Cochrane, Fiscal Policy, Interest Rates and Neo-Fisherites Again

John Cochrane's latest paper has raised a few eyebrows, due to some of the distinctly post-Keynesian ideas which seem to have crept into his recent thinking.  His focus is specifically on a world with interest on reserves, but his analysis involves a very significant role for fiscal policy.  This comes down to a point Cochrane has made before about the idea that private sector expenditure can be seen as the counterpart of a demand by the private sector for holdings of public debt.  This concept underlies some important ideas in post-Keynesian economics.

Cochrane considers a model with no government expenditure other than transfer payments and, for the most part, with government debt all of single period maturity.  His main equation (slightly restated here) is:

                                P = D_-1 . ( 1 + i_-1 ) / E(s)

where P is the price level, D is the nominal value of government debt* and i is the nominal interest rate on that debt.  So the top part of the expression is the level of debt left at the end of the previous period plus the interest thereon.  E(s) is the expected real value of current and future primary budget surpluses, discounted at the household rate of time preference.  Because Cochrane assumes no government expenditure, this is basically the expected value of the future net tax burden.

So what this equation amounts to is a statement that the current equilibrium price level is the ratio between the nominal amount of government paper outstanding, divided by the total real value of tax liabilities that will have to be paid using that paper.  The idea here is as follows.  Households expect to have to pay a certain amount of taxes in the future and they hold government debt to cover this.  If the value of the debt they hold is greater than the value of the taxes they expect to pay then, even with consumption smoothing, they can afford to increase current consumption.  This would push up prices, reducing the value of the debt, until the equilibrium price is reached.

So we have here the idea that the real value of the overall government debt is being driven by the future tax liability, and that the price level then depends on the nominal amount of debt available to cover this real value.  This might be said to be essentially a Chartalist position.  But it is also possible to analyse this in terms of backing.  In this view, the value of the debt is driven by the backing of the real value of the expected future tax receipts.  Within this model, these could be said to be just alternative ways of looking at the same thing.

Amongst other things, Cochrane uses his model to look at the relationship between the interest rate and inflation.  One feature of this is easy to see from the above equation.  The growth in the nominal value of government debt depends directly on the nominal interest rate.  If the interest rate is increased by 1%, with no change in expected real primary surpluses, the price level needs to grow at an additional 1% to compensate.

This result should not be a great surprise to post-Keynesians.  In a simple Godley & Lavoie model with only short term debt, they also show how an increase in the interest rate would be expansionary (section 4.5.1).  There are certainly differences between the assumptions in these models, but in essence the reason is the same.  An increase in interest rates transfers nominal value from public to private sector.  If this results in the private sector holding more government debt than it wants it will try to spend to get rid of the excess.

We can see that in Cochrane's simple model, when we have perfectly flexible prices, the price level would rise immediately.  So a rise in nominal interest rates would lead to an immediate inflation, with no temporary deflationary period - the neo-Fisherite result.  I have pointed out before that this is a much less likely result with anything other than single period debt.  This model actually provides a good way of showing this again.

Let's assume instead that government debt also includes some longer term bonds, previously issued at a discount and maturing in the current period.  We now need to write our equation as:

                                P = [ DS_-1 . ( 1 + i_-1 ) + DL ] / E(s)

where DS is the nominal value of the short term debt and DL is the redemption value of the longer dated bonds.  Because these longer bonds were already in issue, their payout is not impacted by any change in the current interest rate.  It is immediately obvious that a 1% increase in the current interest rate now translates into a less than 1% increase in the equilibrium price level.  But if inflation rises by less than the nominal interest rate, the real interest rate has risen which will have real effects.  In fact, the only way that flexible prices could eliminate any real effect is if the price level falls in the period in which the increased interest rate is set.  So we get an initial deflationary period, and only thereafter can inflation increase.  This effect with longer dated debt is also illustrated in Godley and Lavoie (section 5.7).

Cochrane's methodology is clearly mainstream and he excludes many things heterodox economists might consider important.  Nevertheless many of the results he derives are consistent with post-Keynesian analysis.  Cochrane tends to be very dismissive of those who consider themselves Keynesians, but I've been increasingly wondering whether he isn't a closet Keynesian himself.  I hope that at some stage he will be able to come to terms with this.

* Cochrane uses the redemption value of discounted debt as his variable.  I have used issue value, because it helps illustrate my point. 

His B = my D. ( 1 + i )