Incidentally, I wrote about the problem of trying to do intergenerational cost-benefit analysis earlier this year:
The biggest problem is the easiest one to state: what is a cost and what is a benefit? How do you value the changes?As I read it, Stern sort of punts when faced with these impossible calculations. Instead, it relies on status quo bias; now is good, so we should bequeath a world to our descendants that looks as much as possible like the one we live in today. Obviously, there are huge problems with status quo bias, most notably that none of us would like it at all if our ancestors had been at all successful in applying it. On the other hand, "better the devil you known than the devil you don't" is not an entirely awful heuristic. At any rate, that seems to be the underlying assumption of the report. The quickest way to produce that result financially is to set the pure rate of time preference to effectively nothing, and (says William Nordhaus) to rely on the more pessimistic forecasts.
Now, I actually find the moral intuition behind a zero rate of intergenerational time preference pretty compelling, but the practical implications are rather daunting. (A John Quiggin post responds that
"Strange as it may seem to Economist writers, there are phenomena in the world that aren’t particularly illuminated by applying economic concepts. Attitudes towards abortion have nothing at all to do with discounting rates."Which doesn't strike me as illuminating, because the question at the heart of the Stern Report's choice of discount rates is no more a matter of economic concepts than abortion is. It's a moral philosophy problem: are we, or are we not, entitled to privilege our own interests over the interests of those who are not yet born, but probably will be? Otherwise, the low social discount rate is just a pseudomathematical attempt to dress up your preferences as science.)
Can one reject a compelling moral precept just because it's nearly impossible to live by? That's a question that devout Christians wrestle with every day. I am still thinking through this question. But my instinct to reject the precept simply because it would require me to overthrow half of my policy positions is not, at first glance, an admirable one.
But even if you accept a zero rate of intergenerational pure time preference, you can't just smack the pure time discount rate to zero and leave it. Discounting covers a multitude of financial sins by literally making them disappear. For example, if you have a very low rate of discounting, you run into a problem with future generations: there are too damn many of them. Because there are so many of them, even trivial income streams have extremely high net present values.
This is easy to illustrate with a basic equation, such as a discounted cash flow. Let's say that in year one, we have $100 in income, growing at 3% a year. In year 1,000, this will have turned into an annual income of $687 trillion, give or take a few trillion. If, just to keep things fair, we discount this by the rate of growth, we will find that the net present value of income over the next 1,000 years is $100 x 999 or $99,900.
A 0.1% increase in future income over the next thousand years thus has a discounted present value of about a dime a year, which sums to $99. Using these sorts of discount rates, a cost benefit analysis indicates that we should be willing to surrender up to $89.99 in order to produce this small increase in future cash flows, a patently ridiculous result. Discounting takes care of this problem, because even with a low discount rate, the present value of constant income streams quickly declines to nothing. If you don't use discounting, you have to account for this in some other way, by selecting a utility threshold or something. And measuring utility is a rather tricky business.
Another problem is wealth disparities between generations. As I read it, the Stern Report basically assumes that there are low diminishing returns to income (it sets the elasticity of marginal utility of consumption, or η, to 1). It strikes me as odd to see the left half of the blogosphere supporting this proposition; I'm fairly sure that John Quiggin, who is a social democrat, thinks it is higher than that. (Or at least I hope he does). Heck, I think it is higher than that; this is why I support a progressive, indeed negative, income tax, rather than a flat tax. (Yes, yes, I know: I'm not a real libertarian. You may have my card and my secret decoder ring back.) Discounting takes care of this problem by getting rid of very rich future generations; having done away with it, we are now stuck with them, the lucky bastards. I don't even know how you value marginal utility of even large income streams when incomes are $6 trillion, but it has to be pretty trivial. (Or maybe that's what our ancestors thought about incomes of $30K.) Anyway, I'm unhappy with Stern's approach. I'm not sure that you can reconcile owing anything to that thousand year generation with even moderate utilitiarianism, unless you keep ratcheting up the price of Cape Cod views.
Then there's uncertainty. There's still an awful lot of it, and I am not picking up the banner of the global warming sceptic here--when Ron Bailey has switched sides, I think it's safe to say that this particular debate is over. But we are still left with all kinds of uncertainties about what exactly will happen, and about what the world will look like, economically, technologically, and so forth. Climate stabilisers may kick in; they may make everything worse; in fifty years we may have batteries that let us use solar and nuclear energy for basically everything, meaning global warming will go away. We could find other ways to abate climate change. We could be preventing the recurrance of a new ice age--don't laugh, from what I understand, we're about due. At the risk of sounding like a broken record, normal discounting takes care of this problem, because things become more uncertain the farther they are in the future. Discounting progressively lowers the weight placed on future income streams, until they rapidly vanish.
A fourth problem was pointed out by an economist of my acquaintance: if you do away with time preference, you can't just apply this to the environment; you have to apply it to everything. Perhaps our descendants would prefer flying cars to Bangladesh. If you deliberately apply these low discount rates selectively, that's not a serious intellectual effort; it is at best cargo cult science, at worst intellectual fraud. I, too, have a strong intuitive preference for leaving the planet to our descendants in as good as, or preferably better, condition than we found it. But I recognize that there are strong practical and moral challenges to this desire, and the costs of advancing my preferences by random application of high discount rates outweigh the benefits. Let me make it clear that I am not accusing Mr Stern or anyone else of acting in bad faith. I am just saying that I think committing to the discount rate also entails committing to its use in a range of other applications, or justifying your environmental preferences on other grounds. I presume that Mr Stern and all of his supporters are prepared to do so, or to convince me that I am wrong and that ultra low pure time discount rates are uniquely applicable to the environment.
Which of course raises the fifth, and possibly the biggest problem with Stern: who the heck knows what our descendants want? Again, discounting takes care of this problem by essentially saying, "to hell with those young whippersnappers!" But if you don't do this, you have to attempt to grapple with changing preferences, a task at which, if Fifties SF is anything to go by, you will almost certainly fail.
This is not support for the "do nothing" crowd; like Megan, I think we should do rather a lot, starting with (in America) really whopping gas and carbon taxes. I am against subsidies for alternative fuels as a policy matter; I want to use a cap-and-trade system on greenhouse emissions with declining annual quotas that includes gasoline. (Yes, yes, I'll never use the secret handshake again, either.) But having endorsed these methods, I don't know how much we need to shoot for--and given the crudeness of the Stern Report's methodology, after reading it I still don't know.
Oh good God are you returning to the scene of that train wreck? JQ pointed out about a million times that the discount rate in the Stern report was more or less exactly consistent with market rates - the assumption of eta=1 is equivalent to setting the discount rate equal to the rate of growth of per capita consumption, which is about 2%, which is the historically realised real rate of return on high grade bonds.
That's odd, D2, because in the comments, Quiggin says he agrees, nor does your disagreement make much sense to me, as I seem to have been specifically discussing the problem of discounting by the growth rate. Perhaps you are thinking of a different post?
and also in the comments, Michael Sullivan notes that Quiggin was being much too polite and that you are still trying to pretend that the Stern report used a "low" discount rate.
I'll jump right to the end of the thread in question where I said "And conversely the central claim of the right-to-life group is that foetuses are (currently, not potentially) human beings with all the rights of other human beings. This has,as engels says, diddly squat to do with discounting."
As regards the actual discounting issues, I said my piece here (a revised version is forthcoming in Climatic Change.) As DD says, the real bond rate is the obvious choice here, and that's what Stern uses. If you have an ethical problem with that, you need to take it up with the financial markets first.
There is a lot more subtle complexity in Stern's utility analysis than dsquared implies.
First off, as Megan points out, there is more in question than just the temporal rate of discount to future utility rho. Stern's low value for eta, the rate of decrease of utility with income, is equally important to his strong results, because it gives the very much higher expected incomes of future generations a lot of weight. While mathematically consistent, it is ethically unusual to say that future generations are very important, but that income inequality is not very important. (There is, for example, no way that current rates of progressive taxation could be justified under an analysis using Stern's value of eta.)
Next, while Quiggin is absolutely correct that Stern's discount rate is a market rate, it certainly isn't the market rate. As Nordhaus has pointed out with numerous examples, Stern's discount rate implies that people would make certain intertemporal trade-offs that they clearly do not make in practice. This disconnect is really just another instance of the equity premium puzzle, the emperically observed but economically not well-understood phenomenon that people appear to apply different discount rates to situations that look the same to economists.
So, to be clear, Stern's choices for rho and eta are both entirely defensible. But they are also entirely debatable. Given a range of acceptable choices for rho, Stern picks the one that makes future climate change look worst. Given a range of acceptable choices for eta, Stern picks the one that makes future climate change look worst. Stern is careful to take into account the full range of possible climate change scenarios, including low-probability scenarios which makes future climate change look worst. But he doesn't extend his analysis to a range of values for rho and eta, other values for which are likely to make climate change look less bad. Seeing a pattern yet?
Really, the best response to all this loaded analysis comes from Lombard, who basically says: Use any value of eta and rho you want, and I won't argue with you. But apply it to all possible ways that we could sacrifice wealth today to improve the lives of poorer and future people: vaccene research, malaria eradication programs, GM crop development, etc. You results are going to tell you that we should sacrifice a lot more today than, in the end, we actually are willing to sacrifice. Then when we decide how much we are willing to actually forgo, put it toward those programs that our analyses tell us will buy us the most integrated utility.
Generally good points! Just one more idea…
I think we should do rather a lot, starting with (in America) really whopping gas and carbon taxes. I am against subsidies for alternative fuels as a policy matter; I want to use a cap-and-trade system on greenhouse emissions with declining annual quotas that includes gasoline.
What about NOT subsidizing greenhouse emissions? Which we do?
BTW - for a cap-and-trade system one needs CO2 accounting? Should CO2 emissions be passed on like VAT?
[While mathematically consistent, it is ethically unusual to say that future generations are very important, but that income inequality is not very important.]
It's not ethically unusual at all. This is a simple consequence of expected utility theory. You're criticising Stern here for not reinventing more or less everything written since Bentham.
(There is, for example, no way that current rates of progressive taxation could be justified under an analysis using Stern's value of eta.)]
Of course they could. You don't understand eta if you think that. Eta=1 means that if you have twice my consumption, an extra unit is worth twice as much to you as it is to me. It's a log utility function. Quiggin proves that, for example, eta=1 would justify a policy which took $1000 from a person with $100,000, wasted 93% of it and gave the remaining $70 to someone with $7000.
I think you've made this mistake because, although Megan uses the correct term to describe eta (the elasticity of the marginal utility of consumption) she then writes about it incorrectly (as if eta=1 meant that a dollar of income was worth the same no matter who got it, rather than meaning a 1% increment to income was worth the same no matter who got it) and then claims that eta=1 would rule out progressivity in the income tax schedule, which it doesn't.
Isocrates - that passage from Varian is a mistake (a rare one as Varian is a very good economist) and he's admitted as much in email exchanges with John and Brad DeLong.
ref for Quiggin's paper above, supporting the point that eta=1 would rule in progressive taxes
http://johnquiggin.com/wp-content/uploads/2006/12/sternreviewed06121.pdf
Megan(or whoever), I'm not an economist at all so I have some questions on the Pigovian taxes. I can see the need and, as a liberal-ish type, I'm all for reducing CO2 and I'm not allergic to the word taxes. But I always find myself wondering if you really understand the distances that people have to travel if they live outside of major metros and west of the Mississippi.
I keep picturing some single mom in Kansas making $35,000 with a 45-mile commute and gas is suddenly going to cost her $7 a gallon. Do economists have some way planned to make the gas taxes progressive? Has anyone considered weighting the tax by population density so we can roughly account for how neccessary the travel is? It just seems to me that rural flight is bad enough as it is.
Air travel is nearly as big a CO2 source as ground travel and I'd bet the demand's a lot more elastic. That seems like a better starting point to me than gas. Especially since folks that routinely make private flights produce more CO2 in a year than most people will in their lives.
No, dsquared, I have not confused eta=1 for eta=0. I am well-aware that eta=1 corresponds to a log utility function, and I stand by my original assertion that such a utility function could not justify our current tax regieme.
Only a small minority of taxes represent transfer payments from rich to poor. Mostly taxes are a "price of civilization" whoose benefits are highly diffuse. From a utilitarian perspective, then, a fair tax system is one that costs everyone an equal ammount of utility. For eta=0, that would mean a "flat fee" tax, e.g. everyone pays $1000 regardless of income. For eta=1, that would mean a "flat rate" tax, e.g. everyone pays 10% of his income. But our tax system is actually progressive; the tax rate rises with income. The shape of tax rate as a function of income (Figure 5 at http://www.irs.gov/pub/irs-soi/petasa98.pdf) is somewhere between a line and a parabola, corresponding to a value somewhere between eta=2 and eta=3. (Nordhaus has run utilitarian analysis with Stern's rho values but eta values in this range, and finds that the case for CO2 reductions becomes marginal.)
By the way, I don't know what Varian has said by way of clarifying his remarks quoted above, but I don't see any error to confess. Quiggen is fond of playing a "gotcha" game where he acts like anyone who calls rho a discount rate has made some fundamental error. Rho isn't the discount rate of future dollars, but it is the discount rate of future utility, which seems a perfectly reasonable thing for Varian call the "social discount rate".
Only a small minority of taxes represent transfer payments from rich to poor. Mostly taxes are a "price of civilization" whoose benefits are highly diffuse.
The transfer from rich to poor isn't one of the biggest parts of the government but its not small. The majority of government spending in the US (and I think most other rich countries) is transfer payments. It doesn't have to be "from rich to poor" to be distinct from "the price of civilization".
Tim: The accounting here is a bit tricky. You are absolutely right that most government spending is transfer payments, but almost all of that is social security payments. (1) They are not, by and large, from rich to poor, and therefore eta will have nothing to say about whether they are justifed. (2) As defenders of social security like to have it, they are not really transfers at all, but just a retirement savings annuity program that happens to be government-mandated.
Now I am perfectly willing to admit that the issue is subtle and that these counter-points have weak points, but I also think that after you are done with a careful accounting, you will indeed find that the money the government transfers, in the net across lifetimes, from rich to poor, is a very small fraction of its budget.
Your link to the IRS is broken, but I doubt that the income-elasticity of the tax system as a whole is greatly above 1. For example, the evidence I've found says in Australia total tax paid rises from 36 per cent of gross income for the bottom quintile to 51 per cent for the top quintile. It's almost exactly proportional for the middle three quintiles since the regressivity of sales taxes and fixed charges offsets the progressivity of income tax. IIRC, the income gap is about four to one from top to bottom so the implied elasticity is something like 1.1.
PS I haven't had much sleep, so I may be doing something wrong here. Feel free to set me straight.
David: Well most of it is either Social Security or Medicare. Medicare is still smaller at this point but its growing faster.
re: "They are not, by and large, from rich to poor"
I don't understand the significance of this point. They are transfer payments, even if they are not only to the poor. They aren't part of the "price of civilization".
re" As defenders of social security like to have it, they are not really transfers at all, but just a retirement savings annuity program that happens to be government-mandated."
They are transfers. My money goes to current retirees. When I retire (assuming the program is still active and solvent) someone else's money will go to me.
Also if you consider it a retirement savings program its a lousy retirement savings program. The real rates of return are pathetic and can even be negative, and that's before any possible reduction in benefits or increase in taxes to try to keep the program solvent. Also you recieve payments, but you don't own the "returns on investment". You can't take it out and re-invest elsewhere. Your can't give the money to your children or favorite charity after your gone.
re "you will indeed find that the money the government transfers, in the net across lifetimes, from rich to poor, is a very small fraction of its budget."
Its relatively small, but not very small. And that's considering programs not aimed at the poor as not going to the poor. If you include money the poor receive from programs like social security than the total increases. But really its not a distinction I care about. If anything transfers to the poor have more justification than transfers to the not poor. My issue is with all the transfers not who the money goes to.
Yes, like Megan, there is a strong feeling for taxing the bejesus out of the American public. a tax for carbon feet, gas guzzling monsters (Mini Coopers, etc.), the standard fare for the Progressives (yes, Megan, you're turning much more progressive since joining the Atlantic group).
Ma'am, its time to turn in your Libertarian card for a MoveOn website.
Tim: The reason to call out "transfers to the poor" is that the utility function used by Stern and other modelers only depends on income, so transfers to the poor are the only kind of transfers it can justify. Now you could certainly construct a model where old people get more utility out of the same marginal dollar than young people, and tranfers from young to old could be justified using that model. But since that isn't the model Stern used, the parameters you got from fitting it to observed transfer payments wouldn't tell you anything about the appropriate value of eta for Stern's model. (Also, such a model probably wouldn't accurately reflect most people's ethics. The reason we have social security isn't because old people enjoy money more than young people; it really is an attempt at a forced retirement savings plan.)
John: Thanks for chiming in. Megan's software made the closing parenthesis part of my link; you can get to the IRS report by using the URL without that parenthesis.
From the utility function u=(i^(1-eta))/(1-eta), you can derive a tax rate r=(Di)/i that produces the same utility decrease Du for every daypayer. For very small Du, it's just r=i^(eta-1)Du. For more realistic larger Du, it's r=1-(1-(1-eta)(Du)i^(eta-1))^(eta-1). This exhibits all the expected behaviors: r is bounded between 0 and 1, r falls with i for eta < 1 and rises with i for eta > 1; as eta increases, r becomes more suppressed at small i.
When I do a visual fit to the graph I cited I find eta~3 reproduces American tax rates pretty well. I don't have the same data for Australia, but if the bottom quintile already pays 35% and the top quintile only pays 20% more, then I can certainly believe that a fit would produce an eta only slightly higher than 1. (You will get eta > 1 for any system where r increases with i. But for eta > 1, all these models have r=0 at i=0, so none of these models is going to fit Australia very well.) Clearly, Australia's tax system is much less progressive than America's! Perhaps Australians should be convinced by Stern's report but Americans shouldn't!
OK, now I can read the link. It only covers income tax, which is the main progressive component of the tax system. Once you add in payroll and sales taxes and fixed charges, you'll get something much closer to the Australian result. In fact, most of the work I've seen suggests that the US system is less progressive than most, though I don't have any links to hand.
Regarding sales taxes, I certainly agree, but those are very small in the U.S.: none at the federal level except on a few items like gasoline, and a few percent in most states.
Regarding payroll taxes, I don't agree. Payroll taxes in the U.S. fund social security. (True, there is some loaning back-and-forth between social security and the general fund, but the idea, and the approximate reality, is that the tax is dedicated.) As I have argued with Tim, this tax should therefore not be considered either a cost of government or transfer payment within the context of the model; it's more or less just a government-mandated retirement annuity savings plan. (Unlike the public pension system in many other countries, there is almost no progressive component to social security: your payments at retirement are nearly proportional to what you have payed in.) Surely if the government took, on top of current taxes, 40% of everyone's income, then returned it 10 years later, you wouldn't say that our income tax is nearly flat because effective tax rates range only between 40% and 60%. No, you would say that the right analysis would be to ignore that 40% component and look at the remaining fraction that is actually spent and/or redistributed. Why should your analysis be different if they take 10% and return it 40 years later?
If public pensions in Australia have a strong progressive component (e.g. everyone pays a flat rate while working, then recieves a flat payment in retirement), then this analysis doesn't apply there. It will also be less easy to subtract out the pension component if Australia doesn't fund it via a dedicated tax. But in the U.S. neither of these considerations applies.
The right way to settle this debate, I assume you would agree, would be to view i as lifetime income and u as lifetime utility. One would then need to use longitudinal data to determine lifetime effective tax rates (total taxes payed minus total payments recieved from government, divided by income), and then fit eta to that curve. For the reasons I argued above, I think you will get a result for the U.S. similiar to the one I got by ignoring the payroll tax. If you can point me to the relevent data, though, I am happy to be proved wrong.
High grade bonds. Yes being the vast majority of our economies, they are clearly the correct choice for a discount rate.
David Wright - Re: "As I have argued with Tim, this tax should therefore not be considered either a cost of government or transfer payment within the context of the model; it's more or less just a government-mandated retirement annuity savings plan."
It could be considered a "government-mandated retirement annuity savings plan", but in addition to the fact that is a rather poor one, there is the more relevant fact that considering it as such does not make it something other than government spending. There is a tax, then there is a check from the government. Even if the check was going back to the same tax payer,it would still be tax combined with spending. In this case it doesn't go to the same tax payer. My SS tax money goes to current retirees. When I retire, if the program is solvent and operating than future workers SS taxes will go to my SS payments.
As for it being "a cost of government", well it certainly is a cost imposed on the tax payer by the government. If that's what you mean by "a cost of government" than your correct, but I don't see any relevance to the point. If OTOH you mean its a necessary cost of government, and that without it we would not have government or would have an anarchy then that claim is false. Maybe you mean something different than either of those two things. If so please explain what you do mean.
If the government took an additional 40% of my income from from me, than (in addition to being forced to sell my house and maybe my car) I would indeed consider it a 40% tax. Them giving it back to me 10 years later wouldn't change the fact that taking it in the first place is a tax. Even if it was somehow inevitable that I would get it back, even with a good rate of interest, it still wouldn't change the nature of the initial taking. And it would be far from inevitable that I would get it back. In addition to the possibility that I might die before 10 years have passed, the government could cancel the program, or they could modify it in any number of ways.
A real forced annuity program would be a requirement that I put money in to an annuity that I own and control. Than instead of the government taxing my money away they would be regulating my use of it. I'm not a big fan of such government regulation either, but my point is SS is not such an annuity. My projected future SS benefits are not by law or in any other way something that I own.
RE: "lifetime effective tax rates (total taxes payed minus total payments recieved from government, divided by income)"
Lifetime effective tax rates are total taxes paid divided by total income. Receiving a benefit from the government doesn't reduce the amount of taxes you paid.
tramyard convoker notebook estrepement circumarticular scottishly seamster readmit
http://mdc.mo.gov/nathis/arthopo/crayfish/recip.htm >Crayfish, Crawfish, Crawdads
http://www.lakepemaquid.com/