We know that inflation targeting failed. But we don't know why it failed.
One theory is that inflation targeting failed because inflation targeting made the Phillips Curve flatter. It made the Phillips Curve so very flat that keeping inflation close to target wasn't enough to keep output and employment close to potential. Inflation targeting contained the seeds of its own destruction. It destroyed the usefulness of inflation as a signal of whether money should be tightened or loosened.
We want to test that theory.
The trouble is, it is hard to distinguish econometrically between: inflation targeting made the Phillips Curve really flatter, and; inflation targeting made the Phillips Curve look flatter.
Take for example a simple standard Phillips Curve:
1. Pt = E[Pt] + bYt + Xt
Where Pt is inflation, Yt is output, E[Pt] is expected inflation, and Xt is some exogenous variable.
The structural parameter b is the slope of the Short Run Phillips Curve, holding expected inflation constant. And the slope of the Long Run Phillips Curve, where actual equals expected inflation, is infinite. (If you prefer, you can replace Yt with -Ut, where Ut is the unemployment rate, so that -b is the slope of the Short Run Phillips Curve).
In this model, by construction, the slope of the Phillips Curve is fixed. In this model, inflation targeting cannot make the Phillips Curve really flatter. Nothing can make the Phillips Curve really flatter.
But inflation targeting can make the Phillips Curve look flatter.
There are two ways that inflation targeting can make the Phillips Curve look flatter.
1. Inflation targeting tries to make expected inflation constant.
If both actual inflation and expected inflation vary, and if the two are positively correlated (which they would be unless inflation were totally unpredictable or people had totally irrational expectations), then any observed correlation between Pt and Yt would be some sort of average of the Short Run and Long Run Phillips Curves. To the extent that inflation targeting succeeds in making expected inflation constant, we would only observe the Short Run Phillips Curve and never observe the Long Run Phillips Curve. Since the SRPC is flatter than the LRPC, if inflation targeting made expected inflation more constant it would make the Phillips Curve look flatter.
2. Inflation targeting tries to make actual inflation constant.
Assume that inflation targeting succeeds in making expected inflation constant. The observed correlation between Pt and Yt will depend on whether the exogenous variable Xt is correlated with Yt.
If Xt and Yt are uncorrelated, we will observe a positive correlation between Pt and Yt, with a slope equal to the structural parameter b. We would observe the Short Run Phillips Curve, plus random noise.
But inflation targeting will try to make Xt and Yt perfectly negatively correlated. To keep inflation perfectly on target, the central bank would need to adopt a monetary policy that ensured that Yt=-(1/b)Xt.
If Xt and Yt are negatively correlated, the observed correlation between Pt and Yt would have a slope less than b. If the central bank had a crystal ball, and kept inflation perfectly on target, the Phillips Curve would look perfectly flat, because Yt would vary but Pt would stay constant.
3. Putting both 1 and 2 together: the better the central bank is at targeting inflation, the flatter the Phillips Curve will look, even though it doesn't make it really flatter.
If econometricians could observe E(Pt) and Xt, they could estimate equation 1 and estimate the parameter b directly. They could eliminate the omitted variable bias that comes from looking at simple regressions when multivariate regressions are appropriate. If they saw that b became smaller after central banks started targeting inflation, that could help us understand why inflation targeting failed.
Now econometricians might have some information on E(Pt) and Xt, that they could use when estimating equation 1. But it is unlikely they will observe E(Pt) and Xt without error. So we get errors in variables bias, unless the observation errors in E(Pt) and Xt are uncorrelated with Yt, which will probably not be the case. Because remember: the whole point of inflation targeting is to make the Phillips Curve look flat, and the way to make the Phillips Curve look flat is to make Yt perfectly negatively correlated with E(Pt) and Xt.
I think we need some other sort of evidence if we want to find out if inflation targeting made the Phillips Curve really flatter.