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.