Brad DeLong calls it my "self-imposed Sisyphean task". He's probably right. But it seems worth a try, as long as there's a small chance he's wrong. I have a Cunning Plan.
Like it or not (and there is much to like as well as dislike), New Keynesian macro has become the main accepted approach for teaching, research, and policy. It would be hard to persuade economists to ditch it. Rather than ditch it, I want to reinterpret the New Keynesian model as a model of a monetary exchange economy (and argue that it only makes sense as a model of a monetary exchange economy). Then I want to make small changes to the model so that the stock of money enters essentially (and argue that it only makes sense if the stock of money enters essentially). My Cunning Plan is a bait-and-switch.
Simplify massively, to clear the decks of anything that is not required for me to make my points. Large number of identical infinitely-lived self-employed agents who produce and consume haircuts (the only good). So wages and prices are the same thing, and output, consumption, and employment are the same thing. All agents set the same price (which may be sticky or flexible). The central banks sets a rate of interest (somehow, and this is a question that must and will be answered). To make it even simpler, we can assume the central bank indexes the nominal interest rate to the inflation rate, so it sets a real rate of interest. No shocks, nothing fundamental ever changes, and full employment equilibrium is 100 per period.
Suppose the central bank sets the rate of interest too high. Will this cause unemployment?
No. Any unemployed agent would simply cut his own hair.
Suppose we change the model so agents can't cut their own hair, to motivate trade. Can we get unemployment now?
No. Two unemployed agents would simply do a barter deal to cut each other's hair.
We need to change the model so that monetary exchange is essential -- they can't trade without using money as a medium of exchange. So let's do that.
You can't cut the hair of anyone who cuts your hair. So we get a Wicksellian triangle. And agents can only meet pairwise, and have bad memories for names and faces and can only remember the central bank. Or whatever. So they have to use central bank money to buy haircuts. Every agent has a chequing account at the central bank. The central bank pays a rate of interest r on positive balances, and charges the same rate of interest r on negative balances. And the sum of the positive balances equals the sum of the negative balances, so the central bank has no other assets or liabilities and zero net worth and zero income.
Now we can get unemployment if the central bank sets the real interest rate too high. Each individual wants to accumulate a positive balance in his chequing account by spending less money than he earns, which is impossible in aggregate.
Reinterpreting the New Keynesian model as a model of a monetary exchange economy, where every agent has an interest-earning chequing account at the central bank, kills two birds with one stone (it explains how the central bank can set the rate of interest, and explains how this can cause deficient-demand unemployment). Yet it leaves the equations of the model unchanged. No sensible New Keynesian macroeconomist should object to this reinterpretation. It's a friendly amendment -- and not even really an amendment.
That was the easy part -- the bait part of my Cunning Plan to bait and switch. And I'm just recapitulating my old post on solving the riddle of the New Keynesian Cheshire Cat.
Now for the harder part -- modifying the model to make the stock of money essential. That's the switch part.
There are two definitions of the stock of money that would be useful in a model like this:
- The Net money stock = the sum of positive balances minus negative balances.
- The Gross money stock = the (absolute) sum of positive balances plus negative balances.
In the model I have sketched above, Net money is zero by assumption. The central bank could make Net money positive by buying some asset, or negative by selling some asset (open market purchases or sales).
In the model I have sketched above, Gross money will be zero, because all agents are identical. Holding Net money constant, aggregate receipts of money must equal aggregate payments of money by accounting identity, but if agents are identical this also is true for each individual agent. Each agent's receipts and payments of money are perfectly synchronised, so his inventory of money will always be zero.
If we add individual-specific shocks to agents' receipts and/or expenditures of money, we can change the New Keynesian model so that agents' receipts and payments of money are not automatically perfectly synchronised, which means the Gross money stock is now strictly positive.
Assume that the central bank sets a spread between the interest rate it charges on negative balances and the interest rate it pays on positive balances. Assume it is costly for agents to synchronise their payments and receipts of money (for example by agents with a positive balance lending to agents with a negative balance). We now have a demand for gross money as a negative function of the spread set by the central bank.
We now have something that looks a bit more like a traditional macro model, because it does have a money demand function.
Hold that thought. Because I now want to take a detour, and talk about the New Keynesian IS equation.
There is a very big problem with the New Keynesian Macro model. It simply assumes, with zero justification for this additional (hidden) assumption, that agents in the model expect an automatic tendency towards full employment. As I explained in my old post, Old Keynesians would be screaming blue murder if they understood that New Keynesians were making this illicit assumption. Because it is precisely this question that Keynes wrote the General Theory to address.
To repeat the point I made in that old post, if the central bank always sets the real rate of interest equal to the natural rate of interest, that is a necessary but not a sufficient condition for output being at the natural ("full employment") level. There is a continuum of equilibria, with anything from 0% to 100% unemployment being an equilibrium. This result follows immediately from the Consumption-Euler equation. In the simple case of log preferences, where n is the rate of time preference proper, it is: C(t)/C(t+1) = (1+n)/(1+r(t)). The real interest rate only pins down the expected growth rate of consumption, not the level of consumption. And New Keynesians evade this problem by simply assuming that in the limit, as t approaches infinity, C(t) approaches the full employment level.
That's a problem with the New Keynesian model. A very big problem. How can we fix it?
This big problem with the New Keynesian model is the result of the New Keynesian Long Run IS curve being horizontal. It is horizontal at the natural rate of interest. So if the central bank sets the real rate of interest equal to that natural rate, the long run equilibrium level of output is indeterminate. As any second-year economics student knows, if you have a horizontal IS curve, you need an upward-sloping LM curve to determine the level of output.
Back to that thought you were holding, about how we can modify the New Keynesian macro model so there is a well-defined demand function for the gross stock of money. What else do we need to get something like a standard upward-sloping LM curve? You guessed it: we need a supply function for the gross stock of money. And if we want the LM curve to slope up, so that the level of output is determinate, that supply function cannot be perfectly elastic at any given rate of interest.
It is not sufficient for a central bank to set a rate of interest (or one rate of interest plus a spread) and let the stock of money be determined by demand at that rate of interest. Long run output (not to mention the price level) is indeterminate if it does that, even if it sets the correct rate of interest. It needs to control the nominal quantity of money too. The central bank needs to set some nominal anchor, not just to make the price level determinate, but to make the level of output determinate.
The only mechanism that can provide an automatic tendency towards full employment (if, and that's a big "if", the central bank does the right thing) is the hot potato mechanism. If we reinterpret and reform the New Keynesian model the way it needs to be reinterpreted and reformed, we end up with Keynso-monetarism.
I ought to talk about "haircuts" in the financial market sense, and how collateral constraints mean the central bank puts limits on individual agents' negative balances, and how this creates a link between the Gross and Net stocks of money, and how Open Market purchases increase both Net and Gross money. But this post is already too long, so I will stop there.
Update: In a comment on my previous Cheshire Cat post, Brad DeLong asks: "If it isn't an RBC model minimally-tweaked to deliver Old Keynesian conclusions, why is it what it is at all? What other telos could it possibly have?"
On Thursday I heard Michael Woodford give a talk at a Bank of Canada conference. He started his talk by saying he visited the Bank of Canada in the late 1990's, spent time talking with Chuck Freedman and Kevin Clinton about how the Bank of Canada conducted monetary policy, which had been very influential in his subsequent work. I understood him to be talking about his "Interest and Prices". Indeed, the only important difference is that it is commercial banks, and not regular people, who have chequing accounts at the Bank of Canada. Otherwise, the model fits pretty exactly. I think that is the telos. Blame Canada.