Increased Government Purchases Right Now Are Self-Funding...

…and reduce the effective debt-to-GDP burden of a country:

• For a multiplier μ of 1.5 and a marginal tax revenue share of GDP τ of 1/3…
• When a credit-worthy government can borrow at a real interest rate r of zero…
• If the hysteresis parameter η--the share of this year's demand-side production shortfall that turns into a persistent supply-side potential output shortfall next year--is larger than the decay parameter ρ--the speed with which persistent but not permanent hysteresis effects go away.

This is a very, very easy hurdle to jump. For any credit-worthy sovereign--or for anybody who can borrow on the credit of any credit-worthy sovereign--it is fiscal expansion now that reduces the effective debt, and fiscal austerity that increases it.

This is really not rocket science, people. Arguments that austerity makes sense are arguments that the multiplier μ is not 1.5 but 0.5, and that the relevant interest rate r is not the interest rate currently on offer or any future interest rate forecastable off of the term structure but rather something much much higher that will appear with the imminent arrival of the bond market vigilantes.

We in the North Atlantic have now been waiting for the bond market vigilantes for five years. Here in Japan they have been waiting for the bond market vigilantes for 25 years.