We introduce and assess the use of supervised learning in cross-domain topic classification. In this approach, an algorithm learns to classify topics in a labeled source corpus and then extrapolates topics in an unlabeled target corpus from another domain. The ability to use existing training data makes this method significantly more efficient than within-domain supervised learning. It also has three advantages over unsupervised topic models: the method can be more specifically targeted to a research question and the resulting topics are easier to validate and interpret. We demonstrate the method using the case of labeled party platforms (source corpus) and unlabeled parliamentary speeches (target corpus). In addition to the standard within-domain error metrics, we further validate the cross-domain performance by labeling a subset of target-corpus documents. We find that the classifier accurately assigns topics in the parliamentary speeches, although accuracy varies substantially by topic. We also propose tools diagnosing cross-domain classification. To illustrate the usefulness of the method, we present two case studies on how electoral rules and the gender of parliamentarians influence the choice of speech topics.