How High Should Taxes Be?

How high should taxes be? High enough to cover expected outlays going forward — but no higher.

That’s because any additional revenue would be used to pay down the federal debt, which is a bad idea. It was almost surely a mistake to run up this much debt in the first place, but now that we’ve got it, the best thing to do is to keep it forever.

Here’s why:

Every $100 in outstanding debt commits the government to making payments with a present value of $100, and hence to collecting tax revenues with a present value of $100. In a world where the interest rate is 3%, the options include collecting (and paying off) $100 immediately, or $50 this year and $51.50 next year, or $11.38 a year for ten years running, or $3 a year forever. Because deadweight loss (i.e. the economic damage due to the disincentive effects of taxes) is roughly proportional to the square of the tax rate, it turns out that the latter — the policy of paying interest forever without ever making a principal payment — is (at least roughly) the policy that minimizes the present value of deadweight loss.

(For those checking this at home, use the fact that tax revenue looks roughly like At-Bt2 where t is the tax rate.)

In other words, as far as the existing debt goes, we’re hosed no matter what we do — it’s painful to pay it off, and painful to keep paying interest forever. But at least if we pay interest forever, we’re minimizing the deadweight losses associated with raising taxes.

The right policy, then, is to estimate future outlays including interest on the existing debt but not including any principal payments on that debt, and to set tax rates so that revenues match those outlays in a typical year. Insofar as Mr. Obama asks for more than that, he’s either a) planning higher future spending than he’s admitting to or b) embarking on a reckless policy of debt reduction.

Note: The above assumes that spending policies and tax policies can be set separately (subject to the constraint that tax revenues are at least high enough to cover interest payments). Things of course get more complicated if you believe that debt levels and/or tax rates constrain future spending through some political mechanism. I’ve often heard this alleged, but I’m unaware of any strong evidence for this assertion.

Share/Save

69 Responses to “How High Should Taxes Be?”


  1. 1 1 James Knight

    In the UK we’re hearing that the favourable European tax jurisdictions that Geoogle, Amazon and Starbucks use for their UK businesses (i.e. tax avoidance) makes us worse off. I think there might be a case though that it’s not true. Say Amazon pays its taxes, it then puts up its prices, meaning the consumer pays more. Given the choice between paying £2 less for a book on Amazon, or the government having that money (to probably spend unwisely), I think I prefer things as they are.

  2. 2 2 Dirk

    are all these arguments assuming nominal or real income, rates, etc?

  3. 3 3 ryan p

    I agree that it’s going to be difficult to get a convincing amount of data where we really believe the changes are exogenous (I can point to how spending went up in the 80s when taxes went down, or how spending went down in the 90s when taxes went up, but maybe you think that’s because the people who want the one also want the other?). Still, that whole “demand curves slope down” thing is pretty solid elsewhere. So I’d have to see a lot of solid political economy evidence before I adjusted my prior all the way to “deficits aren’t a subsidy for big government”.

  4. 4 4 Daniel

    1. Is the right policy to keep the debt stock constant in (a) nominal terms, (b) real terms, or (c) as a % of GDP?

    2. How do you assess a policy of repudiating the debt through total default and then running balanced budgets and never issuing any more debt in perpetuity?

    3. How do you assess a policy of completely monetizing the debt by using newly printed currency to buy back and cancel the entire debt stock, followed by a policy of running balanced budgets and never issuing any more debt in perpetuity?

  5. 5 5 nobody.really

    The right policy, then, is to estimate future outlays including interest on the existing debt but not including any principal payments on that debt, and to set tax rates so that revenues match those outlays in a typical year. Insofar as Mr. Obama asks for more than that, he’s either a) planning higher future spending than he’s admitting to or b) embarking on a reckless policy of debt reduction.

    Almost certainly Obama is planning higher future spending. What responsible president would NOT make contingency plans for unanticipated needs (natural disasters, wars, etc.)?

    Or are you suggesting that we don’t need to pay off debts in anticipation of contingencies because we could simply print money instead?

  6. 6 6 Andy

    Maybe Obama thinks the interest rate of the debt will be higher when it comes to refinancing the debt…

  7. 7 7 TjD__

    Greetings,

    in my economy 101 classes, I was told that there is a limited amount of money borrowers in the economy. And that each dollar borrowed to the government is a dollar not borrowed to a new business venture, which is not a good thing.

    Is this in your calculations?

    T.

  8. 8 8 Matthew

    Economies with large debt burdens (relative to GDP) don’t typically reduce the burden by paying it back. The ratio falls due to either 1) restructuring (creditors take a haircut) or 2) inflation. I think the US is headed for inflation.

  9. 9 9 Jonathan Kariv

    Steve: I’m missing the reason why we care about the difference between principle and interest. Why is the optimal policy to pay off exactly the interest rather than something less than the interest and letting the debt grow some more and have even less dead-weight loss? Come to that if it was a mistake to rack up the debt in the first place why is it optimal to run things in a balanced way instead of spending less than received in revenue and having someone else owe the us?

  10. 10 10 David Wallin

    TjD r7/ Gotta love my Kindle. I can write a responce or “steal” Steve’s ultimately better written one:
    It is argued that government borrowing uses resources that could be better employed in the private sector. This is wrong because government borrowing does not use any resources. What consumes resources is government spending. If the government buys a million tons of steel, then a million tons of steel become unavailable to the private sector. This is equally true whether that steel is bought with tax revenues or with borrowed funds.

    Landsburg, Steven E. (2007-11-01). The Armchair Economist [revised and updated May 2012] (p. 138). Simon & Schuster, Inc.. Kindle Edition.

  11. 11 11 Joseph Zaccardi

    The U.S. Gov. does not borrow money in perpetuity. They borrow at specific maturities and then roll the debt as needed. If they set the tax code up to pay interest payments in the future, is it feasible to constantly adjust the tax-code for the changing interest rate environment?

    Further, if the U.S. did issue debt in perpetuity and collected taxes to exactly cover Gov spending and interest payments, wouldn’t the debt-holders essentially have a residual claim on U.S. tax revenues? This would make U.S. debt more similar to an equity position on the coercive power of the U.S. Government, and I do not see that ending well.

  12. 12 12 Bearce

    That’s because any additional revenue would be used to pay down the federal debt, which is a bad idea. It was almost surely a mistake to run up this much debt in the first place, but now that we’ve got it, the best thing to do is to keep it forever.

    Have you considered the possibility of war and/or another recession/depression? Deficit spending is going to be needed in either case. This will increase the principal amount of the debt, thus causing long-run increase in interest payments, thus causing long-run higher tax rates, and thus a larger long-run deadweight losses.

    Sounds pretty bad.

  13. 13 13 iceman

    Regarding the note caveat: It does seem to me (sans data of course) that the only practical way to reduce spending is to “starve the beast”, and therefore the one good aspect of public misperceptions about debt / deficits is that this seems to be the only way to get actual follow through on the spending side. This suggests a strategy of cutting taxes whenever you can by as much as you can (i.e. “irresponsibly”), then giving back some of it during the inevitable negotiation to a ‘balanced’ solution. Of course the converse is what we seem to get more often – overspend and then demand a balanced response.

  14. 14 14 Bearce

    Jonathan K. wrote:

    Why is the optimal policy to pay off exactly the interest rather than something less than the interest and letting the debt grow some more and have even less dead-weight loss?

    This too. If the economy is in a boom, you should pay off the principal because that will lead to long-term lower tax rates and diminished deadweight losses.

  15. 15 15 TjD__

    Hmm, English is not my native language, replace borrower with lender.

    T.

  16. 16 16 David Wallin

    r/11 Joseph Zaccardi
    I suggest your first paragraph details an unimportant technical issue. As far as your second paragraph, why would turning current debt into permanent debt be any different than the essentially permanent and growing debt of my lifetime? Why would debt holders be able to exert any coercive power of the U.S.? One might argue that such a situation exists in Greece (and other euro countries). But, that is because they no longer have the drachma (or lira, etc.). Plus, if the U.S. debt is fixed at current levels into the future (as Steve suggests), the total debt will seem trivial at some point in the future. Even if there were no inflation, the increase in GDP at historic levels would make current debt amounts seem trivial to the President’s grandchildren. $16.3 trillion won’t sound so large in 50 years. Gosh, imagine if they did what Steve suggests 25 years ago. We’d be looking at total debt of under $3 trillion. Heck, if Reagan had done it in 1981, we’d have about $900 billion. I can predict two things with essentially 100% certainty. First, if we did what Steve suggests, the citizens of 2050 would not be bothered by the $16.3 trillion of debt we hand them (and the people of 2075 would consider it trivial). Second, we won’t do what Steve suggests in our lifetimes.

  17. 17 17 Jimbino

    We should just stop paying off the debt entirely, leaving the problem to future generations–the brood of the wanton breeders for whom I’m paying through the nose to medicate and mis-educate.

    I want my money spent on me now, and I have no interest in future generations. If I did, I would have bred, too. Let the breeders and their kids bear the costs of the stupidity.

  18. 18 18 Mike H

    @Steve in your solution, haven’t you assumed that the country at least pays the interest each year? If you relax that assumption, isn’t it better to borrow to pay the interest, and pay off the debt some time in the distant future?

    Or if you allow payments to be negative, isn’t it better still to borrow huge amounts now to invest or give tax breaks, again paying the debt off in the distant future?

    I get : if G0 is current GDP, and Qn is the present value of the payment in year n, I need to minimise Sum(Qn^2/1.03^n)/G0^2 subject to Sum(Qn) = 100. This is best done by making the early Qn as small as possible, hence zero (if this is allowed) or negative (if this is allowed)

  19. 19 19 Mike H

    OMG!! Does this mean Steve’s economic model shows that the government should immediately embark on a massive debt-financed stimulus package of infrastructure works and tax breaks???

  20. 20 20 Mike H

    Grr… that should be “minimise Sum( (Qn+Sn)^2 / 1.03^n )/G0^2 subject to Sum(Qn)=100. Whene Sn is the PV of spending (except interest payments) in year n.

    Steve, is it still true that “deadweight loss is … proportional to the tax rate” when the tax rate is negative?

    PS – in case people are wondering how I cooked up “stimulus spending on infrastructure” in #19, I figure that to make Qn negative, one way is to borrow to invest. Invest means “spend on stuff that earns or saves you money later”. My impression is that in the USA, people are unusually leery about the government actually owning stuff that earns money, so if the government is going to invest, they can spend on things that save spending later or helps them earn more tax later. Eg, infrastructure and education.

    Feel free to pick this argument apart, but I won’t join in, I’m more interested today in whether I got the maths right.

  21. 21 21 Mike H

    Argh! In the above, I meant “Steve, is it still true that deadweight loss is proportional to the tax rate squared when the tax rate is negative>”

    Sorry to use up so many comments. If we run out of comment numbers this time, I accept the blame. My intuition says we won’t, but I present my apologies in advance in case I’m wrong.

  22. 22 22 Max

    I’m not following the argument. In the first place, you seem be assuming exactly zero GDP growth. Otherwise, running a balanced budget would either send the debt/GDP ratio to zero (for a growing economy) or infinity (for a shrinking economy).

    If you revise the tax rule to stabilizing the debt/GDP ratio, it’s still a mystery how you conclude that the current debt/GDP ratio, whatever it may be, is automatically the ideal one to maintain.

  23. 23 23 James Knight

    Steve>> It was almost surely a mistake to run up this much debt in the first place, but now that we’ve got it, the best thing to do is to keep it forever. <<

    But we cannot keep the debt forever, because those to whom we owe the money are going to want it back at some point, aren't they?

  24. 24 24 James Knight

    David Wallin – your argument would work, except that your model overlooks the interest paid on the debt.

  25. 25 25 nobody.really

    Sorry to use up so many comments. If we run out of comment numbers this time, I accept the blame. My intuition says we won’t, but I present my apologies in advance in case I’m wrong.

    ???

    Maybe this comment was meant for the Accounting for Numbers thread…?

  26. 26 26 Steve Landsburg

    Mike H:

    @Steve in your solution, haven’t you assumed that the country at least pays the interest each year? If you relax that assumption, isn’t it better to borrow to pay the interest, and pay off the debt some time in the distant future?

    No. Solve the optimization problem per my reply to Max.

  27. 27 27 Steve Landsburg

    Bearce:

    This too. If the economy is in a boom, you should pay off the principal because that will lead to long-term lower tax rates and diminished deadweight losses.

    What assumptions went into this? Can you share your calculation?

  28. 28 28 Steve Landsburg

    Joseph Zaccardi:

    This would make U.S. debt more similar to an equity position on the coercive power of the U.S. Government,

    That’s exactly what US debt is in any case.

  29. 29 29 Advo

    The debt should DEFINITELY be paid down to some degree.
    There is evidence that a particularly high debt load is not good for economic growth (you don’t want your debt to be at 120% GDP) and at some point it also puts the creditworthiness of the country at risk, leading to increasing interest rates, capital flight, etc.

    Unfortunately, at some point in the future there’s going to be some emergency that will require prolonged deficit spending. Most likely this will occur a decade or two after the GOP deregulates the financial sector again.
    Since such financial meltdowns drive up government debt typically by 20-50% of GDP (or more, see Japan), you will want to maintain debt at a level where such additional debt doesn’t cripple the country. A reduction to 40% sounds like a good idea.

  30. 30 30 Steve Landsburg

    Jonathan Kariv (#9):

    Why is the optimal policy to pay off exactly the interest rather than something less than the interest and letting the debt grow some more and have even less dead-weight loss?

    Because, at least under reasonable assumptions, this leads to more deadweight loss, not less. If you have a calculation that shows otherwise, you’re either a) making different assumptions or b) making a mistake. If you’ll share your calculation, I’ll be glad to try to figure out which.

  31. 31 31 James Knight

    Here’s the important distinction between paying off the debt and the interest attached to the debt. In the future the debt aggregate is going to be a lot more trivial (and a lot less painful) to future generations than it is to us – so if we keep up the interest payments but have a moratorium on the aggregate debt payment, then paying it off for future generations will seem a lot like to charity to them (and we all like charity, don’t we).

    Think of it this way – suppose our bankers had run up the equivalent debt (pro rata) in the 1880s, and suppose the then president had had the foresight to set up a policy immediately to pay off the interest every year for 120 years up to our present day – our current Government would be faced with a meagre debt of tens of thousands of pounds. Much better to pay off that than see our great-great-grandparents’ generation miss out on important Government spending because they were yoked to a crippling debt. The same situation is true for us and our future progeny.

  32. 32 32 Bearce

    What assumptions went into this? Can you share your calculation?

    If you pay down the principal you have lower interest payments, 5% of one billion is a lot less than 5% of 1 trillion. Furthermore, if the economy is at the natural rate of unemployment fiscal policy dictates you ought to have contractionary policies in order to avoid inflationary problems.

    You didn’t address my earlier point concerning the case of war and/or depressions/recessions.

  33. 33 33 Steve Landsburg

    Bearce:

    If you pay down the principal you have lower interest payments, 5% of one billion is a lot less than 5% of 1 trillion. Furthermore, if the economy is at the natural rate of unemployment fiscal policy dictates you ought to have contractionary policies in order to avoid inflationary problems.

    This is not a calculation.

    You didn’t address my earlier point concerning the case of war and/or depressions/recessions.

    The ongoing level of taxation should be calibrated to expected future spending, including wars etc.

  34. 34 34 Bearce

    This is not a calculation.

    What exactly do you want then? Let’s use your hypothetical case of $100 at 3% interest. (ignoring the fact that the interest rate fluctuates.)

    Society could pay the $3 dollars forever, or instead pay off $50 now and then pay only $1.50 forever. It seems it would be preferable to have to pay off $1.50 forever as opposed to $3. Why not the $100 right away if possible? I’d imagine you say something to the likes of “Then you miss out on $3 dollars that you could accrue from saving that $100.” So what? I miss out on earning $3 from saving one year as opposed to $3 dollars every other year that I get to keep for myself as opposed to merely paying off interest (assuming government doesn’t run up any debt afterwards).

    The ongoing level of taxation should be calibrated to expected future spending, including wars etc.

    Wait, your telling me the government has some powerful algorithm that can predict things such as wars, natural disasters, recessions, and depressions? How the heck did the economy crash in the first place in 2008 or have to go through 9/11?

    You can (reasonably) predict growing outlays such as social security and medicare, you can’t do this with calamities I’ve listed above. You’re going to end up with more debt and higher interest payments (dollar terms, not percentages) in the long run.

  35. 35 35 Steve Landsburg

    Bearce:

    What exactly do you want then?

    A well-specified optimization problem and its solution, of course. Anything else (e.g. the rest of your comment) is just blather. (Though the blather content of your comment is in fact particularly high, even for someone who refuses to address the issue.)

  36. 36 36 Bearce

    A well-specified optimization problem and its solution, of course. Anything else (e.g. the rest of your comment) is just blather. (Though the blather content of your comment is in fact particularly high, even for someone who refuses to address the issue.)

    So it’s blather then.

    Let’s see….

    Advo:

    Unfortunately, at some point in the future there’s going to be some emergency that will require prolonged deficit spending. Most likely this will occur a decade or two after the GOP deregulates the financial sector again.
    Since such financial meltdowns drive up government debt typically by 20-50% of GDP (or more, see Japan), you will want to maintain debt at a level where such additional debt doesn’t cripple the country. A reduction to 40% sounds like a good idea.

    Max:

    I’m not following the argument. In the first place, you seem be assuming exactly zero GDP growth. Otherwise, running a balanced budget would either send the debt/GDP ratio to zero (for a growing economy) or infinity (for a shrinking economy).

    Johnathan Kariv:

    Steve: I’m missing the reason why we care about the difference between principle and interest. Why is the optimal policy to pay off exactly the interest rather than something less than the interest and letting the debt grow some more and have even less dead-weight loss? Come to that if it was a mistake to rack up the debt in the first place why is it optimal to run things in a balanced way instead of spending less than received in revenue and having someone else owe the us?

    nobody.really

    Almost certainly Obama is planning higher future spending. What responsible president would NOT make contingency plans for unanticipated needs (natural disasters, wars, etc.)?

    They all are asking the same essential question I asked, which we currently see as a critique to your argument. Since you’re presumably a professor, it would seem rather helpful if you could clear it up and explain where us ‘rubes’ have made an error.

    Or perhaps you realize you’re wrong, don’t want to admit it, and are continuing to be an ass about it while still leaving us as confused about your position as before. No, instead of helping readers of your blog and also probably consumers of your books you decide it’s better to blow them off and label reasonable questions as blather. Maybe you were too dense to see this as a problem, which would explain your rudeness. Either way, your just coming off as a disgruntled blogger on a soapbox with a giant stick up your stupid ass.

  37. 37 37 Steve Landsburg

    Bearce:

    They all are asking the same essential question I asked, which we currently see as a critique to your argument.

    I answered this question briefly in the post itself and in greater detail in an earlier comment. Here it is again:

    With linear demand and supply curves, tax revenue is of the form At-Bt^2 (where t is the tax rate); deadweight loss is of the form Ct^2. Let Ri be revenue in year i and Di be deadweight loss in year i. Write down the optimization problem: Minimize present value of deadweight loss subject to (present value of tax revenue = current debt level), use the functional forms I just gave you (and PV of revenue = sum(beta^i Ri), PV of DWL = sum(beta^i Di)) and you’ll find that the solution (unless of course I’ve made a mistake, which I’m sure you’ll be happy to point out) is to set each year’s tax revenue equal to the interest on the debt.

    Of course you’ll want to raise additional revenue above and beyond this to cover expected future spending. But there too, the solution will be to equalize revenue across years (as you’ll see if you take the trouble to solve the problem).

    This all makes a lot of simplifying assumptions — straight line curves, zero growth, etc. If you want to argue that those assumptions are leading me significantly astray, you might very well have an excellent point — in which case you should tell me *your* assumptions, write down the appropriate optimization problem, and present your solution. Really, anything else is blather.

  38. 38 38 Mike H

    Here’s my calculation (I didn’t see your (Steve’s) reply to Max). The government has to pay off $100, which means the sum of the present values of the payments is $100. If the payment in year n is Pn, the present value is Qn = Pn / 1.03^n. We want Sum{Qn} = 100.

    The tax rate in year n is (Rn + Pn)/Gn, where Gn is GDP in year n, Rn is non-debt-related spending in year n. The deadweight loss is proportional to Dn = [(Rn + Pn)/Gn]^2. The present value of this is [(Rn + Pn)/Gn]^2 / 1.03^n.

    Assuming Gn = G0 x 1.03^n, and letting Sn = Rn / 1.03^n, the present value En of Dn is [(Sn / 1.03^n + Qn / 1.03^n)/(G0 / 1.03^2)]^2 / 1.03^n, which is (Sn + Qn)^2/G0^2 / 1.03^n.

    We want to minimise Sum{(Sn + Qn)^2 / 1.03^n} / G0^2. We can drop the G0^2 to get this problem :

    Minimise Sum{(Sn+Qn)^2 / 1.03^n} subject to Sum{Qn}=100

    Using lagrange multipliers, we need to minimise

    Sum{(Sn+Qn)^2 / 1.03^n + lambda x Qn} – 100 x lambda.

    the derivative with respect to Qn of this is

    2(Sn + Qn)/1.03^n + lambda, hence the solution is to make (Sn+Qn)/1.03^n a constant.

    Your solution (Q0=Q1=Q2=Q3=…=3) doesn’t make (Sn+Qn)/1.03^n a constant, except for certain specific Sn sequences.

    Instead, the optimal solution is when Qn = K x 1.03^n – Sn. We still need Sum{Qn} = 100, so this can’t be solved except for finite sums/sequences, unless K=0, which makes lambda=0, which messes up the lagrange multiplier method (I think). Plowing on, however, and letting K=0, the optimal solution is to let Qn=-Sn, and sum{Qn}=100. Clearly, this is also not a solution in general.

    With more care, I’m pretty sure I could make the case that there’s no optimal solution, and that any proposed Qn sequence can be improved by finding the first Qn which is not equal to -Sn, changing it to be closer to -Sn, and adjusting some Qm (with m>n) to keep Sum{Qn} constant.

  39. 39 39 Daniel

    No strong evidence for the assertion that debt levels constrain future spending? See Australia versus the rest of industrialized world for a clear example. Low debt levels in Australia allowed for a sufficiently large stimulus packages and kept unemployment rates low.

  40. 40 40 Daniel

    Also Steve, your assumption that the supply curve is linear is a little bit ridiculous. I’m not very good at solving maximization equations but what would the result be if we have a linear demand curve, but instead the supply curve is horizontal and also how about if it is vertical? What difference would this make to the calculation? Can someone else do this for me?

  41. 41 41 Harold

    The reason you and Bearce disagree is the political caveat. It wouldbe a good idea forGovt to tax now in anticipation of future disasters, but the peoplewon’t take it. The only practical alternative is to maintain an ability to borrow when such a contingency arises.

    Maybe a better policy would be for Govt to explain why they need to do such a thing. That wouldrequire bravery and leadership, and might still be doomed to failure given the sound-bite reporting we get. I fear no succesfulpolitician would be reckless enough politically to reduce the recklessness of their economics.

  42. 42 42 Max

    The “reply to Max” seems to be missing, your browser ate it. The assumption is that the interest rate is 3%+GDP independent of debt level, correct?

    In reality, the government doesn’t fund itself that way. The interest rate is variable, and typically negative (relative to growth). This negative realized rate isn’t a free lunch, however, because it’s not guaranteed. Do you feel lucky?

  43. 43 43 nobody.really

    The right policy, then, is to estimate future outlays including interest on the existing debt but not including any principal payments on that debt, and to set tax rates so that revenues match those outlays in a typical year. Insofar as Mr. Obama asks for more than that, he’s either a) planning higher future spending than he’s admitting to or b) embarking on a reckless policy of debt reduction.

    Almost certainly Obama is planning higher future spending. What responsible president would NOT make contingency plans for unanticipated needs (natural disasters, wars, etc.)?

    The ongoing level of taxation should be calibrated to expected future spending, including wars etc.

    Agreed. That is, ideally (absent political constraints) we’d set tax levels to cover average projected spending, which hopefully would exceed typical projected spending. Yes, generating those projections may be difficult, but that doesn’t mean they shouldn’t be the goal.

    Nevertheless, this strategy is akin to saying that a homeowner should save to cover the average cost of incurring a fire in any given year in lieu of having homeowners insurance. I humbly suggest that homeowners insurance may be the better way to go. It may be a sub-optimal strategy in the long run, but the short-run benefits should not be discounted.

    In other words, a government should seek to maintain its power to acquire even unanticipated levels of resources in the event of an emergency. Borrowing is one way to acquire resources. Paying down debt is one way to maintain borrowing capacity.

    Let me concede that paying down debt in order to protect future borrowing capacity might be a sub-optimal way to ensure that government will have the financial resources to respond to an emergency. Maybe government can simply rely on the ability to commandeer assets or, somewhat similarly, the ability to print money. In that case, I’d withdraw my objection.

    But in that case, we encounter another curious paradox of libertarianism: Libertarians (as the rest of us) favor keeping taxes low. Yet a policy that would keep taxes low would appear to rely implicitly on government’s ability to appropriate assets without consent.

    Thought for the day.

  44. 44 44 Mike H

    Erratum : “Your solution (Q0=Q1=Q2=Q3=…=3) doesn’t make (Sn+Qn)/1.03^n a constant, except for certain specific Sn sequences”

    Steve’s solution is P0=P1=P2=…=3, but this still doesn’t make (Sn+Qn)/1.03^n a constant.

  45. 45 45 Nathan

    Re Daniel @ 39 – Don’t overstate the Australian experience. Our two rounds of fiscal stimulus totaled 50 billion AUD while the two rounds of US fiscal stimulus totaled 945 billion USD. It’s a bit hard to adjust for exchange rate because there was a huge drop in the AUS/US exchange rate during the GFC, but the long term exchange rate has been close to parity on average over the last decade so I’ll just assume dollars of equal value (and I’m definitely not about to get into PPP adjustment).

    This means the US stimulus was approx 19 times bigger in absolute terms. Factoring in population sizes, the US has 314 million people and Australia has 23 million. Assuming relative growth rates haven’t changed radically in the last couple of years that means that the US population was about 13 and a half times Australia’s.

    So while I’ve only done a rough comparison, it seems pretty clear to me that the US got a bigger per capita fiscal stimulus than Australia did. That fact could be used to support a lot of arguments but probably not one that debt constrains future spending.

    I find it interesting that you assume that because Australia’s economy is doing (a lot) better we must have had a bigger stimulus. Nothing wrong with falling victim to bias – there is a lot of information in the world and limited time to learn it so we’re all bound to get caught making incorrect assumptions based on our worldviews at some point. But this does show that there’s something far more powerful than fiscal stimulus driving economic fortunes – wouldn’t it be interesting to try and figure out what that is?

  46. 46 46 Mike H

    @Nathan when the Nation Building and Jobs Plan was announced, the Australian dollar was worth about US$0.65, (down from $0.97 before the crisis). It started to climb back up in March, shortly after the stimulus started rolling out. The average for 2009 was about US$0.80 per AU$.

    There is no way to justify the statement “the long term exchange rate has been close to parity on average over the last decade”. Being “close to parity” is a very recent phenomenon, only dreamed of for a couple of months in 2008, and since mid-2010.

    Also : If you want to argue about whether debt constrained the size of the stimulus package, it is odd that you would care about the size of the stimulus per capita. Surely you should look at the size of the stimulus as a percentage of GDP, for that purpose?

    In 2009, the GDP of the USA was about 14 times Australia’s. Using US$0.80 = AU$1.00 (rough average for 2009), the US stimulus package was 28 times larger that Australia’s AU$42B package, hence twice as much, as a fraction of GDP.

    Your case is strengthened (in this instance) if you use the data correctly.

  47. 47 47 Nathan

    @Mike H – thanks for the corrections.

  48. 48 48 djp

    I’ll put in a non-progresive MMT view (there really are some things about functional finance that make sense if you can separate them from the political views espoused by most MMT’ers.).

    Comment1:
    Why does the govt even need to raise taxes to pay the interest? The Fed essentially borrows at 0 (or at worst the discount rate, but they can easily revert back to 0) to buy gov securities (see the SOMA portfolio at the nyfed) and all ‘profits’ meaning the coupon payments are remitted back to the Treasury. So, if the Fed owns all of the debt in SOMA then the servicing of the debt is self-sustaining and needs no tax revenue to fund it. Treasury pays the Fed the coupon, and the coupon is remitted back to the Treasury from the Fed.

    Comment2:
    What sets the “right size” of the debt? I think many discussions about this topic suffere from a logical fallacy akin to the following: Many of us are told stories in school about why there’s some limit to the size of living organisms through the following naive argument — volume grows as the cube of distance and surface area as the square, so as organisms get bigger it’s harder for them to get enough food in through their surface to “feed” the volume. Well, that’s all well and good for why there aren’t any creatures of inifinite size, but it tells me nothing about why things should break down at some particular length scale. Likewise, I can accept that the debt shouldn’t be infinite, but I don’t know what the right size is.
    I suspect that many people look at the debt in the wrong way (as something to be paid down — which you have just argued against). Without the debt there are no dollars for our pockets, so surely there needs to be some level of debt to satisfy our desire to hold some dollars. But how much is the right amount? I don’t know. What is the right amount Steve? Is there an answer that doesn’t involve sticking your finger in the air to see what it’s been in the past, and how things have turned out?

    Comment3:
    What likely really does matter is that when the govt accumulates debt it gets something of reasonable value in return. A new bridge that gets lots of use, or maybe even a trip to Mars to inspire our imaginations and provide a sense of achievement are likely good candidates. Parties in Las Vegas, unnecessary bureaucratic jobs, lavish pensions, and graft are likely not a good value. The MMT’ers seem to think it doesn’t much matter what it gets spent on, but somehow disagree that giving it all to me would be a good thing ;) And, oddly, they always seem to think it should go to funding certain progressive projects.
    MMT in general says it should be enough to keep the debt high enough to satisfy savings demand, and that the best barometer for that is to see when unemployment drops to a reasonable level. I’m mostly inclined to agree with that position, and find it a useful gedanken experiment to try to answer the question about how large the debt should be in a world where the gov really did just print dollars to fund the deficit — a world not too different from the one we are in once the Fed accumulates all of the US Treasuries.

  49. 49 49 Daniel

    @Nathan,

    I’m aware that the other reason Australia’s economy did much better in this situation is more strict financing requirements. Given the depth of the recession was much smaller, it also stands to reason that the stimulus was adequately sized for the gap in potential GDP, whereas as anyone who bothered to do the calculation ahead of the US stimulus would tell you that based on a multiplier of about 1.5-1.7 (the most reasonable estimate for a deep recession such as this one), the stimulus was approximately 1/3 the size of what an adequate stimulus should have been. I take your point that it’s a much harder comparison to make, since the governments were in a much different situation and had a much different type of recession.

  50. 50 50 Mike H

    Steve, using your approach, you can set the deadweight loss Dn and revenue Rn to any (fixed) function of Tn and get the same result.

    Eg, to minimise Sum{D(tN) x betaN} subject to Sum{R(tN) x betaN}=K, taking lagrangians, we get Sum{D(tN) x betaN – lambda x R(tN) x betaN} + K x lambda. Differentiating with respect to tN gives D’(tN) – lambda R’(tN) = 0, which (if D and R are fixed functions of tN), can be solved to express tN in terms of lambda, which doesn’t depend on N. Hence the revenue R(tN) doesnt depend on N either.

    What, exactly, is being assumed if you assume R and D are functions solely of tN ? Obviously something different from what I assumed.

  51. 51 51 MGH

    I’m biased, but would it be appropriate hijack your argument to say that reductions in government spending are a more effective way to reduce deficits than raising taxes?

  52. 52 52 Steve Landsburg

    MGH:

    I’m biased, but would it be appropriate hijack your argument to say that reductions in government spending are a more effective way to reduce deficits than raising taxes?

    I have no idea what “more effective” means.

  53. 53 53 Ken B

    @Steve 52: I think he means less deadweight loss.

  54. 54 54 nobody.really

    I’ll put in a non-progressive MMT view (there really are some things about functional finance that make sense if you can separate them from the political views espoused by most MMT’ers.).

    What, exactly, is being assumed if you assume R and D are functions solely of tN ?

    What hope is there of distinguishing valid ideas from political views? Even in our equations, we can’t help but see the world in terms of R’s and D’s!

  55. 55 55 Ken B

    This is why calculus is such a cool subject nobody.really: you can imagine what happens when you make the Rs and Ds vanish …

  56. 56 56 nobody.really

    @51: [W]ould it be an appropriate of hijack your argument to say that reductions in government spending are a more effective way to reduce deficits than raising taxes?

    @52: I have no idea what “more effective” means.

    @53: I think he means less deadweight loss.

    At the risk of becoming an accomplice to a hijacking: Almost.

    The Deadweight Loss function clearly demonstrate that we can minimize the loss by minimizing taxes, not necessarily spending. Thus, to minimize deadweight loss we should set taxes to 0.

    And then what consequences would ensue, do you imagine?

    Moral: As applied to public policy, the term “deadweight loss” is propaganda. Yes, if you have incremental taxes, some mutually-beneficial transactions will not occur. But what DOES occur instead? Government services, a relatively stable currency — generally, the absence of the harm that would have resulted if we had set taxes equal to 0. Thus, there is a loss, but the loss is incurred to secure a gain. Outside the context of the Deadweight Loss graph, economists refer to this kind of dynamic as a “price.”

    In other words, there’s no way to compare the consequences of reducing government spending to the consequence of raising taxes without knowing what the spending is buying.

  57. 57 57 Max

    Nick clears things up here:

    http://worthwhile.typepad.com/worthwhile_canadian_initi/2012/11/precautionary-taxation-vs-tax-smoothing-on-paying-down-the-debt.html

    To summarize, you ideally want nice smooth tax rates, not tax rates that go predictably up then down, or down then up.

    Ok, that’s not too crazy. It only gets controversial when you try to translate it into actual policy, since that requires making forecasts. Steve is a pessimist with his 0% growth forecast. For some reason, Steve didn’t optimistically consider the possibility that Obama is a fellow pessimist, only pessimistically assuming that Obama wants to increase spending or reduce debt. :-)

  58. 58 58 djp

    @54

    “”"
    What hope is there of distinguishing valid ideas from political views? Even in our equations, we can’t help but see the world in terms of R’s and D’s!
    “”"

    Very funny!

  59. 59 59 Nathan

    Question: If you are not intending to ever take on additional debt, is there any argument in favour of servicing existing debt instead of just defaulting?

  60. 60 60 Paul T

    SL:”… tax revenue is of the form At-Bt^2 (where t is the tax rate); deadweight loss is of the form Ct^2.”

    This is news to me, so I’ll ask: in what units is this tax rate variable? ‘tax rate’ is hardly self-explanatory.

  61. 61 61 Martin-2

    Steve, are your calculations of dead weight loss assuming a sort of optimal consumption tax? I’d be surprised if all the inefficiencies of US tax policy added up to such a nice formula. Or do the coefficients account for this?

  62. 62 62 Harry

    Steve:

    This issue is not with your math. The math is fine. The issue is with the stability of the system. You are assuming that at any given level of debt (or debt/GDP, which is held constant over time in your optimization) there is zero probablity of interest rate risk, zero probability of roll-over risk, and zero probability of negative growth.

    This combination (any given level of debt or debt/income, zero interest rate rate, zero roll-over risk, and zero probability of negative growth is exactly the set of assumptions that created the housing/mortgage bubble. The problem was not with the math in this case either, it was with the stability of the system at increasingly higher debt and debt/income levels.

    How much is too much debt for macro stability? The Maastricht Treaty put the limit at 60% debt/GDP, long since exceeded across the Eurozone. Reinhart-Rogoff put it at 90%. Italy is at 120%. Greece is well beyond 160% with a preposterous objective of 120% only because Italy is already there. Japan is well beyond 200%. And all of those countries (and plenty more) are doing nothing but increasing their debt ratios because – for now – most of them can. But your approach, which optimizes deadweight losses from taxes, assumes the US (and presumably any currency issuing country) will always be able to do so as long as the debt/GDP ratio is held constant.

    That means, among other things, that 1) there is no debt/GDP level at which interest rate risk or roll-over risk exists, let alone increases, and 2) there is no risk of a currency crisis like the kind that sank Mexico in 1994, or most of Southeast Asia in 1997, or Argentina many times in the past few decades (to pick countries and regions with debts denominated in their own currencies and having printing presses, thus bypassing the MMT money-printing chicanery).

    In other words, the financial truism that leverage kills does not exist because exogenous or endogenous shocks to the national balance sheet don’t exist. Indeed, in this scenario, there is no national balance sheet to shock because the model and the changes in the system are 100% related to flows and 0% related to stocks. (This puts your model to the left of Krugman’s by the way. At least he has some proposals to deal with the excessive stock, i.e., too much debt/GDP, however implausible they may be.)

    Ultimately, what happens is that when an over-leveraged system becomes unstable (for any number of reasons) it does not deflate or quietly drop to a lower equilibrium level, it collapses. Everyone rushes for the exists and the illusion of stability collapses. This is what happened to the housing/mortgage markets in the US, Spain, Ireland, and many other countries, is happening to the PIIGS in the Eurozone, and will happen in the US, Japan, and other similarly over-indebted countries despite their own-currency denominated debts and their printing presses.

    You are 100% correct that “It was almost surely a mistake to run up this much debt in the first place, but now that we’ve got it, the best thing to do is to keep it forever.” The problem is that the higher the debt levels the less likely “forever” lasts forever.

  63. 63 63 Steve Landsburg

    Harry: Thanks for this thoughtful contribution. You’re right of course that I’ve made a thousand simplifying assumptions. Welcome to The Big Questions.

  64. 64 64 Harry

    Steve:

    Thanks for your kind comment. Two typos in my original write-up. The first line in the second paragraph should read “zero interest rate risk” not “zero interest rate rate.” The fourth line in the next to last paragraph should read “Everyone rushes for the exits…” not “Everyone rushes for the exists…”

    One final substantive comment on the stability of our over-leveraged system. The US, just like every other over-leveraged country (or currency union) with debts denominated in its own currency and a printing press, is certain it can extricate itself from any system disturbance at any debt/GDP level with little or no real economic pain. This is central to the arguments of Bernanke, Krugman, Draghi, the MMT crowd, etc. and contra to the evidence of Reinhart-Rogoff, the IMF, and the US financials who’d rather hold more than $1T of excess reserves rather than make loans. A more succint way of putting it would be as follows: We have debts we cannot repay, promises we cannot honor, a standard of living we cannot sustain, and 300 million Americans who depend on those three statements not being true. This is a story that ends badly no matter how we deal with taxes versus expenditures.

  65. 65 65 AMTbuff

    A new Tax Notes article refutes the Diamond/Saez claim that 73% would be an optimal tax rate, using the same criteria that Diamond and Saez claim to have used:

    http://www.aei.org/files/2012/11/19/-should-the-top-marginal-income-tax-rate-be-73-percent_085518416524.pdf

    This excellent and accessible article omits one other long-term influence on elasticity: financial aid for college expenses. Need-based aid operates like a large add-on to the marginal tax rate from about $50,000 to $150,000 income, with the range moving higher at more than the inflation rate.

  66. 66 66 Daniel

    Harry, You cite politically unstable regions, which after their crisis pretty much returned to their pattern of volatile expansions and contraction. You use this evidence to state that America is in for some rough times because of debt to GDP levels which are still lower than those following World War II. The crisis you cited occurred because investors believed that these regions may not be able to pay off their debt because their governments were unstable. Japan has operated with a debt to GDP ratio that is much higher than your supposed safe levels for many years now without any consequence to their financial stability.

    Can you enlighten us on how this supports your argument that the US is headed for disaster any day now since the consequences you stated were not nearly as bad as you think they will be for the US in these regions and the reasons for the crisis were not nearly as simple as you had stated?

  67. 67 67 Mike H

    “Ultimately, what happens is that when an over-leveraged system becomes unstable (for any number of reasons) it does not deflate or quietly drop to a lower equilibrium level, it collapses. Everyone rushes for the exits and the illusion of stability collapses.”

    But which exits do they run for?

    “This is what happened to the housing/mortgage markets in the US,”

    which led to the collapse of the housing bubble, and the GFC.

    “Spain, Ireland, and many other countries, is happening to the PIIGS in the Eurozone,”

    You already said Spain. The exit here appears to be Euro-denominated bonds. Spain can’t print Euros. Ditto Ireland and the other PIIGS (GIPSI) countries. These governments could literally run out of money, in theory.”

    “and many other countries”

    The Asian financial crisis? I was in Malaysia when that hit, in 1997. The governments could print their own money, so when confidence disappeared, the exit people ran for was the currencies. The value of the Ringgit, Rupiah, Baht, etc collapsed (and has never fully recovered). Much government and private debt was denominated in US dollars, and suddenly the debt increased by 50% or more. This presented a serious problem for many of them. Malaysia solved it by fixing the exchange rate and instituting strict controls on the flow of capital.

    “and will happen in the US, Japan,”

    Which exit will people run to?

    If they start selling off bonds – the governments won’t run out of money, they can always print more. As in the Asian financial crisis, this would cause people to start sell off the currency. However, if the value of the US dollar drops, the burden of debt drops also. Unlike the countries of the Asian financial crisis, the US and Japan owe money in their own currencies. A drop in the value of those currencies would lower the value of the debt.

    So, the US is immune to the troubles faced by Spain (since it has its own currency) and to the troubles faced by Malaysia (since it borrows in its own currency). A lower US dollar would hurt some industries, but help exporters and manufacturers. If there’s some disaster in this story, it’s quite different from the Euro crisis or the Asian crisis. What do you imagine it might be?

  68. 68 68 Frozen

    However, if the value of the US dollar drops, the burden of debt drops also. Unlike the countries of the Asian financial crisis, the US and Japan owe money in their own currencies. A drop in the value of those currencies would lower the value of the debt.

    So, the US is immune to the troubles faced by Spain (since it has its own currency) and to the troubles faced by Malaysia (since it borrows in its own currency). A lower US dollar would hurt some industries, but help exporters and manufacturers. If there’s some disaster in this story, it’s quite different from the Euro crisis or the Asian crisis. What do you imagine it might be?

    Honestly the issue isn’t the current debt. As others have pointed out, if we could simply bring the budget into balance tomorrow and just service the interest, then time and inflation will slowly dwindle the debt to nothing. The issue is that we have trillions in debt that is hiding in unfunded entitlement liabilities. And, since SS is formally protected from inflation and Medicare is de facto protected from inflation, simply printing money won’t make that problem go away. You are still stuck having to run the presses ever faster in a race against yourself and destroying the economy in the process.

    My question to Steve is just how do we set the ongoing level of taxation to account for these future entitlement liabilities? It seems to me that we are forced to choose between the one extreme of collecting a surplus today and paying the debt down in order to be in balance on average between the present day and any arbitrary future date, or we say that the whole system is Pay Go and tell future generations that they’ll just have to cough up more for Grandma and Grandpa who didn’t contribute an adequate amount when they were paying taxes. What am I missing here?

  69. 69 69 Paul T

    Frozen: “… The issue is that we have trillions in debt that is hiding in unfunded entitlement liabilities.”

    According to these gents:
    http://tinyurl.com/wsj-future-shock

    the entitlement liability is a wee larger than generally suspected.

    I have no idea where their number comes from.

  1. 1 How High Should Taxes Be? « Politics & Prosperity
  2. 2 Steve Landsburg says paying off the national debt would be a bad idea « Quotulatiousness
  3. 3 Steve Landsburg Thinks the Current Debt Level Is Juuuuust Right
  4. 4 Steve Landsburg Thinks the Current Debt Level Is Juuuuust Right | Liberty on the Rocks™ Denver
  5. 5 Steve Landsburg Thinks the Current Debt Level Is Juuuuust Right - Unofficial Network
  6. 6 Potpourri
  7. 7 Potpourri - Unofficial Network
  8. 8 Seven reasons why U.S. will never pay down the debt | Economic Collapse News
Comments are currently closed.