Social media and Web data offer new opportunities to improve demographic knowledge and to complement more traditional data sources. Facebook, for example, can be thought of as a large digital census that is constantly updated. However, its users are not representative of the underlying population. The American Community Survey relies on smaller samples that may be noisy for small areas and that are published with a substantial delay from data collection. However, the respondents are representative of the entire population. The two data sources have complementary features. We generate predictions of migration stocks that combine the best of the two sources. Facebook data, obtained via the Adverts Manager API are timely, but lack demographic constraints on age patterns that we extrapolate from time series of the American Community Surveys. Although the focus of this article is on migration, our methods are general and can be applied to other substantive areas.