Appendix 1: The effects of attrition
Sample attrition can arise due to survey non-response or to individuals being excluded for any of the reasons discussed in the text (other than ageing out of the sample). A probit model was used to estimate the probability of attriting in the next survey wave. Table 9 shows the estimated parameters. The score vector from this estimation provides the generalised residuals (equivalently, the inverse Mills’ ratio). These are then included in the main model to control for the possibility that the unexplained component of attrition may be correlated with the residuals of any of the equations of our system. Included in the probit model is a variable showing whether the interviewer changes between survey waves. This is likely to affect response because panel members may feel more comfortable about responding to a familiar interviewer. The variable is not included in our main model and so acts as an instrumental variable to help with identification.
Appendix 2: Returns to lifelong learning from the unrestricted model
Table 10 shows the results of the simulation for the version of the model in which the learning terms in the “stayers” equation are not restricted to zero. The coefficients on the learning terms are very close to zero and poorly determined (Table 5). It is therefore to be expected that there is little impact on the mean effects and that the results are much less well determined.
Appendix 3: A fixed effects model
Table 11 shows the results of estimating a fixed effects model. In this model, each man’s initial educational attainment is absorbed into the individual-specific fixed effect. The term “No upgrade” shows the effect of acquiring a qualification which does not result in any change in the attainment level; the coefficients by the other terms show the effects of acquiring a qualification at this level during the course of the survey, when it is at a level higher than previously. Upgrading to level 1 or to level 3 or higher has a significant effect on the hourly wage, while acquiring a qualification without upgrading does not.