The TIMSS 1995, 1999, and 2003 data have been gathered from Hong Kong before and after its sovereignty switch from the United Kingdom to China in 1997. Built on a reciprocal relation theory from the research literature, this investigation is designed to examine models of student self-concept and mathematics achievement during the political transition. Along with a perceived "brain drain" from the population migration, there was a non-monotonic change in the reciprocal relationship between self-concept and mathematics achievement. In addition, indicators of mathematics achievement and self-concept have demonstrated different linkages to the permanent emigration of Hong Kong residents with valued or desirable skills and qualifications. Interpretation of these empirical findings entails a need of enhancing cross-cultural understanding in mathematics education. (Contains 1 figure and 3 tables.)