When you have cognitive dissonances with the Phillips Curve it is NOT your fault but rather a sure sign of mental health. The Phillips Curve is misspecified since Samuelson/Solow. To make matters short the elementary version of the correct structural Phillips Curve is shown on Wikimedia.#1 The structural Phillips Curve consists alone of measurable variables and is therefore identical with what you call the observed Phillips Curve.
For the derivation see Sections 5 to 7 of the working paper Keynes’ Employment Function and the Gratuitous Phillips Curve Disaster.#2
#1 Wikimedia AXEC36
|Structural Phillips Curve|
Related 'Rethinking the Phillips curve'