Knowledge producers conducting research on a particular set of questions may respond to supply and demand shocks by shifting resources to a different set of questions. Cognitive mobility measures the transition from one location to another in idea space. We examine the cognitive mobility flows unleashed by the influx of Soviet mathematicians into the United States after the collapse of the Soviet Union. The data reveal that American mathematicians moved away from fields that received large numbers of Soviet émigrés. Diminishing returns in specific research areas, rather than beneficial human capital spillovers, dominated the cognitive mobility decisions of knowledge producers.

It has been difficult to open up the black box of knowledge production. We use unique international data on the publications, citations, and affiliations of mathematicians to examine the impact of a large, post-1992 influx of Soviet mathematicians on the productivity of their U.S. counterparts. We find a negative productivity effect on those mathematicians whose research overlapped with that of the Soviets. We also document an increased mobility rate (to lower quality institutions and out of active publishing) and a reduced likelihood of producing “home run” papers. Although the total product of the preexisting American mathematicians shrank, the Soviet contribution to American mathematics filled in the gap. However, there is no evidence that the Soviets greatly increased the size of the “mathematics pie.” Finally, we find that there are significant international differences in the productivity effects of the collapse of the Soviet Union, and these international differences can be explained by both differences in the size of the émigré flow into the various countries and in how connected each country is to the global market for mathematical publications.

Many economists believe knowledge production generates positive spillovers among knowledge producers. The available evidence, however, is mixed. We argue that spillovers can exist along three dimensions: idea, geographic, and collaboration space. To isolate the key channel through which knowledge spills over, we use a unique data set to examine the impact of a large post-1992 exodus of Soviet mathematicians on the output of the nonémigrés. Although the data reveal strong competitive effects in idea space, there is evidence of knowledge spillovers in collaboration space, when high-quality researchers directly engage with other researchers in the joint production of new knowledge.

We compare winning and losing firms in lotteries for H-1B visas, matching administrative data on these lotteries to administrative tax data on US firms and to approved US patents. Winning one additional H-1B visa crowds out about 1.5 other workers at the firm. Additional H-1Bs have insignificant and at most modest effects on firm innovation. More general evidence from the universe of US firms and the universe of H-1B visas using alternative estimation strategies is consistent with these results. Firms that hire H-1Bs grow faster and innovate more because they are different in other ways from firms that do not.