Correlation and causation By Scott Sumner

On January 23rd, I made the following claims:

Consider the following two paradoxes: 1. Falling wages are associated with falling RGDP. Falling wages cause higher RGDP. 2. Falling interest rates are associated with falling NGDP growth. Falling interest rates cause higher NGDP growth.

I argued that people often confuse correlation and causation, and it didn’t take me long to find some examples. Three days ago Tyler Cowen suggests that the fact that wages fall faster when unemployment is high counts as evidence against the sticky wage theory, when it is actually exactly what the theory predicts. Today Tyler suggested that because negative interest rates are associated with economic weakness, a negative interest rate policy might not be helpful. The post linked to above explains why both these claims are false. BTW, the recent adoption of negative rates in Japan provides a beautiful example. The yen fell on the news, but later rose even more on fears that policy in Japan is still too tight.

Here I’d like to add a third paradox:

3. At very low levels of NGDP growth (but not otherwise) rising levels of monetary base are associated with slowing NGDP growth, even though rising levels of the monetary base (i.e. QE) cause higher NGDP growth.

If you want a detailed explanation of this paradox then read this earlier post . Here I’ll just summarize the argument.

Tight money leads to slower NGDP growth, which leads to lower nominal interest rates, which leads to an increase in the ratio of base money to NGDP. That’s not controversial. If you start from high rates of NGDP growth (say Zimbabwe), then the rise in the base/NGDP ratio is not enough to offset the lower growth in NGDP itself, so the quantity of base money is lower. But at very low rates of NGDP growth (i.e. near the zero bound), the demand curve for money flattens out.

Thus suppose that since 2007 Australia’s monetary base stayed at 4% of GDP, the US base ratio rose from say 6% to 25%, and the Japanese ratio rose from say 10% to 60%. (I made up these numbers, but they are in the ballpark.) Australia’s had the fastest NGDP growth, and Japan has had the slowest. Normally that might be associated with faster growth in the base in Australia, and relatively slow growth in Japan. But near the zero bound it is exactly the opposite, the base tends to grow fastest when NGDP growth is slowest (or more precisely is slowing the most.) The dramatic increase in demand for base money at zero rates overwhelms the (slightly) slower growth in NGDP, and thus in absolute terms the base often grows fastest in the more depressed economies, even though the impact of any exogenous increase in the base is expansionary.

In this article, Stephen Williamson makes the same sort of mistake Tyler Cowen made in the two examples cited above, but for the monetary base, not interest rates or wages:

Indeed, casual evidence suggests that QE has been ineffective in increasing inflation. For example, in spite of massive central bank asset purchases in the U.S., the Fed is currently falling short of its 2% inflation target. Further, Switzerland and Japan, which have balance sheets that are much larger than that of the U.S., relative to GDP, have been experiencing very low inflation or deflation.

Williamson is right that this evidence is consistent with the view that QE is ineffective, but it’s equally consistent with the view that QE is highly effective.

Update: Let me add one more paradox. States with more fire fighters tend to have more forest fires. And yet fire fighters actual cause a reduction in forest fires.

Do you see the analogy to wage cuts, lower IOR, and QE?

PS. Commenter Giles recently asked me why lower market rates (holding the base fixed) are contractionary while lower IOR is expansionary. IOR applies to base money, while market rates apply to base money substitutes. Here’s an analogy. A lower tax on oil boosts demand for oil. A lower tax on natural gas reduces demand for oil.