The growing availability of data linking students to classroom teachers has made it possible to estimate the contribution teachers make to student achievement. While there is a growing consensus that teacher quality is important and current evaluation systems are inadequate, many have expressed concerns over the use of value-added measures (VAMs) in high-stakes personnel decisions. We conduct a new test of the validity of teacher value-added models. We apply traditionally estimated VAM models to an outcome that teachers cannot plausibly have a causal effect on: student height. Any estimated "effect" of teachers on height should raise questions about the extent to which VAMs cleanly distinguish between effective and ineffective teachers. We also examine two potential interpretations for effects of teachers on height. The first is that these effects reflect bias, sorting to teachers on the basis of unobserved factors related to height (that may or may not be related to achievement). The second is that these effects reflect measurement error or other forms of random "noise." Both have implications for the use of VAMs in practice. The findings raise important questions about the extent to which VAMs cleanly distinguish between effective and ineffective teachers. This is especially important when personnel and compensation decisions are tied to individual VAM estimates.