Nick Rowe, Brad DeLong, and Me on Whack-A-Mole General Gluts and Money

The other day I took some issue with the idea that general gluts are just excess demand for [bonds, money, secure assets] and excess supply of goods and services. The idea isn't absurd, of course. If there happens to be no excess demand for money but there is an excess demand for bonds and surplus of goods and services, that will sure feel like a recession to workers and look like a recession in the data. In that sense I don't think Brad DeLong's version of the story is wrong per se. In all likelihood we've had many downturns characterized by this sort of general glut. But there's something ultimately unsatisfying about this approach when you're going through a downturn that just doesn't bounce back - when you have a stable underemployment equilibrium. Why would this "whack-a-mole" general glut not work itself out? Brad provides several great reasons why not: disrupted credit channels, the zero lower bound, etc. All of these reasons are very good reasons for why a whack-a-mole general glut would lock in for a while. And perhaps that's all there is to it.

But I have my doubts that that's all there is to it, and so does Nick Rowe. However, Nick takes a somewhat different approach from me an in a lot of ways, my approach to why the whack-a-mole theory is incomplete is closer to Brad.

Nick starts with a review of some quantity-constraint material which is very good to look over. He was the one that first alerted me to how important Janos Kornai's work on socialist economies was for understanding market economies - because of these quantity constraints (supply constrained under socialism, demand constrained under the market).

Then Nick gets into the monetary stuff:

"If there are n goods, including one called "money", we do not have one big market where all n goods are traded with n excess demands whose values must sum to zero. We might call that good "money", but it wouldn't be money. It might be the medium of account, with a price set at one; but it is not the medium of exchange. All goods are means of payment in a world where all goods can be traded against all goods in one big centralised market. You can pay for anything with anything. In a monetary exchange economy, with n goods including money, there are n-1 markets. In each of those markets, there are two goods traded. Money is traded against one of the non-money goods. Each market has two excess demands. The value of the excess demand (supply) for the non-money good must equal the excess supply (demand) for money in that market. That's true for each individual (assuming no fat fingers) and must be true when we sum across individuals in a particular market. Summing across all n-1 markets, the sum of the values of the n-1 excess supplies of the non-money goods must equal the sum of the n-1 excess demands for money.

Walras' Law describes an economy with one market with n goods traded and n excess demands. In a monetary exchange economy there are n-1 markets with 2 goods traded and 2(n-1) excess demands.

OK. So can't we just re-state Walras' Law as saying that the sum of the values of the excess supplies (demands) for the n-1 non-money goods must equal the sum of the n-1 excess demands (supplies) for money?

The short answer is: "No, you can't". Or rather: "You can if you like, but it's a very different beast from the original Walras' Law, and is totally useless"."

I like to think in terms of a linear system, because when we worry about recessions we're worrying about slack, and with a linear system it's very easy to conceptualize exactly what the source of the slack is. So Nick talks about n-1 markets and n goods (one being money, which crucially has no market, and is instead traded in all markets). When he says "market" think of a linear system with a supply and demand schedule. So:

Qs=a+bP
Qd=c-dP

Putting this in equilibrium (Qs=Qd) and moving things around:

Q-bP=a
Q+dP=c

...and the solution is trivial. That system is a "market". There are n-1 goods out there and then Nick adds money which makes "n", but he says money isn't traded in a market, so that's n goods, n-1 prices, and 2(n-1) market relations (because you have a supply relation and a demand relation for each market). I think Nick is wrong here. Why? Let's go back to our system of equations - "money" gets a column because it's a good, right? Does it get a row? Nick implies no - because there are n-1 markets. But this seems wrong. It oughta get a vector of prices, right? That's what the "price level" is, after all - it's the inverse of the value of money. So while Nick tells us there are n-1 markets which have 2(n-1) market relations and n goods, and n-1 prices it seems to me there are n goods, n-1 prices, and the price level.

This, I think, is what Brad was thinking in this post where he took issue with my claim that the nature of the interest rate as one price operating in two markets implied an overidentification. Brad wrote: "In the language that Dan is talking, I think that the right thing to say is that if the price level is sticky then the Walrasian system is over-identified. If the price level is flexible then the Walrasian system is just identified--the thing that is supposed to move in order to eliminate the excess demand for financial assets is the price level, and it does not, or it does not move fast enough."

This thinking from Brad seems very close to what Nick is saying to me: n goods (including money), n-1 markets, and one "price level" producing a perfectly identified system. In this system, you need sticky prices to get slack, Brad is right on that.

But the problem is, we don't live in this system. And you know who drove this home for me? Brad DeLong.

Everything comes down to money and the interest rate, and everything comes back to Keynes. In this post, Brad explains why the interest rate is really one price functioning in two markets: the bond market and the money market. People want loanable funds and people want liquidity. Let's bring this back to our system of linear equations where Brad is an out-of-the-closet Walrasian (who is open about the fact that the price level squares the system of linear equations) and Nick is a still-in-the-closet Walrasian (who still insists we have n goods and n-1 markets even though it's clear that that n-th good - money - is related to all the other goods through the price level). What does the interest rate do to this system of equations?

It overidentifies the system, introducing the very real potential for slack. Before we had n-1 goods, n-1 prices, and money for a total of 2(n-1)+1 columns. We had 2(n-1) market relations (supply and demand in each of the n-1 markets) and the price level for a total of 2(n-1)+1 rows. This is a well-identified system where we can have whack-a-mole general gluts but no reason to think those gluts won't be arbitraged away eventually (by adjustments in the price level, a la Brad's point, if nothing else). But Keynes points out that we are missing one row - one market relation. We are missing the money market or the market for liquidity - that market that Nick says doesn't exist. This is the liquidity preference theory of the interest rate - the interest rate is determined by the desire to stay liquid. The problem is that while we add this market relation as a row in our linear system, we don't add another column so that the system remains identified. Why? Because we already have the interest rate as a column - because the interest rate is the inverse of the price of bonds (which are presumably already there as one of our n-1 goods and n-1 prices).

This is a major problem. Now we have 2n rows and 2(n-1)+1 columns. That introduces slack. Now, where that slack shows up isn't entirely clear. Keynes said investment was made based on the investment level that would equalize the marginal efficiency of capital and the interest rate. So he thought a lot of the slack would show up in investment. It's not a bad approach - we do see the sharpest drops during recessions in investment. Keynes was a sharp guy. Hicks took a slightly different approach that was perhaps better suited to the new wave of national accounts measurement. In his model, he forced the loanable funds market to actually clear at the same interest rate as the money market. This means no slack in the loanable funds market, so the slack would be felt in the prices or quantities of goods and services. Hicks strikes me as being a little more presumptuous than Keynes in this respect, so I somewhat prefer Keynes - who left the question open.

Anyway - hopefully this clarifies where I agree and where I differ with Brad and Nick. I think Nick's system is relatively Walrasian once you think about the role of the price level. I think Brad's unashamedly Walrasian system ignores his own prior writing about the interest rate. And I think the interest rate is key: it is one price operating in two markets. You can arbitrage your way out of whack-a-mole gluts. You cannot arbitrage your way out of an overdetermined system. You have to hack the system - you have to get the interest rate to a level that is consistent with full employment.

UPDATE: And this, I should add, is why despite Brad's quite justifiable praise of Say, Bastiat, Mill, Bagehot, Fisher, and Friedman - there is a very good reason why Skidelsky calls Keynes "the master", and why I write so much about him on here.

*****

The blogosphere can get heated when people disagree with each other. Let me nip that in the bud. Nick and Brad are quite simply the best bloggers that I follow right now. Most of this stuff I ultimately, at some point picked up from them anyway!