http://www.brookings.edu/~/media/Files/Programs/ES/BPEA/2012_spring_bpea_papers/2012_spring_BPEA_delongsummers.pdf
this bravura effort
contains a nice gimmick calculation
that gets public investment to pay for itself and then some
you got
the this period multiplier m some fraction of the change in G(n ) ^G(n)
--- ^ = change n = now ---
ie m^G(n)
the increase in future potential output ^Yn + k
(get ready here comes the ab-rah ka bab-rah)
now
assume growth potential g is less then the rate of time discount r
g<r
then
after lots more building blocks i may fill in later
we get this :
"For a policy-relevant multiplier of 1.5, a hysteresis parameter of 0.1, and a tax share of 1/3, "
the critical rate is 10%/year:
that is
if the spread between the Treasury borrowing rate r and the real growth rate of GDP g
is less than 10% points"
"present-period fiscal expansion improves rather than degrades the long-term budget balance of the government. "
ie
FREE LUNCH
more soberly
with " a policy-relevant multiplier of 1.0, a hysteresis parameter of 0.05, and a tax share of 1/3, the critical rate is 2.5%/year: if the spread between the Treasury borrowing rate r and the real growth rate of GDP g is less than 2.5% points, present-period fiscal expansion improves rather than degrades the long-term budget balance of the government. "
ie
r-g < 2.5 % => you improve long run budget balance
FREE LUNCH
--------------------------
Parameter Values: Baseline Case
Parameter Interpretation Value
Net-of-monetary-policy-offset present-period spending 0-2.5
multiplier
r Real government borrowing rate, social rate of discount .025-?
g Potential GDP growth rate 0.025
Marginal tax-and-transfer rate 0.333
Reduction in output from raising additional tax revenue 0.500
Hysteresis parameter 0-0.2
"Since World War II it is only in the early 1980s, in the immediate aftermath of the Volcker disinflation, when the permanence of the reduction in inflation was uncer-tain, was the ten-year Treasury bond rate minus the previous year’s inflation in the range in which expansionary fiscal policy would impose any substantial financial burden on the government—if, that is, the multiplier μ has even a moderate val-ue."13
