Stop Me Before I Vote Again

Of course in my account book the legendary Marx sublator and mechanical debt nut, Stevie Wonder of Keentown, leads all comers from the little down-under. But more conformitory post-Keynesian types -- like Johnny Q, the people's credit quigsling -- are not too far behind.

Speaking of dear Johnny, here's a recent Quigogram from the outback of the collective white male brain:

"The US needs more stimulus now!...combined with a substantial increase in tax revenue in the long term."

"Here's John Quiggin at Crooked Timber writing that the US needs "a substantial increase in tax revenue in the long term" and backing it up with the claim, "I assume [the optimal debt-GDP ratio is] finite, which would not be the case under plausible scenarios with no new revenue and maintenance of current discretionary expenditure relative to national income." ...Given the historic pattern where GDP growth is above the interest rate, this statement is simply false."

Let b be the government debt and d the primary deficit (i.e. the deficit exclusive of interest payments), both as shares of GDP. Let i be the after-tax interest rate on government borrowing and g the growth rate of GDP (both real or both nominal, it doesn't matter). Then we can rewrite the paragraph above as:

We can rearrange this to see how the debt changes from one period to the next:

Now, what happens if a given primary deficit is maintained for a long time? Does the debt-GDP ratio converge to some stable level? We can answer this question by setting the left-hand side of the above equation to zero. That gives us:

What does this mean? There are three cases to consider. If the rate of GDP growth is equal to the interest on government debt net of taxes, then the only stable primary balance is zero; any level of primary deficit leads to the debt-GDP rate rising without limit as long as its maintained. (And similarly, any level of primary surpluses leads to the government eventually paying off its debt accumulating a positive net asset position that grows without limit.) If g > i, then for any level of primary deficit, there is a corresponding stable level of debt; in this sense, there is no such thing as an "unsustainable" deficit. On the other hand, if g < i, then -- assuming debt is positive -- a constant debt requires a primary surplus."

Yup, we don't need no stinking tax rate increases or friendly loopholes closed (like the mortgage deduction or the earned income tax credit) or new tax bases found, like on existing entitlement benefits -- err, which is not to say that (f'rinstance) a lifetime income tax, "the stealth way to tax wealth away", wouldn't be a grand byway to service Uncle's debt, eh?