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.

Value of State Currency When it's not Medium of Exchange

There's been some interesting posts speculating on how things might pan out if the Greek government were to switch from the euro to a new currency (drachma, say) for state finances.  For MMT theorists, the use by the state of such a currency, specifically for taxation, is the essential feature for establishing it as the basis for a medium of exchange.

An old post by Warren Mosler provides a simple outline of such a proposal (h/t Peter Cooper).   As I understand it this would work like this:

- All tax payments would be required to be made in drachma;

- All government expenditure payments would be made in drachma;

- Government contracts for goods and services would be re-denominated to drachma.

- Existing private contracts in euros (including existing bank loans and deposits) would remain in euros.

- The drachma would trade freely against the euro.

- Payments on existing euro denominated government debt would be suspended (this is necessary because the government is no longer raising euro revenue and is likely to undermine the value of the drachma if it attempts to use it to buy euro).

The idea here is to rely on the "taxes drive money" principle to ensure demand for the new drachmas. This would then allow the government to use them for domestic expenditure, removing the budget constraints it has in euro.

This idea raises some interesting questions.  The first question is what currency the private sector would use for quoting prices and making contracts.  Would they stick with euro, switch to drachma or use both?  When the drachma was originally replaced with the euro, this was of little consequence, since the exchange rate between the two was fixed.  When the exchange rate floats, it becomes an important question.

I'm inclined to agree with JP Koning that it would not be easy to shift private commerce onto the new currency.  I'm not sure that Mosler's steps alone would be sufficient, although maybe with some further measures that end could be achieved.  Here, however, I want to assume that the private sector chooses to stick with euro, because I wanted to think through the consequences.

The new drachma must carry some value, as it is needed to pay taxes.  Any taxpayer in Greece will need to acquire drachma at some point.  However, they do not need to hold drachma for any material period.  They can acquire the drachma on the same day that they pay the taxes.

When should a Greek taxpayer consider acquiring drachma?  If they wish to minimise their exposure to the drachma / euro exchange rate, then they need to buy drachma on the date when the tax liability is determined.  I am not at all familiar with Greek tax legislation in terms of calculation and timing of payments, but this probably involves a period of not more than a year on average between when the liability arises and when it is paid.  So, taxpayers may want to buy their drachma a year in advance, if they wish to avoid any exchange rate exposure.

On the other hand, if the drachma is perceived as weaker than the euro, then they may wish to defer that purchase until the tax is due, hoping to pick up the drachma cheaper.  Either way, the aggregate stock of drachma that the private sector wishes to hold would appear to be limited to taxes accrued but unpaid.

At the same time various private sector entities will be receiving government payments in drachmas.  Unless they have a tax payment due, they will be wanting to sell these for euro.  In some cases, people who are due to receive future government payments of known amounts of drachma might want to try and hedge their exposure to the exchange rate by forward selling these amounts.

So it would appear that the drachma / euro exchange rate would be directly determined by the supply and demand arising from government finances. 

It helps to consider some simple numbers.  Let's say that GDP is 100 euros and the exchange rate is one to one.  The tax rate is 20%, taxes are paid one year after they arise, and there are 20 drachmas is issue.  Each year the government spends 20 drachma, which is matched by 20 of drachma receipts from the previous year's tax, leaving issued drachma constant at 20.

What now happens if the government decides to try and boost activity by handing out 10 of drachma (in addition to its 20 of spending)?  At this point, the outstanding unpaid tax of 20 drachma is unchanged, so no-one would naturally want to hold the extra 10.  As people try to sell their additional drachma, the exchange rate against the euro falls.

When the exchange rate reaches 1.5 drachma to the euro, then annual GDP in drachma terms will work out as 150 drachma and the tax liability (at 20% of GDP) will be 30 drachma.  At this point, people may be willing to hold the full stock of 30 drachma and the decline in value will halt.  This is not exact though.  It depends a lot on expectations.  As described above, if people percieve the drachma as weak, they may decide not to match their liability exactly, but to wait and see if they can pick up the drachma more cheaply at a later date.  In which case the rate will fall even further.

It's useful here to consider the Quantity Theory, in the form MV = PY, for any money supply measure M, with P as the price level, Y as real output and V as the residual "velocity".

With P being fixed in the short term, an increase in M (brought about say by government expenditure) must correspond with changes in Y or V.  The question then becomes how much of each, and whether and to what extend this subsequently leads to changes in P.  (A monetarist would claim that P will eventually change so as to eliminate any temporary change in Y and V).

However, if P can change easily, then there is no traction to have any impact on V or Y.  In the scenario we are considering, all of P is captured by a single exchange rate that is freely traded.  This is very different from a situation made up of numerous individual prices and contracts.

In conclusion, I think it makes a big difference whether the euro or the drachma is used as the unit of account, for the setting of prices and the making of contracts.  The fact of price stickiness is what makes monetary economies behave as they do.  Unless the adoption by the Greek state of a new currency also entails the Greek economy switching to that currency, the power of fiscal policy to have real effects would be severely hampered.