We study the relationships between ageist stereotypes - as reflected in the language used in job ads - and age discrimination in hiring, exploiting the text of job ads and differences in callbacks to older and younger job applicants from a resume (correspondence study) field experiment (Neumark, Burn, and Button, 2019). Our analysis uses computational linguistics and machine learning methods to examine, in a field-experiment setting, ageist stereotypes that might underlie age discrimination in hiring. In so doing, we develop methods and a framework for analyzing textual data, highlighting the usefulness of various computer science techniques for empirical economics research. We find evidence that language related to stereotypes of older workers sometimes predicts discrimination against older workers. For men, we find evidence that age stereotypes about all three categories we consider - health, personality, and skill - predict age discrimination, and for women, age stereotypes about personality predict age discrimination. In general, the evidence that age stereotypes predict age discrimination is much stronger for men, and our results for men are quite consistent with the industrial psychology literature on age stereotypes.