Take a look at the Phillips Curve, another statistical correlation regarded as an eternal truth that our inflationary era has just undermined.
From 2007 to 2019, the standard observation was: “The Phillips curve has flattened.” Large changes in unemployment correspond to very small changes in inflation, or small changes in inflation correspond to huge changes in unemployment, depending on which causal (mis)reading of the correlation you choose. For an optimist, allowing for a small amount of inflation can drastically reduce unemployment. It would take huge unemployment for a pessimist to do something about inflation, if necessary.
Then came the pandemic. Unemployment jumped without changing inflation, right on the curve.
Then inflation came. Phillips curve woke up. Almost vertical! (The scales of the two axes are different).
Much of the thinking of the Fed and commentators is based on the Phillips curve. According to conventional thinking, this is the main way that interest rates affect inflation. High interest rates raise real interest rates, reduce aggregate demand, cause unemployment, which through the Phillips curve causes lower inflation.
It is clear that something is very wrong here. Perhaps expectations are changing. Maybe supply disruptions do matter. Of course, one should start with a serious dynamic Phillips curve, as is done in most macro literature. Maybe the Phillips curve is flexible up but sticky down, and the natural speed is shifting. Maybe the prices are sticky until they are. As Bob Lucas showed For a long time the slope of the Phillips curve depends on the volatility of inflation. Countries with unsustainable inflation do not get an increase in output at the expense of additional inflation. There are thousands of epicycles to add, and this post is kind of an invitation to do so. Or maybe the Phillips curve was just a correlation hiding a deeper reality. (My opinion, but for another blog post).
In the meantime, this is another good warning not to take statistical correlations too seriously, and certainly not with the same causal relationship as we usually do. For example, inflation will always be 2%. For example, do real interest rates have a constant downward trend?
This time of inflation will force us to rewrite a lot of macroeconomics.