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Don't really see the point of this exercise, given that neither a balanced budget nor a fixed debt:GDP ratio make much sense.

The optimum deficit, as Keynes explained, is whatever reduces unemployment as far as is consistent with not too much inflation. Or as he put it, "Look after unemployment and the budget will look after itself."

I apologize for wasting your time.

Out of curiosity, has there been much work on exploring the feedback effects on government debt and interest rate? Your napkin-math assumes that the interest rate is known a priori, but at some level of government debt we'd expect to begin seeing crowding-out effects that would change the underlying interest rate even for a fixed central bank response function.

Another back-of-the-envelope calculation I like to make is: suppose we held the level of debt constant in real terms (so there is no deficit if we adjust everything for inflation). Multiplying the 30% debt ratio by the 2% inflation target (so the nominal debt rises at the same rate as the price level) gives us an extra 0.6% of GDP of government spending (or tax cuts). That's \$12.5 billion, or half of your own calculation.

Ralph: I see the point of this exercise is to allow the government to run deficits in bad years and surpluses (or smaller deficits) in good years, while having some Long Run target for the debt ratio that makes that policy sustainable over time.

Will you do the math for the US?

G/Y = T/Y - iDR + gDR

What happens when one year treasury rate matches growth? Here is the USA chart:
https://fred.stlouisfed.org/graph/?id=A191RL1Q225SBEA,#0

In the last eight years, we would have balanced the budget three times to keep DR constant.

Matthew,

The average remaining maturity of U. S Treasury debt is almost 6 years (up from a low of 4 years in 2008).

https://www.yardeni.com/pub/usfeddebt.pdf
Page #15

The interest rate on 5 year Treasuries is about 2.06%.
https://fred.stlouisfed.org/series/DGS5

More importantly total interest paid / total debt outstanding = 2.43% and U. S. Federal debt held by the public has been growing at about roughly 5%.
https://fred.stlouisfed.org/series/A091RC1Q027SBEA
https://fred.stlouisfed.org/series/GFDEBTN

U. S. Nominal GDP growth has been about 4%.
https://fred.stlouisfed.org/series/GDP

Assuming that government receipts and government spending grow at the same rate as economic growth, interest expense is growing about 3.43% faster than receipts.
Right now interest expense consumes about 13.5% of all U. S. government receipts.

Assuming no changes (interest rate, economic growth, debt growth), interest expense will equal government receipts in:

I1 / T1 = 13.5%

I2 = I1 * exp (X * ln (1 + 5% + 2.43%))
T2 = T1 * exp (X * ln (1 + 4%))

I2 / T2 = 0.135 * exp (X * ln (1.0743/1.04))

Setting I2 / T2 = 100% (1.00) and solving for X

X = ln (1.00 / 0.135) / ln (1.0743 / 1.04) = 62 years.

Mind you, that is after all other government expenditures (defense, education, social benefits, etc.) have been cut to zero.

Frank,
Let us make it even simpler. Congress pays the ten year rate (interest expenses/debt equals ten year rate) So lets plot NGDP vs the Ten year rate:

https://fred.stlouisfed.org/graph/?id=DGS10,#0

Using this scale, I see two points in the last eight years that would have balanced the budget, and a third point coming up in 2018.

The theory proposed has a reversion to zero in it, it is a predictive filter and will bounce around zero to keep DR constant. A good idea, actually, but it means balancing the budget every 3-6 years if you do it right.

Matthew,

The only problem is that interest rates on federal debt are unlikely to go negative.
Who other than central banks would buy them?
Nominal GDP growth can go negative. See:

https://fred.stlouisfed.org/series/GDP

And so guaranteeing a stable debt ratio (DR) is dubious at best.

"... replacing the fiscal anchor of balanced budgets to one of a fixed debt-GDP ratio allows the federal government to increase spending by 1.2 percentage points of GDP, or by about \$25 billion."

I'll take your word for it, and you can count on my commitment to oppose this terrible idea.

Just one small question though... what "fiscal anchor" you are talking about? I haven't seen a balanced budget since 2007.

I would be very interested to lean your thoughts about a recent analysis of monetary and fiscal policy. http://necsi.edu/research/economics/econuniversal

Why not have a debt service cost ratio target, rather than a debt ratio target ?

Tony,

"Why not have a debt service cost ratio target, rather than a debt ratio target ?"

That's not a terrible idea. Limit interest expense to say 15% of available tax revenue.

To do that, the federal government would need to do one of several things:
1. Manage interest rates directly (bye bye central bank).
2. Manage it's quantity of debt issuance with regard to interest rate changes instead of with regard to the business cycle (bye bye countercyclical debt financed fiscal policy).
3. Switch to all zero coupon bonds and manage it's debt duration with regard to interest rate changes (100 year, 1000 year, 10000 year bonds).
4. Sell equity claims on it's future revenue in lieu of or in conjunction with bonds.

With #4, central bank independence is preserved, countercyclical fiscal policy becomes possible without additional debt issuance, and duration of government securities (debt / equities) can be limited.

FYI, with traditional government bonds, coupon interest payments are made semi-annually and thus those coupon payments are regularly occurring government expenditures. With zero coupon bonds, interest and principle are returned to the investor when the bond matures - no coupon payments are made.

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