Inference and forecasting in the age-period-cohort model with unknown exposure with an application to mesothelioma mortality

Background: There has been extensive discussion of the workings of the English system of higher education income contingent student loans. Major focuses have been on what former students are likely to pay and when, distributional characteristics and how much the Government guarantees made to students about having their loans forgiven after 30 years are likely to cost the budget of the Department of Business, Innovations and Skills (BIS) in the longer term. Leading contributions to this work includes Barr(2004), Goodman et al (2008), BIS Ready Reckoner (2012) and Chowdry et al (2012). Here we look at a vital but entirely unstudied area, the actual cost the Government faces in financing these loans through borrowing in the gilts market1. We use a financially conventional “liabilities matching” approach, just as we would if we were trying to match or value pension obligations. To do this we identify financial instruments which proxy the behaviour of the time series of former student expected repayments. This allows us to estimate each year the direct cost to the state of providing these student loans. The results are remarkably different from the conventional calculations used by H. M. Treasury to charge BIS in their Departmental account2. The reason for this is very simple to explain, it relies entirely on the next observation. Once that is accepted all of the other arguments are conventional economics and the conclusions follow immediately.