Numerous studies find that U.S.-born Hispanics differ significantly from non-Hispanic whites on important measures of human capital, including health. Nevertheless, almost all studies rely on subjective measures of ethnic self-identification to identify immigrants' U.S.-born descendants. This can lead to bias due to "ethnic attrition," which occurs whenever a U.S.-born descendant of a Hispanic immigrant fails to self-identify as Hispanic. This paper shows that Mexican American ethnic attritors are generally more likely to display health outcomes closer to those of non-Hispanic whites. This biases conventional estimates of Mexican American health away from suggesting patterns of assimilation and convergence with non-Hispanic whites.