“Ken Rogoff of Harvard and Carmen Reinhart of Maryland have studied the impact of high levels of national debt on economic growth in the U.S. and around the world in the last two centuries. In a study presented last month at the annual meeting of the American Economic Association in Atlanta, they conclude that, so long as the gross debt-GDP ratio is relatively modest, 30%-90% of GDP, the negative growth impact of higher debt is likely to be modest as well.

“But as it gets to 90% of GDP, there is a dramatic slowing of economic growth by at least one percentage point a year. The likely causes are expectations of much higher taxes, uncertainty over resolution of the unsustainable deficits, and higher interest rates curtailing capital investment.

“The Obama budget takes the publicly held debt to 73% and the gross debt to 103% of GDP by 2015, over this precipice. The president’s economists peg long-run growth potential at 2.5% per year, implying per capita growth of 1.7%. A decline of one percentage point would cut this annual growth rate by over half. That’s eventually the difference between a strong economy that can project global power and a stagnant, ossified society.”

As a rather extreme illustration posted at 3AM, how could it not be? :-) But not too much so.

Look, in your argument …

“the number to be concerned with is the amount of government spending. Not the manner in which the government pays for its expenses”

… you are really saying two different things:

1) In dollar amounts (at present value) spending always equals taxes — whether the taxes are collected up front to pay for the spending right away, or on a deferred basis to carry the national debt.

This is entirely true. The tax cost of an expenditure paid up front equals the present value of tax-financed interest on a perpetual bond used to debt-finance the same expense. So there is no “extra” dollar cost of debt financing, via interest or whatever. (As Milton Friedman used to say, spending determines taxes.)

*and*

2) Because that dollar cost to be paid is always the same, “the manner in which the government pays for its expenses” makes no economic difference.

This is false, because of the deadweight loss cost of taxes. Different taxes have different deadweight cost, so that matters. And timing matters, because e.g. if taxes are deferred to “pile up”, their deadweight cost rises with the square of the increase in the tax rate. So a 10% rate increase ups DWL by 21%, etc. And that’s very un-economical!

The paper doesn’t say anything about the effects on period 3 from no taxation in periods 1 and 2….

It’s simple: DWL increases by the square of the increase in the tax rate. There are plenty of ready references (e.g. Mankiw “if we double the size of a tax, the deadweight loss increases four-fold; if we triple the size of the tax, the deadweight loss increases nine-fold. The graph of the deadweight loss as a function of the tax takes the shape of a parabola.”)

Any serious tax discussion has to consider deadweight loss. If not for it, we could have tax rates of 100% with no economic loss at all! So DWL *is* the cost of taxes.

Lets say the government taxes yearly. You earn $60k/year….

Let me re-stylize my own example, at an hour when I’m still awake.

Scenario #1: As per our world (sort of) GDP = 100, govt spending is 30% of GDP, paid for with taxes at 30% of GDP, tax rate is 30%, growth and the interest rate are real 3%, and as per Feldstein the deadweight loss cost of taxes is $0.76 per dollar of tax. Over three years…

[not knowing if the formatting will work]

Time: …T1 … T2 …. T3

GDP …100 …103 …106 … etc., forever
SPD…… 30 ….. 31….. 32
TAX…… 30 …. 31….. 32
Trt…….. 30% ..30% ..30%
DWL….. 23….. 23…… 24

Scenario #2: In T1 and T2 taxes are cut to $0 so former DWL is added to GDP … In T3 deferred taxes to cover all the spending are collected — they total the same 93 as in Scenario 1, but now require a 71% tax rate in T3 … This 71% is 2.37 times the 30% rate, squaring that is 5.6, times the original $0.76 cents DWL gives a new DWL of rate of $4.25 per dollar of tax … x 93 of tax = DWL of 395 … subtracted from potential GDP of 130 is not good.

GDP … 123 … 127 … 130 … end of sequence.
SDP …… 30 ….. 31 ….. 32
TAX ……. 0 ……. 0 ….. 93
Trt………. 0% …. 0% …71%
DWL …… 0 ……. 0 ….. 391

NET GDP in T3 …….. negative.

Yes this is an extreme stylized example, but you’ll see it does not support the hypothesis that collecting the same 93 of tax in different ways makes no difference.

The only way to avoid net-losing DWL in T3 is for persons to save dollar-for-dollar the exact amount of gov’t spending in years 1 and 2, instead of consuming any of it in spite of their “tax cut”, then pay it to the gov’t in T3 through a 100% lump sum tax.

Which, in effect, is the exact same as paying a 30% tax rate in T1 and T2 through an escrow account. In that case, where’s the tax cut and supposed deficit financing? (Talk about “Ricardian Equivalence”, we can see why Ricardo argued against it!)

Here in the US personal savings have hardly risen dollar-for-dollar to match our fast-rising mega-billion now trillion-dollar deficits. Not quite! We are solidly on the course of using large scale debt finance to defer taxes to “pile up” higher and higher in the future, by arithmetic, requiring higher tax rates to collect them, etc.

If this course isn’t changed the rest follows, as per exponential rise of the deadweight cost of taxes, as shown in the CBO’s economic projection and S&P’s projection of the US credit rating falling to “junk” by 2027, linked above.

And this is the what Mr. Sakowicz should have known to answer that question. Yes he should have known it. In fact, all talk show hosts should know it. If they did, we wouldn’t always have so many pundits pushing so called “tax cuts” with no matching spending cuts, that as a result are only tax deferrals, which just pile up future taxes yet higher, making everything worse.

Your example is a bit off. The paper you linked says, as best that I can determine, that deadweight losses quadruple as taxes double, all else being equal. But all is not equal. In your example, the deadweight losses in period 3 are, at a 3Z tax rate, nine times the deadweight losses of period 3 at a Z tax rate. No more, no less. The paper doesn’t say anything about the effects on period 3 from no taxation in periods 1 and 2.

Lets say the government taxes yearly. You earn $60k/year and the government taxes you $10k/year. You keep $50k/year and live a life.

Now say the government is going to take taxes every 3 years. You not only earn $60k/year, but because you get to keep all your wages, you work a few extra hours a week and actually take home $65k/year (leisure time being relatively more expensive, and thus you consume less of it). You know your tax bill is going to come due down the road and buy up $10k of government debt a year. Year 3, you earn your $60k (you don’t work more hours, preferring to avoid accumulating tax burden) and the government taxes you $30k to pay for its projects. You cash your $20k of bonds and end up in year three with $50k of income.

This is not precise, of course, because I haven’t accounted for interest on either side. Interest on the debt will raise the amount the government taxes you. But it will also raise the amount you receive when cashing your debt. The deadweight loss in year 3 will stem largely from the fact that you -could- have consumed immediately or invested in more risky ventures (with consequently higher returns) but did not in order to cover your future tax burden.

Saevar: Say this: “the deadweight cost of taxes on the economy increases with the square of the increase in the tax rate“.

For instance:

Say that in each of periods 1, 2 and 3 the gov’t spends $X, or $3X total, which could be covered with a steady tax rate of Z%. But instead, in its wisdom, the gov’t decides to entirely deficit spend during periods 1 and 2, and to defer all the tax cost into period 3, in which it collects tax of $3X.

You may say: “It doesn’t matter. The gov’t still collected the exact same $3X in taxes. By not collecting $X in each of the first two periods it just left that much more available to be collected in the third period. It’s a wash.”

But it is *not* a wash! Because in period 3 the tax rate needed to collect all the tax is 3xZ% , triple the steady tax rate that would have done the job. Thus, in period 3, the deadweight cost of taxes is nine times (9X !) what it would have been otherwise.

Let’s define the deadweight cost of taxes as 1 unit per time period for the tax rate of X%, if applied steadily over all three periods. Then tripling the tax rate in period 3, increasing the deadweight cost nine-fold in that period, to nine units, which also triples the deadweight loss to the economy over the entire three-period stretch.

That’s no wash!

Now, if you think the current deadweight cost of taxes to the economy is trivial, then you can ignore all this. But if you think it is significant already, this is something to seriously be concerned about.

Feldstein puts the current deadweight cost to the economy of income taxes at $0.76 per dollar of tax collected at the margin. Boskin puts it closer to $1.40. So, if they are right, we are talking about an already serious cost — which large-scale deficit financing will multiply geometrically.

I refer you again to CBO’s projection of, and explanation of, our economic future if it is deficit financed. (charts 3 & 4). And S&P’s picture of the US credit rating in 2027 if projected spending increases are financed with debt.

Reinhart & Rogoff’s new book documents 40-odd countries that have defaulted on their national debt since 1970, at great cost to themselves, due to excess debt. In many cases on domestically owed debt, not debt owed to foreign creditors. If the amount of debt a nation incurs really doesn’t matter, that is a very bizarre fact.

1) Please define the “excess burden of government debt” that allegedly is being relieved.

In the numerical example above the dollar cost is identical both ways, so where is the “relief”?

Checking the original Slate piece where I first read this idea (btw, I still remember it because I am a fan of yours, but this one always irked me) the claim was that by buying enough bonds to get back in interest what one pays in taxes to service the debt…

“For all practical purposes, you’ll have opted out of the debt burden entirely”.

That certainly reads like one is getting out of something, some “burden”.

Yet the “debt burden” is the tax cost of servicing the debt — what else? — and using this tactic leaves that tax cost, the transfer to the gov’t, exactly unchanged, both in amount and timing. So exactly what has one “opted out of”?

If nothing at all has changed, apparently nothing.

It would seem to be much more clear to say: “There is no excess burden of government debt, over the cost of the taxes needed to cover government spending.”

Yet that is something very different. In that case there is nothing to opt out of, and the whole exercise of buying bonds is pointless.

2) A major economic cost of piling up debt is still being ignored. See below.

If the government debt-finances the spending, you must sacrifice the $100k assets buying government debt (or, if you are willing to take more risks, some other higher-yield assets). But the government debt you hold earns interest in an equal proportion to the yearly burden in order to service the debt.

In either situation, the number to be concerned with is the amount of government spending. Not the manner in which the government pays for its expenses.

To buy the $100,000 of govt bonds I have to get $100,000 cash from somewhere — either from reducing my consumption, or by liquidating investments — reducing my welfare accordingly.

Yes, and buying that $100,000 bond is exactly as painful as paying a $100,000 tax, which is what you’d be paying under a pay-as-you-go plan.

Nobody claimed that buying bonds could relieve you of the burden of government *spending*; the claim is that it can relieve you of any excess burden of government *debt*.

I hope this isn’t the old: “I can avoid the cost of the national debt (or other taxes) by buying enough of the debt to receive the cost back in interest payments *from* the government” fallacy!

Illustration: The govt spends money on something and debt-finances it, adding the cost to the national debt. Say that “my share” of the debt increase is $100k and the interest rate is 5%, so “my share” of the income taxes used to pay it = $5,000. I incur a new $5,000 income tax cost.

I am out of pocket by $5,000 cash every year — my annual consumption/savings must decline by that much, reducing my welfare accordingly.

But, of course, I could get that $5,000 cash right back from the govt by buying $100,000 of its bonds. That makes the tax cost/inerest income cash flow a wash. Have I eliminated the tax cost landing on me? Not at all, not by a cent.

To buy the $100,000 of govt bonds I have to get $100,000 cash from somewhere — either from reducing my consumption, or by liquidating investments — reducing my welfare accordingly.

If one could “very well buy government bonds to cover the cost of higher taxes”, then one could buy yet more government bonds to more than cover the cost of taxes — and profit outright!

If only!!