The question, once again, is: "Does government debt impose a burden on future generations?" I took a crack at this question back in January, and my answer is still the same, but I'd like to phrase it more concretely.
Here's how I like to think about this question. In my mind, to "impose a burden on future generations" means "to decrease the consumption possibilities of future generations". So the question is really whether or not the size of today's stock of government debt reduces the total consumption possibilities of people not currently born. In other words, if government debt is $1,000,000,000 today, does that mean that the consumption of future people must be lower than if government debt were $1 today?
Let's assume a closed economy. In that case, the economy's maximum potential consumption at any point in time is determined by the productive capacity of the economy at that time. Productive capacity is determined by the size of the capital stock, the labor force, the availability of natural resources, and the level of production technology. (For convenience, I'm defining the "capital stock" as including all consumer durables, and defining "consumption" as including the flow of services from those durables.) Now let's assume that the technology level, the labor force, and the amount of natural resources are all completely exogenous, so that the government cannot affect these things (this may not be realistic but we could always drop that assumption later). So the productive capacity of the economy at any point in time is just a monotonic function of the economy's capital stock - more capital at time T means more potential consumption at time T.
Now let's define "burden on future generations". That means that at some time T > 0 (t=0 being today), the potential consumption of the economy will be lower. Since the potential consumption of the economy at any time t is determined entirely by the size of the capital stock at time t, what we are really asking is whether or not the following proposition is true:
∀{D_t},{C_t} ∃T>0 s.t. K_T = f(D_0), where f'(D_0) < 0
Here K is the capital stock, D is government debt, f is some function, t=0 is today, D_0 is today's stock of government debt, {D_t} is the path of government debt between t=0 and t=T, and {C_t} is the path of consumption between t=0 and t=T. If this proposition is true, then no matter what anybody does in the future, higher debt today necessarily means a smaller capital stock at some point in the future.
Note that this proposition is not stated as formally as it could be or really should be, for which I apologize.
So now, let's think about what determines the capital stock at a future time T. This is determined by the sequences of consumption and investment from t=0 to t=T-1. In order for K_T to be constrained to be lower than it would otherwise be, it must be the case that K_T-1 is lower than it would otherwise be (this follows easily from the assumption that the production function is monotonic in the level of the capital stock). By backwards induction, the above proposition can only hold if the following proposition holds:
K_1 = f(D_0), where f'(D_0) < 0
Remember, t=1 means tomorrow. In other words, only if tomorrow's capital stock depends in a negative way on today's stock of government debt can it be true that a higher D_0 forces K_T to be lower at some point in time.
Tomorrow's capital stock depends entirely on today's level of investment (today's level of production is fixed, because today's capital stock is fixed). So our question now reduces to:
Question: If I_0 = g(D_0), where I_0 is today's investment and g is some function, what is the sign of g'(D_0)?
If g'(D_0) is positive, then a higher government debt stock today means that the economy will invest more today; this means that government debt will impose no burden on future generations.
So is it possible that g'(D_0) > 0? In other words, given two societies that are identical in all respects except that Society 1 has a higher stock of government debt than Society 2, is it possible that Society 1 will invest more today (and consume less today) than Society 2?
Of course it's possible. The investment/consumption choice is entirely behavioral. And when I say "behavioral" I am including the behavior of the government. If Society 1's government chooses to cut welfare and use the money to build a bunch of roads, for example, it could easily invest more and consume less today than Society 2; the high level of D_0 in Society 1 would not prevent it from being able to do this.
So government debt need not be a burden on future generations. It all depends on how economy-wide consumption/savings decisions react to the size of the stock of government debt. And that is heavily dependent on the behavioral model one chooses. Might a higher stock of government debt outstanding induce a society to invest less and consume more (which would constrain future consumption to be lower under certain additional assumptions)? Sure.
So the answer to the question is: It depends. What does it depend on? It depends on how consumption/savings decisions react to the size of the stock of government debt, which depends on the behavior of the government, firms, and households. Modeling that behavior is a major challenge.
Also, note that this does not answer the question of "Does government borrowing impose a debt on future generations?" This is because the economy's consumption-savings choices may respond differently to changes in debt than to levels of debt. But in general, the answer will have the same form.
So to sum up:
- Must higher government debt today lead to lower potential consumption sometime in the future? No.
- Does higher government debt today lead to lower potential consumption sometime in the future? Maybe; I don't know.
- Does higher government debt today lead to lower actual consumption sometime in the future? Maybe; I don't know.
- Must higher government borrowing today lead to lower potential consumption sometime in the future? No.
- Does higher government borrowing today lead to lower potential consumption sometime in the future? Maybe; I don't know.
- Does higher government borrowing today lead to lower actual consumption sometime in the future? Maybe; I don't know.
(Just in case you were wondering: The example Nick Rowe creates here is a case of higher government borrowing today leading to lower actual consumption in the future. He uses a "fruit-tree economy" with no capital (or if you prefer, with K fixed), so potential consumption in each period is fixed. In that sort of economy, it is impossible for anything to "impose a burden" on any cohort, using my definition of "imposing a burden".)
Update: More interesting conversation between me and Nick over at his blog, as well as in the comment section of this post. We look deeper into the issue and get some more interesting results.
Update 2: Nick and I have been discussing the issue. I think we agree on everything now, and a number of interesting conclusions have emerged. Let me see if I can translate them into plain English...
The "Burden" Result: It is possible that the existence of past government transfers can ensure that either currently living people or as-yet-unborn (or both) must get screwed, relative to the baseline in which no transfers occurred. These past government transfers can be accomplished by government borrowing and spending; in that case, the past government transfers will affect the value of today's government debt. This is the upshot of Nick's model.
The "No Future Burden" Result: However, no matter what transfers happened in the past or how much government debt we have today, then given some simple assumptions, it is always possible to get away with only screwing people who are currently alive (and yes, you can quote me on that!). This is the upshot of my proof.
Note that these two results are not incompatible at all. So Nick and I don't disagree.
The "Dues Paid" Result: Given some more simple assumptions, it is always possible to limit the total amount of screwage (in consumption terms, not utility terms) to the amount of consumption that was, in the past, transferred away from people who are currently alive. In other words, the total amount of screwage never has to be bigger than the total "dues" already paid by currently living people. This is something I realized while talking to Nick over at his blog. I think it's kind of interesting.
The "Debt Does Not Equal Burden" Result: This means that the govt. debt number may not equal the burden number (and in general does not). The size of the current stock of government debt may be much larger than the total amount of the aforementioned screwage. In other words, govt. debt may be $10,000,000,000 today, but the total amount of necessary screwage might be much smaller, or might even be zero. This can happen, for example, if the government spends money on the same people it taxes, or if people leave government bonds to their children in a certain way. So debt is not a book-keeping device that faithfully records the amount of necessary future screwage.
(Note that this means that government debt's effect on society is very different from the effect of one household's debt on that household. If I borrow $10,000 and spend it today, I'm going to need to take a $10,000 hit in the future in order to pay it back. But if the government borrows $10,000 today, it's quite possible that nobody ever has to take a hit at all. I am not sure, but I think that this might be Paul Krugman's main point.)
(Update: Antonio Fatas thinks that this last result should be the main takeaway from the debate.)
In conclusion: When you ask "Does debt impose a burden on future generations?", you have to be very careful about exactly what you mean when you ask that question. But if you are careful - if you use math in your explanation, state all definitions and assumptions clearly, and above all think clearly and don't get mad - then the truth will out.
If I'm skimming (lol) your post correctly, the gist is that the answer depends on present allocation of spending, with the implication being that greater net investment now in relation to entitlement spending could lead to future growth?
ReplyDeleteYep. The people who are saying "Debt imposes a burden on future generations" have a model in which higher debt today (or higher additional borrowing today, which is different) makes people consume more today, thus making future generations poorer. Basically, they are saying that government debt makes us act like grasshoppers instead of ants.
Delete"Now let's define "burden on future generations". That means that at some time T > 0 (t=0 being today), the potential consumption of the economy will be lower"
ReplyDeleteI'd say that's the wrong definition. That would be the definition of "burden on future times" (or some such phrase). Since you have used the word "generations," you shouldn't be talking about time but about people (i.e., cohorts). A "burden on a future generation" would mean that the total lifetime consumption possibilities for that generation were reduced. That could happen regardless of the capital stock, because the capital stock determines only the quantity of output at a given time, not the distribution of output among cohorts that are alive at that time. Then a "burden on future generations" would mean that there will be at least one future generation whose consumption possibilities will be reduced. Holding the capital stock (and total consumption at any given time) constant, government debt can still be a burden on future generations (and will be under certain conditions, of which I believe an exogenous path of total consumption, the absence of bequest motives, the absence of a stable Ponzi game in government debt, and standard Homo economicus behavior would be jointly sufficient but not necessary).
You're right that I could use that alternate definition of "generation". But the result would be the same, since a negative result for future times implies a negative result for future generations, since future generations live only during future times.
DeleteIn other words, if it is possible for today's debt level to have no effect on consumption possibilities at any time in the future - i.e., if it could leave consumption unchanged or increased for every individual at every t>0 - then it immediately (and somewhat) trivially follows that higher government debt today need not necessarily lead to lower potential consumption for some cohort not alive at t=0.
DeleteNo, the result would not be the same. A negative result for future times does not imply a negative result for each future generation, because times do not map one-to-one onto generations. It implies such a result for the total of all current and future generations (which map to the total of all current and future times), but it implies nothing about the the distribution among those generations, which could involve an increase for a generation alive today and a decrease for some generation not yet alive.
DeleteA negative result for future times does not imply a negative result for each future generation, because times do not map one-to-one onto generations.
DeleteYes it does. Think carefully.
No, times do not map one-to-one to generations. But if total consumption rises for all t>0, then a system of government transfers can raise consumption for every individual i at every time t>0. This mechanically leads to an increase in consumption for every future cohort, since a future cohort's consumption is just the sum of the consumption values for various (i,t>0) pairs. QED
I guess I shouldn't get to say "QED" for just restating the Second Welfare Theorem...
DeleteAlso note that to state my point more completely, in my response above I should have written "a future cohort's consumption is just the union of the consumption values for various (i,t>0) pairs."
DeleteNoah, I think you redefined "generations" to mean "time periods" so that you could make a case for public goods.
Delete(Just like I think Nick Rowe is spreading FUD about the debt to push NGDP targeting.)
But you're avoiding the subject of future generations. (Or perhaps the current generation.)
I don't think saying you can harm the present generation to benefit the future addresses the subject. (I think you may have deleted my comment below.)
I don't think their is a semantic disagreement. I think maybe you've created a semantic disagreement. (The public and the politicians may be confused, however.)
So, Nick is warning that borrowing money today *may* burden future generations, and you're warning that *not* borrowing money today *may* *harm* future generations. (But you may be trying to harm the present generation.)
The debate *was* about whether growth rates will keep pace with the interest burden over the long-term. (And how much a burden it really is.) (And now whether this "burden" is any different than inflation under NGDP targeting or private sector bubbles.) (This is my interpretation, anyway. I think for Nick it was at least in part about disproving that it was *impossible* to burden "our grandkids.")
Btw, I don't think Nick ever said, the debt (or deficit spending) will burden future generations, only that it could. (Although, as I keep saying it's not the debt, but the interest that's the problem.)
I think (almost) everyone agrees (at least they say they do) that we should spend money on worthwhile projects. (I'm not sure "everyone" includes Republicans. At least, at the moment. Maybe if Romney gets elected they'll start to care again.) Perhaps, if you had a more specific (detailed) project than "a bridge." (To advocate for.)(Ironically, you've made a case against investing in the future as it may work against the present.)
(I'm not saying it would work against the present in today's economy, only that you don't seem to be making that case. There's, of course, good reason to spend money, now.)
Noah, I think you redefined "generations" to mean "time periods" so that you could make a case for public goods.
DeleteNope. I did not.
But you're avoiding the subject of future generations. (Or perhaps the current generation.)
Nope. Not that either!
What are we talking about then? Intergenerational communism? A real-time "smart" tax and transfer? (Would this work?)
DeleteAndy hits the nail on the head.
DeleteNoah: in my simple counterexample, consumption is fixed at all present and future time periods. But the lifetime consumption of the current cohort is increased at the expense of lower lifetime consumption of some future cohort.
Deletehttp://worthwhile.typepad.com/worthwhile_canadian_initi/2012/10/what-part-of-counter-example-dont-you-get.html
Noah: "Also note that to state my point more completely, in my response above I should have written "a future cohort's consumption is just the union of the consumption values for various (i,t>0) pairs." "
DeleteNo it is not. Not if you have overlapping cohorts.
Oh God. This is just so incredibly frustrating. If a smart guy like Noah can't get my point!
DeleteLook. I deliberately set up an example in which aggregate consumption is a constant at all future time periods and is unaffected by the debt. So there is not, and cannot be, a
"burden" in the sense in which Noah defines "burden". But I also showed that a current cohort could have higher lifetime consumption at the expense of lower lifetime consumption of some (unborn) future cohort.
I could also construct an example in which the current cohort has higher lifetime consumption resulting in lower lifetime consumption of *all* future cohorts (with the burden on all future cohorts asymptotically approaching zero as time approaches infinity).
Assume all output is consumed. Assume people live for 2 periods, produce 100 when young and 100 when old. Assume one person per cohort 9so population is always 2). So aggregate consumption is 200 at all time periods.
In the baseline scenario life time consumption is 200 and consumption per period is 200.
Now suppose:
In period 0, the young in cohort A consume 100.
In period 1, the old in cohort A consume 200, and the young in cohort B consume 0. Aggregate C=200. Lifetime consumption of cohort A is 300.
In period 2, the old in cohort B consume 150, and the young in cohort C consume 50. Aggregate C=200. Lifetime consumption of cohort B is 150.
In period 3, the old in cohort C consume 125, and the young in cohort D consume 75. Aggregate C=200. Lifetime consumption of cohort C is 175.
In period 4, the old in cohort D consume 112.5, and the young in cohort E consume 87.5. Aggregate C=200. Lifetime consumption of cohort D is 187.5.
And so on.
The government borrowed 100 and gave it to cohort A to consume, then slowly reduced the debt at the rate of 50% per period.
Every single future cohort has lower lifetime consumption, even though aggregate consumption is always 200 at all time periods.
Noah: if you don't get it after this, and post a comment saying: "Wow!!!!! Nick Rowe is just so totally right!" I am really going to despair of all humanity.
I didn't mean "post a comment". I meant to say "write a post".
DeleteYou are now (or should be) at exactly the same point where Bob Murphy had his epiphany and totally saw my point and did a 180 degree turn on the burden of the debt question.
Nick Rowe, Just so you know, you have successfully converted me. Do not despair for ALL of humanity, just for some of your fellow economists :)
DeleteNick:
DeleteYou are totally right ("Wow!!!!!") about the validity your model and about its implications. So don't despair for humanity.
However, if you think that your model is a counterexample to the proof I have written in this post, you are not right about that.
Noah: in my simple counterexample, consumption is fixed at all present and future time periods. But the lifetime consumption of the current cohort is increased at the expense of lower lifetime consumption of some future cohort.
This I understand. But your "counterexample" is not a counterexample to my proof. Look at my proof again and think carefully.
Noah: "Also note that to state my point more completely, in my response above I should have written "a future cohort's consumption is just the union of the consumption values for various (i,t>0) pairs." "
No it is not. Not if you have overlapping cohorts.
Yes, it is. A "future" cohort is defined as a cohort that is not alive at t=0. The letter i represents an individual. The consumption of a cohort is a set consisting of the union of the lifetime consumption sequences of every member of that cohort. Therefore, the consumption of any "future" cohort is the union of some set of (i,t) consumption points, where t>0 for all of those points (because a person not alive at t=0 cannot consume at t=0).
Think carefully about this. Are our definitions of "future" cohorts the same? Or does your definition include some people who are alive at t=0?
Oh God. This is just so incredibly frustrating. If a smart guy like Noah can't get my point!
Don't get frustrated...it interferes with careful thought.
I understand your model perfectly, and I think I understand your point perfectly. I also understand that your model is not a counterexample to my proof, which is valid in full generality.
What's probably happening is that our definitions are different.
I have defined a "future" cohort as a cohort that is not alive in the first period.
I have defined "burden" as a constraint on the consumption possibilities set (as you note).
I have allowed for three alternative definitions of "impose" (see the end of the post) and two alternative definitions of "higher debt".
To reiterate: I need no epiphany. I understand your model, and I understand your point (as I did last year). Your model has no errors. The only error you are making is if you think that your model invalidates the proof I have written in this post.
(I went over this fairly carefully last night with Miles Kimball, and this is the conclusion we reached. Miles realized quickly that my proof hinges on my definition of "future cohort".)
Noah: OK, I'm sorry if I'm not getting the fact that you *are* getting my point.
DeleteBut does your proof really amount to saying "If the government wanted to, it could borrow and spend, and then immediately pay off the debt by taxing all the people who are still alive but who weren't born when it made that decision to borrow and spend"?
This comment has been removed by the author.
DeleteBut does your proof really amount to saying "If the government wanted to, it could borrow and spend, and then immediately pay off the debt by taxing all the people who are still alive but who weren't born when it made that decision to borrow and spend"?
DeleteNo, my proof is more general than that.
It says that no matter how much debt we wake up with on Monday, anyone born on Tuesday or later has the same set of feasible consumption bundles.
An extension of the proof is to say that no matter how much the government borrows on Monday, anyone born on Tuesday or later has the same set of feasible consumption bundles.
Of course, implementing some of those consumption possibilities might require doing something exactly like what you're talking about. It depends on lots of stuff (like whether there is productive capital, etc).
Noah: "Of course, implementing some of those consumption possibilities might require doing something exactly like what you're talking about. It depends on lots of stuff (like whether there is productive capital, etc)."
DeleteIf so, that's a very big admission.
But I still don't understand this very well. Since I (think I) understand the role of investment in productive capital in this debate, it would help my intuition a lot if we assumed aggregate C was exogenous at all time periods (so there is no burden in your sense) and then asked whether implementing some immediate tax increase on those alive when the debt was incurred would be necessary to prevent a burden on the unborn. In other words, what happens if the government borrows and buys a last supper for those about to die the very next minute? They eat that supper, then explode!
Ooops! I just realised. The government could tax those people who were alive at the time of the last supper, but who didn't partake, and didn't die immediately.
DeleteOK. So what I think you are saying is that a borrow-and-consume strategy is still reversible in its effects on unborn cohorts up until the time that all those who were alive at that time have died.
But that would require date-of-birth contingent taxation. (I expect we have that at age 65). I can't really see the government saying "OK, there's going to be a special tax on all you guys who were alive when we ran up the debt!"
If so, that's a very big admission.
DeleteAdmission? But I never claimed otherwise.
The proof holds in general, given the assumptions. If you come up with a particular case in which a certain type of govt. behavior requires a certain type of countervailing govt. behavior in order to keep future cohorts' consumption unchanged...well, that's kind of interesting, I suppose.
OK. So what I think you are saying is that a borrow-and-consume strategy is still reversible in its effects on unborn cohorts up until the time that all those who were alive at that time have died.
Yes, that's right.
But that would require date-of-birth contingent taxation. (I expect we have that at age 65).
Yep. In your model, the govt. has to temporarily implement reverse Social Security if it wants to hold the consumption of future generations constant.
I can't really see the government saying "OK, there's going to be a special tax on all you guys who were alive when we ran up the debt!"
DeleteAlso, consider this example. Suppose at date t=-132, the govt. made a consumption transfer from young to old, and then just kept making identical transfers from young to old in every period (and suppose it used debt as both a bookkeeping device for these transfers, and as a way of justifying its promise to keep the chain of transfers going).
Now we find ourselves at time t=0. The government can choose to end the chain of transfers now. In that case, the series of government decisions from t=-132 through t=-0 create a net transfer from the t=0 old to the t=-132 old (as you would put it, "time travel"). BUT, the inherited stock of debt at t=0 does not then reduce the consumption of the t=1 young, the t=2 young, etc. So in this example, the stock of debt inherited at t=0 requires that either, the consumption of t=0 old, the consumption of t=0 young, and/or the consumption of future generations be reduced, relative to the counterfactual in which the chain of transfers never started. So the current stock of debt can impose a burden on the union of current and future generations, because currently living people have already contributed to the chain (and so not reimbursing them by keeping the chain going would mean that overall they lose out).
So this is why I think your model makes a good point. Miles agrees.
Noah: OK. Thanks. But even if we keep the chain going, if the rate of interest exceeds the growth rate, lifetime utility would be lower even if lifetime consumption is the same, because consumption would be unsmoothed.
DeleteNoah: OK. Thanks. But even if we keep the chain going, if the rate of interest exceeds the growth rate, lifetime utility would be lower even if lifetime consumption is the same, because consumption would be unsmoothed.
DeleteYes! If We keep the chain going. But remember, according to Smith's Lemma (hehehe), in any period we can break the chain and get away with just screwing over one single (currently living) generation.
But if keeping the chain going would result in lower welfare than screwing over one single generation...then that is an interesting result!
Noah, so what's the point? A progressive tax system could mitigate some of the burden, but we're still prone to cyclical burdens?
DeleteOr is a "smart" tax like you're suggesting a practical possibility. If not, could we still easily determine each individual's burden? (People could look it up on the internet.)
Let me say, I think the semantics matter, at least a little bit. If I am born in the year 2100 and there is outstanding government debt that needs to be repaid (i.e. no stable Ponzi scheme), and if I anticipate that it will be repaid in my lifetime, then I would think of myself as having a burden. My lifetime consumption possibilities would be lower, because I would have to give up some of my consumption to the generation before me in order to pay the taxes that are used to pay off the debt. Whereas if the government debt hadn't existed when I was born, I could consume everything I produced (leaving aside other redistribution, public goods, etc.), because I would have no obligation to the generation before me. There is a burden -- in the sense of reduced consumption possibilities -- on me, as a person born in 2100, and as such a person, I am not comforted by the fact that the generation of people already alive by 2100 will get to consume more at the same time I am consuming less. As that person born in 2100, I will be pretty pissed at you and Dean Baker and Paul Krugman for using a semantic trick to deny that I have a burden.
ReplyDeleteIs this question in some ways related to (or perhaps it's the same question) as the issue of whether or not government spending -- either generally or in specific circumstances -- crowds out private investment? It would seem that this paragraph:
ReplyDelete"So the answer to the question is: It depends. What does it depend on? It depends on how consumption/savings decisions react to the size of the stock of government debt, which depends on the behavior of the government, firms, and households. Modeling that behavior is a major challenge."
...is a different way of stating that if issuance of new government debt, or a reaction to the existence of a "large" stock of government debt, elicits a negative investment response from the private sector thereby reducing future accumulations of capital and thereby lowering K_T then that is what imposes a burden on future generations. This essentially sounds like "crowding out" via the mechanism of higher interest rates a la the loanable funds model or something similar.
Or perhaps I'm thinking too simplistically? Is there a way for this process to occur other than through a rise in interest rates?
Let me say, I think the semantics matter, at least a little bit.
ReplyDeleteOK. I think the whole Rowe-Krugman debate is semantic in the first place. The key word being "burden".
If I am born in the year 2100 and there is outstanding government debt that needs to be repaid (i.e. no stable Ponzi scheme), and if I anticipate that it will be repaid in my lifetime, then I would think of myself as having a burden.
Not necessarily. Suppose you inherit a large trust fund full of government bonds. Your lifetime consumption possibilities would be higher than if the government defaulted, or had never borrowed in the first place.
As that person born in 2100, I will be pretty pissed at you and Dean Baker and Paul Krugman for using a semantic trick to deny that I have a burden.
But suppose that the government in 2012 was considering borrowing money to invest in infrastructure. But because you and Nick Rowe convinced everyone that "debt imposes a burden on future generations", the government canceled the infrastructure-building plan AND the concomitant borrowing. A person in 2100 might then be pretty pissed at you and Nick Rowe.
Yes, this is changing the semantics. It is using "debt" as shorthand for "deficit spending". But this semantic usage is very common in practice.
If we're going to make useful, helpful statements about how the economy works, we should define our terms in ways that are not ambiguous and open to misinterpretation; otherwise we risk doing more harm than good.
Paul Krugman's point is that a high level of existing debt does not mean that society as a whole has to bear a lot of "pain", since it owes most of that money to itself, thus making it qualitatively different from a household that has borrowed money from outside lenders. This is a good and valid point.
Nick Rowe's point is that if the government borrows to consume, then it can effectively be shortchanging the future generation, whether that shortchanging is accomplished by reduced investment or by durable government commitments to future net transfers. This is also a good and valuable point.
The points do not really conflict. But the semantic ambiguity of the terms being used has convinced both parties that the other party disagrees with them. This, to my mind, is not good.
"But because you and Nick Rowe convinced everyone that "debt imposes a burden on future generations", the government canceled the infrastructure-building plan AND the concomitant borrowing"
DeleteYou mean we should assume that the government is too dumb to know the difference between borrowing to finance an asset and borrowing to finance consumption? And that future generation should blame Nick and me for not anticipating the government's stupidity? Or for not tricking the government into buying an asset it didn't think was worth buying by pretending that there was no cost?
I basically think that the Keynesians are technically right, or at least that the David Brooks' of this world are technically wrong.
ReplyDeleteBurden of new debt = new debt inheritance - new credit inheritance.
That is, in aggregate, in a closed economy with no imports and exports there should be an aggregate burden of 0 as the new credit inheritance balances out the new debt, even without considering the additional economic activity from the debt-fuelled spending.
In the real world, the credit burden can make this problematic in several ways. Firstly, the debt may be owned by non-citizens, which means that (especially for an internationalised currency like the dollar) that the US people owes money to non-citizens, and that money once paid may not come back to the US economy any time soon (what Paul Krugman has referred to as quantitative diseasing)... So in reality the debt burden won't equal zero if debt is going abroad (and of course the future distribution of the debt is unpredictable) but even so it would surprise me if the Keynesians cannot muster up a strong case that the impact of the new economic activity is significantly likely to outweigh the level of transfer from the domestic economy to the rest of the world.
The more interesting factor for me is that "credit inheritance" is not distributed evenly. To calculate an individual's new debt burden, we should take their proportion of the national debt (or even better their income level that will go to paying the national debt) and subtract their new credit inheritance. People who inherited a lot of bonds and their interest (including in the form of property, etc), will do better than those who didn't. Again, while it is not possible to say what will happen in the future (either in aggregate or for individuals) we can say that income inequality has been rising in Japan in tandem to their growth in government debt, and indeed income inequality has tended to be associated with high levels of government debt in the past around the world (http://sdsu-dspace.calstate.edu/bitstream/handle/10211.10/613/Takanami_Keiko.pdf?sequence=2)
So the argument that is stronger against debt-fuelled stimulus is that it may transfer wealth upward. That is not the argument that the right particularly wants to make, as it suggests that a possible counterbalance to this effect is making sure that programs and spending concentrate the money toward lower income groups and the middle class. (That said, I am still very sceptical as on a practical level I do not trust politicians to redistribute wealth downward, they are more likely to claim they want to do such a thing but still end up enriching crony corporations, think tanks, consultants, etc etc etc)
This is much, much smarter than most of the commentary on this subject.
DeleteAziz, it may be a good argument against deficit financed tax cuts for the wealthy, since they'd be buying the bonds. The interest would be like a transfer payment.
DeleteDeficit financed stimulus should be fine so long as long term growth keeps pace with the interest burden.
The goal should be full-employment so that low incomes have an opportunity to rise. Inequality would be reduced.
(I believe some of the MMT crowd advocate doing away with bond financing. They say they could still control inflation with interest on reserves and raising taxes.)
Agree with much of this: the net effect of most of Government debt expansion is associate with an upward distribution of future tax dollars.
DeleteThat has some interesting implications in terms of possible public policy remedies that I haven't heard in any cogent political narrative.
"there should be an aggregate burden of 0 as the new credit inheritance balances out the new debt"
DeleteI don't understand this. Are you just assuming that each generation will inherit offsetting credits? There's nothing that obligates people to leave bequests for the next generation. The ownership of government bonds means that old people have a claim on the country's output. If they wish, they can pass that claim on to their children. Or if they wish, they can exercise the claim during their own lifetime and consume something that their children could otherwise have consumed.
Andy Harless —
DeleteIt's just double-entry book-keeping. The credit and debt adds up to zero in aggregate. If the older generation all sell their debt to younger people then the younger people still inherit the proceeds. There is no net burden unless the debt is hugely offshored..
The thing that concerns me is that the interest payments are a transfer from the taxpayer to creditors. But that's not the same thing as a generational burden, because all the interest will still end up being inherited.
Aziz,
Delete"It's just double-entry book-keeping. The credit and debt adds up to zero in aggregate. If the older generation all sell their debt to younger people then the younger people still inherit the proceeds."
Since the credit and debt cancel each other out, any money paid for the credit is a net loss for the younger generation. So only if the money paid for the credit is zero - that is the credit was literally inherited or otherwise handed over for free - is there no net loss for the younger generation.
I think you've missed the point. Rowe and others were talking about the case where government debt has no real effects--that is, how much the government borrows has no impact on aggregate consumption or GDP in any period in the future. From the social planner's perspective, the debt is not a burden on future generations because all of the intra-temporal allocations across generations are still feasible regardless of debt level. But from the individual's perspective, debt is indeed a burden on future generations if and only if it must be paid off at some finite date in the future. The reason is that we cannot pay off the debt without limiting the inter-temporal allocation possibilities of at least one future generation (provided that the generations are finitely-lived and self-interested so that there is no ricardian equivalence).
ReplyDeleteSo to be clear, there is no direct loss of efficiency due to debt, but there is a loss of inter-generational equity if some generation in the future has to pay the taxes to pay off the debt.
I think you've missed the point.
DeleteNope.
Rowe and others were talking about the case where government debt has no real effects--that is, how much the government borrows has no impact on aggregate consumption or GDP in any period in the future.
Yup. I actually pointed that out at the bottom of this post. Check it out!
From the social planner's perspective, the debt is not a burden on future generations because all of the intra-temporal allocations across generations are still feasible regardless of debt level.
Yup.
But from the individual's perspective, debt is indeed a burden on future generations if and only if it must be paid off at some finite date in the future.
Nope! Let me show you why you're not right. Suppose that the government pays off the debt by taxing Generation 3. However, suppose it now levies a tax of the same size on Generation 2 and hands the proceeds to Generation 3.
If this happens, Generation 3 is unaffected on net. On net, Generation 1 received rents from Generation 2. So Generation 2 is harmed.
However, Generation 2 was alive in period 1, so they are not "future generations".
See? ;)
I think that's just a semantic argument. The point is that there is inequity between generations caused by the debt. Whether you are talking about today's young bearing the cost or the young who have not yet been born yet is irrelevant. (Most politicians talk about today's young bearing the cost, don't they?)
DeleteYour argument is really just a statement of the second welfare theorem, in a way--we can always reverse the intergenerational inequity caused by the debt through redistribution. Of course, if the government does this for all the generations, then the government's net debt in each period is actually zero anyway.
caused by the debt
DeleteWhat does "caused by the debt" mean? The debt is not an agent, and makes no decisions. The debt was neither a necessary nor a sufficient condition for the generational inequity.
Well it is certainly not necessary--you get the exact same effect with a pay-as-you go pension scheme, for example, if it has some finite end date. As for sufficiency--it is sufficient if the debt has to be repaid at some finite date in the future. Either the government's net balance is zero in all periods, the government never repays the debt (it gets rolled over indefinitely), or some generation gets screwed.
DeleteNope. Debt is not a sufficient condition for generation inequity, because there can be borrowing within generations. Think about that...
DeleteNoah,
ReplyDeleteFirst, I hope to something akin to god that this is not your idea of Saturday fun. I’m not an economist and am not competent to comment on your model, except to note that to me it seems more than a little contrived. For the record, I mean that in the most respectful way possible. I believe your answer of “it depends” is correct, but I don’t think you’ve got the right dependency. The key is who owns the debt and how do they behave. If the creditors choose to make the obligation burdensome, they will be constrained in their ability to do so by the extent to which future citizens view the debt as legitimate. A kindhearted liege is less likely to smile down on his people from the end of a pike. In reality all of the notes are drawn on the First Bank of Bullshit anyway. They might just as easily choose to go on peacefully adding a couple of zeros to the end of their balance while the government continues to re-borrow the same money over and over. The consumption capacity of the super wealthy is not constrained by the number of zeros in their accounts but by the limits of their capacity to consume. If you look at a copy of Forbes’ Life you can get an idea of what a difficult challenge this is. The thing that’s a mystery to me is where the notion that markets represent a free exchange of value comes from. It is so obviously not what happens in the real world.
anon: "I think for Nick it was at least in part about disproving that it was *impossible* to burden "our grandkids.")
ReplyDeleteBtw, I don't think Nick ever said, the debt (or deficit spending) will burden future generations, only that it could. (Although, as I keep saying it's not the debt, but the interest that's the problem.)
I think (almost) everyone agrees (at least they say they do) that we should spend money on worthwhile projects."
Yep. We could haggle over whether it's the debt or the interest on the debt that creates the burden. If the real interest rate is *always* negative, or *always* less than the growth rate, there will only be a burden if the government is stupid and doesn't just roll over the debt.
Here is my simple thought experiment since this is all that is being discussed. I was born in 1947 and the US was in debt. The US has been in debt for this entire time and that debt has escalated (unfortunately FRED only has data back to 1966; fun to see the exponential nature of the debt graph!). I'm now a middle generation guy, parents are gone now and kids are out of college and are themselves consumers. So I ask myself, has this increase in US indebtedness affected my consumption? My answer is not one bit. Thus far it's also not affected either of my daughters. OK, this is real time and historical data with a very small 'N' but I suspect that everyone who has posted comments here over the last 24 hours would probably give the same answer.
ReplyDeleteSometimes it isn't clear what is meant by consumption versus investment. I think everyone would agree that if the economy is operating at its long run output level and all resources are fully employed, then deciding to eat more seedcorn today will mean less seedcord tomorrow. But is feeding an unemployed labor force "consumption" (e.g., unemployment insurance, food stamps, etc.) or human capital investment? Traversing along the economy's long run output level can be very bumpy and each bump affects the amount of capital stock at any given point in time. If the government borrows from the private sector for the purpose of absorbing idle private saving that would otherwise leak from the GDP flow, then deficit spending can crowd-in investment. This might shock some folks, but sometimes there is economic slack.
ReplyDeleteOne other last point. When talking about the effect of debt on future generations, we should not be looking at gross domestic product, or even gross national product if we want to talk about an open economy. Instead we should be looking at net product, and here our NIPA accounting fails us. For example, while the NIPA tables do try to adjust for depreciation, this is done rather crudely and does not fully account for depletion of natural resources, does not distinguish between one-hoss shay and straightline depreciation, and ignores the way human capital can influence the depreciation of physical capital, global warming, etc. If we're worried about future generations, then we should probably worry more about those kinds of NDP/NNP issues rather than debt. Sometimes an increase in government debt can have a positive effect on NDP/NNP even if it has a negative effect on GDP/GNP.
I think it is pretty remarkable that Major_Freedom hasn't yet showed up in this discussion (even under Captain_Freedom)
ReplyDeleteAccording to the Federal Reserve, in 1970, GDP and total debt (public and private) were about equal.
ReplyDeleteToday, total debt is $53 trillion, while GDP is $15 trillion.
It seems that GDP has not kept pace with debt, which indicates the extra debt was beneficial for only a short time period, certainly not across generations.
Don Levit
I suggest even a simpler answer, with no math.
ReplyDeleteWhat is to prevent us from consuming everything that is available for consumption today? It certainly has nothing to do with what "money" we might owe to someone else. In aggregate, if we wished to, we could consume everything available right now. The only constraint is our desire to have some stuff for tomorrow. But tomorrows generation has the exact same decision tree to consider. At what rate do they wish to consume the resources available to them. Nothing we do today can keep them from still having that choice. Unless we consume everything........ and then there IS no future generation. Future generations owe us nothing "real". You cant pay back stuff to previous generations.
Monetary "burdens" arent real, they are imagined.
Noah,
ReplyDeleteIt would be much more helpful (unless the task has been catered elsewhere in greater force) to hear stylized historical examples of how sovereign borrowing affected future consumption.
The issue in the street relies on people's reasoning-by-exemplar intuition of the economy. So the American Economy is like a business who needs to maximize exports (credits) and minimize imports (debits). Fallacy. And the American Government is like lazy Uncle Lenny borrowing from Cousin Sam, and of course Sam will want his money back.
The real impact of the political economy of the question is I think posed from the Uncle Sam and Cousin Lenny perspective. And from that perspective, the old Chicago quip that we're borrowing money from ourselves, not from Cousin Sam makes a lot of sense. Could you address that if you think it's a bad dismissal of the issue?
And again, what matters is the evidence. And the best we have is ex post and anecdotal, probably. So what of it? Has government borrowing appreciably and reliably skewed consumption and production possibilities down over successor generations? My (cursory) understanding is that in fact the evidence seems to lean both ways, and not at large magnitudes. That suggests to me that government borrowing is just not a large elasticity variable on growth in the long run, which would take a lot of air out of the zany political fight that's always going on about the deficit.
I appreciate George Lakoff's perspective here -- the debate over fiscal austerity seems to have a *lot* more to do with the ethical symbols of profligacy versus responsibility involved.
Keep up the strong work.
The other day I thought of you when I wrote this...
ReplyDelete"Right now I'm just like Noah. I'm building pragmatarianism like Noah built his boat. Noah had his skeptics just like I have my skeptics. Jetboogieman is certain that pragmatarianism is one of the stupidest ideas ever. Even though I'm very confident he's wrong...I would never force him to board my boat. Yet, he believes there's nothing wrong with forcing taxpayers to board bogus boats. How can that be right? He's a skeptic who doesn't appreciate the value of skepticism, doubt and disbelief." The Interests of Consumers are the Interests of the Human Race
Did you click on the link that says "doubt"? If so you'd have read where Arnold Kling said, "I doubt the business model." Oh man, for some reason that line really cracks me up. "We doubt the business model!!!" is exactly what all the skeptics were saying when Noah was building his boat. How many times throughout history have people doubted the business model? I mean...isn't that our history in a nutshell?
A few times people have brought up the issue of borrowing in a pragmatarian system. My response has been that it would be completely up to each government organization and its supporters/taxpayers. In other words...the entire government wouldn't be able to default on its debt because each government organization would be solely liable for any money that it borrowed. Obviously you're a big fan of public education...so I'm sure you'd give them some of your taxes if you had the opportunity. How much money could the Dept of Education borrow before you started to get nervous? But the more important issue would be what they were planning to spend the money on...right?
It's no different than having a close friend mortgage his home to finance a business idea. The more you trusted the business model the less nervous you'd be for your friend. But the real truth of the matter would only be revealed by how much of your OWN money you'd choose to invest in his business. And that's why markets work and why the government does not work. But getting the government to work would be as simple as allowing taxpayers to put their taxes where their mouths are. And if you doubt my business model then really take a long hard look at the value of having the freedom not to board my boat.
Incidentally...being one of your fiercest trolls and all...I really hope you detest Noah and the Ark references. The first time I met an old Army buddy named Frank I distinctly remember him telling me, "yeah yeah yeah...a currency, open and earnest and a hot dog."
Hey Xerographica, don't look now, but my PhD advisor is a fan of something that looks suspiciously like...dare I say it...tax choice...
Deletehttp://blog.supplysideliberal.com/post/30196025443/no-tax-increase-without-recompense
You're right...it does look very suspiciously like tax choice! How cool is that? Thanks for pointing out that Easter Egg. Well...I guess since we're close to Halloween it would be more appropriate to say thanks for connecting me to another person who believes in the Great Pumpkin. And it's your PhD adviser no less! Haha...nothing like good ole confirmation bias.
DeleteBased on the rule of threes...all you need is to stumble over one more believer and then you'll believe in the Great Pumpkin as well! Pretty soon the belief will reach the tipping point and then it will go viral.
Man, how in the world did the idea of trick or treating go viral? Kids dress up as goblins and then go around threatening violence if people don't give them candy. Given that economics is based on the concept that there's no such thing as a free lunch...I think we can blame Halloween for all our economic problems.
Incentives matter...right? Instead of shouting "trick or treat" kids should shout..."check out my report card!" Hmmm...yeah...Christmas gets the incentive aspect right. It also at least tries to instill the idea that giving is better than receiving...nobody likes a Scrooge. Yet, who doesn't become a Scrooge when it's time to pay their taxes?
I really like how your adviser recognized that taxpayers are alienated altruists...
"There is joy in giving, and by providing a choice of which organization to give to, my hope is that the joy of giving would be only partially muted by the requirement of giving to some appropriate organization."
Tax choice is going to turn tax day into the best holiday ever! Well...except for the minor detail that taxpayers would be able to make their contributions at any time throughout the year. But I'm sure that there will be a week of festivities and celebrations leading up to April 15. Perhaps we'll build giant figures that represents the deficit and then burn them on April 15. Kinda like the Fallas in Spain.
Noah,
ReplyDeleteAnyway we could get a concise summary of the commenting between you and Rowe in the main article?
Yep, coming soon...
DeleteTransfer resources through time is a difficult task. Especially to the past.
ReplyDeleteI think people who worry about how society is transferring resources from the future to the present are really optimistic in our ability to time travel.
Even transferring resources to the future is quite difficult. We usually do that by using our productive capacity to create goods that have the lowest possible depreciation rate.
But given how much we do transfer to the future I think it's quite impressive that people think we are actually stealing from the future.
If someone come to you complaining about what we are leaving to our children say: "A gigantic, never before seen capital stock, along with some of the best institutions yet to be in the world"
Actually I think if time travel were possible we should redistribute resources from the future to the past on a utilitarian basis. We should also have open time borders so people could go to the future or to the past if they wanted.
That being said, of course we can transfer resources from one generation from another quite easily if they are sharing the same time-frame. And I worry deeply about it. But I think people often confuse one thing for another.
OK, start with a Rowe-type model with no capital or private debt. You will get your result that the maximum burden on a generation is determined by the amount of consumption they forego when young, and of course this is true regardless of how much debt there is. On the other hand, the older generation owns the debt, and they have the right to redeem it (if we assume it's rolled over each period) and use the proceeds for consumption. So in principle, they can impose an arbitrarily large maximum burden on the younger generation up to the total value of the debt, and indeed any debt that is not part of that maximum burden -- debt that is not redeemed to use for consumption -- is debt they will own when they die and will therefore show up as a bequest. So (assuming the government doesn't pass any new laws mandating transfers across generations or do any new borrowing), the maximum burden on the young equals the total debt minus the total bequests they will receive. So what happens if the debt is really huge, so huge that the younger generation is not even able to forego enough consumption to pay for it (for example if it's bigger than the country's total product)? In that case, the older generation is mathematically obliged to leave bequests, even though they are legally able to consume as much of their assets as they wish. What will happen if they try to leave infeasibly small bequests? Default of some sort, either outright or via inflation. So, in other words, when the debt is very large, the older generation's willingness to leave bequests determines whether the debt is sustainable. I just thought that was interesting.
ReplyDeleteThat is interesting, but let's make it the topic for another post! :)
DeleteI think this is all very interesting, but I find it somewhat disturbing that this is all framed outside of the voluminous existing literature on intertemporal debt dynamics. In particular, the "it depends" result of the comment stream seems to be similar to the original Diamond result. Much more interesting is what's been derived since then particularly on the provision of liquidity track, as in Woodford (1990) and Holmstrom and Tirole (1998). These are clear areas where government debt decreases the "burden" on future generations, and are broadly consistent with recent empirical facts on interest rates and wealth inequality.
ReplyDeleteEven Andy's above comment (which I agree is very interesting) is very reminiscent of Drazen's article on debt in an economy with human capital transfer.
It's just (my opinion) much nicer to see these results (positive and negative) in fully worked out models with fully fleshed out assumptions.
These are clear areas where government debt decreases the "burden" on future generations, and are broadly consistent with recent empirical facts on interest rates and wealth inequality.
DeleteThat's neato.
Noah,
ReplyDeleteI've written an atrociously long comment over at Rowe's blog. While I'm hoping for some feedback as to just how wrong it is, I thought I'd try to ask something of it here.
To what extent is there agreement that none of this matters when we're not at full employment?
Doesn't all economic activity, including NGDP targeting, imply possible burdens? If so why do we focus on the debt? Couldn't inflation grow faster than GDP under NGDP targeting? Wouldn't this burden the young?
How much does progressive taxation and social insurance mitigate the harm done by debt burdens? So that when rg, at worst, the wealthy have improved their position relative to each other.
The last paragraph should have read:
Delete"So that when r is less than g, like now, bonds allow the wealthy to save with relatively low risk. But when r is greater than g, at worst, the wealthy have improved their position relative to each other."
Noah,
ReplyDeleteFirst off: I disagree with your framing mainly because as far as I can tell very little government debt has ever been repaid. The vast majority is depleted through inflation and the remaining principle rolled over. Which doesn't seem to come into your model and I think has a very large effect. To be precise about it as long as once in while real rates go negative it's more than possible for the debt stock to remain bounded in the limit which means this isn't a Ponzi scheme. (incidentally I can't prove it yet but I think this happens pretty much automatically assuming rational government responses).
Moreover, say we didn't have government debt at all. That would be a massive limitation to the capital market which would effect not only present and alive generations but future generations too- take institution with very long intergenerational liabilities, basically life insurers and pension funds. Having a positive debt balance may actually be socially very useful.
Finally, you allude to this but I'm not sure the effect is given a strong enough weighting: inequality seems to be stubbornly persistent and there's not too much of a leap of faith to assume that this happens due to a large number of intergenerational transfers within families. Say we have a progressive tax system and therefore the wealthy pay most of the taxes. But these same people own most of the debt and therefore the net transfer is greatly reduced for these individuals. So we’re only really limiting the consumption possibilities of the wealthy, who have the lowest marginal utility anyway….
Your answer of ‘it depends’ is obiosully true. But I’m not convinced the simple model works to think about these issues…
Brett
I rally don't see how your proof works. In short: K_T equals K_0 plus the sum of investment between t=0 and t=T-1 (possibly with correction for physical depreciation)... How van you then conclude that only I_0 matters? Couldn't, just to focus on something, D_0 have no effect on K_T-1 and still depress I_T-1 in which case K_T would be force lower?
ReplyDeleteDo public assets benefit future generations?
ReplyDeleteWhat if debt is used to build public assets that increase in value over time?
The argument about debt burden only makes sense if BigG privatizes everything so there are no public assets. If people believe that BigG can create assets that are more valuable in the future, then they will be less likely to favor tax cuts for the wealthy and spending cuts on the public as many of our wealthy elites wish to achieve. The debt burden argument is made to support tax cuts for the wealthy. Of course it is a bogus, Machiavellian, argument intended to mislead the public.
-jonny bakho
Which members of future generations?
ReplyDeleteI could see that government debt might, under most circumstances, hurt the descendants of John D Rockefeller or Sam Walton, relative to the "no government debt" option. For the average person, the situation is different.
funny how as economists you just have theoretical concepts about "investment" and "consumption". what about the cost effectiveness of government spending or the level of returns on investments? seems to me that these are not fixed, and the increased borrowing today is leading to lots of waste that with a little bit more discipline (imposed by lack of money) could be avoided.
ReplyDelete