This paper develops a model of earnings and applies this to an examination of the effect of lifelong learning on men’s wages. Using data from the British Household Panel Survey, a variant of the mover–stayer model is developed in which hourly wages are either taken from a stationary distribution (movers) or closely related to the hourly wage one year earlier (stayers). Mover–stayer status is not observed, and we therefore model wages using an endogenous switching regression, estimated by maximum likelihood. Methodologically, the results support the mover–stayer characterisation since the restrictions required for the simpler specifications popular in the literature are rejected. Substantively, simulation of the estimated model shows some statistically significant effects from acquiring qualifications of a higher level than those previously held, but not from acquiring qualifications of the same level.
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This is to avoid the complications around female labour supply, where fertility decisions are more important.
Across all waves, 10.5 % of the sample are dropped due to being self-employed, 13.4 % of workers. To provide some sense of how this might affect our results, we re-estimated the econometric model described later, excluding individuals who were self-employed at any point. The resulting estimates of lifelong learning are similar to those found when not excluding those self-employed at any point.
Results available on request showed that our findings are robust to assuming that attrition is random.
The General Certificate of Secondary Education (GCSE) is normally taken by children at the age of sixteen, while AS-levels are taken at age seventeen and A-levels at age eighteen. Two A-levels are the minimum qualification required for study at university although in practice most universities require three A-levels. Scotland has its own system of qualifications; these have been converted into the equivalents from the rest of the UK.
Costs of courses vary very greatly, so it is not possible to draw any generalisations.
This is a derived variable wPAYGU.
The original mover–stayer model (Goodman 1961) considered a population on which categorical data were observed. Some members, movers, were subject to a Markov process, while others, stayers, retained their initial category.
An academic qualification is one which is normally taken in a school or university. Thus academic qualifications are GCSEs, AS and A-levels, and their Scottish equivalents or university degrees and diplomas.
It should be noted that the model in differences is not simply the model in levels. In the former, variables explain growth in wage rates, while, in the latter, they explain the level of wage rates.
The confidence intervals are calculated from the simulations; we do not make the assumption that the returns are normally distributed. The lower limit of the 95 % confidence interval of the estimate of the return is given by the 2.5 percentile of the ranked returns. We show in Table 7 the proportion of simulations which result in a reduction in the discounted wage and, when this is more than 2.5 %, the estimate is not significant at a 95 % level. When it is more than 5 % the estimates are not significant at a 90 % level.
They did include initial qualification level as a control variable, but this is not sufficient to distinguish upgrading from simply acquiring a qualification.
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We are grateful to the Economic and Social Research Councils for supporting this research through the LLAKES research centre at the Institute of Education and the National Institute of Economic and Social Research. We also gratefully acknowledge comments from participants in seminars at the Institute of Education and the National Institute. The British Household Panel Survey, used in this study, is funded by the Economic and Social Research Council and is available from the data archive at the University of Essex.
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.
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Dorsett, R., Lui, S. & Weale, M. The effect of lifelong learning on men’s wages. Empir Econ 51, 737–762 (2016). https://doi.org/10.1007/s00181-015-1024-x
- Lifelong learning
- Returns to education
- Switching regression
- Wage dynamics