We present and calibrate a dynamic model that characterizes the labor market for computer scientists. In our model, firms can recruit computer scientists from recently graduated college students, from STEM workers working in other occupations, or from a pool of foreign talent. Counterfactual simulations suggest that wages for computer scientists would have been 2.8%-3.8% higher and the number of Americans employed as computer scientists 7.0%-13.6% higher in 2004 if firms could not hire more foreigners than they could in 1994. In contrast, total computer science employment would have been 3.8%-9.0% lower and consequently output smaller.