Do severe economic downturns increase intergenerational economic mobility by breaking links between generations, or do they instead reduce mobility by limiting opportunity for the young? To answer this question, I estimate rates of intergenerational mobility during the Great Depression for individuals in American cities that experienced downturns of varying severity. I create two new historical samples, digitizing and transcribing archival data on individual earnings and linking fathers to sons before and after the Depression. To build these longitudinal samples, I develop a new machine learning approach to census matching, which enables me to link individuals accurately and efficiently between censuses in the absence of unique identification numbers. I find that the Great Depression lowered intergenerational mobility for sons growing up in cities hit by large downturns. These results are not driven by place-specific mobility differences: for the generation before the Depression, mobility between 1900 and 1920 is unrelated to future downturn intensity. Differential directed migration is a key mechanism to explain my results. Although sons fled distressed cities at similar rates, the sons of richer fathers migrated to locations that had suffered less severe Depression effects. The differences in rates of intergenerational mobility for sons in the most and least Depression-affected cities are comparable to the differences between the United States and Sweden today.