Neo-Fisherism and Term Debt

I just got round to having a look at John Cochrane's recent paper on the neo-Fisherian hypothesis, that higher nominal interest rates raise inflation.  A main theme of this paper is the issue of whether there is a theoretical basis for thinking that, even if this holds as a long-run equilibrium condition, the short run impact is the reverse.  It is commonly believed that the initial response to a higher interest rate will be lower inflation; Cochrane looks at whether we are right to think this.

The paper makes a good case that the basic New Keynesian model does not in fact imply the conventional result.  Cochrane also looks at several possible variations but concludes that these do not providing a convincing case for an initial deflation.

In my view, there is a very simple reason explanation of why we might expect an initial deflation and it's to do with term debt.  This is easy to see within Cochrane's model.

He starts with two of the three equations from the basic New Keynesian model: an equation for output (y) based on the nominal interest rate (i) and the inflation rate (π) and a NK Phillips curve.

y_t = E[y_t+1] { β ( 1 + i_t ) / ( 1 + E[π_t+1] ) }^-σ

1 + π_t = ( 1 + E[π_t+1] )^β y_t^κ

The third equation (the central bank reaction function) is replaced with an interest rate peg.

Cochrane also considers the inclusion of a public sector budget constraint:

B_t = ( B_t-1 -  s_t p_t ) ( 1 + i_t )

where B is the nominal stock of single period government debt by face value (which we'll call bills), s is the real primary public sector surplus and p is the price level.  This accounting identity can be extrapolated to show that the current real value of public debt is equal to the discounted value of future primary surpluses.  In turn, taking the historical level of public debt together with expected future surpluses and real interest rates gives us a current equilibrium price level, as follows:

p_t = B_t-1 / E[S_t]

where E[S] is the expected present value of future surpluses.

Cochrane uses this to distinguish between the multiple equilibria that are admitted by the simple two equation model, but finds that this does not convincingly point to an initial deflation.

From looking at how SFC models work, the thing that I would do at this point is try to incorporate some term debt.  The easiest way to do that here is to suppose that some part of the public debt consists of an annuity which pays a fixed nominal amount.  The public sector budget constraint (assuming no new issue of annuities) is now:

B_t = ( B_t-1 + a -  s_t p_t ) ( 1 + i_t )

where a is the nominal value of the annuity payment.  The equilibrium price level now becomes:

p_t = ( B_t-1 + A_t  + a ) / E[S_t]

where A is the nominal present value of the future annuity stream based on expected future interest rates (and assuming here that this is valued and discounted at the same rate as is paid on bills).

Examining this formula, we can see why a rise in expected nominal interest rates might create an initial deflationary effect.  Whilst the interest rate change has no impact on the value of bills, it does effect the value of the annuity.  A rise in expected nominal interest rates reduces the value of the annuity and therefore reduces the equilibrium price level.  If annuities make up a sufficient part of the public debt, this results in an initial deflation.

The charts below show what this looks like in Cochrane's model.  I have used the same parameters and the charts are the equivalent of Cochrane's Figure 1, but with 25% by value of public debt assumed to be in the form of annuities.

The first chart shows the result of an expected increase in the nominal rate.  This chart is essentially the same as Cochrane's Figure 1.  This is what we would expect, because if everything pans out in line with expectations, there is no difference between bills and annuities.

The second chart shows the impact of an unexpected rate increase.  This is very different.  Not only do we get a much greater fall in real output but we now also get a temporary fall in inflation.  This is the result of the shock revaluation of term debt.

Of course, this result should be of no surprise to anyone familiar with SFC modelling.  These dynamics are typical of what happens in models which combine long run and short run debt and are relatively insensitive to assumptions about expectation formation or inter-temporal preference. 

[Edited to conform a bit more closely to Cochrane.]

The "Moneyness" of Shadow Bank Liabilities

I was recently involved in an interesting discussion regarding the sense in which shadow bank liabilities might be considered money.  Along with many people, I feel that there is a qualitative difference between claims on banks and claims on non-banks, but I find it hard to put my finger on exactly what that difference is.

One possible approach is simply to say that claims on non-banks are not generally transferred to others as a means of payment for goods, services or other assets.  However, this answer overlooks the fact that bank deposits are not transferred as payment either.  Instead, what happens if I make a payment to you is that the balance of my account is reduced as consideration for my bank procuring that the balance of your account (potentially with another bank) is increased.  This may look very much like I have transferred a deposit to you, but the distinctuion is important.

Shadow bank liabilities are generally held by large institutional investors, so it's useful to look at how investors like this manage their funds.  Such investors will typically hold their liquid funds in a range of short term investments.  The most liquid of these, between one day and the next, will be overnight instruments.  These may be simple overnight bank deposits, but they may also be overnight repo (reverse repo from the cash investor's viewpoint) or other instruments, which may be with a bank or a non-bank.

To make and receive payments during the day, investors will have transaction accounts with banks.  These will typically pay little or no interest overnight.  They may also have provision to be overdrawn, either during the day - if payments are to be made from the account before receipts are confirmed - or overnight.  It is inefficient for institutions with large liquid asset pools to carry a significant positive or negative balance in their transaction account overnight.  Such institutions will therefore seek to place as much of their net cash inflow into overnight instruments during the course of the day.

At the start of each new business day, all of the overnight money placed the previous day has to be reinvested.  Likewise, all of the institutions that had borrowed through these overnight instruments need to refinance.  The money markets are therefore most liquid at the beginning of the day when there are lots of buyers and sellers.  As the day goes on and more and more positions are filled, the market becomes thinner and it can become harder for someone trying to match a position to get a good price.  Money managers will therefore try and estimate their daily cashflow and place it as early as possible, rather than wait till the end of the day.

When money is placed into an overnight instrument, the value is agreed at which it will be redeemed the next day.  However, there is no guarantee of the current day's value.  If an investor places $100 early in the day and then changes his mind later in the day, he cannot expect to get $100 back.  It will depend on what has happened in the money market during the day and may be less or more than the $100 placed.  The only certain value is the redemption value the next day.

In contrast, balances in transaction accounts retain their value during the day.  So $100 paid in early in the day may be paid out as $100 later in the day.  When we compare this with overnight instruments, it seems that that this is much more money-like, whereas overnight instruments, including deposits, are more like what we think of as bonds, albeit with a very short maturity.

I'm not sure that this enables us to answer the question of whether shadow bank liabilities are money.  However, I think there are some useful observations that can be made.

1.  Transaction accounts are qualitatively different to overnight instruments, and shadow banks are not on the whole in the business of operating such accounts.  We could think of transaction accounts alone as being money, as these are the only means with which general payments can be made, and everything else as bonds.  However, this approach makes it difficult to say anything meaningful about the quantity of money.  The balance of transaction accounts is managed down to minimal levels by the end of the day, which is the only point in time at which the balances can be meaningfully measured.  The picture given by the end of day balances bears little relationship to all the activity that takes place during the day.

2.  From point of view of the holder, the liquidity of an overnight instrument does not depend on whether it is issued by a bank or a non-bank.  When we come to think about implications for the financial markets generally and the real economy, we should not therefore expect investors to behave differently when they hold bank claims as opposed to non-bank claims.  In this sense, there is nothing special about banks.  

3.  When a payment is made between transaction accounts, one account is credited and one is debited.  If both accounts start at zero, this means one balance becomes positive and one becomes negative.  Negative balances can be avoided if the account from which the payment is made is positive in the first place.  Either way, each payment has balance sheet implications for the bank (or system of banks) providing the accounts.

We have looked at a situation where holders of liquid assets attempt to manage their transaction account balances to close to zero by the end of each day.  However, this process involves a mass of individual transactions with little coordination.  If a bank processes a payment from one account, it cannot be sure that this will be covered by subsequent receipts, so it faces a potential credit exposure.  In order for a bank to be able to do this, it therefore needs a balance sheet of some size.  Part of this will be constituted by the issue of overnight instruments.

So, whilst bank issued overnight instruments may be no more money-like that those issued by non-banks, in the hands of investors, they are important in creating the balance sheet depth necessary for banks to be able to process payments through transaction accounts.  It's not so much that overnight bank deposits are money, but rather that they facilitate monetary exchange.

Expectations and the Infinite Future

Neo-Fisherism is on the blogs again (e.g. Noah Smith, John Cochrane and Nick Rowe).  This is the idea that if the monetary authority raises the nominal interest rate and holds it there permanently, that it will eventually lead to higher inflation.

I think this discussion says something important about the way expectations and the infinite future are used in models.

It is not hard to construct models which behave in a neo-Fisherite way.  However many of these models involve GDP initially responding negatively to the interest rate rise.  For example, the charts below show the response to a permanent increase in the nominal interest rate in the SFC / DSGE hybrid model described in my recent post.

Some models may not show this negative effect, but only really those that abstract away from all the real world features that would be typically be expected to give rise to it.

So can we draw something useful from models that show a permanent increase in the nominal interest rate eventually leading to inflation?

Monetary policy impacts on the economy in two different ways.  It matters what the current policy is.  But it also matters what policy is expected to be in the future.  The monetary authority can control what policy is now, but as regards what policy is expected to be in the future, it can only hope to have an influence.

In models, specifically those with rational expectations, the monetary authority has much greater power.  In order to determine the expectation of future policy, it merely needs to actually carry out that policy in the future.  In a model, it's very easy to say that the monetary authority raises the nominal interest rate and holds it there to eternity.  In reality, this is not a policy choice that the authorities can make today.  They may intend today to hold the rate at that higher level forever.  But that is no way the same as ensuring it will happen.

So, realistically what would happen if the monetary authorities hiked the nominal rate and the economy plunged into a prolonged downturn as many models suggest it would?  Would the authorities stick to their neo-Fisherite plan, maintaining the high rate for ever in order to validate their original policy?  Or is it more realistic to assume that events might overtake them, some time before eternity?

Preferred policies come and go.  We live in a world of inflation targeting, but have not always done so and will not be doing so at some point in the future.  The longer a monetary authority or the government persists in pursuing a policy with sustained adverse effects, the more risk there is that they are forced by political expediency (or maybe revolution) to change.

And it is therefore entirely rational for economic agents to expect this.  Economic models can often display explosive results, where continuation of a particular policy makes the outcomes tend to zero or infinity.  But all these results should tell us is that the assumption of a particular policy being maintained to eternity is absurd.

We have to think of fiscal and monetary policy as endogenous in the long run.  It is useful in models to examine what happens if a policy is continued forever - indeed we are often forced to assume something like this.  But these are just useful fictions. 

What these models say will happen today is often critically dependant on what the agents in the models expect to happen in the future.  But we then attribute to them the belief that policy will pan out exactly as the authorities today decide.  This may be a rational belief in the world of the model, but it's hardly a rational belief in the real world.