s true that if the central bank holds the interest rate constant than the price level becomes indeterminate in the NK model”
It might be worth pointing out that this is also true in monetarist models. If the central bank tries to keep the nominal interest rate constant then the price level is indeterminate, even if the CB is controling the money supply.
This is a feature of every model.
Adam, when I said the indeterminacy goes away if the central bank controls the money supply I meant instead of the interest rate. But when you say it’s a feature of every model isn’t that a bit sweeping? Again, I refer to that Bénassy OLG model. Part of what he’s trying to do is explore the conditions in which these problems arise. (That’s not his aim in that particular paper but it’s a major theme of his book, Money, Interest and Policy.)
Kevin, I did know what you meant. I pointed out because there is the tendency for people to take a statement like you made out of context and say “well that shows Keynesian models make no sense”. Yet no NK model actually assumes the CB tries to keep the nominal rate constant.
On the other hand, while I admit I don’t really have an OLG structure in my head it seems to me the result is true of any economy with money and something like a Fisher effect (even just in the long run).
To give an example, a couple of years ago Nick had a post that said something like “we used to know that an interest rate target left the price level indetermintate but after 20 years in which it appeared to work we forgot…” (I’m paraphrasing).
While I don’t think Nick was being intentionally disingenuous this was a very silly post. The price level is indeterminate if the CB tries to keep the nominal rate constant forever, that is not the same as using a target that is adjusted according to some rule, like a Taylor rule. So the whole premise of his post was nonesense.
Adam,
Yes, I’ve often noticed that any little oddity in a Keynesian model will be enough to put some reader off. I think the NK model would get a better press, from conservatives at least, if it was called the Mankiw-Taylor model or something like that.
The nominal indeterminacy business doesn’t seem all that important to me, but in case I’m missing something it might be worth spelling out how I understand it: if the natural interest rate (real, obviously) is r, and i is the nominal interest rate (both constant for simplicity) then, at least in a flexible-price setup, if expectations are exactly fulfilled we must have:
Log[P(t+1)/P(t)] = i – r
It’s clear that if a sequence {P(t)} satisfies that equation so does {kP(t)} for any k>0.
But that’s all that Fisher-type thinking gets us. It doesn’t rule out the possibility that some other equation in the model will nail down P(t) for just one period, which is all we need to draw the entire path. In RBC and NK models there is no such equation available. But in a monetary OLG model there is, because the older generation has a stock of financial assets to preserve it from starvation. So there is a nominal anchor. The crucial difference seems to be that, in models with a constant population of immortal agents, there are no ‘outside’ financial assets. The same feature that gives us Ricardian equivalence in RBC/NK models robs us of a determinate price level when i is held constant.
And you’re right: I should reiterate that no economist actually calls for constant interest rates, so it’s not a matter of practical importance.
Kevin, we are actually talking about slightly different types of indeterminacy.
First off, the NK model (as presented by Woodford) does have another eequation to pin down P. It is the government budget constraint (the government is assumed to issue nominal debt). I tried to explain it here: http://canucksanonymous.blogspot.com/2011/06/price-level-determination-without-money.html
If there were no government then it could be done if there is a stock of privately issued nominal debt, the collective budget constraint of the debtors would pin down P.
But what I was thinking off was actually the instability associated with attempting to maintain a constant interest rate. That is the Wicksellian cumulative process, if the some noise or shock makes i want to rise then CB supplies more money which increases inflation, causing i to want to rise, causing the CB to supply more money…
The indeterminacy you’re talking about in you last comment doesn’t appear to have anything to do with the nominal rate being constant, it would not even be solved by a taylor rule. A taylor rule only controls inflation without some stock of nominal debt.
Adam and Kevin, You misunderstood me. I certainly understand that a Taylor rule allows you to control the rate of inflation, but it takes the current price level as a given. It doesn’t tell us where that price level comes from. Why are prices in Japan 100 times higher than in the US? I don’t see how you can answer that question looking at interest rates and output gaps. Even looking at the money stock will not give you a precise answer, but it puts you in the right ballpark.
Here’s another way of putting my point. Describe the path for the fed funds rate that’s likely to lead to a 470-fold increase in the US price level over the next 5 years. Not 470 percent, a 470-fold increase. I say it can’t be done. I don’t even know whether you’d need a lower or higher interest rate to make it happen. But I can describe a path for the monetary base that will at least put you in the right ball park.
Joe, I’ll have plenty to say about Krugman when I return. I left a comment over at his post that cites his Vox essay on Keynes.
Adam, thanks; I was afraid that the word was used in different ways by different authors.
Scott, I can’t see what your problem is. Just put your preferred money-supply process into a Mankiw-Taylor model and it will give you the interest-rate path you need. 🙂
Professor Sumner,
You said….I certainly understand that a Taylor rule allows you to control the rate of inflation, but it takes the current price level as a given. It doesn’t tell us where that price level comes from.
Why can’t you just plug in the expected inflation rate into the Taylor rule? You could just use the market’s TIPS rate as the inflation rate for the Taylor rule. No?
Joe, Inflation and the price level are different things. Explaining the inflation rate isn’t the same as explaining the price level. A Honda that costs 25,000 in the US costs 2,500,000 in Japan. Why the big difference?
Kevin, I’m glad you added the smiley face, at first I thought you were serious. 🙂
Scott, I wasn’t being entirely facetious. The model typically comes with a log-linear money demand function as an optional attachment: m(t) – p(t) = y(t) – ki(t), where k is just a parameter. You know what path you want p(t) to follow and you are probably willing to assume full employment (at least for a first stab at the problem). So if you believe that putting m(t) on a particular path will do the trick, why not simply plug your sequence {m(t)} into that equation and get the sequence {i(t)} you need to put m(t) on your desired path?
The obvious objection is that you may get values like -20% or less but you don’t accept that negative interest rates pose any particular problem – or do you?
Scott: “Everyone, Thinking about this discussion, and reading Krugman’s new Keynes essay, makes me wonder whether there is any other field where even well-informed people think about basic concepts in such different ways.”
That is deserving of a blog post.
Take me and Scott, for example. In many ways, we are very much alike. Same age, same field (except Scott does history), same intellectual antecedents. We are both Milton Friedman’s grandsons. Scott’s PhD Chicago, mine UWO. (Which Serge Coulombe once described as “succursale Chicago” (succursale = “branch plant”). Both quasi-monetarists, in some sort of sense. And yet, even in this case, we think of AD and the AD curve in very different ways. And AD is a totally basic and key concept in our thinking. And most economists are far more different than me and Scott.
Nick, I’ve become obsessed with the pragmatist maxim: “That which has no practical implications, has no theoretical implications.” So we need to figure out the practical implications of our two views of AD. (I’m still not sure about the practical implications of our two views of the essence of money (medium of account or exchange).)
Based on the comments of you, Adam, and Kevin, am I correct in assuming the following:
The standard Keynesian view is that if Canada gains 10 million new immigrants, and this causes the AS curve to shift right, and this causes prices to fall and the real quantity of goods and services being purchased to increase, that you’d say “real aggregate demand has increased.” Even if the AD curve didn’t shift. If that’s true, I need to rethink everything I thought I knew about AD.
You are right that a post would be interesting, but I think you are better at this sort of thing. I’m afraid I’d misrepresent standard Keynesian reasoning, as I’m still not sure I understand it.
Maybe part of the problem is that I tend to assume nominal shocks (the entire AD curve), which are immediately split between output and price changes. Keynesians assume real demand shocks, that lead to price changes with a lag.
Scott, it’s really hard to imagine immigration on that scale without an associated increase in the demand components C, I, and G. If the immigrants are drawn in by a booming economy that contradicts the assumption of constant AD. If causation runs the other way, C and G must surely increase since the immigrants will have a demand for goods and services. Investment must also increase because firms will revise their estimates of future capacity requirements.
I’m never sure what you and Nick are on about when you refer to ‘the’ AD curve. Why not focus on one particular model, so that you both know how the curve is derived?
“To show that interest rates are not sufficient in the transmission mechanism, imagine a world with barter rather than monetary exchange…”
I’m in Bishkek now, Kyrgyzstan… here, as in most developing economies, short interest rates have no direct role in whatever transmission mechanism exists for monetary policy into the real economy, I don’t need to imagine a world with barter exchange, I just need to observe the significant lack of financial sector architecture around me… and yet, what role do monetary aggregates play in these countries?
I really like your posts Nick, and the exchanges that one is truly compelled to print out, but the last 3 posts on this matter really came across at odds with the paper that has been on my mind lately: http://www.bis.org/publ/work269.pdf . It seems that it is not only for New-Keynesians that monetary aggregates and velocity are meaningless concepts…
Regards from Kyrgyzstan
Joao