THIS APPENDIX provides additional detail on particular aspects of our methodology. The first two sections of the appendix relate to the model of student outcomes that is introduced in Chapter 4 and also used in Chapters 5–7. The third section relates to the sample of completion cohorts used for one of the tables in Chapter 9.
This section describes the empirical model of student outcomes that is introduced in Chapter 4.1 In the model, time is discrete and measured in years. We directly model student transitions from one year to the next. Given that a student is in a PhD program in a particular year, he or she may continue on in the program the following year, leave the program without completing it, or complete the program and receive the PhD before the start of the following year. Thus given that the student is in the program in year t – 1, the three transition probabilities that we are interested in are the probability that the student will still be in the program in year t, the probability that the student will have dropped out of the program by year t, and the probability that the student will have received the PhD by year t.
We specify these transition probabilities as functions of explanatory variables using a multinomial logit form. We allow the parameters of the model to vary freely across years. The sample of students used to estimate the model for a given year is the subsample of students in the program at the beginning of that year. (For years 1–3 we do not allow the completion option, so we simply have a binary logit model for continuation versus attrition.)
1 For a more technical discussion of competing-risk duration models, see Aaron Han
and Jerry A. Hausman, “Flexible Parametric Estimation of Duration and Competing Risk
Models,” Journal of Applied Econometrics 5 (January–March 1990): 1–28.