Evan Soltas
Jan 25, 2012

Why 70% Makes No Sense

A response to Brad DeLong on the top marginal tax rate

In one of his own posts he deems "worth reading"--one is tempted to ask what he considers the remainder--UC Berkeley professor Brad DeLong discusses work by economists Peter Diamond and Emanuel Saez. The Diamond-Saez study purports to show that a 70 percent top marginal income tax rate would be optimal policy in the United States, and they derive this result from modeling utility with diminishing returns on marginal increases and income in combination with a "Laffer curve" model which posits that the maximum revenue on a tax occurs at a value 0 < t < 100, where t is the tax rate, because as t -> 100, the incentive for tax avoidance rises. 

The problem with their work is that they've worked from a model that is oversimplified, in that it leaves out important considerations--namely, as Scott Sumner points out, capital gains.

But allow me to add that the study is now out of date in terms of academic literature. It fails to include findings from Benjamin Lockwood and Matthew Weinzierl which demonstrate that, considering heterogenous preferences, a term which we will explain momentarily, the optimal top marginal income tax rate falls dramatically.

What are "heterogenous preferences"? In the Lockwood-Weinzierl model, it means that, in short, people placing different relative marginal values on increases in income versus increases in leisure.

They matter because in a conventional Mirrleesian model, which assumes total homogenous preferences, the only explanations for differences in income are luck and differences of ability. This explains the Diamond-Saez finding, as Lockwood and Weinzierl argued, that the United States' marginal income tax rate structure is insufficiently progressive and redistributive to maximize social welfare.

Enter preference heterogeneity, and the differences in income can be explained by differences in preferences as well as luck and differences of ability (i.e. the three factors can receive different weights as explanatory variables). Obviously, preference heterogeneity means that the utility calculations aren't as simple as before, but because we know now that the distribution is by some measure closer to optimal then a random question of luck and ability, the economic case for redistribution is meaningfully weakened.

The results from theory are clear: taking preferences into account lowers optimal redistribution for themost plausible specifcations of the model. We start by showing that, if preferences and ability are the same for all individuals with a given income (as in the standard model), attributing more of the variationin incomes across individuals to preferences rather than ability lowers the optimal linear tax rate. Then, we show that if preferences and ability vary conditional on income, preference heterogeneity is even more likely to reduce optimal redistribution relative to standard results.
There is so much more in this fascinating study, too. A gem.