RDP 2014-02: Fiscal Policy and the Inflation Target Appendix B: FRB/US Fiscal Equations

This appendix presents key equations in the fiscal block of FRB/US, modified to include the effects of countercyclical stimulus, dt as defined in Equation (3). The model's full equation list is available at www.petertulip.com.

Real transfers (GFT) equal the trend share (GFTRT) of transfers in potential output (XGDPT) plus deviations from that trend (GFTRD) plus a quarter of the stimulus, dt * XGDP, where XGDP is real GDP.

Real government consumption purchases before the stimulus, excluding employee compensation, (EGFOBASE) is a function of own lags, a stochastic time trend, EGFOT, and the output gap, GDPGAP.

EGFO is EGFOBASE plus a quarter of the total stimulus, in real dollars. The separation of EGFO and EGFOBASE ensures that the endogenous persistence in EGFOBASE does not amplify the stimulus.

Nominal personal tax receipts (TFPN) equal the tax rate (TRFP) times taxable income (YPNADJ) minus half the stimulus in nominal dollars.

The tax rate (TRFP) is a function of the trend tax rate (TRFPT), own lags and the output gap (GDPGAP). I shock TFPN rather than TRFP so that the endogenous persistence in TRFP does not amplify the stimulus.

The trend tax rate (TRFPT) adjusts to stabilise debt (GFDBTN) at 55 per cent of nominal GDP (XGDPN)