AbstractThis paper applies the theoretical literature on nonparametric bounds on treatment effects to the estimation of how limited English proficiency (LEP) affects wages and employment opportunities for Hispanic workers in the United States. I analyse the identifying power of several weak assumptions on treatment response and selection, and stress the interactions between LEP and education, occupation and immigration status. I show that the combination of two weak but credible assumptions provides informative upper bounds on the returns to language skills for certain subgroups of the population. Adding age at arrival as a monotone instrumental variable also provides informative lower bounds. Copyright © 2005 John Wiley & Sons, Ltd.