  Measuring and forecasting migration patterns, and how they change over time,
has important implications for understanding broader population trends, for
designing policy effectively and for allocating resources. However, data on
migration and mobility are often lacking, and those that do exist are not
available in a timely manner. Social media data offer new opportunities to
provide more up-to-date demographic estimates and to complement more
traditional data sources. Facebook, for example, can be thought of as a large
digital census that is regularly updated. However, its users are not
representative of the underlying population. This paper proposes a statistical
framework to combine social media data with traditional survey data to produce
timely `nowcasts' of migrant stocks by state in the United States. The model
incorporates bias adjustment of the Facebook data, and a pooled principal
component time series approach, to account for correlations across age, time
and space. We illustrate the results for migrants from Mexico, India and
Germany, and show that the model outperforms alternatives that rely solely on
either social media or survey data.
