This study examines issues of algorithmic fairness in the context of systems that inform tax audit selection by the United States Internal Revenue Service (IRS). While the field of algorithmic fairness has developed primarily around notions of treating like individuals alike, we instead explore the concept of vertical equity—appropriately accounting for relevant differences across individuals—which is a central component of fairness in many public policy settings. Applied to the design of the U.S. individual income tax system, vertical equity relates to the fair allocation of tax and enforcement burdens across taxpayers of different income levels. Through a unique collaboration with the Treasury Department and IRS, we use access to detailed, anonymized individual taxpayer microdata, risk-selected audits, and random audits from 2010-14 to study vertical equity in tax administration. In particular, we assess how the adoption of modern machine learning methods for selecting taxpayer audits may affect vertical equity. Our paper makes four contributions. First, we show how the adoption of more flexible machine learning (classification) methods—as opposed to simpler models—shapes vertical equity by shifting audit burdens from high to middle-income taxpayers. Second, given concerns about high audit rates of low-income taxpayers, we investigate how existing algorithmic fairness techniques would change the audit distribution. We find that such methods can mitigate some disparities across income buckets, but that these come at a steep cost to performance. Third, we show that the choice of whether to treat risk of underreporting as a classification or regression problem is highly consequential. Moving from a classification approach to a regression approach to predict the expected magnitude of underreporting shifts the audit burden substantially toward high income individuals, while increasing revenue. Last, we investigate the role of differential audit cost in shaping the distribution of audits. Audits of lower income taxpayers, for instance, are typically conducted by mail and hence pose much lower cost to the IRS. We show that a narrow focus on return-on-investment can undermine vertical equity. Our results have implications for ongoing policy debates and the design of algorithmic tools across the public sector.