Because of data limitations, virtually all studies of the later-generation descendants of immigrants rely on subjective measures of ethnic self-identification rather than arguably more objective measures based on the countries of birth of the respondent and his ancestors. In this context, biases can arise from "ethnic attrition" (e.g., U.S.-born individuals who do not self-identify as Hispanic despite having ancestors who were immigrants from a Spanish-speaking country). Analyzing 2003-2013 data from the Current Population Survey (CPS), this study shows that such ethnic attrition is sizeable and selective for the second- and third-generation populations of key Hispanic and Asian national origin groups. In addition, the results indicate that ethnic attrition generates measurement biases that vary across groups in direction as well as magnitude, and that correcting for these biases is likely to raise the socioeconomic standing of the U.S.-born descendants of Hispanic immigrants relative to their Asian counterparts.