Friday, May 4, 2012

The Cotton Blight Problem

Like most market monetarists, my approach to monetary policy emphasizes alternative regimes.  Which is best, (or from my rather pessimistic turn of mind, which is least bad?)

One test for monetary regimes is the cotton blight test.  What happens when there is a decrease in the supply of a particular good?   

Suppose we have an economy with ten goods, one of which is cotton.   Unfortunately, there is a cotton blight that ruins Mississippi for growing cotton.   Initially, the value of the cotton crop makes up about 10% of the entire economy.  

The effect of the blight is so severe that the price of cotton doubles and the production of cotton falls in half.   With cotton initially making up 10% of the economy, the price level has risen by 5% and aggregate real output has decreased by 5%.

Because the demand for cotton happened to be unit elastic, spending on cotton remains the same.   At least initially there is no reason to suppose that the prices or quantities of other goods change.   Total spending on those other goods and  total spending on all goods together remains the same.

However, real income has fallen.  The same total spending generates an equal nominal income, but with prices 5% higher, real incomes are all 5% lower.   This, of course, matches the 5% reduction in real output.

The increase in the price of cotton provides an appropriate signal and incentive to conserve on the use of cotton.   It also provides an appropriate signal to cotton farmers in South Carolina to intensify their production efforts (and to work hard to keep the blight from spreading.)  It creates an incentive to come up with a cure for the blight.

Of course, there would likely be second order effects.   The demand for substitutes, like synthetic fibers, would rise.   The demand for complements, like bleach might fall.   The demand for products preferred by cotton farmers in South Carolina could rise, while the demand for the products preferred by the cotton farmers of Mississippi might fall.  With real income falling by 5%, the demand for luxuries would fall more than 5%, while the demand for necessities would fall by less than 5%.   But it is difficult to see why the higher price of cotton and the need to pay more for cotton would fail to provide the proper signals and incentives to make these adjustments.

Suppose one of the other 9 goods, call it gold, serves as medium of account.   The unit of account, the dollar, is defined as a fixed amount of gold.    The result is approximately as described above.   The price of cotton doubles in terms of gold.   The prices of the other 8 goods are little changed, and the dollar price of gold remains fixed.   Cotton production is halved, and real output falls by 5%.   The price level rises 5%.   While total spending on output and nominal income is unchanged, real income falls by 5%.

Of course, it is usual to think of a gold standard as including more than using gold to define the unit of account.   Gold might also be used as a medium of exchange.    Does that make any difference?

The increase in the price level by 5% reduces the real supply of money by 5%.    However, the lower real income reduces the demand for money.   If the real demand for money were exactly proportional to real income, then even if gold served as money, the effect would be the same.   The price level rises 5%, spending on output remains the same, nominal income remains the same, and real income falls 5%.  

Now, suppose instead that cotton is the medium of account.   The cotton blight still reduces the supply of cotton, and its relative price doubles and the quantity falls in half.    With the dollar defined as an amount of cotton, the dollar price of cotton cannot rise.   Instead, the dollar prices of all the other 9 goods must fall by 50%.    With the price of cotton unchanged, the equilibrium price level falls by about 45%.   (No change for 10% of the economy and a 50% decrease for 90% of the economy.)   Nominal spending falls by 50%, with 50% less cotton purchased at the same price and assuming prices are sufficiently flexible, 50% lower prices for the same amounts of the other goods.  Nominal incomes fall the same amount.   But with the price level falling 45%, real income falls about 5%, matching the 5% decrease in real output.
With a Walrasian auctioneer, this adjustment in prices could be accomplished easily.   An economist doing these calculations can solve for the 50% lower prices for each of the 9 other goods just as easily as he can solve for the 50% higher price of cotton.    In a decentralized market economy, the signal each seller is going to receive for the need to set lower prices is lower sales at the previous prices.   Frequently, lower sales imply a shift in demand away from a particular good towards other goods and so the need to reduce production and release resources for the production of the other goods.   The likely effect of the cotton blight would be a general depression of production throughout the economy and at best only a gradual recovery as prices fell.

To avoid problems associated with picking a commodity as a medium of account, suppose that instead a fiat currency is issued and its quantity is fixed.   The fiat currency is solely demanded as a medium of exchange, and it serves as medium of account.   The dollar is defined as unit of the fiat currency.
Now, return to the cotton blight.   As before, the immediate effect is a 50% increase in the price of cotton and a 50% decrease in the quantity of cotton.   With cotton being 10% of the economy, that is a 5% increase in the price level and a 5% decease in real output.    It would appear that nominal expenditure would be unchanged in aggregate as would nominal income.   Again, with the price level rising 5%, real income falls with real output.

But what of the fiat currency?   The 5% increase in the price level is a 5% reduction in the real quantity of money.   However, if money is a normal good, the reduction in real income also reduces the real demand for money balances.   If the demand for real money balances is exactly proportional to real income, then the real quantity of money falls exactly in proportion to the decrease in the real demand for money.   There is no shortage of money to force a return of  the price level to its initial level.    The 5% increase in the price level is consistent with monetary equilibrium.

A "blight" on currency should be easy to avoid.    Assuming the demand for the fiat currency hasn't changed, don't decrease the quantity of currency.   Print more to replace any that wears our or is damaged.

On the other hand, it is possible that the demand to hold the fiat currency might change, and the effects of those changes might be roughly similar to using a good that is subject to a blight as medium of account.    In particular, the quantity of the fiat currency could be managed so that is perfectly elastic--it changes according to the demand to hold it.  

What happens if the quantity of a fiat currency rises beyond the demand to hold it?   Those with excess money balances spend them, increasing the demands for the various goods in the economy.    Other things being equal, this tends to raise their prices, and so the price level.

On the other hand, if the quantity of the fiat currency is less than the demand to hold it, those receiving money in payment build up their holdings by refraining from spending it.     Other things being equal, the reduced demands for various products would result in lower prices for them and so a lower price level.

It appears that the proper rule for a fiat currency is to stabilize the price level.   If the price level rises, this suggests that too much money was created, outstripping the demand to hold it.  If the price level falls, this suggests that too little money was created, failing to meet the demand to hold it.

Unfortunately, appearances can be deceiving.  Return to the scenario of the cotton blight.   If a fiat currency was being managed to stabilize the price level, then the immediate effect of the 50% increase in the price of cotton is a 5% increase in the price level.   To reverse this inflation, the quantity of the fiat money would need to be reduced by approximately 5%.   This would result in the prices of all goods falling about 5%.   The price of cotton would fall 5% as well, but that would leave it about 47.5% higher than its initial level.   The prices of the other 9 goods in the economy would fall about 5%.    Nominal spending in the economy would be approximately 5% lower.   Nominal income would be 5% lower.    The 5% lower nominal income with the price level remaining the same implies 5% lower real income, matching the 5% reduction in real output.

This could easily be managed by a Walrasian auctioneer.  And, of course, an economist can do these calculations quite easily.  It is really not much more difficult than calculating what happens to the price level when the price of cotton simply rises 50% and stays there.   Unfortunately, in a decentralized market economy, the only way all of those selling the other 9 goods get a signal that they need to cut their prices by 5% is lower sales at current prices.  Lower demand usually means that prices perhaps should drop, but production should drop so that resources can be freed up to produce other goods.   In this situation, it is the wrong signal.

If the quantity of the fiat money is managed according to nominal GDP targeting, then when the blight increased the price of cotton by 50% and the price level by 5%, no change in the quantity of money would be necessary.   Because spending on output  and nominal income are unchanged, there is nothing to be done.   Nominal GDP targeting has the same effect as a gold standard (assuming there is no blight on gold itself) or a fixed quantity of fiat money.   Nominal GDP targeting simply avoids an inappropriate monetary intervention to force the prices of other goods to fall enough to offset the effects of increase in the price of the good with reduced supply.

Backward-looking inflation targeting has the same consequences as nominal GDP targeting.   Suppose the inflation rate is targeted at zero percent.    When the cotton blight raises the price of cotton by 50% and so the price level by 5%, nothing is done.   The rule just seeks to avoid any further change in the price level.    Unfortunately, forward-forward looking inflation targeting still requires a monetary contraction in anticipation of the cotton blight.   In order to keep the price level from rising, the quantity of money would be decreased by 5%, so that the price of cotton will only rise 47.5%, and all the other prices be cut 5%, leaving the price level stable.

Generally, a forward looking posture would seem sensible.   For example, if the demand for money were to fall, it would be better to reduce the quantity of money before it had a chance to cause prices to rise.   With a backward looking inflation target, nothing would be done until after the price level had already risen, with the aim of preventing further increases.

Flexible inflation targeting allows the monetary authority to allow inflation whenever it believes it is appropriate.   In that case, it would have discretion to decide whether it should reduce the quantity of money to partly offset the effects of developing cotton blight on the price level.   Unfortunately, with this discretion comes a need to build credibility.   Allowing a developing cotton blight to generate a 5% increase in the price level appears to create worries that the quantity of fiat currency will be allowed to greatly surpass the demand to hold it, resulting in "unanchored inflation expectations."

Worse, a flexible rule is hardly a rule at all.

Nominal GDP targeting looks to be the least bad response to the cotton blight problem.   It is much better than a price level rule, forward looking inflation targeting, and it is an actual rule, unlike "flexible" inflation targeting.

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