This chapter focuses on the 5% Public Use Microdata Samples of the 1980 and 1990 US Censuses of Population and Housing to study the Asian underemployment. The rankings of the ethnic groups by education in 1980 show three distinct clusters: Hispanics, Vietnamese, and blacks at the one extreme; whites, Koreans, and Japanese in the middle group; and Filipinos, Chinese, and Indians, at the other extreme. Simple averaging of ranks across education, occupation, and nativity for 1980 show that Vietnamese, Japanese or Filipinos, and Chinese are the candidates for multivariate modeling. Sample selection occurs when part of a population cannot be studied because of exclusion based on criteria inherent in the choice of the dependent variable. Education is represented in the sample selection model by the HSPLUS variable. The chapter considers four levels of underemployment. These are the unemployed, the underemployed based on low hours, the underemployed based on low income, and the underemployed based on job mismatch.