## Simple Deficit Reduction Arithmetic: A Comment on Kash Mansori

Mark Thoma sends us to Kash Mansouri: http://streetlightblog.blogspot.com/2011/05/some-simple-deficit-reduction.html

I think things are actually much worse than Kash states. If recessions cast a shadow of s--that is, if a fraction s of an austerity-induced output decline turns into a permanent reduction in potential output--and with a multiplier of m and a marginal tax rate of t, $1 of spending cuts this year lowers future annual tax collections by tms.

And with an interest rate of r, $1 of spending cuts lowers the future annual debt service burden by r - rmt.

This means that the burden of the debt rises if you cut spending at the margin this year if:

mt > r/(r + s)

With mt roughly equal to 0.5 and r currently less than 2%, this means that if even 1/50 of the austerity-induced decline in current output flows through to reduce the economy's productive potential, that austerity today worsens the debt burden.

This is an unusual result: it applies only to a country with a substantial fiscal multiplier that can fund its debt at very low interest rates. But we are a country with a substantial fiscal multiplier that can fund it's debt at very low interest rates...