First I am going to give you the intuition behind the model in John Cochrane's new paper. It's a very good paper, though I confess I've only skimmed it, because it's very long, and I don't understand all the math. Then I'm going to explain what I think is wrong with it. Then I'm going to explain why I think my model works better.
You start a company, financed by issuing non-voting shares. The total market value of those shares (the market cap) is equal to and determined by the expected present value of your company's profits.
There are two sorts of shares: Fixed-Dividend shares (F-shares); and Variable-Dividend shares (V-shares).
Dividends are not paid in cash; they are paid in newly-issued V-shares. They aren't really dividends; they are annual (or daily) stock splits.
You set up an independent Finance Office to choose dividend policy for the V-shares. The Finance Office can also decide the financing mix between F-shares and V-shares by trading one for the other in the stock market.
Suppose the Finance Office increases the dividend rate on V-shares by 1%. What happens?
If there were only V-shares, and no F-shares, the answer is easy. It's an ongoing additional 101 for 100 annual stock split, so the V-shares will now depreciate at 1% per year relative to the counterfactual of an unchanged dividend policy.
With both types of shares the answer is a little more complicated. Clearly the F-shares will instantly fall in value relative to the V-shares when the new dividend policy is announced, because their dividends don't increase. But the (weighted) average share price will not change immediately, because the number of shares hasn't changed yet, and the present value of the profits hasn't changed at all. Therefore the price of V-shares must instantly rise when the new dividend policy is announced, and only thereafter begin falling at 1% per year (relative to the counterfactual).
Now call your company "the government", call your profits "primary fiscal surplus", call your Finance Office the "central bank", and call the Finance Office's dividend policy the central bank's "interest rate policy". And assume your V-shares are the unit of account, so call them "money".
So if the central bank sets a 1% higher interest rate, the result is an immediate fall in the price level, followed by a 1% increase in the inflation rate.
And if you assume that the price of V-shares is sticky, that immediate fall in the price level takes a year or two to happen, so becomes a temporary fall in the inflation rate, followed by a permanent increase. So you get orthodox results in the short run, but Neo-Fisherian results in the long run.
Damn it's clever. But is it right?
Let me make one small change to John Cochrane's model. Let us assume your V-shares are a highly liquid asset and people value liquidity. In fact, let us assume that your V-shares are the most liquid asset in the whole economy, so that when anyone buys or sells anything, they always buy or sell it for your V-shares. Your V-shares are the medium of exchange. And because your V-shares are unique in that way, you face a downward-sloping demand curve for your V-shares as a function of the opportunity cost of owning them (the rate of return on other assets minus the rate of return on your V-shares).
That small change in the assumptions has big consequences.
First, we can now understand recessions. If there is an excess demand for your V-shares (remember their price is sticky) that will disrupt trade in the whole economy, because people will have difficulty selling anything else, so the volume of trade will decline.
Second, the Modigliani-Miller theorem no longer applies; the decisions of your Finance Office will now affect the total market capitalisation of your company. You should start to think of your Finance Office as a profit centre. For example, if people are willing to hold your V-shares even at a negative real rate of return (which is very realistic), you could run your company with permanently negative profits and still have a positive share price. If the Finance Office is truly independent, then it is the Finance Office which is now running the company, by telling you how big the losses are that you are allowed to make.
What would John Cochrane's model look like if we made that minor change to the assumptions? And would it still generate Neo-Fisherian results?
Well, by sheer fluke I just happen (ahem) to have written a post a couple of days ago sketching out just such a model. And by sheer fluke Gerard MacDonell asked me that very question about Neo-Fisherianism in the comments, and I thought about it and answered it.
They key question to ask is this: when the Finance Office central bank announces an increase in the dividend rate interest rate that it pays on V-shares money (call it Rm), what does it announce about the growth rate of the stock of V-shares money?
If the central bank announces that Rm increases by 1%, and at the same time announces that money growth increases by 1%, then we get Neo-Fisherian results. The inflation rate increase by 1%, but the opportunity cost of holding money is unchanged (the increased Rm and increased inflation cancel out), so there is no initial jump up or down in the price level.
But if the central bank announces that Rm increases by 1%, and at the same time announces that money growth will not change, then we get an initial drop in the price level, because the opportunity cost of holding money has fallen so the demand for money has increased, but there is no subsequent change in the inflation rate.
If we assumed prices are sticky rather than perfectly flexible, that initial drop in the price level would take a few years of deflation to work itself out.
It's not enough to ask what happens if the central bank changes the deposit rate of interest. We must also ask what the central bank does with the money supply. And the New Keynesians (Neo-Wicksellians) are to blame by deleting that second question, by deleting money from their model.
And by the way, my model is bog-standard ISLM, except that the central bank pays interest on money, and you can make the IS curve New Keynesian if you like, and add flexible prices or an expectations-augmented Phillips Curve.
What actually happened in the Great Recession? Why wasn't there a deflationary spiral when central banks were constrained by the ZLB? The answer is simple: the price level (and real output too, if prices are sticky) did not spiral down to zero because central banks did not let the money supply spiral down to zero. In fact, they did the opposite. They did "QE" (aka Open Market Operations). Empirical puzzle solved.
Which does not mean there is no empirical puzzle. Given the recession, why didn't inflation fall more than it did? But that is a puzzle about the Phillips Curve, not a puzzle about why Aggregate Demand (or Nominal GDP) did not fall more than it did.