Taxation curves and poverty traps

Dan Lakeland has been thinking about taxation curves and the poverty trap.

The short story goes as follows: a graduated tax rate reduces the incentive to increase your income. At the high end, this is probably fine: do we really care if Tiger Woods or Bill Gates makes more money? Really it would be fine if they were to follow the example of Greg Mankiw and reduce their working hours and spend more time with their kids. As he wrote:

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.

But at the low end, maybe it’s more of a problem if people have little economic motivation to increase their income. Mankiw displayed this graph:

implicit tax rates 2.png

This picture doesn’t tell the whole story. Despite the flat curve, you’re probably better off making $40,000 then $20,000; for one thing, if you’re at the $40,000 point, it seems like you have a chance to go from there into that happy upward-sloping range.

But, setting practical concerns aside for a moment, Lakeland plays around with some mathematical models of the curves. Perhaps could be useful to some economist somewhere, so I’m linking here and here. Enjoy.

12 thoughts on “Taxation curves and poverty traps

  1. The surprising thing to me, when I did these models, was that a few simple rules that seemed intuitively helpful actually produced the poverty trap, and then in the second case, a simple utility function toy that traded off earnings and slope in a qualitatively correct way produced a curve that I would almost say we should implement immediately, it seems intuitively to be the right type of tax structure if you're going to do redistribution.

    Andrew, you've criticized the concept of utility in the past, so I had hoped you might have something to say on utility functions and when you felt that the concept was or was not useful.

    Probably though, the utility of debating utility during holidays is rapidly diminishing :-)

  2. This topic is worthy of study, but the chart greatly overstates the issue. Mankiw himself says: "Producing this kind of chart correctly is not easy (and I cannot fully vouch for the accuracy of this one) because a variety of different government programs are involved, and their rules are often complex."

    The first problem is to assume that everyone qualifies for such programs and takes advantage of them. Some programs have time limitations, making them irrelevant when talking about poverty traps. It is also the case that many of those who qualify do not take advantage of them for a variety of reasons. It is considered unacceptable to some, others do not understand them (even Mankiw, a smart guy, says they are complex), and it is costly to go to all the offices and fill out forms.

    An additional problem is that analysis at the margin is basically useless here. The decisions that are being made by these households are not, "Should I work one more hour and get $8 more". The decision is whether an unemployed spouse should continue to look for work. Or if one of them should finish college/other training.

    Again, I'm not denying that the point itself is valid. It's just a strong overstatement to claim that low income families have no or little incentive to increase their incomes.

  3. Dan: In brief:

    I think the concept of utility is extremely useful, and I've used it in my own applied work (see my papers on the utility of voting and on radon mitigation or the chapter on decision analysis in BDA). Utility is a model, and it's great.

    My problem is when people think that the utility model can/should explain everything.

    For example, as I've discussed on the blog, I don't think the utility model is particularly useful for explaining uncertainty aversion, seeing as the essence of the "uncertainty aversion" phenomenon is that preferences can depend on how they are framed and how they are set up in terms of probabilities–two things that violate the classical von Neumann axioms in which preferences should only depend on the ultimate outcomes and their total probabilities, not on where these probabilities come from.

    I think it's just sad that utility functions have become a default way of explaining all sorts of psychological processes that don't fit the model so well (requiring the sort of epicyclic adjustments that can make the model more trouble than it's worth). I can respect the general endeavor to take a model and push it as far as you can–to see what tweaks can be done to make it work further than it was originally intended–but, at some point, I think it makes sense to recognize the practical limitations of any mathematical model.

    So, yes, I don't think utilities (or, for that matter, preferences) "exist" in some Platonic sense. But I still think utility theory is great. I think the normal distribution is great, too, even though it can be misused in all sorts of ways!

  4. Andrew, here's an alternative concept for utility in situations where von Neumann axioms fail, what do you think about this concept?

    People make decision approximately according to maximization of utility but in the presence of several kinds of errors:

    1) Errors in the estimation of the welfare that an alternative will bring

    2) Errors in the interpretation of the importance of various probabilities, especially those that are either small, or near 1.

    3) Errors in the importance assigned to the method of stating the problem (1 in 10 will die, vs 90% will be saved type stuff)

    However, even in the presence of these errors, for a given person, there could be a stable "average" which could be considered "true" in the sense that it is stable through time to some extent. Just as there are no families with 2.3 kids the average itself is more descriptive of something around which individual decisions will be clustered.

    In this framework, people's failure to make rational choices that correspond to maximizing the average utility function can still be interpreted in terms of psychologically based random deviation from their time-averaged behavior, but the time averaged behavior might still be something that they "should" strive to maximize if they are going to use a formal decision process.

    I can certainly see utility theory as failing to explain actual decision making adequately, but in the context of formalized decision making, where we seek to make a decision that will affect many people, or we seek to allow one person to make a difficult decision in a way that will lead to the best outcomes for that person on average, the individual's failures to obey utility theory axioms seem less important.

    when decisions are viewed as a stochastic process with natural deviations from some semi-stable long-term or cross-sectional average the utility of utility seems to be much expanded, especially if we can model those deviations (for example the way in which the questions are posed can alter the decision even though they are equivalent logically, and those effects are relatively deterministic).

  5. but, at some point, I think it makes sense to recognize the practical limitations of any mathematical model.

    But hang on. Utility theory isn't the end of the analysis of actual human behaviour. What about, for example, cumulative prospect theory? It gives you a well-defined mathematical model that can, among other things, account for the uncertainty aversion you mention. And I don't think it's particularly epicyclic: it makes two motivated changes to how you calculate "utility", and then can explain many observations that utility theory can't.

  6. Nathan (and Dan): I think prospect theory is great. I just don't like trying to explain uncertainty aversion using a nonlinear utility function of money (which, as I and others have shown repeatedly, makes no sense at all when you try to look at it quantitatively), and I really really don't like having to explain this to people over and over again, people whose technical ability is such that they could've realized in the first place the impossibility of explaining uncerttainty-aversion-at-any-scale using a curving utility function. And I also don't like the term "risk aversion" casually used in a way that blurs three different pheonomena: aversion to risk, aversion to loss, and aversion to uncertainty.

  7. first here
    "Why not just work part time at a coffee shop with wages of 0.4 of median income (about $17.5k/yr?), sign up for tons of government programs, and take home around 0.6 of median income (about $26k dollars/yr?). If you work harder to get double that wage, you still don’t take home anything more!"

    The problem is that if the person does take a higher wage job elsewhere then the coffee store owner still needs someone to do the original job.

    Someone has to be in that low paid job for the business to exist.

    This isn't a personal poverty trap – it's a government subsidy to businesses to maintain a low wage workforce.

  8. You cannot eliminate notch effects altogether as long as you rely on means tested welfare programs (where welfare is very broadly defined). The US system of relatively progressive taxation and means-tested benefits keeps aggregate taxes low, but cannot eliminate these notches — as the cost of health care increases, they will only get worse. However, the alternative, making benefits universal, probably means doubling the tax take and I doubt that we are ready for that.

  9. I would like to challenge the assumption "At the high end, this is probably fine: do we really care if Tiger Woods or Bill Gates makes more money?". Consider a 55-year old professional working hard, with some money put by. It is in the interest of the economy that they continue to work full time, rather than tapering off into part time work or early retirement.

  10. Regarding you statement that "At the high end, this is probably fine", you might want to look at the work of Hal Varian amongst others on optimal taxation and luck versus skill (c.f. Luck and Skill link).

    High taxes at the upper end may work well respective of Bill Gates and Tiger Woods, but may not work well when considering the near-mythical (per Paul Kedrosky, at Myth link amongst others) serial entrepreneur. The issue applies to their abilities to garner enough resources to make starting follow-on ventures easier, and to their incentives for so doing.

  11. I don't really care if Tiger Woods or Bill Gates make more money, and I respect Greg Mankiw's stated choice, under the Obama taxation regime, to spend more time with his kids and less time earning money.

    On the other hand, I certainly think society benefits if I keep working! At this very moment, I'm blogging at $0/hr, but I also am working on a project that I hope will bring in some money. If my personal income were being taxed at a 100% marginal rate, I'd still be working on this project, but I'd be thinking harder about how to channel the funds to avoid taxation, for example by having the money go directly to employees and expenses. On the other hand, I'm thinking about that anyway, so I don't know how different this is.

    P.S. It's funny how this connects to the recent thread on consulting fees.

  12. "I don't really care if Tiger Woods or Bill Gates make more money…."

    I think this statement makes sense for these types of people because on the margin, their real productivity is near zero. They can earn millions more by having signed some paper without altering their activities in any significant way. In other words, the transactions are near zero sum.

    On the other hand, there are productive entrepreneurial people like for example Mark Shuttleworth who has founded several technology based companies including Canonical, the developers of Ubuntu Linux, and if I remember correctly Sipphone/Gizmo project who were bought out recently by Google

    For someone like him to decide that it doesn't make sense to found the next startup he might be considering… that decision could have strong real economic consequences for the people who would have benefited from that companies products.

    when it comes down to it, it seems the difference is between Monopolists (Tiger Woods and Bill Gates who have copyright/trademark/patent protections and therefore a lot of leverage to earn more without increased production) and non monopolists (a developer of a conveniently packaged version of a free software product that competes with every other packager of linux software).

    Many but not all people at the upper end of incomes have government facilitated monopolies and this is one reason why it seems that high marginal tax rates on upper incomes are unproblematic. A better way to deal with that would be to eliminate the governmental monopoly though.

Comments are closed.