Social media data donation through data download packages (DDPs) is a promising new way of collecting individual-level digital trace data with informed consent. When linked with survey data, data donation is an even more promising tool that helps answer novel research questions. Nevertheless, given the novelty of this approach, little is known about whether and how people would share their data with researchers, although this could seriously affect selection bias and thus, the outer validity of the results. To study the determinants of data-sharing and help future data donation studies with detecting the conditions, under which the willingness is the highest, we pre-registered two vignette experiments and embedded them in two online surveys conducted in Hungary and the U.S. In hypothetical requests for donating social media data via DDPs, we manipulated the amount of the monetary incentives (1), the presence or lack of non-monetary incentives (2), the number of requested platforms (3), the estimated upload/download time (4), and the type of requested data (5). The results revealed that data-sharing attitude is strongly subject to the parameters of the actual study, how the request is framed, and some respondent characteristics. Monetary incentives increased willingness to participate in both countries, while other effects were not consistent between the two countries. Non-monetary incentives and time to download/upload data influenced willingness in the U.S. sample but not in the Hungarian one, whereas the type of data affected the willingness to participate only in the case of the Hungarian respondents. Our findings help design more effective future data donation requests and provide insights into the potential patterns of selection bias in data donation studies.