Education, life expectancy and family bargaining: the Ben-Porath effect revisited

Abstract

Following Ben-Porath [1967. “The Production of Human Capital and the Life-Cycle of Earnings.” Journal of Political Economy 75 (3): 352–365], the influence of life expectancy on education and on human capital has attracted much attention among growth theorists. Whereas existing growth models rely on an education decision made either by the child or by his parent, we revisit the Ben-Porath effect by modelling education as the outcome of bargaining between the parent and the child. We develop a three-period overlapping generations (OLG) model, where human capital increases life expectancy and shows that as a result of the unequal remaining lifetimes faced by parents and children, the form of the Ben-Porath effect depends on how bargaining power is distributed within the family, which in turn affects long-run economic dynamics. Using data on 16 OECD countries (1940–1980), we show that introducing family bargaining helps to rationalize the observed education patterns across countries.

Keywords:

• education
• life expectancy
• family bargaining
• OLG model

JEL Classification:

• D13
• J10
• O41

Acknowledgements

The authors are grateful to Daniel Cohen, Marion Davin, Colin Green, Volker Meier and to two anonymous referees for their comments on this paper.

Notes

1. The intuition for using period life expectancy for cohorts born in 1940–1980 goes as follows. Agents, when choosing their education ex ante, have access to the currently available demographic statistics, which are period lifetables. Cohort lifetables are only known ex post, that is, once the entire cohort is dead. Hence cohort lifetables are not really relevant for the Ben-Porath effect, which is about individuals making schooling decisions ex ante.

2. This is taken into account in models with endogenous mortality, such as Cervellati and Sunde (2005) and de la Croix and Licandro (2013).

3. See Boucekkine, de la Croix, and Licandro (2003), Cervelatti and Sunde (2011), de la Croix (2008), de la Croix, Lindh, and Malmberg (2009), Cohen and Soto (2004, 2007), Acemoglu and Johnson (2007), Lorentzen, McMillan, and Wacziarg (2008), and Cohen and Leker (2013) for a discussion at the empirical level. Those studies give quite mitigated results regarding the influence of life expectancy on education and growth.

4. In our model, education is time consuming. The education investment takes the form of a fraction of time that the parent and the child must spend together. This specification is general: one can think of a father watching his child, but also of a professor teaching a student, or of a senior worker helping a junior worker.

5. For simplicity, we assume here a fixed fertility, equal to the replacement level. On the determinants of education under endogenous fertility, see Barro and Becker (1989), Ehrlich and Lui (1991), Soares (2005) and de la Croix and Licandro (2013).

6. For simplicity, we assume that there is no savings decision. Although widespread in the literature (Blackburn and Cipriani 2002), that assumption is strong and requires some justification. In our context, the justification is merely that our model focuses on a part of the lifecycle where agents are either studying or working, without considering the retirement age. The absence of an inactivity period in our economy makes the savings issue less important.

7. Note that, for the sake of simplicity, we restrict ourselves here to a model with only two possible lengths of life. See Ponthiere (2011) for a study of asymptotic age structures in an OLG model with endogenous fertility.

8. Many studies show that the level of human capital has an important impact on longevity, through knowledge on prevention and treatments of diseases. See Easterlin (1999).

9. The parent's motive to educate his child is here purely egoistic. This explains why the utility derived from the child's education is conditional on survival of the parent, unlike in altruistic models, where this would be unconditional on the parent's survival.

10. That objective function already includes the time constraints for the different periods. In period 1, the parent's own education reduces his consumption, while in period 2 the parent's consumption is reduced by the education he provides to his child, .

11. The concavity of the time-horizon effect is standard in the literature. See for instance the increasing and concave effect of life expectancy on the propensity to save in Chakraborty (2004), which also relies on log linear utility.

12. The myopic anticipation assumption amounts to assume that human capital enters here the survival probability as an externality. Indeed, we have , so that the child affects, by his education choice, his future survival chances. Assuming amounts to assume that children do not internalize the impact of their education choice on their life expectancy.

13. Given that the parent and his child bargain and discuss about the future, it makes sense to assume that they share the same beliefs on longevity prospects. In particular, it is plausible to suppose that the parent, thanks to his older age, is better informed about the survival process (explaining that his foresight is perfect), and shares that information with his child.

14. Note that, if the child faced, because of some cohort-specific circumstances (e.g. wars), a shorter expected life horizon than his parent, then the differential in remaining lifespans might go in the other direction. Throughout this paper, we rule out those cases, and focus on the general situations where children have a higher remaining life expectancy than parents.

15. Those dynamics is actually quite close to Azariadis and Drazen's (1990) threshold effects in human capital accumulation.

16. Figure 2 shows the transition function and the 45° line.

17. See, for instance Lam and Schoeni (1993), who show that women with higher education and income have more bargaining power in their household, which implies higher schooling for their children.

18. The distribution of bargaining power may also vary in a nonmonotonic way. Yet, for simplicity, we will only consider a monotonic relation between the distribution of the bargaining power and human capital.

19. In that proposition, the reference to a ‘poverty trap’ means that there exists a threshold in human capital such that if the initial condition is below this threshold, then the human capital stock shrinks over time. On the contrary, an ‘area of perpetual growth’ refers to the existence of a threshold in human capital such that, if the initial condition is above that threshold, then the human capital stock will grow indefinitely in the future.

20. The considered countries are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Sweden, the UK and the USA.

21. We use period life expectancy, since cohort life expectancy requires the death of all cohort members before being known. That assumption is too strong in our context, since education decisions take place quite early during the lifecycle. We thus consider that period life expectancy statistics are more adequate than cohort life expectancy statistics.

22. The reason why we proceed in that way goes as follows. We would like to investigate here whether the model where the parent decides alone can better replicate the data than other models, including the one where only the child decides on his education. Given that the does not affect education when the child decides alone, but that strongly affects the chosen education when the parent decides alone, it makes sense to select the level of that best fits the education data when only the parent decides.

23. Sources: the World Values Survey questionnaires are available online at http://www.worldvaluessurvey.org/wvs/articles/folder_published/survey_2005

24. Sources: for European countries, we use data from the study Voter Turnout in Western Europe, published by the International Institute for Democracy and Electoral Assistance, 2004. For Australia, we use data from the Australian Electoral Commission website (http://www.aec.gov.au/About_AEC/25/theme1-voting-history.htm). For Canada, we use the Amendment to Canada Election Act (1970). For New Zealand, we use the website New Zealand history online (http://www.nzhistory.net.nz/politics/milestones). For the USA, we use the Amendment XXVI to the US Constitution and Voting Rights Act Amendments (1971).

25. On this, see Ponthiere (2010).