## Greg Mankiw’s utility function

From 2010:

Greg Mankiw writes (link from Tyler Cowen):

Without any taxes, accepting that editor’s assignment would have yielded my children an extra \$10,000. With taxes, it yields only \$1,000. In effect, once the entire tax system is taken into account, my family’s marginal tax rate is about 90 percent. Is it any wonder that I [Mankiw] turn down most of the money-making opportunities I am offered?

By contrast, without the tax increases advocated by the Obama administration, the numbers would look quite different. I would face a lower income tax rate, a lower Medicare tax rate, and no deduction phaseout or estate tax. Taking that writing assignment would yield my kids about \$2,000. I would have twice the incentive to keep working.

First, the good news

Obama’s tax rates are much lower than Mankiw had anticipated! According to the above quote, his marginal tax rate is currently 80% but threatens to rise to 90%.

But, in October 2008, Mankiw calculated that Obama’s would tax his marginal dollar at 93%. What we’re saying, then, is that Mankiw’s marginal tax rate is currently thirteen percentage points lower than he’d anticipated two years ago. In fact, Mankiw’s stated current marginal tax rate of 80% is three points lower than the tax rate he expected to pay under a McCain administration! And if the proposed new tax laws are introduced, Mankiw’s marginal tax rate of 90% is still three percentage points lower than he’d anticipated, back during the 2008 election campaign. I assume that, for whatever reason, Obama did not follow through on all his tax-raising promises.

To frame the numbers more dramatically: According to Mankiw’s calculations, he is currently keeping almost three times the proportion of his income that he was expecting to keep under the Obama administration (and 18% more than he was expecting to keep under a hypothetical McCain administration). If the new tax plans are put into effect, Mankiw will still keep 43% more of his money than he was expecting to keep, only two years ago. (For those following along at home, the calculations are (1-0.80)/(1-0.93)=2.9, (1-0.80)/(1-0.83)=1.18, and (1-0.90)/(1-0.93)=1.43.)

Given that Mankiw currently gets to keep 20% of his money—rather than the measly 7% he was anticipating—it’s no surprise that he’s still working!

I don’t think Mankiw has fully thought this through.

In which case, the marginal tax rate doesn’t have anything to do with it. Sure, it’s fun to get these little checks—just the other day, I received a bank deposit from the Wall Street Journal for an article they didn’t publish—but let’s not kid ourselves that we’re doing it for the money, or even for our kids (who I think will do just fine without that extra \$1000 in their inheritance).

What Mankiw could do with the money

The last time this came up, a couple of years ago, Mankiw wrote the following in response to Obama’s threatened 93% marginal tax rate:

The bottom line: If you are one of those people out there trying to induce me [Mankiw] 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. They will be poorer when they grow up, but perhaps they will have a few more happy memories.

And here’s what I wrote at the time:

To start with, it does sound like Mankiw’s kids are already well provided for, and, although I’m sure they’d disagree with me on this, it’s not clear that they would benefit from having more money in the bank when their parents are gone.

So, from that point of view, the question is why Mankiw isn’t already spending more time playing with his kids?

I can’t speak for him, but for me, I have to say that it can be fun to work (or even to write blog entries). But, more than that, I feel a sense of obligation to get things done. At some level, getting paid is part of the motivation, but in any particular example I’m not quite sure how it fits in. I do lots of work things that pay me \$0; I think they’re important, so I do them.

When I get extra money, one thing I spend it on is students, assistants, and postdocs. But, for that, the marginal tax rate is nothing close to 90% or even 80%. For Mankiw, I’m not sure; maybe he makes enough from his textbooks that he doesn’t need much of his academic salary and could possibly do more by converting it into postdocs and research assistants. Or maybe he already has more research assistants than he knows what to do with; I don’t know. But his division of waking hours into “working” or “playing with kids” is, I would guess, not very sensitive to the marginal tax rate.

Back to taxes

In writing the above, I’m not trying to suggest that the tax rate be X% or Y% or Z%. I don’t know anything about macroeconomics and have nothing to offer you, the readers, on this topic.

My real point: economics is hard. Greg Mankiw is one of the world’s experts on macroeconomics, but when it comes to a seemingly simple problem in micro—anticipating his personal reactions to taxation—he messes it up, making the classic error of considering only monetary motivations and, bizarrely, suggesting that he’s not out playing with his kids because he’d rather make a thousand bucks writing a newspaper article. It’s not that I think Mankiw is insincere; I think he just underestimates the difficulty of thinking clearly about decision making. (I know much much much less than Mankiw about economics, but I’ve done enough research in decision analysis to know the challenges that arise in analyzing even the simplest decisions.)

The irony is that Mankiw (like so many people, particularly economists!) is conditioned to be hard-headed and think that it’s all about the benjamins, when, really, he’s writing newspaper articles for the completely sane reason that he wants to make the world a better place, and he’d like to do this by presenting cogent arguments that can help convince people that his views are correct. I assume that Mankiw sincerely believes that higher taxes on the rich are a bad thing and will ultimately make everyone less well-off (just as Krugman, say, believes the opposite). But he feels uncomfortable characterizing his actions as idealistic and, as a result, ends up placing his work and child-care decisions into a nearly nonsensical framework of dollars and cents.

P.S. More here.

Update (2014):

All questions of tax policy aside, I think the above story is important, in that it illustrates how a smart guy can get trapped inside a mathematical model and not even realize it, sort of the philosophical equivalent of a person living on a large, interesting island who naively thinks that this island is the entire world.

As I wrote in the comments thread, I don’t think Mankiw is being insincere. My guess is that he’s being sincere but is working within an impoverished model that does not fully account for non-monetary rationales for his work. He can accept that he plays with his kids for non-monetary reasons; why is it so difficult to accept that he writes newspaper columns for nonmonetary reasons also? I’m not saying he should not write more columns; I just think it’s a bit silly to analyze that decision based on his dollar compensation for them, given that this has got to be the most minor reason for writing them.

1. Fernando says:

This is one example where the work being done is an end in itself. Mankiw wants his voice heard and would presumably do it for free.

But rich people often do things as a means to an end, like earning money to endow charity. In this case after tax money matters. Would Bill Gates have built MS if all earnings above 500K had been taxed at 100%?

I suspect many rich people do not amass money for its own sake or for conspicuous consumption. Some do so so they can eradicate poverty or build technology to fly to Mars.

I suspect most entrepreneurs believe they can make much better use of their marginal income than the government.

• Andrew says:

Fernando:

Exactly. I’m not disagreeing with Mankiw’s statement that a change in the tax rate will affect behavior. What bothers me is his implicit characterization of economic motivation seems to be limited to (a) doing it for the money, and (b) playing with the kids. The classic income vs. leisure tradeoff. Mankiw’s own op-eds clearly aren’t for the money, nor do they represent leisure; rather, he (like Bill Gates or that Tesla car guy) has goals other than money and leisure.

• Nate K says:

Other than Amartya Sen I have yet to read an economist who could really think and write well about goals other than money and leisure. I’m not sure why that deficit persists, as it’s a change that could easily be made within the standard framework of rational actors and utility functions. Rationality doesn’t have to imply self-interest. In fact, I don’t see that rationality necessarily has to imply anything about one’s ultimate ends, it only applies to means and intermediate ends (i.e. ends that are also means to other ends). But perhaps it’s this very focus on means rather than ends that has left much of the economics profession without a good way to characterize end goals. Mankiw, like many economists, is comfortable talking about trade-offs and marginal utilities between labor and leisure or other goods, but economists haven’t really spent that much time looking at the non-economic motivations that influence behavior. (And yes, it makes sense that economists would focus on economic motivation. It just becomes a problem when they then attempt to prescribe public policy or talk about the choices individuals make to maximize their utility without fully considering non-economic motives).

• Rahul says:

How does one incorporate non-economic motives in ones models? It seems all so vague & subjective.

• ezra abrams says:

very perceptive
let me add, I think many rich people are rich because they are hyper competitive – thats where they get the drive from.
And being hyper competitive, they need a way to keep score; money is convienent (money serves as a store of value, a medium of exhcange, a unit of account, in economics jargon)

also, being hypercompetitive, they need to outscore the other guy; one guy I know was truly sad cause in his new house he could only afford a 4 car garage, while his more successful college friend could afford a 10 car garage with turntable… it is not how many yachts can you waterski behind, it is Nah nah !! I’ve got more yachts then you do…

2. Ram says:

As Fernando points out, Mankiw’s op-eds may not be the best example of financially motivated output. Still, if financial incentives supplement, rather than substitute for, non-financial incentives, then diminishing financial incentives would reduce rational agents’ output. Putting aside the question of how rationally these decisions are in fact made, the key question is whether financial incentives supplement or crowd out non-financial incentives. An op-ed is the kind of output that is most likely to feature crowding out, but many kinds of output produced by high-income people probably feature less crowding out, since the non-financial motivation for performing these activities is often non-existent (e.g., most people think bankers are a bunch of crooks, so it seems likely that few people would elect to work in finance without being generously compensated). Maybe high income activities are disproportionately unproductive from a social point of view, but surely many activities by high income individuals are both highly productive and unpleasant to undertake without great financial rewards, and high enough marginal tax rates could deter such activities noticeably.

3. Tim says:

My argument with Mankiw’s narrative is that he completely neglects other, perhaps more compelling, economic principles. Perhaps his marginal utility of a single dollar is very low due to his large overall income, but there are equally capable young economists waiting in the wings to be recognized, and for whom a single dollar and the in-print exposure both still have a high marginal utility. Let the publisher do what sports teams do, and recruit new talent when the existing talent is pricing itself out of reach. Mankiw may grump about how the incentives to get him to work are distorted, but that’s because of the position he holds, not the incentives themselves. There are doubtless hundreds of hungry young economists who would be more than happy to write for amounts that Mankiw disdains.

4. MikeM says:

One of my favorite quotes, from a Gigerenzer book:

“One philosopher was struggling to decide whether to stay at Columbia University or to accept a job offer from a rival university. The other advised him: “Just maximize your expected utility—you always write about doing this.” Exasperated, the first philosopher responded: “Come on, this is serious.”

His column is an indictment of how economics is practiced by far too many.

5. jonathan says:

I followed the link to GM’s 2008 marginal rate calculation. It’s bullshit. It’s so much bullshit I have to say it’s nothing more than a political calculation designed to make a case appear as bad as possible.

It’s not a model. It’s an argument. It’s not a logical model but one of an advocate, meaning it’s slanted.

I understand you focused on the prestige rewards of public writing. That could be treated in a rational model as an investment: you write publicly so you get more offers and some of those offers don’t pay enough but some might and maybe some are really great. It’s the same kind of investment model used to analyze education but with a harder to evaluate population.

As to GM’s calculations, why assume corporate tax? Why assume money earned by him personally is invested in a corporation? Why assume it’s taxed at the maximum rate? Why assume money is received from this corporate investment? (That would more sensibly feed into “if I put \$x into y investment” and take dividend yields or index fund returns, etc., but not “money goes into corporation, corporation pays 35% if your guy wins or 25% if my candidate wins”.) Why assume estate tax given estate planning? And so on. Nonsense.

• Andrew says:

Jonathan:

I don’t buy the investment model. I don’t think Mankiw is writing op-eds primarily to raise his market value. I think he’s doing it for the (quite reasonable) goal of affecting policy, because he wants the world to be a better place. He just seems not so comfortable saying that or even thinking it, because it falls outside the standard investment-and-consumption framework. As Aaron Edlin and I (and others) have written in various places, there’s no logical reason why rationality should imply selfishness, but that connection seems to be deeply embedded into the unwritten constitution of economics, to the extent that, even if an economist is himself behaving unselfishly, he hardly has the language to express it.

• Haynes says:

Andrew said: “. . . that connection seems to be deeply embedded into the unwritten constitution of economics . . .”.

That is right. There are utilitarian models with interdependent preferences, and with the welfare of others explicit in them, but they are essentially unsolvable in the same sense as one’s own utility function, so they are essentially ignored.

As one of my colleagues told me when I noted a particularly untenable assumption in his formal analysis: “without that assumption I can’t say anything”, meaning no nice closed form solution. To which I always reply “what makes you think you’re saying anything?”

Mankiw like so many on the right suffers from motivated reasoning. I think this is a form of intellectual dishonesty, and we should be pointing it out.

• Daniel says:

Haynes, you might be interested in an article from Willers et al. in the Journal of Mathematical Sociology:

WILLER, DAVID, ERIC GLADSTONE, und NICK BERIGAN. „Social Values and Social Structure“. The Journal of Mathematical Sociology 37, Nr. 2 (2013): 113–30. doi:10.1080/0022250X.2011.629067.

>The exchanges that individualist, prosocial, and competitive actors will make and the kind
>of negotiations they will carry out in dyads and power structures are predicted here for the
>first time. The predictions are generated by bridging two previously independent streams of
>thought, network exchange theory and social value orientations. In so doing, this article
>shows that formal, mathematical theory and metric predictions are not threatened by using
>multiple actors with contrasting utilities. Results offered here are hypothetical and provide
>a baseline against which empirical studies can be compared. A later paper will compare
>these predictions with experiments now ongoing

The article challenges the view that only simple rationality assumptions can be modeled. It’s at least interesting but it does not seem to have seen a lot of attention so far.

• Alex Godofsky says:

Oh come on. Do you really think Mankiw has not been exposed to this idea before? Rather, he was using the example of him writing for money as a pedagogical tool.

The idea that Mankiw is somehow blind to the objections raised here is ridiculous; every economist is able to make this sort of argument easily.

• Andrew says:

Alex:

Yes, I think that if you were to ask Mankiw if he has goals other than savings, investment, and consumption, he would either readily agree or else define “consumption” so vaguely as to include all possible goals. But I also think that, when he’s not being directly pressed on the issue, he’d spring back to the implicit attitude that the only things that really matter are money and leisure. I think that, in some way, he’s almost embarrassed to admit that he’s writing his columns in an attempt to educate people and improve policy, as this runs counter to the idea of economist as hard-headed scientist who sees to the core of human motivation.

Again, sure, I agree that Mankiw or any other economist is able to make this sort of argument easily, but I also think that in a way he thinks of such an article as cheating: for a classically oriented economist to introduce something other than savings, investment, or consumption into an economic model would be sort of like a physicist arbitrarily introducing a fifth, sixth, seventh . . . force of nature in order to explain some phenomenon, rather than doing the work of modeling reality using the four forces that we know exist.

The difference is that, as I noted above, there’s nothing in economic theory that requires consumption to be the only ultimate motivation (indeed, from the perspective of a political scientist, the point is obvious), so it’s more of an aspect of the culture of economics than anything else.

• Alex Godofsky says:

I think your problem begins and ends right here:

the idea of economist as hard-headed scientist who sees to the core of human motivation.

Economists are very self-aware of this stereotype. I can’t find it right now, but there was a survey where a bunch of economists were asked to respond to the prompt “gifts are a waste because the incur deadweight loss”. A handy majority responded “no, that’s stupid”, and I’m betting the rest are just the sort of people for whom gift-giving really is a pain. Economists don’t talk a lot about alternate motivations because those alternate motivations don’t really alter the predictions of the models much.

In the particular example of Mankiw writing for money, you can choose to model him as mainly deriving non-pecuniary value from the writing – but you can get pretty similar answers by instead modelling him as having a much shallower supply curve for it. And metaphysically there isn’t really a big difference between the two.

• Andrew says:

Alex:

I agree with you that economists are self-aware of this stereotype. Nonetheless, it can be possible to be aware of a problem and to still have it. For example, I am aware that I spend too much time on the internet, I’m aware that this is a problem for me, but the problem still exists.

And indeed the problem is existing in your comment above in that you don’t seem to accept that Mankiw is writing columns not for the money and not for consumption. To imagine that Mankiw is putting in the effort to write these columns because of the money, that just seems ridiculous to me. Of course you might be right but I really really doubt it. Rather, I think that you have a preference for explaining motivations in terms of savings, investment, and consumption (as is indicated by your statement “you can get pretty similar answers by instead modelling him as having a much shallower supply curve for it”—which to me sounds like Ptolemy in action, adding epicycle after epicycle in order to keep the earth at the center of the universe. You can do it but at some point it seems to be missing the point.)

Again, there’s no reason from economic theory why consumption should be the only ultimate motivation, nor is there any requirement that rationality should require selfishness (or that selfishness should be some sort of default explanation, to be departed from only when absolutely necessary). But these ideas are clearly part of the culture of economics, and ultimately I believe they lead to misunderstandings (in this case, Mankiw misunderstanding his own motivations because he is viewing them through the filter of classical econ-culture).

• Fernando says:

I think Mankiw was just trying to make a point with a simple example.

Moreover, some of his critics fall in the analogous trap that just because they are happy doing X for a small wage Y, so they think most people don’t need to earn more than Y. What could possibly be wrong with 90\% marginal taxes? After all, the marginal dollar is worthless right?

I think diminishing marginal utility is way overrated – some people dream big and expensive. Should we tax their dreams just bc ours are small? For someone like Alexander the Great the unit of consumption is an Eurasian landmass (ok, maybe _he_ should have been taxed!).

In fact, if we take utilitarians at their word, we should tax all those content early retirees living in a farm with one horse, and give the money to the big dreamers whom, despite having a big house and yatch, still have a higher utility for marginal resources.

• Alex Godofsky says:

A supply curve in which the good is exchanged for money doesn’t reduce the economics to purely “he writes columns for the money”. His other reasons for writing it can be embedded in the supply curve. If he really likes writing columns, he has a shallower supply curve (lower price); if he likes writing them enough, it could even go negative (he’s willing to pay to publish them). These aren’t Ptolemaic epicycles; we are just gathering a bunch of important but non-modeled variables and bundling them up into one chunk of information, the supply curve, which we take as exogenous.

If you are working on the economics of oil extraction, you might also omit the actual details of geology from your calculations, and just summarize them with a table of values for “known oil reserves profitably extractable at a price of \$X/bbl”, which you populate from some outside source. The geology is obviously in extremely important – maybe the most important thing! – but if it isn’t what you are studying then the above step is reasonable.

• Anon says:

“I think diminishing marginal utility is way overrated – some people dream big and expensive. Should we tax their dreams just bc ours are small? For someone like Alexander the Great the unit of consumption is an Eurasian landmass (ok, maybe _he_ should have been taxed!).

In fact, if we take utilitarians at their word, we should tax all those content early retirees living in a farm with one horse, and give the money to the big dreamers whom, despite having a big house and yatch, still have a higher utility for marginal resources.”

there’s actually no agreement on how to compare your “utility” of x dollars to mine. Even though there are a few technical ways of making utility functions comparable across people in a technical sense, no one accepts them at succeeding at the task of interpersonal utility comparison. I think this is because no one actually believes utility functions to be something that maps onto any real, important quantity.

they’re great for characterizing trade-offs and choice but they’re not an explanation of what goes on under the hood.

• Fernando says:

Yes, I agree.

My point is that many redistributive arguments based on equalizing marginal utility implicitly assume comparability of utilities.

I just take them at their word, and show how this may also justify redistribution from satiated hippies to unsatiated plutocrats.

But yes, the whole enterprise is very dubious. Partly why utilitarianism has received so much criticism.

6. People who work in organizations face external pressures that affect how much they work. I would guess that it’s those forces, more than tax rates, that determine their decisions. Will a trader at Goldman tell them that he’s taking Fridays off because what with the taxes and all, it’s just not worth the effort? Is Mankiw so out of touch with what jobs are really like for most people, even the very well paid?

Only wealthy free-lancers have that kind of autonomy, and I have my doubts as to whether a change of 3-4 percentage points in the income tax has much impact on how much they work. When the Bush tax cuts kicked in, did Mankiw rub his palms together and say, “Boy, now I can take all those consulting gigs I’ve been turning down”?

7. Phil says:

I have a more basic problem with Makiw’s math. He says ” First, I pay the combined income and payroll tax on the dollar earned. Second, I pay the corporate tax rate while the money is invested in a firm. Third, I pay the dividend and capital gains rate as I receive that return. And fourth, I pay the estate tax when I leave what has accumulated to my kids.” He then gives a simple formula that he claims he can use to calculate how much \$1 of his income will increase his kids’ wealth. That formula is wildly wrong. How can I take this guy seriously as an economist?

• Philip says:

Having not looked at Mankiw’s math, I’d also wonder how to square (a) the federal government takes in, what, 20% of GDP? (perhaps he includes all levels…), and (b) the top earners (top 5%? 1%?) control a huge proportion of GDP. Where does all that tax money go that Mankiw and his ilk are paying if they’re paying at an effective 90% tax rate? Not sure this disproves him, but perhaps an interesting check from a different direction.

• Entsophy says:

Phil, he was talking about the marginal tax rate. The rate on tax on an additional dollar earned, not the effective rate on his entire income.

• Phil says:

Enstophy, I know. And his math is wildly wrong!

• Philip says:

Ahhh, poor logic on my part.

But where is the extreme rate increase with income to get to 90% marginal rates if averages are substantially lower? Federal tax rates increase but not that dramatically (climbing from 28% to 35% as income grows to \$400K+); Massachusetts where Mankiw lives has I believe a flat ~5% income tax (12% on investment income?), no variation with income (this seems surprising). Maybe it is the estate tax where the marginal effect hits the strongest in his calculations?

• Philip says:

Just looked at Mankiw’s NYT article, and there is nothing marginal about its analysis of tax rates, unless you consider the different choices he makes with his first vs marginal dollar and how that choice affects his tax rates as ‘marginal’.

By far the biggest impact of the 4 main taxes he cites (federal + medicare, state, corporate, estate) is corporate, which takes the 30 year 1000% increase in his money at 8% growth down to a roughly 300% increase at a roughly 5% post-tax annual growth rate.

The other taxes are straightforward and believable – yes, in fact, with no tax management Mankiw is paying state and federal income tax at about a 50% rate (a bit lower average-wise, but not much if it approaches at least a million/yr) on his income, and the repub vs democratic argument revolves around whether that should be, say, 35% (at one extreme) vs 55% (at the other) – big differences in terms of government income but much more muted in terms of Mankiw incentives vs the 10x effect he cites. He needs rates to hit 80-90% so that small changes have huge impacts on his ‘incentives’.

Note that at this point, any dollars he spends for consumption, no more tax, and his marginal tax rate argument doesn’t apply.

But his marginal effect is to say all new income he’ll save for his kids – hence the huge loss due to lower growth rates on investment from corporate taxes, and then the ~50% hit due to the estate tax.

That’s where his argument gets a little screwy.

If we (a) assume taxes as a percent of GDP are at steady state (with rates unchanging), but also (b) that wealthy people like Mankiw invest the majority of their income at an 8% rate which leads to huge compounding (10x over 30 years), then Mankiw has created an implied world where people like him asymptotically approach 100% ownership of the country and so owe all of the taxes. I mean, if almost every \$1000 you make grows to \$10,000 in 30 years (while GDP growth obviously grows more slowly), and everyone poorer than you invests a smaller share of their income, then you and your ilk own own an increasing share of the country over time and so pay an increasing share of the country’s taxes.

But taxes as a percent of GDP are in steady state, and well below 90%? And yet you claim your marginal rate is 90%? This doesn’t compute. Not perfectly thought out as a comment to a blog post, but clearly there is something terribly off here in him counting lost investment growth as a tax this way.

One other questuon, estate tax related – with all of the huge piles of wealth around, and a 55% estate tax rate, why isn’t the federal government raking in huge sums from the estate tax? My understanding is the bulk of federal tax is income, then corporate… rarely hear about a large contribution from estate taxes. What’s missing in the logic of ‘many big estates->high estate tax rate->should mean large amount of federal income from this’? Maybe it is the perhaps many-year turnover on estates? Or… no one actually pays the effective rate? Or most wealth is held in a way that doesn’t count as an estate? I’m far too young to have thought about any of this.

• Alex Godofsky says:

It doesn’t imply that at all. At the same time as some workers are saving their marginal dollar in a 30-year investment, retirees are drawing down the investments they made 30 years ago. Thus the total capital stock can remain fixed (or fixed relative to the size of the economy) while still providing rates of return higher than the growth rate of the economy. And the 90% MTR also doesn’t lead to taxes collected equaling 90% of GDP because that 90% is collected over 30 years. So you get say 3% of the capital stock is collected each year in taxes.

• Philip says:

Uhh, no. If some people invest a larger percentage of their income in a system at a growth rate higher than the system as a whole, they will gradually own more and more of the system, period. If we divide the world into the Mankiws and the poor people, and both have access to the same 8%/yr investment opportunities in a world growing at a slower rate, and the Mankiws invest more of their income vs. consume it relative to the poor people, the Mankiws will eventually own the world, full stop, independent of drawing down, etc.

Your statement ‘90% MTR also doesn’t lead to taxes collected equaling 90% of GDP because that 90% is collected over 30 years’ has exactly the same issue Mankiw’s argument does. In no year does Mankiw (before he dies) pay substantially above his ~55% tax rate. He just feels that, because he invests his money at 8% the government is screwing him out of a huge compounded return particularly because he’s only going to be investing his marginal dollars, not consuming them.

Note that it isn’t solely the corporate tax that does this in his model – every dollar taken away by federal and state taxes is one which he could have invested.

essentially what mankiw is saying is that anyone who is investing is getting screwed out of a huge chuck of their return because the government taxes the return annually and dampening investment growth (a huge cumulative effect.) That’s by far the biggest loss in his model.

i’m pointing out that at his assumed growth rate the system is not in equilibrium, people like him would be increasing their share of ownership and income (and increasing inequality) at a fairly rapid clip, anyone who doesn’t have a substantial amount of income to invest would over 30 years be left completely behind in wealth-building, and eventually Mankiw and co would be paying 100% of all taxes – but still at the current tax rates. At some point before that their argument must fall apart because they can’t at the same time pay at current rates (well below 90%), also pay the 90% Mankiw calculates due to compounding effects (and don’t make the marginal argument, that’s not at all central to his argument), and own everything. which is where his model ends up.

• Alex Godofsky says:

Philip:

Uhh, no. If some people invest a larger percentage of their income in a system at a growth rate higher than the system as a whole, they will gradually own more and more of the system, period. If we divide the world into the Mankiws and the poor people, and both have access to the same 8%/yr investment opportunities in a world growing at a slower rate, and the Mankiws invest more of their income vs. consume it relative to the poor people, the Mankiws will eventually own the world, full stop, independent of drawing down, etc.

Your premise is the problem. During the years that he is working Mankiw invests a larger portion of his income than the hypothetical non-Mankiw. But after he retires he divests all of it to pay for his retirement! If (for the moment) we pretend population growth and economic growth are 0%, the total capital stock owned by all of the Mankiws doesn’t change, because at the same time the working Mankiws are investing the older, retired Mankiws are divesting in equal amounts. If you add in economic growth and population growth then the total capital stock held by Mankiws grows, but the amount held as a fraction of GDP is constant.

Now, if every Mankiw doesn’t consume all of the wealth and instead leaves some to his children, then you can get an arbitrary increase in wealth, but: the wealth can only keep growing so long as the children don’t actually consume it! So they have big numbers in their bank accounts but those numbers only keep growing until the children (or grandchildren, etc.) actually decide to take advantage of them.

essentially what mankiw is saying is that anyone who is investing is getting screwed out of a huge chuck of their return because the government taxes the return annually and dampening investment growth (a huge cumulative effect.) That’s by far the biggest loss in his model.

Yes, that’s the entire point. That’s the entire point. Repeated taxation of investment income produces very high MTRs.

i’m pointing out that at his assumed growth rate the system is not in equilibrium

Except that it is in equilibrium. The only way for the wealth to grow indefinitely is for both Mankiw and all his descendants to permanently forswear ever actually selling it and using the proceeds to buy stuff (and also commit to forever reinvesting all dividends). That includes using the proceeds to buy “political influence” via campaign contributions, super-PACs, etc.

• Chris G says:

> He then gives a simple formula that he claims he can use to calculate how much \$1 of his income will increase his kids’ wealth. That formula is wildly wrong. How can I take this guy seriously as an economist?

You shouldn’t. Nobody should.

8. Chris G says:

Mankiw has his head so far up his @\$\$ that it’s a wonder he doesn’t suffocate. For example: “Without any taxes, accepting that editor’s assignment would have yielded my children an extra \$10,000. With taxes, it yields only \$1,000.” Right, Greg. And if we went the no tax route then you wouldn’t have any @#\$%ing government-provided roads to drive on or government-provided clean water to drink or a government-provided military to protect your sorry @\$\$ when the 21st century Visigoths close in with their flensing tools to take your stuff and turn you into a pot roast. The cost of a selected path needs to be compared against plausible alternatives. Hey Greg, how much you figure it would cost you out-of-pocket for roads, clean water, protection, and all the other benefits you currently receive from the govt because you and I pay our taxes? You really think you’d have \$10k to hand over to your kids at the end of 30 years if you had to pay for those things yourself? (If so then you’re delusional.)

• Anonymous says:

What a silly rant. Mankiw is not trying to abolish taxes. Just questioning what is optimal.

• Chris G says:

> What a silly rant. Mankiw is not trying to abolish taxes. Just questioning what is optimal.

Work on your reading comprehension. The premise of Mankiw’s argument – numerical and otherwise – is that the taxes he pays result in zero benefit to him. Review his calculations. That’s exactly what he did. It should be a joke but it appears he meant his argument to be taken seriously. What his column reveals is that he lacks the basic skills necessary to make a plausible optimality calculation. It boggles the mind that someone with that level of experience could do something so ridiculous. But there you have it in black and white. As a friend of mine likes to say, “Experience doesn’t mean jack if you’ve been doing it wrong all along.”

• Anonymous says:

No value to him – at the margin.

I think you are the one having difficulties.

I’m not an accountant, but two seconds’ viewing of GM’s calculation in the provided link raises suspicions. My sense is that most common uses of the term “marginal tax rate” are in reference to the current tax year. Not, as GM argues, according to some compounding scheme that goes out to end-of-life.

https://en.wikipedia.org/wiki/Tax_rate#Marginal

As the wiki article points out, the Americans who truly face strong disincentives to work are those at the opposite end of the income curve, due to maladaptive government income support.

10. zbicyclist says:

“making the classic error of considering only monetary motivations”

I guess I’m a case in point. I retired from a high paying job because I had hit the magic \$ I wanted to save in order to retire, and now take care of my 4 month old grandson 3 days a week, teach as an adjunct (not much money there) do a bit of consulting for my former employer, and go on some bike trips. My wife tutors reading part-time.

Economically, it would have made more sense for me to keep working and pay to put my grandson in day care. But WHAT WAS I MAKING THE MONEY FOR, ANYWAY? To provide for my family. I did that well enough, and now can be of service other ways.

• Lao Shan Ren says:

That’s pretty much my experience as well. We collected the magic \$ needed to retire in comfort for the rest of our lives, and leave something to children and charity. Like you I took an adjunct position in another part of the country (moving to a farm that had been in the family for a half a century), which as you say doesn’t pay much but allows a lot of contact teaching young people. My wife was finally able to scratch a long-standing itch to own a horse and she rides it in the countryside near our home. The only thing missing is that the grandchildren are on the other side of the country so we can’t babysit them. :-(

As you say, I could have kept working and stashing money away, but from a marginal utility point of view, those extra dollars are worth a lot less than the rewards we got from doing what we did.

Which seems to me to trash Mankiw’s notions…he’s measuring the utility of dollars as if the marginal utility of the last dollar is the same as that of the first (he hasn’t offered his utility function for money, everything in terms of benefits that he talks about is linear on his money scale), since he only talks about tax rates, not the effective tax rate on marginal utility. Basically he’s comparing apples on the money side and oranges on the leisure side.

Or so it seems to me.

11. My Father and others of his generation and acquaintance took early retirement from school teaching jobs in the UK saying that the difference between pension and salary was so small they would otherwise have been working for almost nothing. They weren’t making a point about tax rates – they’re quite left wing. There’s been a lot of talk about the impact of welfare traps and high marginal tax rates on low earners on employment. Maybe people should also be thinking about the impact of pension arrangements – and whether the economy is losing experienced workers who could manage or mentor younger workers or dead weights whose bosses would rather get rid of them amicably than try to get worthwhile work out of them.

12. Eli Rabett says:

As said by one prize (not Nobel) winner about another (not Nobel)

It’s OK to be wrong, and Dick is a smart person, but most people don’t really understand that one way of using your intelligence is to spin ever more clever ways of deceiving yourself, ever more clever ways of being wrong, and that’s OK because if you are wrong in an interesting way that advances the science, I think it’s great to be wrong and he has made a career of being wrong in interesting ways.

• Chris G says:

>… if you are wrong in an interesting way that advances the science…

Eli,

While I agree with that statement 100% I don’t believe it applies to Mankiw. He’s not a scientist. Say what you will about economics as a field of study, Mankiw is not engaged in a scientific pursuit or otherwise interested in uncovering the truth. He has an agenda. He’s acting politically not as an intellectual who modifies his beliefs based on what he discovers about how the world works.

The most charitable characterization I can manage of Mankiw’s calculation and the philosophy that underlies it is that it is folly rather than error:
“Follies are not errors. Errors are mistakes; they are policies or positions people adopt that can be abandoned when they’ve proved to be self-defeating or to have unfortunate or even disastrous unintended consequences. A folly is a policy so thoroughly associated with the groups that support it that they can’t abandon the policy without destroying themselves.”
-Prof. John Gray of the London School of Economics. (His subject had nothing to do with Greg Mankiw but the statement is broadly applicable.)

13. Wonks Anonymous says:

I recall Mankiw has explicitly written on his blog that, in addition to monetary compensation, he gets enjoyment out of annoying people with his writing.

14. ezra abrams says:

Greg Mankiw is like D Brooks – if he wern’t writing for the NEW YORK TIMES, no one would know who he was

So, why do “we” spend so much time on the Times (eg, the blogoplosion over Kristof’s piece on lack of public intellectuals, see crooked timber)
Is it because the Times is actually that important, or is it that “we” need something to validate our blogging as important, so “we” elevate the TIMES to status of National NewsPaper, and therefore our time spent critoblogging is worth while ?

• Andrew says:

Ezra:

No, Mankiw is a well-respected economics researcher also is well known for a bestselling textbook. Sort of like me! Or like Paul Krugman. David Brooks is not the right analogy here.

15. Phil says:

Here’s one major issue: Mankiw treats his investment in a company as if it is subject to corporate income tax!

Here’s another major issue: Makiw assumes the company pays at the nominal corporate income tax rate!

I can’t figure out which of those is more ridiculous.

• Anonymous says:

On your first point: Look up double taxation. Investment generates income. Company pays tax on it. Then distributes net earnings as dividends. Then investor pays tax on dividends.

On point two, the vast majority of companies are not tax avoiding multinationals.

• Phil says:

On point 1, there are many different investment vehicles and you can probably find some for which the corporate income tax is relevant, but that is not the norm. If you buy a typical mutual fund, the most relevant issue is your capital gains rate, not the putative corporate tax rate.

On point 2: “Earlier this year, the Government Accountability Office, a federal agency, examined corporate tax returns to determine the taxes corporations actually pay. It found that in 2010, profitable corporations based in the United States had an effective federal tax rate of 13 percent on their worldwide income, 17 percent including state and local taxes.” That’s from here. That’s 13 percent as opposed to the 35 percent that Mankiw posits.

There may be some way Mankiw could pay those high rates if he wanted to, but he’d have to work hard at it.

• Anonymous says:

Phil:

On Point 1: You are thinking exactly how the tax man wants you to think. The investment vehicle is 100% irrelevant. No matter how you invest, the money is used to generate income. A share of that income belongs to you as an investor. What matters is whether your business is registered as a sole proprietorship, an LLC, or a Corporation. (Why should the choice of incorporation have any bearing on taxation?) Your logic is like people who say that health care in Europe is free because they don’t pay when they visit the doctor.

On point 2: If you read the entire article you cited:”The independent economist Martin A. Sullivan concluded that the truth is somewhere in between, with the effective corporate tax rate in the mid to upper 20 percent range.” Moreover, the distribution of corporate income, like personal income, is highly skewed. Those aggregate numbers are not very meaningful. Most super rich actually pay low tax rates (though still a big proportion of total tax revenue). Just go ask any small/medium corporation owner how much they pay.

• Phil says:

Anonymous,
Let me guess, you’re a trained economist? If so, you have to realize that you live in a different world from the rest of us. Your Point 1 might be true in EconWorld, but not here in the real world.

Point 2, Mankiw says money he invests would be taxed at 35%, I point out that’s way too high, and you say No, Mankiw is right because the actual number is 20%? WTF?

• Anonymous says:

Phil

I suppose you are not a business owner. If you were you would be familiar with how corporate taxes skew the choice of legal structure, hiring etc.. Business owners are a minority in this country but picture a country without them. Then ask who is in an alternate universe.

On pint 2 I’ll spell it out again: (1) the aggregate figure is ” in the mid to upper 20 percent range”; (2) this aggregate figure is not very informative, as there is a huge skew in corporate income and tax incidence. For the _median_ business the tax rate is likely much closer to what Mankiw has in mind.

• Phil says:

Nobody is disputing that taxes affect legal structure, hiring, etc. What I am disputing is that a dollar of investment is taxed at the nominal corporate tax rate no matter how it is invested. That simply isn’t true.

On point 2 I’ll spell it out again: Even if I granted Mankiw point 1 (which I don’t), Mankiw claims, and uses in his calculation, the assumption that corporations actually pay the nominal corporate tax rate of 35%. And that isn’t true, or even close to true. Even if it’s 25%, that’s still not 35%.

And of course he doesn’t have to invest in the average or median company if he doesn’t want to. Apple paid corporate tax of about 10% last year; Exxon-Mobil paid about 13%.

Mankiw’s math is very wrong, and if you get the same answer he does then your math is wrong too!

• Anonymous says:

Exxon and Apple are hardly median companies.

I cannot reason with unreasonable men.

• Chris G says:

@Anonymous wrote: Exxon and Apple are hardly median companies.

Let’s see Mankiw get 8% average post-inflation return (over 30 years!) from median companies. Now that would impress me. Actually, no, I’d be impressed by his broker.

• Phil says:

The key point to me is that Mankiw’s numbers are way way off. I just can’t take him seriously.

I’m not sure what Anonymous is on about, calling me unreasonable for suggesting that Mankiw isn’t required to invest in “median” companies and that even if he were the median company pays a lot less than 35% tax. Don’t shoot the messenger, man!

• Anonymous says:

Phil:

Any savings you think you might get by investing in a large multinational that pays less tax is already priced in. That is why only the super rich find it worthwhile to invest in things like tax exempt municipal bonds. Its called arbitrage.

Is Mankiw painting a worse case scenario? Probably, he wants to make a point. But considering a median entrepreneur in a median business, I would think his back envelope numbers are close enough. He is not stupid, nor a manipulator.

• Phil says:

Mankiw is not stupid but he is definitely a manipulator. And I don’t agree that exaggerating the corporate tax rate by 25 to 50% is “close enough” when it has such a big effect on his numbers. And I don’t agree that a dollar of investment is, through the magic of perfectly informed rational actors in a frictionless market, implicitly taxed at the corporate income tax rate. When I say “I don’t agree…” in both of those sentences, what I mean is “It’s ridiculous to claim that…”

• Anonymous says:

BTW when you buy a mutual fund the most important consideration should be the management fee. Most don’t beat the index. And those that do are hard to spot ex ante.

• Andrew says:

I know what you mean, but I’m still worried there’ll be a stock market crash and I’ll lose another pile of money.

• Anonymous says:

You are risk averse.

I’ll happily borrow all your liquid assets (\$400,000?) for 10 years at 4%. I am younger than you, and will put up my current and future income, and assets, as collateral.

I’ll invest it in a diversified total stock market index portfolio at 0.3% fee. I’ll bear the risk, and keep the difference between the fund returns and your 4%.

Deal?

(This is not much different than getting a mortgage but unfortunately in the present system we can borrow against unproductive bricks, not against the whole US economy. Beats me.)

16. numeric says:

Without revisiting what I wrote before, my back of the envelope calculation on Mankiw’s marginal tax calculations indicated that (by his reasoning) his marginal tax rate would be over 100% with even a relative modest increase in federal tax rates. As far as his claim that massive rewards to the well-off are necessary or desirable for the functioning of society, I refer people to the latest UN report (http://www.theguardian.com/environment/earth-insight/2014/mar/14/nasa-civilisation-irreversible-collapse-study-scientists) that concludes economic stratification of the type seen a necessary by Mankiw is likely to lead to economic collapse. Any historians out there will remember that Gibbons, in the 18th century, noted that the Roman legions of the 3rd century were far inferior in quality to those of the Republic (which conquered the Mediterranean), due to the evisceration of the “middle class” of Latin farmers on the Italian peninsula and their replacement with slaves/sharecroppers/itinerants. Or recent research

The Son Also Rises:
Surnames and the History of Social Mobility Gregory Clark With Neil Cummins, Yu Hao
and Daniel Diaz Vidal

which shows it takes 10 to 15 generations for privilege to regress to the mean.

• Anonymous says:

Numeric.

On the Romans and inequality you are comparing apples and oranges. One thing is inequality in the US, quite another a rentier state like imperial Rome (or modern oil states). If anything it illustrates how living of off rents is impoverishing. I suspect if the Romans had discovered oil, and put all their middle classes on welfare, their legions would also have been inferior. The manner in which the inequality arises matters.

As for social mobility, your use of the word “privilege” opens up a Pandora’s box that you may want to unpack.

• numeric says:

Imperial Rome and Republican Rome were two separate animals. Gibbon’s point was that Republican Rome was not “rentier” to nearly the same degree that Imperial Rome was, and that the Italian small farmer simply did not exist due to the agglomeration of farms into wealthy estates. Consider that at the battle of Philippi (which marked the effective end of the Roman Republic), over 40 legions were engaged, whereas in the early third century the empire could barely put 50 legions on the entire frontier (granted, with an equal number of auxiliaries, but these were of doubtful fighting capacity). Given that the Roman Republic was able to fight nearly a century of civil wars while at the same time conquering the Mediterranean (and beyond) indicates that there was a large supply of motivated and able soldiers (unless one adopts a top-down view of history and assumes that there were “men” in those days and the leaders from the 3rd century on were much less capable).

As for your metaphor regarding Pandora’s box, one would think one would want to close it, rather than unpack it. Inherited advantage is a better description of what is happening, and there is a hysteresis associated with whatever you call it that is common to many cultures. In fact, one of the reasons the US used to be relatively egalitarian is that there simply weren’t that many generations here (population of 300,000 Europeans in 1700, about 10-15 generations ago–an ecological niche just waiting to expand–think Cambrian explosion). Our current economic policies seem designed to negate this relative equality, though (Krugman’s NYTimes column today–60% of the top 10 wealthy individuals inherited their fortunes).

17. Eli Rabett says:

Ok, so Eli went and read the damn thing more carefully. Manikiw gets a thousand bucks from the WSJ on which he pays \$477 in taxes leaving \$523. That is pretty much in line with what everyone pays in civilized countries, about 50% in all taxes.

His entire tantrum assumes he can invest the untaxed \$1000 @ 8% and if the companies he invested in were not taxed he would grow the \$1000 to \$10,000 which his kids would inherit tax free. Friend Manikiw forgets to apply a discount rate to that 8%, in other words he assumes no inflation in his tax free little heaven. That pretty much tells you that he is dealing seconds. Then again 8% above inflation is a huge return compounded over 20 or thirty years, so you know Manikiw is dissembling.

Of course, he could invest the money after taxes in a triple tax free bond or a trip to Bermuda and put it in tax free instruments, etc. Of course the inheritance tax limit is \$5 million for an individual, \$10 million for a couple and even if Greg and his wife have \$10 million (how about you Andrew?) that means that the effective rate on his estate is a lot lower than the \$10K or whatever he grows the WSJ money into.

He is simply dissembling.

• numeric says:

Thanks for going through this (I don’t have the patience for this type of stuff anymore). Tell me, though, does he actually go above 100% in his marginal tax rate as my back-of-the-envelope calculation indicated? That’s another sure sign of bogusness.

Incidentally, your comment on his dissembling would seem to indicate that, unlike some other commentators in this blog who refuse to assign pejorative character traits to Mankiw’s writings. Existence determines consciousness and people who live up to this reductionist paradigm of humanity deserve opprobrium.

18. Ijlal says:

Next year’s World Development Report carries the subtitle “Mind and Culture.” Further to the point about the centrality of selfish rationality to economics, here’s how it is introduced on the World Bank’s website:

“Economists have long held that the best way to predict human behavior is to assume that people are rational, selfish, and more or less identical. New research shows that this is not necessarily the case.”
http://econ.worldbank.org/WBSITE/EXTERNAL/EXTDEC/EXTRESEARCH/EXTWDRS/EXTNWDR2013/0,,contentMDK:23488439~pagePK:8261309~piPK:8258028~theSitePK:8258025,00.html

The idea that this is new or even an insight just makes me laugh!

19. […] in public health, or even playing with my kids (which, as you may recall, is Greg Mankiw’s preferred leisure option when taxes get so high that he’s no longer motivated to write newspaper […]