They are still at it! (Making totally irrelevant arguments about headline vs core.) How to kill this zombie?
Here is a very simple model of inflation. Don't take it too literally. It's just for illustration.
1. H(t) = aH(t-1) + bC(t-1) - cR(t-1) + e(t)
H(t) is headline inflation at time t; C(t) is core inflation; R(t) is the rate of interest set by the central bank; and e(t) is a serially uncorrelated error. Headline inflation depends on lagged headline inflation, lagged core inflation, the lagged interest rate, and an unforecastable shock. (Everything is in deviations from the mean, so I can ignore the constant term.)
Here is a very simple model of the central bank's reaction function.
2. R(t) = dH(t) + fC(t)
The central bank looks at headline and core inflation, and sets the rate of interest accordingly.
Substitute the reaction function 2 into the structural equation 1, to get a reduced form equation for headline inflation.
3. H(t) = [a-cd]H(t-1) + [b-cf]C(t-1) + e(t)
Two econometricians visit this economy. Both want the central bank to keep headline inflation as close to a fixed target as possible. One argues that the central bank should respond only to core inflation, because core inflation is a better predictor of future headline inflation. The second argues that the central bank should respond only to headline inflation, because headline inflation is a better predictor of future headline inflation.
They agree it is an empirical question, and so agree to settle their argument by estimating a regression of headline inflation on lagged headline inflation and lagged core inflation.
They agree to estimate:
4. H(t) = AH(t-1) + BC(t-1) + e(t)
They agree that if they find that A>0 and B=0 then the second econometrician is right, and that the central bank should respond only to headline inflation. And if they find that A=0 and B>0 then the first econometrician is right, and the central bank should respond only to core inflation. And if both A>0 and B>0 they are both partly right, and the central bank should respond to both headline and core inflation.
Comparing equations 3 and 4, it should be obvious that both econometricians are hopelessly wrong.
The econometricians' estimate A is a very bad estimate of the structural parameter a. Instead, it is a good estimate of the reduced form parameter [a-cd]. And the econometricians' estimate B is a very bad estimate of the structural parameter b. Instead, it is a good estimate of the reduced form parameter [b-cf].
If, for example, the central bank knew that equation 1 was a true description of the structure of the economy, knew the exact values of the structural parameters a, b, and c, and wanted to keep headline inflation as close as possible to a fixed target, then it would choose a reaction function in which d=a/c and f=b/c, so that the reduced form would become:
3' H(t) = H(t-1) + C(t-1) + e(t) = e(t)
And the two econometricians would find that A=0 and B=0, so that neither headline nor core inflation predicted future headline inflation. So, if the central bank were reacting perfectly to both headline and core, the two econometricians would conclude from their regression that the central bank should ignore both headline and core, because both are useless as predictors of future headline inflation.
The correct inference to draw from the econometricians' estimates is not whether the central bank should react to headline, core, both, or neither. It is whether the central bank should react more or less strongly to headline and core than it has reacted in the past.
Now can somebody please explain this to the ECB, and stop this irrelevant debate about the predictive power of headline vs core.
(This is just another way of explaining what I have said many times in the past).