Daniel Schaffa (Richmond; Google Scholar) presents The Regressivity of Complexity at UCLA today as part of its Colloquium on Tax Policy and Public Finance hosted by Kirk Stark and Jason Oh: 

This article argues that complexity in the tax system is regressive. The claim, in essence, is that complexity disproportionally creates burdens for those of lesser means and opportunities for those of greater means. Increases in complexity, thus, generally speaking, result in outcomes relatively less favorable for those of lesser means and relatively more favorable for those of greater means.

Intuitive as some may find this claim, it is not a standard conclusion in the tax complexity literature. It faces two related difficulties. The first is a series of counterclaims, including most notably that many of the features of the tax system that add progressivity also add complexity. The second difficulty is that there is no consensus definition of tax complexity, nor an accepted framework with which to analyze tax complexity, making definitive, general claims about tax complexity elusive.

As a starting point, this article notes that if a change to the tax system results in both more complexity and more progressivity, it does not follow that the change in complexity caused the change in progressivity. If the entire change in progressivity were always attributed to the change in complexity, it would necessarily follow that none of the change in progressivity could be attributed to anything else. Complexity would simply be a catch-all. While this is a logically consistent approach, it relies on a vacuous conception of complexity—and one generally inconsistent with the tax policy literature.

The alternative is to partition the effect of a change in the tax system on progressivity into at least two parts, one of which is the part caused by the change in complexity. To analyze the effect of a change in something, one must isolate it. Isolating the effect of complexity (of anything for that matter) requires counterfactual analysis. In the counterfactual, complexity must be varied and everything else must be held constant. If everything else is not held constant, it is not possible to attribute the effect to complexity. Setting up this counterfactual requires a clearly defined model of complexity, and thus the analysis confronts the second difficulty—disagreement about what complexity is.