Generalized Difference in Differences for Ordinal Responses with a Varying Number of Categories

Ordinal responses often represent verbal descriptions (e.g., happy, neutral, and un-happy). Sometimes, ordinal responses with different numbers of categories have to be used together, as in comparing happiness across different periods/countries. One way to proceed is collapsing some of them such that the same ordinal scale holds for all responses. But this loses information, and how to exactly collapse the ordinal responses is not obvious. We show how to use multiple ordinal responses without equalizing the categories, and apply ‘generalized difference in differences’(GDD) to them; GDD allows nonparallel untreated trajectories across the treatment and control groups, unlike the popular difference in differences (DD). With GDD, Korean data are used to assess the effects on self-assessed health of an aid program for the severely disabled, where four-wave repeated cross-sections appear, with five categories in the first two years and four in the last two; we fnd a signi cant effect with DD, but not with GDD. We also apply our method of dealing with different ordinal responses to the European health data ‘'SHARE'’ where two ordinal scales are worded differently.