## Saturday, June 11, 2011

### Some Fiscal Arithmetic

If we're going to discuss fiscal policy, we should be clear on the accounting relationships involved. So, here are some basic equations describing how the public debt evolves over time. I should say up front that the relationships I'm describing here, while they suggest an unorthodox skepticism about worries about debt "sustainability," are themselves totally orthodox and noncontroversial. And they don't make any behavioral assumptions -- they're true by definition.

We're interested in the ratio of debt to GDP. What will this be at some time t?

Well, it will be equal to the ratio in the previous period, increased by rate of interest, and decreased by the rate of growth of GDP, (remember, we are talking about the debt-GDP ratio; increasing the denominator makes a fraction smaller), plus the previous period's primary deficit, that is, the difference between spending on everything besides interest, and revenues.

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.

There is a further difference between the cases. When g > i, the equilibrium is stable; if for whatever reason the debt rises or falls above the level implied by the long-run average primary deficit, it will move back toward that level over time. But when g < i, if the debt is one dollar too high, it will rise without limit; if it is one dollar too low, it will fall without limit, to be eventually replaced by an endlessly growing positive net asset position.

So, which of these three cases is most realistic? Good question! So good, in fact, I'm going to devote a whole nother post to it. The short answer: sometimes one, sometimes another. But in the US, GDP growth has exceeded pre-tax interest on 5-year Treasuries (the average maturity of US debt is around 5 years) in about 50 of the past 60 years.

The discussion up to now has been in terms of the primary balance. But nearly all public discussions of fiscal issues focus on the total deficit, which includes interest along with other categories of spending. We can rewrite the equations above in those terms, adding a superscript T to indicate we're talking about the total deficit. In these equations, g is the nominal growth rate of GDP.

Again, we define equilibrium as a situation in which the debt-GDP ratio is constant. Then we have:
In other words, any total deficit converges to a finite debt-GDP ratio. (And for every debt-GDP ratio, there is a total deficit that holds it stable.) So defining a sustainable total deficit requires picking a target debt-GDP ratio. Let's say we expect nominal GDP growth to average 5% in the future. (That's a bit low by historical standards, but it's what the CBO assumes in its long-run budget forecasts.) Then 2010's deficit of 8.8% of GDP implies a long-run debt-GDP ratio of about 175% -- a number toward the top of the range observed historically in developed countries. 175% too high? Get the long-run average deficit down to 4%, and the debt-GDP ratio converges to 80%. Deficit of 3% of GDP, debt of 60% of GDP. (Yes, the Maastricht criteria apparently assume 5% growth in nominal GDP.) It is not at all clear what the criteria are for determining the best long-run debt-GDP ratio, but that's what you've got to do before you can say whether the total deficit is too high -- or too low.

One last point: An implication of that last equation above is that if the total deficit averages zero over a long period, the debt-GDP ratio will also converge to zero. In other words, "Balance the budget over the business cycle" is another way of saying, "Pay off the whole federal debt." Yet I doubt many of the people who argue for the former, would support the latter. Which only shows how important it is to get the accounting relationships clear.

EDIT: I should stress: There is nothing original here. Any economist who does anything remotely related to public finance would read this and say, yes, yes, so what, of course -- or at least I sure hope they would. But you really do have to be clear on these relationships for terms like "sustainable" to have any meaning.

For instance, let's go back to that Peterson budget summit. As far as I can tell, five of the six organizations that submitted budget proposals used the CBO's assumptions for growth and interest rates. (EPI tweaked them somewhat.) But given those assumptions, only two of the budgets -- EPI  and AEI -- actually stabilize the debt-GDP ratio. (Interestingly, they do so at about the same level -- 70% of GDP for AEI, and 80% of GDP for EPI.) The other four budgets describe a path on which the entire federal debt is retired, and the federal government accumulates a net asset position that grows without limit relative to GDP. Personally, I am all for public ownership of the means of production. But I didn't realize that's what people had in mind when they called a budget "sustainable". Of course, presumably that is, indeed, not what the people at CAP, Heritage, or the Roosevelt Campus Network had in mind; presumably they just didn't think through the long-term implications of their budget numbers. Which is sort of the point of this post.

UPDATE: ... and not 12 hours after I post this, 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." As we've seen , given the historic pattern where GDP growth is above the interest rate, this statement is simply false.

Of course, John Q. might be assuming this historic relationship will be reversed in the future. But then you could just as logically say that the interest rate is too high, or inflation is too low, as that higher taxes are needed. The view that it must be taxes that adjust implicitly assumes that that longer term interest rates aren't responsive to policy, and that deliberately raising inflation can't even be discussed. In other words, while surpluses later is often presented as part of an argument for deficits now, the case for surpluses in the future rests on premises that also largely rule out more aggressive monetary stimulus in the present.

1. excellent

shows u can you stop the horror easily

the eventual stablity if g>i no matter d
is like the old solow growth model's
final per labor to capital ratio
given solow's constant share of income accumulated
and constant labor force growth assumptions

the i (= or >) g is of course like the domar harrod
knife edge growth model

the key for me is always
to show
the simple feed back dynamic

where the commanding macro ratio
in this case g /i
can be altered at any time
thru adjustments in credit flow
that alter the rate of price level change
and or
by the suppression of the nominal interest rate

too often the assumed fixity
only an artifact of the model's simplification
causes mis apprehensions
ie
i/g is not in reality constant
nor need it be in any sense
optimally be held at some constant
say where g > i

" for terms like "sustainable"
to have any meaning"

we need only to make it double dog clear

a)
the ratio i/g is within our power to alter
at will

and b)
we therefore can alter the debt to gdp ratio
to whatever we choose

so long as
c)
we make the other necessary
as well

of course there can be some nasty fine print on the other necessary steps
like a forex adjustment
that causes an import price tsunami

2. @ Josh:
Some math quibbles: (I don’t know how to write subscripts and superscripts on the computer, apologies, so I write d sub t and d sup T.)

1) In equation 1 (of your 6 equations) should the subscript on the variable d be t or (t+1)?

2) In equation 2, the middle expression gives variable d the subscript (t+1), then in the rightmost expression the variable d subscript is back to just plain t. The middle expression seems to have a typo; I think it should be “(d sub t) + {[(i-g)/(1+g)]b sub t}” or perhaps “[d sub (t+1)] + {[(i-g)/(1+g)] b sub t}”. The way you’ve written it, the middle expression multiplies the term [d sub (t+1)] by the term {[(i-g)/(1+g)] b sub t}, instead of adding these two terms. Is that correct?

3) In Equation 5, on the right-hand side, the term g(b sub t), the nominal growth rate times the previous debt-to-GDP ratio, should be subtracted, not added. (That term should have a negative sign in the middle expression as well.) The way you’ve written it implies that the increment in the debt-to-GDP ratio is always positive whenever there is a deficit and a positive growth rate; under those conditions, the debt-to-GDP ratio would therefore grow without limit. (As you’ve written it, Equation 5 also implies that the larger the growth rate, the larger the increment of debt-to-GDP ratio, which can’t be right.)

A very illuminating post.

willboisvert@aol.com

3. what may get a few folks conflusterated
is the dandy composite term
in equation one
that both figures out the refractioning
of the existing debt for the next periods gdp
ie
( 1/ i+g ) x the period t debt to gdp ratio

and in the ssame infernal fractional expression
show the interest owed on that existing debt
(1 + i) x the period t debt

breaking that apart into two expressions though algebraic ham fistery
has the humble virtue
that one can move to
the expression for total deficit
in a manner that is easier to "see"

4. nice point
recall neumann result
i=g optimally
that's fine because that is with an assumed full employment
ie
no need for stablizing deficits or surpluses

would that our market system with its
firm level profit driven production system
could produce such a fine performance

5. recall neumann result
i=g optimally
that's fine because that is with an assumed full employment
ie
no need for stablizing deficits or surpluses

would that our market system with its
firm level profit driven production system
could produce such a fine performance

6. To be fair to John Q., he explicitly says "current discretionary expenditure". Assuming that non-discretionary spending will rise faster than GDP (debatable but not unreasonable due to medical inflation) his point may or may not hold, depending on the exact math.

7. This comment has been removed by the author.

8. Christian,

What you writes sounds reasonable, but in fact it's incorrect. That's the reason it's important to actually work through this stuff - there are lots of claims that could be true, but turn out not to be.

No matter how high health expenditures rise, they can only push you onto a path where the debt-GDP ratio goes to infinity, if they lead the real interest rate on government debt to rise or the growth rate to slow. Now, either of those things might happen. But it's important to distinguish between the mathematically false accounting claim that John Q. actually made -- under the current mix of spending and revenues, the debt-GDP ratio diverges -- and the empirically testable claims about behavior that he could have made. Note also that those behavioral claims imply that the relationships we observe right now -- dg/db > 0, di/db = 0 -- must qualitatively change at some point in the future so that dg/db - di/db < 0.

Now you might say, OK, but do you really think that if the debt-GDP ratio went to 1,000%, that wouldn't put upward pressure on interest rates? No, I agree, it very well might. So am I just being pedantic, then? No. Because we have to correctly formulate the problem to understand the range of potential solutions.

For instance, one thing we can see from the equations here is that g is just a little higher than i, as it has been in recent decades, then even a small reduction in i can have a very large impact on the final debt-GDP ratio for a given deficit. And if we look historically -- this is going to be the subject of another post soon, I hope -- we see that movements in the real interest rate on government debt have generally been much larger than movements in the primary balance. Together, these two facts might suggest that if we think the long-term trend in the debt-GDP ratio is too high, we should be thinking about policies of "financial repression" to lower long-term interest rates, rather than (or in addition to) reducing fiscal deficits.

One reason to focus on interest rates rather than the fiscal balance is the major practical advantage that it makes our long-term program consistent with our short-term program, instead of contradictory to it. If the world were run by philosopher-kings, saying "Do this now and just the opposite later" might not be a problem, but in the real world I think it's a major handicap both intellectually and politically. Arguments for austerity in the long run have a way of turning into arguments for austerity now. Whereas if we can argue that tighter control of banks and monetary policy that targets longer rates will improve the long-term debt trajectory, those things will help as recession-fighting tools too.

9. "One reason to focus on interest rates rather than the fiscal balance is the major practical advantage that it makes our long-term program consistent with our short-term program, instead of contradictory to it"
" we should be thinking about policies of "financial repression" to lower long-term interest rates"

yes indeed

"One reason to focus on interest rates rather than the fiscal balance is the major practical advantage that it makes our long-term program consistent with our short-term program, instead of contradictory to it"
or at least retain the impact viability
of the elite electorally unaccountable
macro control panel called the fed

its easier to jigger the nominal interest rate when its not on the floor like now
then send the fiscal deficit into barrel rolls

which however
as many moderates like paul krugman
....summers even
have noticed the value of a higher secular inflation rate

so there's almost always some nominal room
to lower the real interest rate

now i prefer a gosmart solution involving a centrally controled price level market in mark up warrants
ala colander/lerner
but that be pie in the sky today
even more so then free running average inflation of 5 or 7 percent

10. Well now I'll be pedantic: the integral/series you write down converges if (a) g > i and (b) d is constant (or bounded same diff). My point was that one could argue that non-discretionary spending and therefore spending as proportion of GDP and hence d provided taxation remains unchanged will increase at above GDP growth rates. In this case the deficit/GDP ratio will not converge.

I do completely agree with your main point btw that one should focus on interest rates rather than fiscal balance (well I'd prefer a revolution and social control of the means of production but there you go).

11. By the way I'm glad I finally looked at your blog a couple weeks ago - it's great, it clarified a lot for me as far as my uneasiness with the things Krugman eg. has been writing is concerned.

12. Paine-

There's a lot of good stuff in your comments (which is why I haven't replied yet...) But you are absolutely right in the last one, higher inflation should be part of the conversation. Both for the ZLB reason you suggest and because -- if we reject Fisher's law, which is at least empirically arguable -- over some range nominal interest rates may be stationary so that higher inflation leads to permanently lower real rates.

Christian-

Yes, of course if the health care share of expenditure rises faster than GDP forever, then other stuff is going to have to get crowded out, whether through taxation or some other measure. That's true, but it's not a statement about the federal budget.

I'd prefer a revolution and social control of the means of production

Hey, me too!

13. on health care i always point out
are we talking about faster sectoral inflation then general inflation
or actual unit growth of the health care sector however fuzzily defined
and after due adjustment for productivity
in labor units
actually exceeding the general product and service economy growth

for the former we could simply impose a mark up market cap and trade system

but as for the actual real unit growth rate
of the sector exceeding
the the real growth rate of the whole

hey made health care is the new food

14. Bill,

Thanks for the corrections. It really doesn't matter if one uses the deficit for the previous period or the current period, but obviously I should be consistent. I think the other error crept in because I was first thinking of writing it in terms of fiscal balances, rather than deficits. Will fix this stuff shortly. (I'm running out the door now.)

Glad you liked the post. That's a first, I think.

15. @ Josh:

The problem in equation 5 is just a sign error that you made in simplifying one of your (unshown) substitutions.

The mistake you must have made in your derivation was writing:
1 - (1+g) = 1 - 1 + g = g, whereas it should be
1 - (1+g) = 1 - 1 - g = -g, which gives the g term in the final expression its correct negative sign.

Maybe this is a stupid question, but is it possible that, if the total deficit is held constant, the interest portion of it can grow so large that it crowds out other government expenditures? D2GDP might still find an equilibrium, but people would be unhappy if most or all of the government budget was devoted to interest payments. If that could happen, political pressures might force a constantly increasing total deficit.

16. Will, at the "equilibrium solution" - that is, when the total deficit as proportion of GDP growth is equal to the debt-GDP ratio - the quotient of interest payments as percentage of GDP (which will be = ib) divided by the total deficit will also be constant provided interest rates are assumed constant as well. When i is approximately of the same magnitude as g, then interest payments will consume exactly the deficit (but of course not the non-deficit portion of the budget).

17. Excellent post! Thanks.

18. A technical/empirical question: what is the correct measure of i?

Just now I calculated i as measured by each year's federal "net interest payments"/"debt held by public" going back to 1948.

G-i was strongly positive in the 50s, 60s and 70s, but slightly negative in the 80s, 90s and 00s.

19. As I said at CT, if you plug in your suggested value of g-i =0.6 per cent, and a primary deficit of 6 per cent, you get b =10, that is a debt/GDP ratio of 1000 per cent, which as you say is unsustainable. And, as you correctly start by saying, it's the primary deficit that you should be working with.

Holding the total deficit constant while debt increases (the basis of your second calculation) can only be done by reducing the primary deficit, that is by cutting spending or raising taxes.

That said, I don't have a problem with the point that the correct objective of fiscal policy is maintaining stable and sustainable ratios of debt and net worth to GDP. "Balancing the budget over the cycle" is intended (by me, at any rate) as a shorthand for this objective.

20. John Q.-

Thanks for the response. I think we are slightly closer to agreement.

First of all, the most important thing from my point of view is that we get some positive content into the slogan of "sustainability" by being explicit about the target debt-GDP ratio and the assumptions about growth and interest rates.

Whether we should work with the primary or total deficit depends on whether we think that spending and tax levels are set by more or less autonomous political processes, in which case we should use the primary deficit; or whether we think the government is targeting the deficit as such for purposes of demand management, in which case we should use the total deficit. In the 1960s and 1970s, "Keynesian" (really Lernerian) macropolicy explicitly did the latter. Policymakers talked about the gap between savings and investment at full employment, which had to be filled by some combination of government borrowing and net exports. For instance, we might think that at full employment, desired savings would exceed desired investment by 5% of GDP. (Again, you can find exactly this kind of language in Economic Reports of the President in the Kennedy, Johnson and Nixon administrations.) Then we have to ask, will filling that gap with a government deficit result in a stock of debt that is too large for the private sector to realistically hold, or not? So either form of the deficit can be appropriate, depending on the context.

Now, if you believe that desired savings do not equal desired investment at full employment, as both Keynes and postwar "Keynesian" economists did, and if you believe that investment should continue to be the responsibility of the private sector (as Keynes did not), then "balancing the budget over the business cycle" is a recipe for stagnation and excess unemployment. You need a long-term average total deficit equal to the savings-investment gap. Whether this corresponds to a primary deficit, balance or surplus depends on g-i.

As I said at CT, if you plug in your suggested value of g-i =0.6 per cent, and a primary deficit of 6 per cent, you get b =10, that is a debt/GDP ratio of 1000 per cent, which as you say is unsustainable.

You can't use 6 per cent for this calculation, tho -- these are long-run calculations and the current deficit reflects the extraordinary effects on government budgets of the Great Recession. A more appropriate number would be the Bush-era primary deficits of around 1 percent of GDP. At which point it is not at all clear that current policy is unsustainable.

This also brings out another point, which is that historically the biggest movements in the long-term budget position have been driven by changes in growth and interest rates, and the effects of changes in growth on the budget. As Dean Baker likes to point out, changes in tax and spending policies contributed exactly nothing to the fact that the federal government ran a surplus in 2000, rather than the deficit that had been projected 5 years earlier. All the real work was done by faster growth.

So, if (1) mathematically, faster growth and lower interest rates are just as important to the long-run budget position as tax and spending levels; (2) historically, faster growth and lower interest rates have contributed more than tax and spending changes to movements in the long-run budget position (this is also true of the shift from rising debt-GDP ratios in the first three postwar decades, to rising ratios in next three decades, tho in this case policy changes did contribute as well); and (3) focusing on higher growth and lower interest rates is consistent with our immediate goals, while lower spending and higher taxes undermines
them; then why present the long-term budget problem in terms of tax and spending levels, instead of lower interest rates (including via higher inflation) and faster growth?

21. Seth,

I have been using the yield on the 5-year Treasury bond (from the Fed via FRED), since the average maturity of government bonds is today around five years. This is a little crude, obviously -- one should really use an average of all maturities weighted by the mix for each year -- and your method might be a better first approximation. Two caveats: First, since today's interest payments reflect the interest rates when the debt is incurred, your method is not going to come up with the same periodization. Second, the correct measure is the after-tax interest rate. Figuring out the appropriate tax rate is tricky but as a first approximation you could simply use the share of federal taxes in total GDP.

Here are some articles with good discussions of these issues:

Arestis, P., and M. Sawyer. 2008. “The intertemporal budget constraint and the sustainability of budget deficits.” In J Creel and M. Sawyer (eds.) Current Thinking on Fiscal Policy.

Aspromourgos, T., D. Rees, and G. White. 2010. “Public debt sustainability and alternative theories of interest.” Cambridge Journal of Economics 34(3): 433.

Darby, M. R. 1984. "Some pleasant monetarist arithmetic," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Spr.

22. Jamie Galbraith makes the same point in this pdf (with pictures!):

http://www.levyinstitute.org/publications/?docid=1379

23. @ Josh,

There's something fishy about the Dean Baker article you cite for your claim that tax and spending policies contributed nothing to the Clinton-era budget surpluses. Baker's main exhibit is a chart that is not actually about the sources of the 2000 surplus. It is instead about the sources of changes in the Congressional Budget Office "projections" of the 2000 budget deficit/surplus during the period 1996-2000. The question the chart addresses is why 1996 CBO projections got it wrong when they forecast a deficit in 2000 instead of the surplus that materialized in later, more accurate CBO projections. The chart does not address the question of why that surplus arose in the first place. (Apologies, I don’t know how to bring the chart into this post.)

Here’s Baker’s gloss on this data:
“As the chart shows, all of the improvement in the budget between 1996 and 2000 was due to the fact that the economy performed much better than expected and that CBO had been overly pessimistic about trends in government spending and tax collections. The legislative changes added by Congress in this period actually went the wrong way.”

Baker’s wording is tricky and misleading. What the chart shows is that changes in CBO “projections” for 2000 during the period 1996-2000 came from 1) “economics changes”—presumably faster growth than anticipated, which added \$230 billion to revenue; 2) “technical changes”—presumably, corrections to the “overly pessimistic” earlier assumptions CBO made about government revenue and spending, which added \$250 billion to revenue; and 3) “legislative changes” during 1996-2000 that shaved \$5-10 billion off of projected revenue, and thus slightly reduced the 2000 surplus.

None of this demonstrates the irrelevance of Clinton’s tax policies. First, Baker implies that the 1996 CBO projection perfectly forecast the future effects of the 1993 tax hikes, and that all subsequent improvements in budget projections must therefore have been the result of “luck” rather than policy. This is an odd gloss to put on a chart that is all about how wildly off the mark CBO estimates can be. It’s quite possible that early CBO estimates erred simply in not properly accounting for the future benefits of the 1993 legislation. The “wrong way” “legislative changes” he cites all came after 1996; they tell us nothing about the effects of the crucial 1993 legislation. Nor does Baker tell us how those 1993 tax hikes affected the baseline revenue for either the 1996 projection or the 2000 actuality—both might have been hundreds of billions of dollars worse without the 1993 tax hikes, but that wouldn’t affect the discrepancy between the two that is highlighted in his post. We also don’t know how much the 1996-2000 “technical changes” might have been due to 1993’s tax hikes. Those changes include unanticipated extra revenues that would not have been captured without higher tax rates, lower interest payments due to prior deficits being reduced by the 1993 tax hikes, etc.

I suspect that your claim about the irrelevance of Clinton’s tax and budget policies is wrong; in any case, you really need better evidence than Baker’s weak article to substantiate it.

willboisvert@aol.com

24. Fair point.

It is my impression that changes in growth rates and interest rates have made a larger contribution to shifts in the long-term budget position than have policy changes in tax and spending levels. (I say policy changes because higher growth by itself improves the primary balance.) But this is a hypothesis to be investigated, not a settled fact. And Dean Baker's piece is suggestive, not dispositive.

25. late to the party again

quig is off the mark here

the point is nominal g and i can be controled
by policy choices

the g/i ratio is of course real
but only some one in fear of inflation can't grasp the options

again the fab 40's show us all we need to see about g's and i's

okay we don't have a a global army and armada
to build and arm
nor anything like
the post war global markets to trade in

but the macro shell is there
and nominality ie shell is the game here
and the pun tells all about how the pro corporate elements play this shell game

the policy pea of a variable controlable i/g
is always
in the merlin econ con's palm
when we start looking under any shell

26. greenwood
seems to have an urge to vindicate clintons that is bondage bob rubins
fiscal policy
well the same mentality is now dropping rabbit turds all over the w3hoite house
and in a time like this
when rubin's poison isn't shielded by macro forces the dino points out existed during bill's second miracle term ....

proof is not needed action is neeeded

deficit reduction chatter
ala rubin even if long range not now heavens no not now
like the GOPers want but ...
well it's completely diversionary

as is silly rain dancing around
the false fire of the fed's QE series

the transfer system is where all eyes must focus
that and the construction sector depression

the transfer system could provide health premium relief and a payroll tax holiday
and needless to say a second term for ohbummer and a repeat of the election of 48
with a donkey congress

a slogan like this
"here's your money back you earned it "
has no viable majoritarian counter

27. Partys' still going strong, comrade.

the point is nominal g and i can be controled
by policy choices

That is exactly the point.

It's like this: Traditional finance says that the state is "small" relative to the economy, just like a household or firm. The Keynesian insight (well, one of them) is that in modern capitalism this is no longer the case. If I am buying stuff with credit, when will I have to stop? When people will no longer willing to lend to me. But logically, people might run out of stuff to sell, before they were unwilling to take my IOUs. That's the position modern states are in (at least some modern states, some of the time; if I have one criticism of the MMT folks, it's that they are more interested in establishing the logical conditions for functional finance to apply, than in empirically investigating the boundary between where it does apply in practice, and where sound finance still does.) Once you accept this perspective, as policymakers did in the decades after WWII, then stuff that had previously looked like parts of the environment, became objects of policy instead, which meant tradeoffs (most famously the Phillips curve), which meant political choices.

The whole point of New Keynesianism is to preserve the functional finance for short-term stabilization while denying the possibility of any genuine economic tradeoffs. It's a program to create an impermeable boundary between macroeconomics and politics. So we are told that appropraite policy can reduce unemployment to the NAIRU level at no cost to anyone, and cannot reduce it below the NAIRU at any cost at all.

This is why it's so wrong and harmful to say that if we want a path of the debt-GDP ratio below that implied by current policy, the only way to get there is by spending less or taking in more. It excludes the tools of macroeconomic policy from the discussion.

28. "we are told that appropraite policy can reduce unemployment to the NAIRU level at no cost to anyone, and cannot reduce it below the NAIRU at any cost at all"

perfect example in fact the center piece of the kalecki mirage taboo

btw
there is no trade off along phillips lines if we
impose a mark up waarant market
and turn price level change into a domesticated macro policy tool

29. We are, I think, closer to agreement on some points, and also closer to understanding where we differ.

Starting with the arithmetic and debt/GDP questions, I'll say the following

1. The primary deficit was rising under Bush from a combination of policy decisions (prescription drugs, wars etc) and long-term trends in Social Security and Medicare

2. Even after cutting bad public spending (defence, ethanol subsidies etc), the US public sector as a whole is clearly underfunded

3. So, given
(a) the public spending I would advocate
(b) no change in taxes from those of the Bush era
(c) economic conditions comparable to those of the 1990s
the primary deficit would be at least 3 per cent of GDP, and probably closer to the 6 per cent I quoted last time.

Even with 3 per cent, if we assume g-i=0.6, we get an equilibrium debt/GDP ratio of 500 per cent which is obviously unsustainable.

So, our main analytical disagreement seems to me to be that you think fiscal and monetary policy can greatly increase g-i, which would both
(a) reduce the primary deficit associated with given tax rates and expenditure policies
(b) reduce the equilibrium debt/GDP ratio associated with any given primary deficit

I'll leave it to you to respond at this point.

30. There are four questions, I think.

First the one you point to. Given that we want a lower long-term debt-GDP ratio, does essentially all the adjustment have to come through tax and expenditure policy, or can some or all the adjustment come through policies targeting g and i?

Second, what is the path of debt/GDP under current policy? Third, what is the acceptable range for the long-term ratio?

Finally, there's a question I have not raised, but should be: is the long-term fiscal stance, independent of the present stance, a possible object of policy at all? Today's government cannot bind the tax and expenditure decisions of future governments. It can influence them, obviously, but the main channel of influence is today's budget. Actually raise taxes this year, and you've increased the probability that taxes will be higher next year. Express the intention to raise taxes next year, the effects are not so clear. If future policy cannot be set except via the persistence of present policy, then there is no sense in talking about the long term budget trajectory except insofar as policies to address it are also desirable in the short run. This is another argument for talking about lower interest rates rather than higher taxes as the solution to the budget problem (assuming the answers to questions 2 and 3 confirm that there is one.)

I will try to put up another post on these issues in the next few days.