After reading Nick Rowe, Brad DeLong, and Paul Krugman, I now understand who bears the burden of the government debt. Any member of the younger generation who reads the stuff that these old guys have written on government debt will be hopelessly confused. And that will be a burden on us all.
The idea that a larger government debt is a burden for future generations is so strongly intuitive as to be part of the standard narrative for anyone who wants to tell you that more government debt is a bad idea. But is that correct? When I teach undergraduates about government finance, I find it instructive to start with the Ricardian equivalence theorem. In a frictionless world, government debt is irrelevant. A tax cut that increases the government debt today has no effect because everyone understands that government debt is just deferred taxation. Lifetime wealth does not change, and everyone saves their tax cut today so as to pay the higher future taxes that are required to pay off the government debt in the future. Ricardian equivalence is a useful starting point, as it makes clear what frictions might cause Ricardian equivalence to break down - and that's a route for thinking about how policy might work to improve matters. Distorting taxes, intragenerational distribution effects from tax policy, and credit market frictions all potentially make a difference. But that doesn't make Ricardian equivalence "wrong" or useless. Indeed, it is an important organizing principle, and needs to be taken seriously.
One key departure from Ricardian equivalence arises because of intergenerational redistribution effects from government tax policy. Ricardian equivalence works because changes in the timing of taxes do not matter for anyone's wealth - the present value of tax liabilities for each individual is unchanged. But what if the government is cutting one person's taxes today, and paying off the government debt in the future by taxing someone else? Surely that comes into play in reality, as the government can cut taxes today, increase the government debt, and potentially not pay off the debt for 100 years, at which time the people who were on the receiving end of the current tax cut are long dead?
Robert Barro had an answer for this. If generations are tied together through altruism (we care about our children) and bequests, then we behave as if we are chained together with our descendants, and might as well be infinite-lived households. If I receive a tax cut today, then I save more, and give my descendants a larger bequest that will allow them to pay their higher future taxes. But surely this is going to far. Following the logic of Barro's argument, chains of altruism tie everyone together in ways that make everything neutral. There is certainly altruism in the world, but I think we all recognize that some collective action is required to make outcomes more efficient.
A standard vehicle for thinking about intergenerational distribution is the overlapping generations (OG) model (DeLong knows that the OG model exists, which is a start, at least). Peter Diamond's version of the OG model, with capital accumulation and production, is useful, but I'll simplify here to get the ideas across. Suppose two-period-lived people, with two generations alive at each date - young and old. The population grows at rate n, and each person is endowed with y units of consumption good when young, and zero when old. Storage is possible, with r the rate of return on storage from one period to the next. This is useful, as it ties down the real interest rate at r (so long as there is some storage in equilibrium). Suppose also that the government has access to lump sum taxes on the young and the old. The government can also issue one-period real bonds, with the real interest rate on government bonds = r in equilibrium.
Suppose that the government increases the quantity of government debt in the current period, T, by an amount b per young person currently alive. Since the real interest rate is constant at r forever, the effect of this change in government debt on economic welfare for each generation depends only on how taxes change for the rest of time. Suppose that the increase in debt is reflected in a lump sum transfer of x(T) to each person currently alive, so
x(T) = [b(1+n)]/(2+n)
Now, clearly the current old are better off as a result. They receive a transfer and are better off. What about everyone else - the current young, and future generations? For those people, it depends.
Scenario 1: Pay off the debt at T+1: In this scenario, to pay off the principal and interest on the government debt in period T+1 requires total taxes per young person alive equal to [b(1+r)]/(1+n). Supposing the government spreads the tax burden equally across people alive in period T+1, the tax per person at T+1 is
-x(T+1) = [b(1+r)]/(2+n)
Therefore, as long as n > 0, so the population is growing, the young people in period T (who are old at T+1) are better off, as their lifetime wealth increases. The old in period T+1 are worse off, as they pay a higher tax.
In this case, it is clear that the government debt is a burden on future generations - specifically the next one, which pays the taxes to retire the government debt.
Scenario 2: Hold the debt constant forever at its higher level: Under this scenario, the government debt per young person in period T+i is
(where x^i is x to the power i). If taxes are the same for young and old during any period, this implies that the tax per person in period T+i is
-x(T+i) = rb/[(2+n)(1+n)^(i-2)]
In this case, the young in period T are better off in present value terms, but anyone born in periods T+1 and beyond is worse off.
Compared to scenario 1, we are now spreading the burden of the government debt across all future generations. Note however, that the government debt per capita vanishes in the limit. The experiment increases the government debt by a fixed real amount and, as the population grows, the burden of the debt in per capita terms falls.
Scenario 3: Hold debt per capita constant at the higher level forever: In this case, if everyone at a point in time bears the same tax, the tax in period T+i is
-x(T+i) = [b(r-n)]/(2+n)
As in scenarios 1 and 2, the young in period T are better off, but now things are more interesting. If r > n, so that the real interest rate is higher than the population growth rate, we get a similar scenario to what we had previously, except we are now spreading the burden of the debt equally across future generations. However, if r < n, we actually make everyone better off. When r < n, it is socially inefficient to use the storage technology, and an optimal arrangement would have government debt driving out use of the storage technology. Diamond's classic paper shows how this works in a more standard neoclassical growth framework. In general, an economy with r < n is dynamically inefficient, and government debt is one means (as is social security) for effecting the appropriate intergenerational transfers. The interesting thing about the scheme in scenario 3 when r < n is that it works as a Ponzi scheme - effectively, each generation borrows from the next, and everyone is better off. Magic!
What's the bottom line? Increasing the quantity of government debt does indeed represent a transfer in wealth from future generations to those currently alive (or, in reality, those currently working). The only important qualification arises if society is not efficiently distributing wealth across generations. In that case, the inefficiency can be corrected with an increase in government debt. But unless we want to argue that the intergenerational redistribution being done by the U.S. social security system is insufficient, that seems a difficult argument to make.
You young whippersnapper you!ReplyDelete
Hey, I was using an OLG framework too, you know?
And did you know you can get exactly the same (qualitatively) results as you got even in a pure consumption economy with no storage? (Which is something I keep having to argue, because people keep complaining I'm assuming time-travel is possible!)
Yes, for example you can do the Sameulson case, and it's essentially the same as the monetary model that Neil Wallace liked to work with in 1982. Then, government debt is important for intergenerational redistribution, and there is some optimal quantity of government debt. Too much government debt, and more of it makes future generations worse off. Too little government debt, and more of it can make everyone better off.Delete
Right. It all depends if r > or < n.Delete
But then I keep reading people saying that deficits can't possibly impose a burden on future generations unless: they crowd out real investment; there are disincentive effects from taxation; some of it gets borrowed from foreigners. Because: "We owe it to ourselves". Or "because the young inherit the bonds as well as the debt burden" (said by people who totally reject Barro-Ricardo!).
So I start another blogosphere war.
"Right. It all depends if r > or < n."Delete
Yes. Samuelson called n the "biological rate of interest." In this context, it's the rate at which the social planner can convert consumption for the young into consumption for the old. For efficiency, you would like the market rate of interest equal to the biological rate of interest, though r > n is also Pareto optimal, as we need to take the inital old into account.
Not sure what these people are on about. I thought this was a standard piece of economics that everyone gets - either in the first year of a PhD program, or perhaps earlier.
I think you guys are missing something here. This stuff comes from models where risk is not an issue, so that the interest rate on government debt is the same as the marginal product of capital, so that the criterion for dynamic inefficiency is the same as the criterion for a stable Ponzi scheme in government debt. But empirically, presumably because of the role of risk, the interest rate on government debt is nowhere near the marginal product of capital. Historically interest rates on government debt in the US tend to meet the criterion for a stable Ponzi scheme, but data on capital and output seem to indicate that the economy has been dynamically efficient.Delete
I think you can make a case that the US economy is dynamically inefficient by arguing that the relevant marginal product of capital is the rate at which increases in the capital stock can safely increase output. Presumably some capital is safer than other capital, and if you add a unit of safer capital, you get less expected additional output than if you add a unit of less safe capital. But since people prefer safety to the extent that they are willing to hold government debt despite its low return, it is inefficient to have so much unsafe capital when we can come up with a more preferred result by using intergenerational transfers.
However, most people don't seem to buy this argument.
Steve: "Not sure what these people are on about. I thought this was a standard piece of economics that everyone gets - either in the first year of a PhD program, or perhaps earlier."Delete
It seems it isn't. (Though for an old guy like me, it wasn't a standard part of my graduate program, and I had to figure it out for myself.)
I think what happened is this: in the 1960's and 1970's, economists used to laugh at rubes who thought that the debt was a burden on future generations. We knew it couldn't be, because we owed it to ourselves (except for debt to foreigners, crowding out of investment, disincentive effects of taxation). Then in the 1980's we started looking at OLG models, and realised that the rubes were basically right. But we were too embarrassed to mention this out loud. And a lot of economists never got the memo.
But, in fairness, there are two ways to define "the future":
1. future cohorts over their lifetimes;
2. people alive in a future year.
If you adopt the second perspective, you get the "we owe it to ourselves" view. If you adopt the first, OLG, perspective, you see the burden.
Andy: I would put it a bit differently. If we were sure that the growth rate of income would always exceed the rate of interest, we would know that Ponzi finance would be sustainable. The risk is that we don't know that.Delete
What I've been trying (and failing) to figure out is how we can still do Ponzi finance in an uncertain world where we don't know future r and g. Because my math modelling skills aren't good enough. And I would really love one of Steve's keen young whippersnappers to try and model my "Trill Perpetuity" plan, to see if it actually works. http://worthwhile.typepad.com/worthwhile_canadian_initi/2012/07/trill-perpetuities.html
No, you've got the effect going the wrong way. You can think of the interest rates on government debt being low because of an extra liquidity premium. Government debt is useful in financial exchange and as collateral, which will tend to increase the difference between the marginal product of capital and the interest rate on safe government debt. Currently, you might argue that there's a shortage of safe assets, but it's not a dynamic inefficiency argument.
Nick: I would quibble with the word "always" (since the r < n condition doesn't have to hold continuously), but I think I see what you mean: the expectation that it will hold, in whatever sense it has to hold, is only an estimate, not a certainty. Presumably, even if we were certain that r < n for government debt, it would still be the case that r > n for the aggregate capital stock, because the capital stock involves different, more expensive risks. The uncertainty associated with future r vs n for government debt doesn't explain why r is so much higher for the aggregate capital stock. So I think you are really getting at a different issue.Delete
Steve: OK, you're going in a direction similar to something I suggested on Twitter yesterday. I was thinking of the government as selling insurance, as if it first borrowed at the MPK and then sold CDS on its own debt. In that case the government isn't running a Ponzi scheme; it's just running a profitable asset insurance business. The case might be more clear cut if, as you do, one thinks of the government as selling liquidity rather than selling insurance. Either way, the government is some sort of super-profitable financial institution that is actually adding value and not running a Ponzi scheme. Note that, while this may be true now to a greater extent than usual, it is not a new phenomenon, since empirically r < n has typically been the case historically for government debt. It's just that maybe we should think of the actual "r" as being much higher than the empirical yield and regard the difference as some kind of premium that the government is earning, separate from the cost of borrowing.
1. Social insurance is another issue entirely.Delete
2. "...empirically r < n has typically been the case historically for government debt." n is at most .01 per annum. For r, it depends what maturity you are looking at. For 30-year bonds, it looks like r > .03 prior to the recent recession.
1. Social insurance? I was talking about asset insurance, like a CDS, insurance for the people who own the bonds, not for society as a whole.Delete
2. For purposes of determining whether the gov't can run a stable Ponzi scheme, the relevant n includes productivity growth as well as population growth (call it "n+g" if you want), so it is at least .02 p.a. (possibly less in the future, but considerably more on average over the past 50 years). Compare actual growth rates for the US since WWII to actual yields, the growth rates have almost always been higher (80's is an exception).
And when social security or comparable schemes are themselves fully funded through bonds, efficient asset insurance converts into efficient social insurance.
And we're in Tobin's world. The point about dynamic efficiency, risk-free and risky rates of capital was also made succintly by him.
Perry Mehrling has an excellent paper on this, on the role of the state as a risk manager, as a social mutual fund.
The last paragraph makes no sense at allReplyDelete
Do you mean zero sense? Or are you just exaggerating? Maybe you mean it's 40% sense? Not sure what your problem is. You need to explain.Delete
It makes sense. But I had to read it twice. It's a bit fuzzy. No big deal.Delete
Wasn't there a g somewhere in there (i.e. r < n + g) if I remember correctly? Anyway, how likely is it that r < n + g (which are about 0.03) under normal circumstances?ReplyDelete
Quite likely, most of the time, from past experience, if we are talking r on safe government bonds. But not all the time.Delete
No, there's no g. In my example, you can allow the endowment of the young to grow, and it doesn't make any difference. In Peter Diamond's model, you can allow for TFP growth, so that per capita income grows in the steady state, and it doesn't make any difference for the efficiency rule. Is there dynamic inefficiency in practice? There is some empirical work on this, and I can't remember the conclusions. Prescott liked to argue that the rate of return on capital (from the national income accounts) was about 4% in the U.S. Population growth is at most 1%. I think it's hard to argue that the U.S. economy is over-capitalized, except for housing.Delete
Steve: are you sure that's right?Delete
Take a simple 2 period model with no capital or storage. Zero population growth. Assume an endowment of 100 when young, and 0 when old. Assume zero time preference proper (B=1). The national debt should be 50. But if the endowment is growing at 10% per cohort (so the next cohort gets 110), we would want the national debt to be growing at 10% per cohort too (so it's 55 for the next cohort). And we do that by paying 10% interest on the debt.
As long as we can roll over the debt forever, and the debt/GDP ratio stays constant, we are OK.
Maybe I'm misunderstanding you.
Had to check my graduate copy of Romer. Government expenditures are expressed in units of effective labor, so once this is taken into account I think debt can grow at n+g.Delete
Mysteries of the OG model. What I said in the post is correct. Now I'm not so sure about my 6:35 am comment (too early maybe). Once you allow the endowment to grow in the endowment model, or allow TFP to grow in Diamond's model, I'm not even sure the Pareto optimum is easy to characterize. Maybe someone knows about this.Delete
Now I'm not sure if I was right either. I need to think about it.Delete
The only OG models I have seen are ones that are stationary - population can grow, but the technology, endowments, and preferences are the same across generations. Maybe it's too hard otherwise.Delete
OK. I'm now fairly sure that as long as r < n+g (permanently) the debt is too small for Pareto Optimality. Because the government can make a lump sum transfer to the current cohort, and then roll over the debt+interest forever, with the debt/GDP ratio falling over time. The current cohort is better off, and future cohorts cannot be worse off, since they don't have to pay higher taxes. In fact, the higher debt will raise r, and make future cohorts better off, since they get a higher rate of return on their savings.Delete
How well does such a model account for the alternative scenario of government not taking on debt?ReplyDelete
I'm currently an undergrad student in Ireland so I can relate to this argument quite well. I'll be part of the generation that will be expected to repay the large government debt currently being accumulated. However, will I actually be worse off with a higher tax burden in the future than I would be if the government didn't take on the debt today?
If the government refused to take on debt in period t by not recapitalising banks, drastically cutting spending (reduced public services, lower public sector pay, reduced welfare payments)and increasing taxes, all to avoid high levels of government debt, would the net effect in t+1 actually be better?
The most obvious impact I could imagine is my education. Avoiding increased government debt here would have a three-fold effect of reducing my parents income, greatly reducing government funding of third-level education and would also reduce banks ability to offer student loans. Therefore it isn't difficult to say that I may not be able to obtain third-level education in this scenario. Wouldn't this reduce my income in period t+1? So is this reduction in income levels greater or lesser than the additional tax burden (but at a higher rate of income) that I would face if the government were to (as they are doing) instead accumulate debt?
My basic point is your model seems to have a very narrow focus, especially given the period of economic history we're living in. When the current context is the aftermath of a financial crisis and with depressed economies, the debt-today/tax burden-tomorrow argument should probably be taken with a bigger picture in mind on how the choices taken impact on future generations.
Sure. I'm not taking on the whole problem of how we should currently determine the quantity of government debt outstanding, let alone its composition. I'm just showing you one aspect of the problem.Delete
To focus on the political debate here though, these results are informative but incomplete. They abstract from a number of relevant factors it seems from a practical policy standpoint.ReplyDelete
The first is that the Republican response to this "burden of debt" issue is to cut programs which primarily help the young (they are promising not to cut the benefits of retirees and near retirees, justifiably). If we do not increase the debt, future generations (either the next or thereafter depending on whether the debt is paid down) will be better off in that regard of lower taxes all else equal, but with less aid to college students, reduced benefits of social security or medicaid/medicare, and other social safety net programs, they will be worse off in those regards. These are inter-generational effects with an intra-generational nature (primarily redistributing to the top). This seems to be the true Republican agenda (if deficits were the priority the only two specifics in the plan wouldn't be 20% tax rate cuts and increased defense spending with loopholes and spending cuts to be named later). Whether they believe this is good for growth is relevant but separate (and they are then being disingenuous about their concern over deficits).
Also, borrowing to finance public investment can have an impact on growth/ future income (contrary to the Barro "Are gov't bonds net wealth" argument where he assumes only transfers), Republican spending cuts which reduce funding on education, infrastructure, and R&D etc are like "eating your seed corn".
"...to cut programs which primarily help the young (they are promising not to cut the benefits of retirees and near retirees, justifiably)."ReplyDelete
If the programs involve government spending on goods and services, that's a different issue. I'm just dealing with the timing of taxation.
"Also, borrowing to finance public investment can have an impact on growth/ future income..."
Again, another issue altogether. For both of these things, you have to consider what the special role of government is. Is there some externality the government is correcting? In any case, all government policy actions involve distributional issues, whether across generations or within the population currently alive. You can't avoid these things.
When I teach my students Ricardian equivalence, I note that if you believe the debt is going to be a burden on your children, you must not like them as otherwise you would increase their bequest by exactly enough to compensate for their added taxes. Maybe we should use that line of argument in public -- think the debt is a problem? Then stop farting around and save, dagnabbit!ReplyDelete
Bravo to Andy.ReplyDelete
I should also point out that this whole discussion is a bit skewed by the fact that the median retiree has non-housing wealth of $30,000, and housing wealth of $150,000.
Bonds are primarily held by the wealthy, not by the old. If you want to talk about intergenerational transfers, then in the U.S. at least, this is always and everywhere as discussion about housing being bought by one generation and re-sold to another, not about bonds.
So, for example, this downturn caused a large hit to the wealth of the median retiree, larger than to other cohorts.
For government bonds, or financial assets more generally, it is more of a transfer between the poor and the rich than between the young and the old.
You and Andy are both confused.Delete
Very helpful post, thanks.ReplyDelete
But I’m embarrassed to say I found your algebraic notation too subtle for my older brain.
Not only that, I keep changing my question regarding the very same point.
But here it is at this time:
x(T) = [b(1+n)]/(2+n)
I assume there that in period T the “normalized” number of old people is 1 and the number of young people is 1 + n (given a growth rate of n), for a total of 2 + n.
... in period T+1 requires total taxes per young person alive equal to [b(1+r)]/(1+n)
Does “young person alive” mean young person in T + 1 or young person in T (and old person in T +1)?
-x(T+1) = [b(1+r)]/(2+n)
If the population grows at rate n, would it not be 2 + 2n at that point?
With the number of old people 1 + n and the number of young people 1 + n?
I know I've erred disastrously - but where?
Hopefully I did the algebra correctly. Everything comes from the government budget constraint, written in per-young-person terms. Government debt is one-period bonds, so if b(t) is the government debt issued in period t, and x(t) is the transfer the government makes to each person alive in period t(assuming everyone gets the same transfer), thenDelete
[(1+r)b(t)]/(1+n) + x(t)[(2+n)/(1+n)]
Everything follows from that.
You write, "A tax cut that increases the government debt today has no effect because everyone understands that government debt is just deferred taxation."ReplyDelete
Please apply such to the two following real data examples.
1. GDP fell after the so called Kennedy tax cut.
The 1964 Tax Cuts and Economic Growth - Paul Ryan Edition
2. GDP Growth Caused By Tax Cuts Has Never Happened
3. Please explain how private borrowing can increase GDP, etc., but not public borrowing. How does the economy or Harvard, for that matter, know the money borrowed to educate the young person who will save the World, tomorrow, came from a public or private borrowing?
"A tax cut that increases the government debt today has no effect because everyone understands that government debt is just deferred taxation."Delete
You're taking my words out of context. I explain above exactly what that means, and how you use Ricardian equivalence to think about the real world.
In any case:
1. So GDP fell after the Kennedy tax cut. How do you know the latter caused the former?
2. The Ricardian experiment, and issues about the long-run effects of changes in the tax structure are two different issues. The Ricardian experiment is: hold government spending constant, change taxes today, with future taxes increasing to pay of the debt. What happens? If we change the income tax code by, say, increasing marginal tax rates, possibly with other changes in the government budget, that's entirely different.
3. This is confused. Someone wants to accumulate human capital, and we all agree this would be a good idea. Suppose that person has zero wealth. They have to borrow to get an education. Maybe a private financial institution will make the loan. Maybe we think there is some market inefficiency, and the loan won't be made unless the government does it. Different issue entirely.
Addendum to the above:Delete
In example 3, you could also imagine at different scenario. Suppose there is someone who has zero wealth. He or she has been admitted to Harvard, and he or she claims that if the government does not give him or her an outright grant, then he or she cannot go to college. There are two decisions to be made: (i) Should the government give him or her the grant? (ii) How should the government finance the grant if they make it? The second decision is independent of the first. The government has two options: tax someone today to finance the grant, or issue debt to finance the grant, and tax someone in the future to pay off the debt. If there is Ricardian equivalence, then it doesn't matter. But, if you think that generations are not linked together by bequests, then the choice is between making someone worse off today to finance the grant, or making someone worse off in the future.
If your explanation of the Ricardian equivalence is accurate, then private debt could not cause growth, either, and we should not permit such, given the risks.Delete
This would be true for example 3, if the student borrows, for this would cause a reduction in disposable income in the future by the amount necessary to pay off the debt.
Of course we know that students borrow exactly because the education makes them more productive and thus able to both pay off the debt and make a decent living for themselves.
The point of the lesson is that the Ricardian equivalence is both false and misleading, for it wholly fails to focus on the real key and that is whether the expenditure increases our productive potential more than it costs. That in turn seems to me to argue that we should be finding the tools to inform our students of the best ways to determine our most productive expenditures, as opposed to worrying about something that is not true.
This might also inform us why GDP falls on tax cuts. Such would be evidence that the tax cuts have hurt the Government's ability to make productive expenditures and that, in reaction to a known future reduction in the standard of living either or both investors or consumers have cut back on spending. This is, in effect, an extension of the arguments of Robert Dugger.
Or said a little differently. There is a true corollary to the false Ricardian equivalence, which would be:
If Gov't fails to spend such will result in lower present investment and consumption to the extent that future expectations are lowered due to a belief that lower gov't spending will result in foregone opportunities to increase productivity.
Doesn't this pretty much explain the last 5 years? We have an immense amount of cash sitting on the sidelines because we have all known that the Bullards and Republicans of this World will keep gov't spending below what we need for future growth.
Look at Obama's stimulus, which was mostly tax cuts. No wonder such was so ineffective.
"...private debt could not cause growth."ReplyDelete
This is unrelated. We typically don't think of private debt as being a cause of macroeconomic phenomena. It's an outcome.
"...whether the expenditure increases our productive potential more than it costs."
Exactly. That's a critical issue. The government's expenditure on goods and services that matters. And the deficit can matter. That doesn't make Ricardian equivalence "misleading." I told you in the post why it's useful.
"GDP falls on tax cuts"
You're stating this as if it's a fact. It's not.
"If Gov't fails to spend..."
Fails to spend how much? On what? How big should the government be and what should it do? There are no obvious answers to those questions, but apparently you think so.
1. You write, "This is unrelated. We typically don't think of private debt as being a cause of macroeconomic phenomena. It's an outcome." I do not agree but think it unlikely that if Minsky cannot teach you where you are wrong it will not be productive for me to attempt such a teaching moment here. I will say that if private debt is not a cause, then neither is public debt for an economy cannot distinguish between the two, so why are you worrying about the Ricardian Equivalence at all?Delete
2. You falsely charge, "There are no obvious answers to those questions, but apparently you think so." To the contrary, I don't think there are "right answers" because of what Soros calls irrationality.
The reason can be simply stated. To be truly effective, gov't spending must meet two tests.
The first question is whether the expenditure increases our productive potential more than it costs.
The second is whether the amount being spent meets the public expectation of what is required or necessary.
If it is widely perceived that the gov't is not making sufficient investment expenditures, the effect will be the duel horsemen of declining private investment and declining private spending.
You and I live in such a State (Missouri). Our public spending, etc. is so bad (lack of support for education, roads, etc., that smart people are running for the exits.). Angry Bear has had several recent posts on the key local driver being the % of college educated adults. A locality that cannot drive that number up faces a bleak future.
My two cents is that the perceived lack of investment by government is why Bush II lead to the Lesser Depression. Look at the rational expectations created by Bush's tax cuts: govn't investment would be insufficient.
Said differently, adequate gov't spending creates the expectation that business can be done safely, efficiently, and profitably. Where are these expectations in Ricardian Equivalence?
I see John D is back. Never believe I won't be here to mock you John, wherever you manifest.Delete
Sorry to keep harping on this, but I’ve taken an interest in how different people have been expressing the same idea in this discussion. Considering it further, it looks to me that there are a couple of errors of algebra in the post, unless you correct my understanding of it. I’m not sure this makes any difference in terms of the directional thrust of your conclusion, so you may wish to leave this. It’s probably not important to the thrust of your post. In fact, I liked the way you presented the algebra as a model.ReplyDelete
But, if you are interested, this is my analysis:
I think the problem I see is that b seems to be defined initially and explicitly as the debt per capita of those buying it (the T young), but in another place (implicitly by equation) as debt in aggregate (also in your comment above).
So, using your original per capita T young notation and meaning for b in the post, I would say:
In period T:
Number of young
1 + n
Number of old
2 + n
Bonds bought by each young person
Total bonds bought
b (1 + n)
Transfer to each person (young and old)
x (2 + n)
Total T transfer = total bonds bought
x (2 + n) = b (1 + n)
Transfer to each person
x = b [(1 + n)/(2 + n)]
(That agrees with the post, although not with your comment above)
In period T + 1:
Total taxes required to retire the debt = Aggregate bonds accrued with interest
b(1 + n)(1 + r)
The T + 1 old pay all the taxes then:
Each T + 1 old pays:
b(1 + r)
(Both the post and your comment seem to identify this as:
b (1 + r)/(1 + n)
All T + 1 alive pay the taxes, the result for one thing depends on the assumption for the size of the T + 1 young population:
You assume the T + 1 young population is 1 + n (which the post apparently does, which I don’t understand)
All T + 1 alive pay the taxes then,
The tax per T + 1 person is:
-x(T+1) = (b(1 + n)(1 + r))/(2 + n)
Both the post and your comment say:
-x(T+1) = [b(1+r)]/(2+n)]
You assume the T + 1 young population is 1 + 2n (which I do)
If the young and the old pay all the taxes then,
The tax per person at T1 is:
-x(T+1) = (b(1+n)(1+r))/(2+2n)
Again, both the post and your comment say:
-x(T+1) = [b(1+r)]/(2+n)]