Technical appendix

Four-Equation VAR

Complete coefficients and actual-versus-fitted charts for the 1995Q1–2019Q4 system.

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The model uses four quarterly lags of core PCE inflation, unemployment, the effective federal funds rate, and labor-productivity growth. Every target equation includes an intercept and every lag of every variable. The table is intentionally preserved in full for reproducibility.

TargetTermLagCoefficient
TargetTermLagCoefficient
Core_PCE_InflationIntercept2.007572
Core_PCE_InflationCore_PCE_Inflation1-0.031032
Core_PCE_InflationCore_PCE_Inflation2-0.051296
Core_PCE_InflationCore_PCE_Inflation30.127479
Core_PCE_InflationCore_PCE_Inflation4-0.085141
Core_PCE_InflationUnemployment10.028992
Core_PCE_InflationUnemployment2-0.036103
Core_PCE_InflationUnemployment30.471242
Core_PCE_InflationUnemployment4-0.503351
Core_PCE_InflationFederal_Funds_Rate10.473938
Core_PCE_InflationFederal_Funds_Rate2-0.392394
Core_PCE_InflationFederal_Funds_Rate30.065760
Core_PCE_InflationFederal_Funds_Rate4-0.110766
Core_PCE_InflationLabor_Productivity_Growth1-0.035008
Core_PCE_InflationLabor_Productivity_Growth2-0.005218
Core_PCE_InflationLabor_Productivity_Growth30.001322
Core_PCE_InflationLabor_Productivity_Growth4-0.006741
TargetTermLagCoefficient
UnemploymentIntercept0.422488
UnemploymentCore_PCE_Inflation1-0.085242
UnemploymentCore_PCE_Inflation2-0.039287
UnemploymentCore_PCE_Inflation30.034413
UnemploymentCore_PCE_Inflation40.068265
UnemploymentUnemployment11.061450
UnemploymentUnemployment20.307003
UnemploymentUnemployment3-0.076432
UnemploymentUnemployment4-0.340390
UnemploymentFederal_Funds_Rate1-0.092254
UnemploymentFederal_Funds_Rate2-0.017605
UnemploymentFederal_Funds_Rate30.102024
UnemploymentFederal_Funds_Rate40.020726
UnemploymentLabor_Productivity_Growth10.010681
UnemploymentLabor_Productivity_Growth2-0.062093
UnemploymentLabor_Productivity_Growth3-0.025481
UnemploymentLabor_Productivity_Growth40.001608
TargetTermLagCoefficient
Federal_Funds_RateIntercept0.153926
Federal_Funds_RateCore_PCE_Inflation1-0.015041
Federal_Funds_RateCore_PCE_Inflation2-0.005112
Federal_Funds_RateCore_PCE_Inflation30.000357
Federal_Funds_RateCore_PCE_Inflation4-0.018921
Federal_Funds_RateUnemployment1-0.147864
Federal_Funds_RateUnemployment20.147703
Federal_Funds_RateUnemployment3-0.017650
Federal_Funds_RateUnemployment40.004307
Federal_Funds_RateFederal_Funds_Rate11.417952
Federal_Funds_RateFederal_Funds_Rate2-0.312971
Federal_Funds_RateFederal_Funds_Rate3-0.069149
Federal_Funds_RateFederal_Funds_Rate4-0.083698
Federal_Funds_RateLabor_Productivity_Growth1-0.006382
Federal_Funds_RateLabor_Productivity_Growth20.063925
Federal_Funds_RateLabor_Productivity_Growth3-0.036244
Federal_Funds_RateLabor_Productivity_Growth40.021748
TargetTermLagCoefficient
Labor_Productivity_GrowthIntercept2.969516
Labor_Productivity_GrowthCore_PCE_Inflation1-0.049059
Labor_Productivity_GrowthCore_PCE_Inflation2-0.246959
Labor_Productivity_GrowthCore_PCE_Inflation30.238596
Labor_Productivity_GrowthCore_PCE_Inflation4-0.065713
Labor_Productivity_GrowthUnemployment10.872088
Labor_Productivity_GrowthUnemployment20.560142
Labor_Productivity_GrowthUnemployment3-2.231272
Labor_Productivity_GrowthUnemployment40.587757
Labor_Productivity_GrowthFederal_Funds_Rate1-0.147081
Labor_Productivity_GrowthFederal_Funds_Rate2-0.467849
Labor_Productivity_GrowthFederal_Funds_Rate31.253006
Labor_Productivity_GrowthFederal_Funds_Rate4-0.545699
Labor_Productivity_GrowthLabor_Productivity_Growth10.342412
Labor_Productivity_GrowthLabor_Productivity_Growth2-0.285425
Labor_Productivity_GrowthLabor_Productivity_Growth30.086576
Labor_Productivity_GrowthLabor_Productivity_Growth40.023878
Actual and fitted Core PCE Inflation
Actual versus fitted values for Core PCE Inflation.
Actual and fitted Unemployment
Actual versus fitted values for Unemployment.
Actual and fitted Federal Funds Rate
Actual versus fitted values for Federal Funds Rate.
Actual and fitted Labor Productivity Growth
Actual versus fitted values for Labor Productivity Growth.

These are in-sample fitted values. A close fit is not equivalent to structural identification or out-of-sample forecasting accuracy.