## The Basic Arithmetic of Self-Financing Fiscal Policy

**Real Treasury 10-Year Borrowing Rates**

From my perspective, it was noteworthy that the one thing that Larry Summers's and my "Fiscal Policy in a Depressed Economy" was not challenged upon at the Brookings Institution last Friday was on our arithmetic.

We were challenged on the proper estimate of the multiplier μ and challenged (quite rightly) on our guesses of the hysteresis parameter η, the share of a current downturn that is the shadow cast on future potential output. We were challenged by those saying that America's debt capacity should not be used now but should be kept ready and dry to be used in some future crisis in which using it could do much more good than it would now. We were challenged by those who think that the U.S. is on the edge of losing not just its exorbitant privilege that allows it to borrow enormous amounts at negative real interest rates but is on the point of seeing a complete revolution in interest rates that will push the rates at which the Treasury can borrow up into high single or double digits.

But on our basic arithmetic we were not challenged: it is that fiscal policy in a depressed economy is self-financing as long as:

where r is the real Treasury borrowing rate--take the nominal Treasury borrowing rates and subtract 2%--g is the growth rate, which is 2.5%; τ is the fraction of GDP that shows up as increased tax revenues and reduced social-insurance transfers, which is 1/3; μ is the (debatable) standard Keynesian multiplier when monetary policy is at the zero lower bound; and η is the (largely unknown) hysteresis shadow a long, deep depression casts on future potential output.

As we, at least, see it, it is possible to be highly confident that the depressed-economy standard Keynesian multiplier when monetary policy is at the zero lower bound μ is greater than 1.0, and substantially confident that the hysteresis shadow η cast by a long, deep depression is greater than 0.05.

The arithmetic means that over the past four years fiscal policy has been self-financing, and would be self-financing unless the real Treasury borrowing rate is rapidly going to become greater than 5%--unless the nominal Treasury rate is rapidly going to burst through 7% heading upwards. It has simply never been at such levels, save for a short span of years during and immediately after the Volcker disinflation.

Thus, even if you think that the United States is on the edge of some kind of fiscal crisis and may be about to transit from a low interest rate "confidence in government" to a high interest rate "panic" equilibrium, increases in debt-service loads relative to GDP from fiscal austerity are more likely to shock the system into the bad equilibrium than are policies of fiscal expansion. Fiscal expansion over the past four years would--exceptionally and extraordinarily--have, for once, by the arithmetic, paid for themselves.

**Critical Real Treasury Borrowing Rates as a Function of the Hysteresis Parameter η: Multiplier μ = 1.0 Case**

**Critical Real Treasury Borrowing Rates as a Function of the Hysteresis Parameter η: Multiplier μ = 1.5 Case**

**Critical Multiplier μ and Hysteresis η Parameter Values: Treasury Real Borrowing Rate r = 5.0% Case**