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Update on Mankiw’s work incentives

Tyler Cowen links to a blog by Greg Mankiw with further details on his argument that his anticipated 90% marginal tax rate will reduce his work level.

Having already given my thoughts on Mankiw’s column, I merely have a few things to add/emphasize.

1. Cowen frames the arguments in terms of the “status” of George Bush, Greg Mankiw, Barack Obama, and their proposed policies. I hadn’t thought of the arguments as being about status, but I think I see what Cowen is saying. By being a well-known economist and having a column in the New York Times, Mankiw is trading some of his status for political advocacy (just as Krugman does, from the opposite direction). If Mankiw didn’t have the pre-existing status, I doubt this particular column would’ve made it into the newspaper. (Again, ditto with many of Krugman’s columns.) So it makes sense that arguments about the substance of Mankiw’s remarks will get tied into disputes about his status.

2. Neither Cowen nor Mankiw address the problem that Mankiw estimates his current marginal tax rate at 80%, whereas only two years ago he estimated his marginal tax rate under a hypothetical Obama administration at 93%. Again, that means he’s keeping 290% of the money he was expecting to keep, based on his calculations from 2008. These calculations are so unstable as to make me doubt any policy implications that would be drawn from them.

3. One might argue that, whether the marginal tax rate is 93%, 90%, 80%, or even 70%, it’s still a lot–it’s a drag on the economy and a disincentive for productive people to work. This might be true, but that gets back to my original point from two years ago, that Mankiw is still working despite these tax rates. In fact, before his recent column came out, I was thinking that Mankiw was working despite what he judged as a 93% marginal tax rate.

4. I agree that, ability to pay aside, there’s something demoralizing about knowing that a large fraction of your marginal income goes to the government, much of it for programs that you don’t approve of. When I do $1200 worth of statistical consulting, I find it a bit frustrating to know that I’ll only take home half of it–so I can only imagine how irritating it would be to feel that you’re only getting 7 cents on the dollar (or even 20 cents, per Mankiw’s latest calculation).

In Mankiw’s case, though, there is a solution: he could use his marginal income (which, as he said, he doesn’t need right now) to hire some research assistants. I don’t know the details of the tax law, but I’m sure his marginal rate would be much much less than 93% or 80% or the other numbers he’s talking about.

5. The discussion of Mankiw’s column seems to have caused him to rethink one of his ideas. Two years ago, he framed his decision as follows:

On a regular basis, I am offered opportunities to make some extra money. It could be giving a talk, writing an article, editing a journal, and so on. . . . The bottom line: If you are one of those people out there trying to induce me to do some work for you, there is a good chance I will turn you down. And the likelihood will go up after President Obama puts his tax plan in place. I expect to spend more time playing with my kids.

The choice was clear: make money or play with the kids. At the time, I suggested that perhaps Mankiw is working not for the money but for the fun and also out of some sense of moral obligation (for example, to do his part to stop a proposed government policy that he opposes).

For whatever reason, Mankiw has added some of these motivations into his calculus and now writes:

I [Mankiw] face a choice among a wide range of activities, each of which offers some combination of pecuniary and non-pecuniary benefits. . . . When the government taxes pecuniary benefits, I spend more time on those activities that yield non-pecuniary benefits. Some of those activities may look like leisure, but others may be better described as “fun work” rather than “income-producing work.”

I think he’s most of the way there. But he still needs to recognize that he does some things for motivations that are neither familial (saving money for his kids), pecuniary, or for fun. Again, I think his formal framework is too narrow and I would find it refreshing if he were to state that he does some things (such as column-writing) because he thinks they will benefit the public good. I’m not saying he needs to be taxed at 93% on these efforts, though; he could perhaps set up a special cookie jar for his extra income and spend it in a productive way on his research so it won’t get swallowed up by inheritance taxes in 30 years. He could, for example, set up a nonprofit foundation for economic analysis, or endow a fellowship at the American Enterprise Institute, or something like that. This could have the effect of furthering his advocacy and policy goals and give him the sense that his extra money is going somewhere useful.

P.S. Cowen argues that details-oriented commenters like me are missing the point: the issue is not Mankiw’s particular circumstances but rather the larger issues of the efficiency and morality of high tax rates. I take Cowen’s point, but, as a statistician, I’m not impressed with an argument when it doesn’t work on the example it’s been applied to.

32 Comments

  1. Dan says:

    Am I missing something, or is the following statement from Andrew really wool-headed:

    "Neither Cowen nor Mankiw address the problem that Mankiw estimates his current marginal tax rate at 80%, whereas only two years ago he estimated his marginal tax rate under a hypothetical Obama administration at 93%."

    It looks to me like the main difference between the 80% and 93% comes from allowing the Bush tax cuts to expire…which hasn't happened yet. Therefore, under Obama's policies, Mankiw expected, and can continue to expect, marginal tax rates of 90+%

  2. TheOneEyedMan says:

    I'm with you about the details. If the details don't matter then why write them down?

    It would be interesting to know if Mankiw is working more now than he expected to be working now two years ago. That would add credibility to his claim of sensitivity to tax incentives.

    A great deal of Mankiw's work cannot be unbundled. His Harvard teaching position is a major reason why his textbook empire continues to be successful. His actual paid work beyond these two sources is probably quite small, but he may not be able to make 75% as much money and do 75% as much work.

    Encouraging Mankiw to invest in tax structures like grad students and think tanks that allow him to get more bang for his buck may be good advice as Mankiw's colleague but isn't a helpful comment about tax policy. If the tax policy is bad the fact that it can be worked around is hardly an argument in his favor.

  3. Darf Ferrara says:

    "I think he's most of the way there. But he still needs to recognize that he does some things for motivations that are neither familial (saving money for his kids), pecuniary, or for fun."

    Why doesn't pecuniary and non-pecuniary choices cover this?

    And personally I think that you are far too focused on the exact tax rate that he thinks that he will pay. I suppose he could have discussed his own personal decision making under uncertainty, his IRA and how he will donate his old pants to goodwill for the tax write-offs, but he chose to keep things simple. It's almost like you are critisizing a parable for being unrealistic.

    At any rate, I hope both you and Greg keep blogging, since I get a great deal of non-pecuniary gain from reading both of you.

  4. Andrew Gelman says:

    Dan:

    According to Mankiw two years ago, he was expecting a marginal tax rate of 93% under Obama o 83% under McCain. But now he's paying 80%. At the very least, his calculations are pretty approximate.

    OneEyedMan:

    I actually think it would be better for Mankiw to hire research assistants than to put his money in a trust for his children. So in that sense the tax policy would be doing a good job.

    Darf:

    I agree that pecuniary/non-pecuniary covers it all. My problem is that Mankiw is identifying non-pecuniary with "leisure" or "fun," which I think is too limiting.

  5. Paul says:

    Even if we accept Mankiw's arguments about his behavior on the face of them, there's a separate question about preferences between the low and high tax realities.

    First, there's a question of inherent preference for high income activities. Things like family time have no direct measurable individual economic gain, but seem to produce better adjusted children presumably increasing the economic value of the future. Similarly, being unconstrained by financial goals can create the opportunity for other non-economic goods: maybe the free time Mankiw has now that he's declining job opportunities will be used for volunteering, or blogging about important ideas, or even just golfing (increasing his own happiness, contributing to monetary velocity, …).

    Then, there's the separate question of the impact of economic inequality: the gap between the rich and poor is already growing, and even if a lower top marginal tax rate encourages more economic value and tax income from the top, it can have negative societal costs. Does a large inheritance discourage success in the next generation? Does the existence of a middle class create a 'ramp' such that the lower class can see a path to success, as opposed to a tiny rich elite that's perceived as insular? Does stratification hurt monetary velocity? Can it serve as a catalyst for hugely damaging revolutions?

    In this regard, I think economics is a bit like thermodynamics: while you can focus on what each individual atom/actor is doing, doing so often distracts from the more important larger picture, where the overall behavior isn't just a trivial sum of the individual behaviors.

  6. wcw says:

    The data indicate that honestly calculated marginal tax rates (Mankiw is calculating something, but it is not his marginal tax rate) at roughly 70% begin on the societal level adversely to affect incentives for productive people to work. Mankiw, at up-to-47%, is a good indication that our tax rates are nowhere near this level.

    That aside, the underlying truth is that Mankiw's work is 100% fungible. He is not Shakespeare. The world loses nothing if he chooses to play with his children and someone else writes the article.

  7. Silas Barta says:

    I'm going to have to agree that a lot of Gelman's points here (well, all) do seem a bit wool-headed.

    - Yes, Mankiw is working despite the high marginal tax rates. But his *whole point* was that he works a *lot less* than he would (i.e. takes fewer individual assignments). And that this reaction, in turn, hurts other people who want his services, not just Mankiw. Did you want Mankiw to come give a talk at your school? Well too bad, you can't afford him now. Did you want to see a new Tom Cruise film for $8. Sorry, you don't have that option anymore, because as much as you might resent it, his $1 million take-home under new tax rules ain't enough to get him out of bed.

    - Yes, Mankiw is calculating the relative value of time with his children vs. future money for his children. Because he has to. Because everyone has to. At some point you have to be able to say "this much future children income is worth as much as this much time with children", or else you open yourself up to preference intransitivity or money-pumping. (While people don't actually money-pump you, you will show dynamic inconsistencies and thus get less of what you — or your kids — want.)

    - On a related note to the two points above: yes, there are non-pecuniary benefits to what Mankiw does, including column writing. But (per econ 101), decisions are made _at the margin_. Mankiw doesn't ever choose between "all work" and "no work". He chooses between some marginal unit of work vs. not that unit of work, and eventually, the non-pecuniary + pecuniary just ain't enough to motivate him. But who cares about dummy Mankiw? Like I said above, let's assume "no one". Care about the people who want to buy him but can't now.

    - Yes, Makiw could use the latest tax code's quirks to divert his income to hiring research assistants. But (per econ 101 stuff again), it's _bad_ when the tax system distorts your behavior on top of the money it takes. (Tax incidence. Deadweight loss. Look them up.) That means it's destroying utility without even a corresponding benefit for the government!

  8. Mark Palko says:

    "When I do $1200 worth of statistical consulting, I find it a bit frustrating to know that I'll only take home half of it–so I can only imagine how irritating it would be to feel that you're only getting 7 cents on the dollar (or even 20 cents, per Mankiw's latest calculation)."

    Maybe I'm misreading parts of Mankiw's op-ed and follow-up, but I believe that reaching even that 80% requires some interesting accounting methods, If I've got this right, every penny of the twenty thousand has to go into an already large estate where no estate planning has been done.

    This is, of course, not the picture you get from a casual reading and, based on various verbal clues in the original text, I suspect that's deliberate.

    More importantly, though, Mankiw's main thesis seems to be that we will have a significant number of creative, inventive people deciding to produce less work if we go back to Clinton-era taxes. Does the historical record support that assertion?

  9. Andrew Gelman says:

    Silas:

    1. When professors from other departments come and talk at Columbia, they do it for free. All we pay is their expenses, which are 100% tax deductible.

    2. The "at the margin" analysis is relevant only to the extent that Mankiw is writing a column (or that Tom Cruise is acting in a movie) for the money. If Mankiw's motivations for writing a column are almost entirely non-monetary, then the marginal tax rate is pretty much irrelevant to his decision.

    Mankiw in fact recognized this in his update (so maybe you should be arguing with him, not with me!). My only amendment to his update was to suggest that his non-monetary incentives include public-spirited duty as well as "fun."

    3. Tom Cruise, like Mankiw, has earned his riches and earned his right to relax. If, in the future, Cruise only wants to make movies for their inherent value and joy, that's ok with me. I don't find it necessary that Cruise make movies just for the money.

    4. It's hardly a "quirk" of the tax code that Mankiw can use his money to hire assistants. I think that it's considered a good thing if productive people hire employees, rather than sticking all their money into trust funds for their children. You might disagree with this assessment, but I don't think it's a quirk. It's more of a goal, no?

    5. You might be right on the "destroying utility" thing. I have no informed opinion on the topic. I'm not expressing any judgment on tax policy here; I'm just addressing some of his individual utility arguments, which I don't think he fully thought through.

  10. Megan Pledger says:

    (I am not an economist but…)

    It seems to me that people at the top end of the incomce scale have a very high ability to be able to set the price for their work. This means that the effective marginal tax rate is not 93% or 80% becasue the earner can ask for more money and pretty much get it – if his/her take home pay decreases because the tax has gone up then she/he can use their star appeal to ask for more salary.

    I would say it effects people at the high end with non-salary income i.e. there is no boss to go to ask for more money. And that kinda money is not producing much for the economy anyway.

  11. Darf Ferrara says:

    wcw, you are completely wrong that Mankiw's writing is fungible. If that column was written by almost anyone other than Mankiw there would not have been anywhere near the hubbub that there has been.

    Andrew, I think that Mankiw has thought through his position very thoroughly. The problem may be that he has internalized the thought process to the point where he is not stating all his assumptions. For example, his claim that, "Absent taxes, I would choose an optimal mix of these activities" assumes that the reader understands that property rights and a price system imply the solution to optimal allocation. Of course my last statement, in turn depends on many assumptions, but that is better left to an article on General Equilibrium Theory, or maybe a micro textbook.

  12. Michael says:

    Gelman response #2 to Silas misses the power of the point that these decisions are made "at the margin". The tax rate is relevant even if "Mankiw's motivations for writing a column are almost entirely non-monetary".

    The reason is that the non-pecuniary benefits are not the marginal benefit. You write this blog for free, and so presumably write as much as you want to, given other obligations, opportunities for amusement, etc. If I wanted to get you to spend another hour a day on it, I'd have to pay you. I know this, because otherwise you would be doing it already for free.

    Technically: labor can provide positive utility; but marginal utility must be negative if you are getting paid to work, and are a rational decision-maker.

  13. Silas Barta says:

    @Andrew_Gelman:

    1. Mankiw sells services other than talks at Columbia …
    2. … or columns, for that matter.

    3. If that's really true, then you're not in the class of people Mankiw is warning. But I don't think it's true: though you aren't a potential buyer of Mankiw's services (or Tom Cruise's), you probably buy some other high earner's services, if indirectly — and as marginal tax rates go up, you will find these harder and harder to buy. Again, forget Mankiw and Cruise — think about the people who want to buy their stuff, the people who aren't even going to get the chance to pay that $8 for another Tom Cruise movie.

    (It seems your real argument is that you don't feel Mankiw has actually earned his income from producing value like Tom Cruise has? Well, I'd actually agree with you there. But the right response to this is to remove the laws and funding sources that make it possible to get rich selling politicians bad economic advice, _not_ to campaign for keeping the high margnal taxes on high earners *in general*.)

    4. I used the term "quirks" because the tax system is a disfigured monster, which will reward different things from day to day. But sure, you like the fact that the tax system incentivizes spending your money on assistants (as well as hole digger/refillers …) rather than trust funds. But it doesn't actually do that in general — it just happens to *result* in that in this case. A policy that generally makes people change behavior away from their first choice will make people generally worse off, even if this is partially mitigated by accidental positive externalities that get thrown off in the process.

    But if you believe there's some sort of uncompensated positive or negative externality, that would be an argument for targeting *that externality* in the tax code, not for keeping the tax system as it is because sometimes coincides with things you wish there were more of, like Mankiw assistants.

    5. Well, the bit about destroying utility was Mankiw's central point; if you don't feel qualified to comment on that, then … ?

  14. Andrew Gelman says:

    Darf:

    It is certainly possible that Mankiw has thought through all the details and just not expressed himself clearly in his column and blog. It may very well be that years of communicating with economists have pushed Mankiw into writing in a kind of shorthand that outsiders whose nuances are not always caught by outsiders such as myself.

    Michael:

    Even at the margin, I expect that Mankiw's newspaper writing decisions are almost entirely motivated by non-monetary gains. So, yes, a change in Mankiw's estimation of his marginal tax rate might affect his rate of writing newspaper columns, but I expect in a negligible way.

    I do agree that the marginal tax rate will affect his decisions to do things just for the money (for example, to write a report for a company, that only the directors of the company will read). So it's not that I'm saying the tax laws will have no effect on his decisions; I'm just questioning the example he's giving.

    Silas:

    One of the joys of blogging is the opportunity to interact with people who disagree with me, so I much appreciate your patience in continuing the back-and-forth.

    In your case, though, I think you're letting your sympathy with Mankiw's political goals get in the way of your reading of what I wrote.

    In particular, you write, "It seems your real argument is that you don't feel Mankiw has actually earned his income from producing value like Tom Cruise has? Well, I'd actually agree with you there." What I actually wrote was, "Tom Cruise, like Mankiw, has earned his riches and earned his right to relax."

    You imply that my suggestion of Mankiw to hire assistants is comparable to hiring someone to dig and refill a hole. I don't think this is correct. Why should Mankiw hire someone to dig and refill a hole? That would be a waste of his (Mankiw's) money. Instead, if he hires an assistant, Mankiw can get something useful out of it. It seems silly to me to treat all hiring as if it is make-work.

    Finally, you question why I blogged on this at all, given my admitted lack of expertise or interesting perspective on tax policy. The answer is that Mankiw's article (and his blog two years ago) were not merely about tax policy; they also touched on decision analysis, which is an area of my research. (See the "decision analysis" category of this blog for more.) And the decision analysis is what I wrote about. As a statistician, I focus on details; in particular the details of Mankiw's example.

  15. Rich says:

    Umm, so maybe this is an ignorant question but exactly how rich do you have to be to have a marginal tax rate of 90%?

    i'm fairly ignorant on tax issues, but i know i pay about 40% on consulting. is there a sliding scale such that if i made a million a year i might pay 90%?

  16. Darf Ferrara says:

    Andrew:

    You write that "[Mankiw] has earned his riches and earned his right to relax." On the other hand you seem to be making the point that giving the money that he has earned to his children instead of to graduate students is a mis-allocation of resources. The disconnect seems to be that Mankiw seems to presume that individuals can make allocation of their own resources better than others can. This is a standard neo-classical econ assumption. You seem to be saying that you know that his giving more money to his children is suboptimal in some way.

    I doubt that Mankiw revealed his actual preferences in the article, but do you agree that he makes a plausible case that 1) changing the tax rates can have a significant influence on the amount of wealth accumulated, and 2) there could be a significant dead-weight loss associated with higher tax rates, especially pronounced in the higher brackets? Given that these are the points that he wants to make, do you think that he could have written an article that made those points in as dramatic and effective manner, for a general audience while incorporating a more realistic decision model? I would actually love to see the same article written by you (or your evil twin who votes (R)) that attempted it.

  17. Michael Lew says:

    Economists might call me naive, but for my straightforward mind Mankiw is not paying anything like 80% or 90% in tax. I looked at his original article and it is pretty clear that his marginal tax rate is actually a little less than 50%. He inflates it by making investment assumptions that have nothing to do with taxation rates. It seems like a distortion intended to bolster a beat-up to me.

  18. Andrew Gelman says:

    Darf:

    I'm not trying to tell Mankiw what to do! He's the one saying that only 7%, or 10%, or 20%, of his marginal earnings will go to his kids, so I'm suggesting research assistants as an alternative way for him to spend his money.

    Beyond this: sure, he's a talented researcher and I'd love for him to do more research, and I'd hope that some well-paid R.A.'s could make his work even better. (It works that way for me, that's for sure!) Similarly, I think Meryl Streep is great and I hope she never stops making movies. But I respect the personal goals of Mankiw and Streep. I'm just expressing my own preferences here; obviously it's their choice how to spend their time.

    People make such suggestions to me too, suggesting I work on X or Y because it's an important problem. I don't think they're exactly saying that they presume they can allocate my resources better than I can. They're just sharing their perspective.

    One reason I shared my perspective above is that I didn't think Mankiw was fully thinking through his decisions.

    An key idea in decision analysis is that the most important decision is often the choice of what options to include in the decision tree. By framing it as work-or-not-work (or even as work-for-money vs. work-for-fun), I think Mankiw is missing some good alternative options. For me to say he might have missed some options or that he hasn't thought everything through, is not to say that I presume I can allocate his resources better than he can.

    In response to your last paragraph: Yes, I think that Mankiw could have written such an article. And I, like you, would love to see it. I think such an article would take work, though. One thing I know from statistical research is that it can be difficult to start with an idea and then look for a good example to make the point. Examples tend to develop a life of their own.

  19. zbicyclist says:

    Most of the "oomph" in the argument comes from the estate tax. You can probably get it up to 97% or so if you assume his kids will drink and smoke their inheritance away — in which case, health of the kids is improved by the high tax rate.

    Mankiw is just doing what every other person does. He's arguing that if somebody has to be taxed, it should be somebody else.

  20. wcw says:

    Darf, that's exactly it: the only thing that distinguishes Mankiw's and Krugman's op-ed work is the *attention* they get. If either retires tomorrow, popular attention will find another target and the world loses nothing.

    Zbicyclist, that's not true. Any number of people, say Warren Buffet, are on record arguing that somebody needs to be taxed more, and it should be him. It doesn't make me special to express exactly the same: my household and all like it on the income scale pay way too little in tax. We should all pay more.

  21. Numeric says:

    I made a previous comment that if Mankiw's argument was true, if the top marginal tax rate was 50%, he would be paying the government money for working, and that since the top marginal rate was 70% from 1962-1978, and even higher from the Depression up to 1962, this means people in the top brackets during this period were paying the government for working. Unfortunately, many writers (including Gelman) continued to use Mankiw's figures as if they were accurate. They are not, and here's why.

    First, a marginal tax rate is the amount of tax you pay on the last dollar of income. Let us say it is 40%. Now, Mankiw is above the level where he is paying any social security tax (12.4%, for both employer and employee), so he doesn't have to pay this. Second, corporate taxes are _not_ paid by Mankiw on this last dollar–they are only paid on the profit he makes if he invests that last dollar. If he sits on the dollar, or puts it into inflation-protected Treasury bonds, he pays _no_ corporate taxes (and since the taxes are deducted from the profits of the corporation, they only affect the amount of the profit).

    As for the estate tax, if Mankiw sits on the dollar, and he is in a high enough tax bracket, and he doesn't buy life insurance with the dollar (thereby avoiding the whole estate tax on the payoff)–in other words, if he is stupid (rather than intellectually dishonest, which he plainly is–but what can you expect of the architect of the Bush destruction of the economy?), if he put the dollar in to TIPS, and lives another 30 years or so, the dollar would double (approximately), so even at a 50% estate tax level, he would still have that 40% (the original marginal tax rate) of one dollar.

    Let us consider a poor ordinary Joe who is below the social security ceiling. Let's say he is in the 30% tax bracket, but then he gets hit for 12.4% on top of that. While paying no estate tax, he still pays a higher marginal tax rate than Mankiw.

    Shills for the accumulation of power and capital go back to the "Divine Right of Kings", the justifications for the (non) taxation of two of the three estates in France before the revolution (why do you think it's called an estate tax?), and supply-side economic. Essentially, in its final form, these individuals are arguing for a return to feudalism. While they won't get to that, look how successful they've been at decimating the middle class after a generation of right-wing rule. The three big costs of the middle class-housing, education and medical care–have gone through the roof, and the governmental funds which might have offset those increases have gone to the top 1% (now up to 24% of the nation's income). One doesn't have to be a Jacobian or a Bolshevik to understand that this is going to create a very unstable society, of which the Tea Party with its emphasis on mindless inchoate mass action is only the tip of the iceberg.

  22. K? O'Rourke says:

    Yes, "Examples tend to develop a life of their own." they run into brute reality which is beyond anyone's control!

    And this "suggesting I work on X or Y because it's an important problem", I believe, is a common problem for most of us.

    Nice post.

    K?

  23. Paul says:

    What's funny is that we're weighing two failures in an idealized capitalist economy against each other. On the one hand, an excessive marginal tax rate on Mankiw's estate is changing his behavior, distorting the market which many assume must be inherently inefficient. At the same time, he wants to avoid that tax so he can give additional millions to his children. That will let his children 'cut' ahead of more intelligent children into top colleges, purchase and run businesses if they desire without proving their ability, and generally allocate resources they only received by virtue of birth.

    I can get an 'eventually efficient' economic hypothesis, that if they don't deserve the money it'll run out after some generations, but lowering estate taxes seems to reduce the 'to each according to his ability' mentality that's supposed to make capitalism work.

    If the rich produce less this generation, but the next one sees a more equally starting footing for all, mightn't that be a more efficient choice in aggregate?

  24. Andrew Gelman says:

    Numeric:

    You write, "many writers (including Gelman) continued to use Mankiw's figures as if they were accurate." I'm discussing Mankiw's decision analysis, which depends on his state of mind. Hence I'm using his stated estimated marginal tax rates (in 2008, an anticipated rate of 93%; today, a rate of 80%), on the theory that he's basing his decisions on these estimates.

  25. Silas Barta says:

    @Andrew_Gelman:

    What I actually wrote was, "Tom Cruise, like Mankiw, has earned his riches and earned his right to relax."

    Indeed, and my response was that this deservedness you deem is completely orthogonal to Mankiw's point. Whether or not either of them have earned the right to relax, their (more frequent) exercise of that right due to higher marginal tax rates will hurt *other people*, since people who want to buy those services have to do without. That's the whole point!

    You imply that my suggestion of Mankiw to hire assistants is comparable to hiring someone to dig and refill a hole. I don't think this is correct. Why should Mankiw hire someone to dig and refill a hole? That would be a waste of his (Mankiw's) money. Instead, if he hires an assistant, Mankiw can get something useful out of it. It seems silly to me to treat all hiring as if it is make-work.

    I'm sorry I was unable to explain at the relevant level of abstraction.

    Paying someone to dig/refill a whole is like hiring an assistant in one very crucial respect: Mankiw doesn't think either one is worth the money under the current tax structure — and even more so as marginal tax rates go up. If the tax system makes people in _general_ move to a lower point in their preference ranking, that's bad: because on taking utility from taxpayers, additional utility (above and beyond the wealth taken) is destroyed. This is called "deadweight loss", and is a fundamental concept in the study of tax incidence.

    Finally, you question why I blogged on this at all, given my admitted lack of expertise or interesting perspective on tax policy.

    Actually, what I said was that you (by your admission) lacked expertise on his point about the tax code _destroying utility_ … which you agree to in the very next sentences:

    The answer is that Mankiw's article (and his blog two years ago) were not merely about tax policy; they also touched on decision analysis, which is an area of my research. … As a statistician, I focus on details; in particular the details of Mankiw's example.

    Then I don't understand why you have a hard time understanding the basic point: "Hey, tax me, I'll sell less of my services, which is bad for people who don't want to buy it"; instead you ask questions like (paraphrasing), "Why doesn't he do something he regards as a net loss for him, like hiring a research assistant? The fact that the tax code happens to incentivize hiring an assistant is conclusive refutation of the fact that it generally moves people down on their utility curves."

    That doesn't sound like a statistician talking.

  26. Paul says:

    If I may interject into this debate:

    You and Andrew are diverging on what you're discussing, him to the micro and you to the macro. Andrew's punted when pressed to generalize this to a general stance on taxes at the top brackets.

    In a macroeconomic sense, I agree with you: nonuniform taxes destroy utility by pushing suboptimal distributions. That's not to say there aren't reasons for it: forcing externalities back to an actor, for example, or handling public commons style resources. But deadweight loss, for example, assumes actors can accurately rate preferences. It's fine for a macroeconomic first approximation, but the study of decision analysis shows it to be just that: an approximation.

    For example, it may turn out I'd love Russian food and if I tried it and far more of my resources would go to obtaining it. Multi-armed bandit studies proscribe an ideal allocation of my resources for figuring out the value in unknown options. But I guarantee my proclivity for trying new things doesn't match any optima, and is culturally rooted such that certain options are not properly explored. But if a friend with similar food tastes recommended it, maybe I'd try it and make better decisions. Strictly speaking, then, I would have been behaving irrationally in not trying Russian food up until that point.

    Thus, at a micro-level it's perfectly valid to critique Mankiw's personal reasoning. His professed utility ranking is just about guaranteed to be wrong on some topic. His framing of it in strictly fun vs. profitable terms may fail to account for an actual preferential variable. Perhaps if he added more assistants he'd find that in fact this was a lot better than he thought, and he is interested in working more. Andrew, being in a superficially similar situation, is in a good position to present alternatives that would reduce deadweight by better matching Mankiw's utility preferences to "reality".

    Personally, I'd agree with you in the macro regard, and agree with Andrew in the individual regard. They're both valid topics people can and do analyze endlessly. But you both seem interested and knowledgeable in orthogonal topics.

  27. Jonathan says:

    Silas is doing a good job, IMO, but let me just address the "at the margin" point a bit more. What he (and Mankiw) are saying is: imagine a world of 40 percent marginal taxes. Mankiw writes N newspaper editorials. This takes into account how much he's paid, how much he likes writing articles, his potential for glory, public-spitirtedness, fun, and all the other pecuniary and non-pecuniary issues there are, including your expansion of his preference set. Now raise taxes. If purely pecuniary gain had even the least scintilla of effect, the effect of an increase in the tax rate, ceteris paribus (as we say), is to reduce his supply below N. Now, it is possible that other effects might increase the supply… for example, he might find some other task so disagreeable at reduced reward that he gives it up altogether, freeing up additional time to write editorials. But the basic point is that there is nothing wrong with the example, and a wide range of non-pecuniary benefits from writing editorials doesn't affect the marginal decision at all.

  28. Phil says:

    My previous comment hasn't even posted yet, but I'm going to add another one.

    What I see in this thread is people talking past each other. There are several different themes, and each person tries to draw other commenters into the one s/he is interested in.

    1. Andrew's original main point: Mankiw wrote his post as though he decides whether to write an article based on the tradeoff between the time it takes to do the writing and the money he would be able to pass along to his children by doing so. Andrew points out that that cannot plausibly be the way Mankiw actually chooses whether to write the article. Andrew is obviously right about this.

    2. Andrew's secondary point (really just the main point from a different angle): Mankiw would be well served by including in his analysis factors other than the money he passes on to his kids and the opportunity cost of his time.

    3. A subtext that many people read into Andrew's post: If, by not writing a few articles, Mankiw spends more time with his kids but gives them less money when he dies, maybe that's a good thing, or at least not a very bad thing. Andrew strenuously denies trying to tell Mankiw how he should spend his time or money, he says he just thinks Mankiw needs to broaden his analysis. I dunno, Andrew, it seems to me that you really did have this subtext in there…but whatever, your main point is still good either way.

    4. A point raised by a few, including me: Mankiw's estimate of his tax effect is bogus. A big error is assuming that money he passes on to his kids will be hit by whatever estate tax is in effect when he dies. But he can simply give the money to his children now — either as a gift or through a trust — and it's tax-free. At least, it's tax-free up to $13,000 per child per year…or $26K if he gives with his spouse, which why wouldn't he? So, unless he and his spouse are already giving each child $26K per year, he can avoid the estate tax on his hypothetical article earnings altogether. That's not a trivial error, considering he assumes the estate tax will be 40% when he dies. But this has nothing whatsoever to do with Andrew's main point, which holds whether Mankiw's numbers are right or not.

    5. A few people are focusing on a key point of Mankiw's argument, which is that if Mankiw doesn't write an article that he would otherwise write, the greater good suffers a loss. That's true, but it misses Andrew's main point: yes, it's true that IF Mankiw doesn't write his article, society loses something. But Andrew's point is that Mankiw isn't going to decide whether to write an article just because of a $500 effect on the value of his estate. People are starting with a false premise — the one that Mankiw handed them, that says that he is motivated only by money when he decides whether to write an article — and reaching a false conclusion that Mankiw is not going to write articles. He writes articles now! He's been doing it for years! If he stops, it's not going to be because they changed the tax code to let him pass along another $39.95 to his kids when he dies.

    6. A few people are interested in other societal issues, like, isn't the estate tax a good thing because it will prevent Mankiw's kids from being freeloaders? Yeah, maybe we lose some of Mankiw's productivity now, but we get it out of his children (and their children, etc.). I think that's a great point, and in fact I am a fan of a fairly high estate tax. But again, this point is different from the ones others are making.

    7. I'll add another one: Mankiw is making a good argument for why government spending rather than a tax cut is the way to provide a stimulus. If all the rich people do with the tax money they save is to sock it away for their kids, that's not at all what we need at the moment.

    All of these are interesting things to discuss, but only items 1 and 2 are Andrew's points, I think.

  29. numeric says:

    Numeric:

    You write, "many writers (including Gelman) continued to use Mankiw's figures as if they were accurate." I'm discussing Mankiw's decision analysis, which depends on his state of mind. Hence I'm using his stated estimated marginal tax rates (in 2008, an anticipated rate of 93%; today, a rate of 80%), on the theory that he's basing his decisions on these estimates.

    I realize subjective probability is a mainstay of Bayesian analysis but Gelman should peruse the game
    theoretic literature to understand that Mankiw is, in the terminology of that field, gaming. Mankiw is well aware of the definition of marginal income and aware that he is misstating it. What Mankiw understands is that by constant repetition of marginal income figures such as 80%, 93%, etc, this is all that will be left in most readers minds. The fact that the marginal rate is much lower than this and that middle class individuals pay a higher rate will be lost. Mankiw's actual decisions in his life will be based on his actual marginal costs, rather than what he states on a blog. He simply states the false figures in the (well-founded) hopes that they won't be refuted. He depends on "useful idiots" to take him at his word.

  30. Silas Barta says:

    @Phil: I think it's comments like yours and Paul's that represent the non-responsiveness of Andrew_Gelman's arguments against Mankiw.

    First of all, yes, you can nitpick here and there are about his personal life and how maybe he could do things more in line with his values. But I don't see why anyone bothers

    I'm going to offer myself as a less-elitist example: I'm a middle class engineer, and even *my* current marginal tax rates make it not worth my time to put my valuable math/science tutoring services on the market (unless I can get paid under the table, which is not what Mankiw's critics have in mind!) Now, you can certainly nitpick me, too. What about the non-pecuniary advantages? Why not fundamentally rearrage myself to take advantage of the tax-code's rewards for tutors (before September 3, 2011 or whatever they agree on)?

    But the thing is, people have generally already adjusted for benefits like these, so you're not telling us anything new. And if you're going to bring up some kind of social optimality that results from Mankiw (or Cruise) *not* selling more of their labor, then fine — but that's an argument for subsidizing that positive externality. In no case is it relevant for you to start digging into Mankiw's parenting choices just so you can make a 90% effective tax rate seem dandy.

    Now, to your specific points:

    1) No, Andrew_Gelman is not obviously right about this: the different factors interplay, and as one cost goes up, the total optimality to Mankiw goes down, leading him to offering less labor. The fact that you find his weighting strange is incidental.

    2) Mankiw's allocation of his time has already accounted for the optimality of spending time with his kids, which is why he probably spends a lot of time with them already — you really can't build a case for the tax on your ability to criticize his lifestyle.

    3) The additional aspects included in such a broadening don't appear to affect the point.

    5) Yes, the obviously is, because all the factors interplay — people act on the margin, remember? You're just introducing an ad-hoc model of Mankiw's psychology that doesn't account for its sensitivity to lower and lower financial gain from his provision of services.

    7) The benefit we're concerned about isn't for Mankiw's kids. The alarm Mankiw was raising is about the fact that, not beng able to divert as much of his marginal earnings to his kids, he sells less of them. The *buyers* of the services are the ones who lose out.

    *Errata*: In my last comment, the quote in the 2nd-to-last paragraph should be: "Hey, tax me, I'll sell less of my services, which is bad for people who do want to buy it".

  31. Numeric says:

    I'm going to offer myself as a less-elitist example: I'm a middle class engineer, and even *my* current marginal tax rates make it not worth my time to put my valuable math/science tutoring services on the market.

    Makes you wonder about why we tax labor so heavily, doesn't it? Instead, we could tax what used to be called in the tax code "unearned" income–that is, the usual suspect–capital gains, dividends, interest, at a higher rate. But hear the howls if
    that happens!

    Pretty much all the problems leading up to the current financial collapse was caused by too much capital chasing too few investment opportunities, because, by subsidizing investment income, we create too much of it (simply economic theory). It then goes into more and more speculative pursuits, as well as activities such as funding right-wing think tanks, and, thanks to the Supreme Court in Citizens United finding that corporations were people, political campaigns. The next collapse will make this current one look like a picnic and might even lead to fundamental changes, many of them likely to be pretty aversive.

  32. Manoel Galdino says:

    I don't know of any of you, but if Mankiw write less, I'll be better off. And if he keep writing (perhaps due to a tax cut) I'll be worse.
    So, it seems to be that it's not a pareto optimum in any case.

    And in case any economist read this, remember: there is no property right defined about the (negative) externality of taking notice about these silly statements by Mankiw.

    Thanks Andrew Gelman for the subtle and smart criticism, being able to criticise the article and the stupidity of it without engaging in any economic theory of the effect of tax increase.

    Manoel