Goodhart's Law is the notion that when a central bank begins to respond to an indicator of monetary conditions, market participants will come to expect those responses and trade on that basis. The result can be an indicator of monetary policy that changes however market participants believe the central bank wants it to change.
For example, simple Keynesian monetary analysis suggests that an increase in the demand to hold money will result in higher money market interest rates. It would seem reasonable that a central bank would watch money market interest rates, and when they rise, increase the quantity of money to accommodate the increase in the demand for money.
Goodhart's law, however, suggests that market participants will come to expect this behavior by the central bank. If interest rates were to rise, there would be a strong tendency by market participants to postpone security sales and an added motivation to purchase securities. Alternatively, lenders would rush to take advantage of the ephemerally higher rates, while borrowers would wait for them to fall again. In the limit, actual market interest rates would not change at all, remaining exactly where the market believes the central bank wants them. With no changes in interest rates actually occurring, such interest rates provide no information on actual monetary conditions.
If the central bank's goal is to keep money market interest rates at a certain level, then this isn't a problem. It is only a problem if the central bank has some other goal, and is using interest rates as an indicator as to whether monetary conditions are consistent with achieving that other goal.
Consider inflation targeting. If inflation expectations are well anchored, then there will be a tendency for those actually setting prices to raise them at the rate the central bank believes is appropriate. Suppose that prices would rise by less. The typical product is relatively cheap, and so there is an incentive to postpone sales and anticipate future purchases. In the limit, prices continue to rise at the rate the market believes the central bank believes is appropriate.
If the goal is to keep inflation on target, then this isn't a problem. Inflation stays on target despite spending on output failing to shift with productive capacity. If, on the other hand, changes in inflation are used as a signal that spending on output is different from productive capacity, then Goodhart's Law suggests the signal is attenuated. Strongly anchored inflation expectations makes inflation a poor signal of an output gap.
Taylor-rule regimes have two characteristics that help solve that problem. Most importantly, conventional monetary policy depends on the output gap as well as the inflation rate. If the inflation rate were very sticky due to Goodhart's Law, then the observed output gap will result in shifts in monetary policy that bring spending on output back into equilibrium with productive capacity.
Those economists (apparently including Taylor himself,) who advocate focusing solely on inflation would take away that benefit of the Taylor rule. Under such a system, fluctuations in spending on output, in real output, and employment could occur even while the inflation rate remains on target. Further, to the degree that output gaps are measured by observing changes in inflation, then Goodhart's Law suggests that output gaps will consistently underestimated, and changes in output in response to changes in spending will be identified as changes in spending and output matching changes in potential output. In other words, inflation fails to change and while output does change, the failure of inflation to change results in a change in the estimate of potential output.
The other characteristic of the Taylor rule that helps solve this problem is inflation rather than price level (growth path) targeting. Suppose that a monetary authority targeted the growth path of the price level. The motivation to keep actual prices on the target growth path would be much stronger if any temporary deviation were rapidly reversed. For example, if prices actually did rise only one percent, they would be expected to rise 3% to return to the trend. This more rapid increase in future prices gives a stronger incentive to postpone sales and increase purchases in anticipation of the price increases relative to a regime where prices are just expected to rise 2% from the current level.
However, much of this intuition implicitly assumes market clearing. If firms are setting prices and wages based upon what they think everyone else will be doing, then the central bank's 2 percent target creates a pretty obvious Schelling point. Our pay offers must be consistent with inflation. Our prices must cover our costs, including the wage bill. Individual firms sales should expand if prices increase slightly less than what other firms are going to charge.
Paradoxically, if every single firm raises prices at the target inflation rate always, then the result is the exact same thing as a price level target. A firm raises prices 2 percent, and sales are disappointing. Do they raise prices less next period? Not if they expect sales to improve enough to clear markets give a 2% price increase.
Suppose they finally give up on the central bank and raise prices more slowly. The central bank now gets the signal that demand is growing too slowly. And what does the firm do next? Do they continue to raise prices more slowly, or do they go back to raising prices 2 percent? The central bank is supposed to raise demand enough so that raising prices 2% will clear markets. And then, does the central bank determine that everything is good because inflation is on target--prices rose 2%?
What is the solution to this problem? Naturally, I would argue that it is nominal GDP level targeting. Suppose Goodhart's Law somehow causes firms to keep nominal GDP on target. In my view, that isn't a problem. Just like someone who believes that the sole goal of monetary policy is to keep inflation on target, I think that the sole goal of monetary policy should be to keep spending on output on target. If market participants keep nominal GDP on target in anticipation of the monetary authority's actions, then that is an advantage. Spending is where it should be.