Two versions of Goodhart's Law

Goodhart's Law is often called a generalization of the Lucas Critique, but it's really not. The "law" actually comes in several forms, one of which seems clearly wrong, one of which seems clearly right. Here's the wrong one:

Any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.

That's obviously false. An easy counterexample is the negative correlation between hand-washing and communicable disease. Before the government made laws to encourage hand-washing by food preparation workers (and to teach hand-washing in schools), there was a clear negative correlation between frequency of hand-washing in a population and the incidence of communicable disease in that population. Now the government has placed pressure on that regularity for control purposes, and the correlation still holds.

Incidentally, this also means that the oft-repeated statement that "Social science can never discover any laws of nature, because human beings react to the discovery of the 'law'" is false. For example, suppose you see that when gas prices rise, people drive less. You place pressure on that regularity for control purposes by instituting a gas tax, which raises the consumer price of gas. Lo and behold, people drive less! Sometimes people actually do what you try to get them to do.

Anyway, here's the version of Goodhart's Law that seems obviously true:

As soon as the government attempts to regulate any particular set of financial assets, these become unreliable as indicators of economic trends.

This seems obviously true if you define "economic trends" to mean "economic factors other than the government's actions. In fact, you don't even need any kind of forward-looking expectations for this to be true; all you need is for the policy to be effective. In other words, this law could as easily describe "Milton Friedman's thermostat" as the Lucas Critique.

An application of this correct form of Goodhart's Law is the suggested use of financial market outcomes as guides for Fed policymaking. At a speech at a conference at Michigan last year (and elsewhere), Narayana Kocherlakota suggested that instead of using its own internal inflation forecasts, the Fed should set policy according to market forecasts of inflation. Specifically, he suggested using the prices of TIPS and other inflation-dependent financial assets to calculate risk-neutral probabilities of future inflation, and to set Fed policy accordingly. His reasoning was that unlike the Fed's own forecasts, risk-neutral probabilities take into account the degree to which people value price stability in different states of the world.

I raised an issue with this approach. The risk-neutral probabilities obtained from financial markets are unconditional probabilities - in other words, markets may have already taken into account what they expect the Fed to do, but they have not yet taken into account what the Fed actually decides to do. The Fed's ultimate policy decision is something the Fed knows and the markets do not. Thus, the Fed is able to make internal conditional forecasts for each possible policy choice, and use only one of those conditional forecasts when making its decision. If it relies on markets, it must necessarily use unconditional forecasts, which may be less informative about conditional outcomes (which is what the Fed really cares about).

This seems to me to be an application of the second version of Goodhart's Law. If you set interest rates mechanically (i.e. according to some rule) based on current market expectations of inflation, you will change those expectations, and markets will move, requiring you to set interest rates differently according to your policy rule. It's possible that markets and policy might converge to some stable equilibrium, but also possible that market volatility might increase once it was known that policy was being set based on market prices themselves.

To link this to Goodhart's Law, if the Fed targeted the prices of inflation-linked assets, those prices would mostly contain information about expectations of Fed policy decisions (which the Fed already knows better than the asset market), rather than about non-Fed economic forces that might affect inflation or people's utility of stable prices (i.e. the things the Fed wants to use the asset prices to ascertain).

So Goodhart's Law, in its obviously true form, seems very important for policymaking.