# Calculating the leak in Okun’s bucket

###### Large blue bucket with money spilling by 350jb, veer.com

Forty years ago, Arthur Okun proposed an interesting thought experiment in his book Equality and Efficiency: The Big Trade-Off. He imagined the redistribution of income like moving water in a bucket with holes in it, and then posed this question: How much water would you be willing to lose as the water moved from the rich to the poor? In other words, how leaky of a bucket would you tolerate before you would stop redistributing income?

Like most thought experiments, the leaky bucket is supposed to spark thinking rather than be a specific test of policy. That was until a recent paper came up with a way of calculating how leaky our current buckets are.

The paper, by Harvard University economist Nathaniel Hendren, tries to figure out how society values an additional dollar going to a specific person based on the causal effects of policies. By looking at these causal effects, Hendren bridges a bit of a divide in economics between those who rely on a theoretical approach verses those who are driven more by empiricism. Hendren is able to provide a theoretical framework that lets economists use empirical results from analyses of specific policies. In particular, Hendren looks at how policy changes affect the U.S. federal budget.

You might think that raising \$1 in government revenue simply requires taking \$1 from a person through taxes. But that’s not true—the person from whom you take the \$1 reacts to the change in their income, resulting in unintended consequences. A person who has their taxes raised, for example, might work less because their incentive to work—has declined. Getting \$1 in government revenue requires taking more than \$1 from the person being taxed as they are making less income. This means the cost of raising \$1 in additional tax revenue is greater than \$1.  At the same time, if less than 100 percent of the value of a program goes to the beneficiary then providing \$1 of benefit increases their income by less than \$1.

Hendren crunches the numbers on policy changes such as tax increases on those at the top of the income ladder; expansions in the Earned Income Tax Credit, or EITC; the Supplemental Nutrition Assistance Program (formerly known as food stamps); and Section 8 housing vouchers. This model, based on previous empirical research on the causal responses to these programs, gives a number that shows the social value of government money going to each policy. The higher the number, the more money society is willing to take from that person to raise an additional dollar of revenue.

These numbers are interesting on their own, but the really interesting results come when the marginal values of these programs are used to estimate the trade-off between each other. Hendren looks specifically at the hypothetical of increasing top marginal tax rates to finance a larger EITC payment. He figures that increased distribution in this case is “desirable” if we prefer for \$0.44 or \$0.66 (depending upon which research estimate is used) to go to an EITC recipient over \$1.00 going to a person making at least \$400,000. To put this in Okun’s terms, are we okay with \$0.56 or \$0.34 leaking out of the bucket in this case?

Of course, redistribution is just one way to reduce our current levels of income inequality. Growth that flows more to those at the middle and low ends of the income ladder would reduce the need for redistribution through taxes and transfers. On the other hand, policies that affect the distribution of income before taxes and transfers but have little efficiency costs might be used more often.

Hendren’s work depends on the underlying estimates of the causal effects from empirical economics papers, so more of that research will help pin down the specific numbers to think about. This would help clarify our thinking even more about the potential trade-offs.

Nick Bunker

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