Anyway, he claims that that the "theoretical case" against nominal GDP level targeting is much stronger than implied by simple work-a-day new Keynesian models. He explains:
If we relax these restrictions, optimal policy becomes a much more complicated beast. It involves [actually this is an informed conjecture not an assertion of analytical fact] a weighted sum of deviations of inflation, nominal wages, consumption by borrowers and lenders (entering separately), interest rate spreads, the capital stock, the real exchange rate… and with weights on inflation of prices and nominal wages an order of magnitude greater than the rest.
So, central bankers are supposed to implement and the general public find credible a rule that sets short term interest rates according to deviations of all of those things? From what, exactly? Estimates of natural levels? Past averages?
And, while I agree with Yates that all of those complications are very relevant, there are many, many more.
The rule Yates proposes is really simple. Maximize social welfare. But there is a distinction between rule and act utilitarianism, and always act to maximize utility doesn't count as a rule.
A monetary authority needs to be subject to a rule that its "bosses," the voting public, can understand.
One interesting point of agreement between Yates and many Market Monetarists would be that he argues that heavy weight should be given to nominal wage inflation.
Anyway, Yates argues that the welfare cost of inflation is that prices are stuck away from equilibrium levels and this reduces welfare. Oddly enough, he then adds that when that occurs people must work and produce too little or too much, and so the opinion of the uneducated masses that "unemployment" is a problem is really a problem with inflation. And so, that is why inflation should be weighed more heavily (by a factor of 20 or something) than deviations of output from potential.
Perhaps I am missing something, but surely people working too much or too little is the same thing as deviations of output from potential. The "costs" of inflation must somehow relate to the changes in prices that actually occur, not the problems that develop because the prices fail to adjust enough.
I thought that the theoretical result of the traditional one consumer good with a sticky price model is that keeping that price at its current value is the best policy. The two percent trend inflation actually pursued by central banks leaves about 1/2 of the firms with prices too low and 1/2 with prices too high all the time.
With a zero inflation target, if somehow the price changes, then that is sad, but nothing can be done about sunk costs. The least bad option is to leave the price where it is rather than bear the cost of changing it again. This is the logic of inflation targeting. Stabilize the price level wherever it happens to be rather than trying keep the price level on a constant target by reversing deviations.
That people might want to plan for the future is not really taken into account. That would be much more complicated. But common sense suggests that a price level rule is superior to an inflation target in that context. If I know that the price level will be 100 for the next 10 years, I have more certainty than if every time the price level changes it will be stabilized at its new level. (Perhaps that is where the complications that Yates believes relating to borrowers and lenders would occur. Perhaps he should look at Eagle's math showing that utility is maximized with level targeting and nominal income is better than the price level.)
Calvo pricing is unrealistic. We have a single good, and a portion of the representative agents get to adjust their prices each period. The others are stuck with prices that may be too high or too low until they have their chance to adjust prices. The result is that changes in aggregate demand impact both prices and output. Prices adjust some, but not enough to clear markets so that real output remains equal to potential.
Well, I agree that prices and wages are sticky and that changes in spending on output impact prices and wages and output and employment, but the notion that Calvo pricing should ever be taken literally is silly.
I have never understood how Calvo pricing is an argument for inflation targeting. Say aggregate demand falls and 20% of the firms get to lower their prices in an optimal fashion and the other 80 percent have prices that remain too high. The price level actually falls, but not enough to clear the market. With inflation targeting, that new price level is made the new target. Now, the other 80% of firms need to lower their prices too. As each cohort lowers their prices, the target price level falls a bit more. All the firms know this, and so only the last set of firms actually lower the prices enough so that markets finally clear at the new lower price level.
Say the price level is 100, and there is an aggregate demand shock that makes the equilibrium price level 105. If 20 percent of the firms immediately raise their prices 5% and the other 80% of firms leave their prices unchanged, then we have one firm pricing optimally and 80% of the firms with prices that are too low. The price level rises to 101. With inflation targeting, the price level will be set at 101 permanently. The first firm will now have a price that still too high, roughly 4%. And the next set of firms get to adjust their prices, and so they set it at a level consistent with a price level of 101.
Now, let's instead suppose that aggregate demand falls, and 20 percent of the firms lower their prices. The actual price level falls below 100, but aggregate demand is increased so that the equilibrium price level is again 100. The 80 percent of firms that did not have an opportunity to lower their price in the first period have no need to make any adjustment in their prices. This certainly seems to minimize the cost of adjusting prices for the entire economy. The cost would be that the firms that have an opportunity to lower prices, lower them by less than with inflation targeting, and so prices fall even less than would be desirable to clear the market.
But suppose that some prices are flexible and others are sticky. The 20 percent of firms that adjust prices haven't just happened to reach their turn, it is rather their prices are set on auction type markets. If aggregate demand increases enough to raise the price level back to the initial value, then those firms are not unhappy that their prices are stuck too low until their turn comes to adjust prices. Rather, they are happy because demand increased again and their selling prices and profits have recovered. And the other 80 percent of firms with sticky prices, while sadly having suffered a loss in demand, see demand recover without ever having to bear the costs of price adjustment.
With the scenario where prices are flexible but wages sticky, then a decrease in aggregate demand results in lower prices and lower output. If the temporary decrease in the price level is made permanent, then wages must be reduced. If the decrease in the price level is reversed, then real output and employment recover with no need to adjust wages.
In my view, the problem with price level targeting is with supply shocks. If "price level shocks" are included as part of the quasi-phillips curve, then if the price level is shocked up, and then later it must be lowered, then in Yates' framework, the problem is that only a certain proportion of firms can lower their prices each period, and those who have not had a chance to lower their prices yet will have them too high.
In my view, if the price of some particular good, such as corn, increases due to a bad harvest, then the inflation in prices is not "bad" at all. The high price signals the greater scarcity of corn and provides an incentive to conserve on its use. Creating a monetary disturbance to force down other prices enough so that the price level returns to target is a bad thing. That some of these prices, including wages, are likely sticky, so output falls below potential, is adding insult to injury.
The benefit of inflation targeting is that if the supply shock is unanticipated, the impact of the higher price of corn on the price level is ignored. However, what is the impact of an anticipated increase in the price of corn? Does an inflation target require that aggregate demand decrease enough so that inflation does not increase?
Since real world aggregate supply shocks typically impact both prices and output in opposite directions, nominal GDP level targeting ameliorates this problem of price level targeting. If the demand for the particular good suffering an aggregate supply shock is unit elastic, then total spending on that good remains unchanged, and so no adjustment in monetary conditions are needed to keep total spending unchanged.
Interestingly, if demand is not unit elastic, so that spending on a good with an aggregate supply shock changes, then depending on the elasticity of supply for the good, changes in spending in the rest of the economy is coordinating. For example, if the supply of corn decreases, and demand is inelastic, what that means is that buyers prefer to spend more on corn and pull resources from the rest of the economy. Reduced spending on other goods is coordinating.
And so, I agree with Yates that nominal GDP level targeting is not optimal compared to an omniscient central bank. But real world central banks are not able to keep track of the elasticity of supply and demand of each and every good that has some shift in supply.