You say: “My expectation [derived from the wage Phillips curve] is that when conditions are sufficiently tight to raise wage growth to the 4 percent range, they will also be sufficiently tight to raise inflation to the Fed’s target.”
You can substantiate your expectation by applying the correct (= non-behavioral) version of the Phillips Curve (2012) which is shown on Wikimedia AXEC36b:
(i) An increase in the expenditure ratio ρE leads to higher employment L (the letter ρ stands for ratio).
(iii) An increase in the factor cost ratio ρF≡W/PR leads to higher employment.
The complete structural Phillips Curve is a bit longer and contains, in addition, public deficit spending and import/export.
Item (i) and (ii) cover the familiar arguments about how effective demand affects employment. Item (iii) embodies the price mechanism. It works such that overall employment L INCREASES if the average wage rate W INCREASES relative to average price P and productivity R and vice versa. The structural Phillips Curve translates consistently into the Atlanta Fed’s chart titled ‘Unemployment and Wage Growth’.
From the theoretically well-founded structural Phillips Curve follows the policy recommendation that the Fed should actively encourage an increase of the (average) wage rate W and discourage an increase of the (average) price P. This increases overall employment without a negative effect on profit for the economy as a whole under the status quo condition for the rest of the variables.
Kakarot-Handtke, E. (2012). Keynes’ Employment Function and the Gratuitous Phillips Curve Disaster. SSRN Working Paper Series, 2130421: 1–19. URL
Related 'NAIRU, wage-led growth, and Samuelson's Dyscalculia' and 'How Wicksell and the rest got inflation/deflation wrong' and 'Full employment, the Phillips Curve, and the end of Gaganomics' and 'Cross-references Employment/PhillipsCurve'.