• Okun’s leaky-bucket experiment

    Okun offers a neat hypothetical to help locate one’s equity-efficiency boundary. He wrote this in 1975, so all dollar amounts are far below what would make sense today. They’re 1974 dollars. In brackets, I’ve inflated them to 2009 dollars (a dollar in 1974 is worth $4.30 today). This is not the same things as recomputing the boundaries and average incomes of the bottom 20 percent and top 5 percent of the income distribution. Still, I think the exercise is worth considering.

    [C]onsider the American families who make up the bottom 20 percent of the income distribution. Their after-tax incomes in 1974 were less than $7,000 [$30,100], averaging about $5,000 [$21,500]. Now consider the top 5 percent of families in the income pyramid; they had after-tax incomes ranging upward from about $28,000 [$120,400], and averaging about $45,000 [$193,500]. A proposal is made to levy an added tax averaging $4,000 [$17,200] (about 9 percent) on the income of the affluent families in an effort to aid the low-income families. Since the low-income group I selected has four times as many families as the affluent group, that should, in principle, finance a $1,000 [$4,300] grant for the average low-income family. However, the program has an unsolved technological problem: the money must be carried from the rich to the poor in a leaky bucket. Some of it will simply disappear in transit, so the poor will not receive all the money that is taken from the rich. The average poor family will get less than $1,000 [$4,300], while the average rich family gives up $4,000 [$17,200]. […]

    I want you to decide how much leakage you would accept and still support [this plan]. Suppose 10 percent leaks out; that would leave $900 [$3,870] for the average poor family instead of the potential $1,000 [$4,300]. Should society still make the switch? If 50 percent leaks out? 75 percent? […] Where would you draw the line? Your answer cannot be right or wrong. […]

    Of course, the leak represents an inefficiency. The inefficiencies of real-world redistribution include the adverse effects on the economic incentives of the rich and the poor, and the administrative costs of tax-collection and transfer programs.

    A more stark thought experiment trading equity and efficiency is hard to imagine. Think about it. (Okun says he’d accept up to 60 percent leakage.)




    • I like this thought experiment as well, though I’d make a small addition:

      Let’s say the people who do the actual carrying figure out a way to capture the leakage, and also realize that they can influence the magnitude of the leakage. We notice that certain bucket-carriers seem to be sloshing the buckets around as they walk, exacerbating the leakage for their own benefit, though not necessarily on purpose. What should be the proper response if we are unable to effectively ascertain the inherent leakage vs. the moral hazard leakage?

    • Interesting that next to this article in my reader is one from Health Populi

      The headline says it all: Lost productivity represents half of all health costs.
      The “leaky bucket” analogy assumes that there is no gain from providing health care equitably. If half of all health costs are due to lost productivity, then there could be a net gain from providing health care to all.

    • I don’t believe this situation accurately portrays the gains/losses from redistribution. Yes, the leakage represents inefficiency, but it’s hard to evaluate it since it’s difficult to see who is the loser of the inefficiency. The rich person loses $4,000 no matter what, and the poor person will gain as long as leakage<100%. Since less leakage benefits the poor person, it implies that the inefficiency hurts only the poor.

      Imagining the two players interacting with the rest of the economy enriches the illustration.

      Also, I believe choosing between a world where everyone earns $10,000 and a world where some make $5,000; most make $25,000; and some make $150,000 is a more stark thought experiment representing the trade-offs.

    • (Okun says he’d accept up to 60 percent leakage.)

      We give SS in order to help the poor but something like 90% of it goes to the rich and middle class, same with Medicare and support for schools. That is why I am for radical reform of those programs. I think that we could transfer plenty of money to the poor and slash taxes.

    • 60% seems very high to me, but let’s think about what happens to that money. In the cases I can imagine, the money goes to program administration, which is to say, government employees and contractors. So, the remaining 40% doesn’t go to the bottom fifth of the income scale. Instead it goes to the people mostly grouped in the middle third quintile. We are still redistributing from the wealthiest 20%, but a good chunk of it goes to the middle class along the way to the poor. As long as the program administrators are doing something valuable in how they direct the money (avoid fraud, make sure it is given to people in a way that makes it more useful), that works for me. Otherwise, not.

      But this raises the obvious next question: how much money actually leaks out in program administration costs for the major social programs for the poor? Medicaid, Food Stamps and many others appear to have much lower leakage than 40%. I would be surprised if either is above 10%.

      Sorry if he answers these questions. I haven’t read the book.

    • @floccina,

      Social Security is not just for the poor. It is for everyone. In fact, it is financed by wages so those who earn more (up to a limit) get more out of it in payments. At it’s heart, it is a middle class program to reduce risk in retirement (from bad retirement investments, being swindled, etc.) and mitigate the human tendency to under-invest when left to one’s own devices (behavioral economics reinforces what we all knew about how people tend to overweight the short term against the long term good).

      Also, the administrative efficiency of Social Security is extremely high. There are very few leaks in that bucket. In fact, your comment makes so little sense to me that maybe I misinterpreted “SS.” Are you talking about a different program?

    • I think the example provides a good way to illusrate the problem. Most of the inefficiency that results from social secutiry is a result of the recipients changing their behaviour. When Okun said he would accept a leakage of around 60%, I would he had in mind that the proportion of income lost by the richest 5% should be in line with the proportion of income gained by the lowest 20%. If a rich person loses 10% of their income, a poorer person should see their incomes rise by the same 10%. In the 1970’s some experiments were undertaken on these kinds of programs. They found that for every dollar transferred from the rich to the poor approximately 50c was lost to inefficiency.

      Relatively the poor could be seen to benefit more from this income as their proportion of income which is disposable (i.e. not lost on fixed costs such as housing, utilities, taxes etc.) is lower than for those on higher incomes. While alot of money may be lost to inefficiency, you can see that gains in the standard of living for these people may outweigh the losses incurred. There are also ways you can reduce the inefficiency, for example by limiting how long people can stay on welfare. Whether programs such as state provided medical care suffer these kinds of problems is far more ambiguous. If those lacking medical insurance were suddenly allowed to see doctors for free would their behaviour change in such a way to incur inefficiency? I would think not.