Historical: Actual FFR vs. Policy Rules (1990βpresent, quarterly)
Live Calculator β adjust inputs to reprice both rules
Sensitivity β Prescribed rate vs. unemployment (other inputs held fixed)
Taylor Rule (1993): R = r* + Ο + 0.5Β·(Ο β Ο*) β 1.0Β·(U β U*)
Adjusted Taylor (1993): R = max(R_T93 β Z, ELB), where Z is the cumulative sum of past Taylor-rule shortfalls below the ELB (Reifschneider-Williams "lower-for-longer" makeup).
Balanced Approach Rule: R = r* + Ο + 0.5Β·(Ο β Ο*) β 2.0Β·(U β U*)
First-Difference Rule: R = FFR_(tβ1) + 0.5Β·(Ο β Ο*) β (U_t β U_(tβ4))
The first three rules are written using the unemployment gap (via Okun's Law), where a 1% rise in unemployment β 2% drop in output. The Balanced Approach doubles the unemployment coefficient from β1.0 to β2.0, prescribing 200 bps of cuts per 1% of excess unemployment vs. 100 bps under Taylor. The Adjusted Taylor rule accounts for periods when the Taylor rule prescribes a rate below the effective lower bound (ELB) by holding the prescribed rate lower for longer once liftoff occurs, to make up for the shortfall in accommodation. The First-Difference rule instead anchors off the prior quarter's actual fed funds rate and reacts to the year-over-year change in unemployment, making it inertial and less sensitive to real-time estimates of r* or U*.
Sources: FRED β FEDFUNDS, PCEPILFE (Core PCE 4-quarter YoY), UNRATE, NROU (CBO NAIRU), quarterly. r* held constant at 0.5%, ELB at 0.125% (standard Fed Research assumptions).