Ordinal response generalized difference in differences with varying categories: The health effect of a disability program in Korea

We consider the use of difference in differences (DD) to evaluate the effect of an activity assistance program on the health of severely disabled Koreans. There are, however, 2 problems in the data: the number of response categories for self-assessed health changed over the waves of the repeated cross-section survey and the "parallel untreated response path" assumption for DD is suspect. We show how to overcome these problems by renormalizing parameters and applying "generalized difference in differences (GDD)." We find a significantly positive effect of the program with DD, but not with GDD. Our solutions should prove useful in applications in which one or other of these problems arise.