The effect of life expectancy on education and population dynamics

This figure replicates the corresponding figures from Chesnais (1992) and Livi-Bacci (1992), see also, Cervellati and Sunde (2011). See also Kirk (1996), Caldwell (2006), Dyson (2010), and Canning (2011) for a discussion of the literature on the demographic transition.

As discussed in more details below, the instrumentation strategy builds on the work by Acemoglu and Johnson (2007).

Technically, modeling this effect requires considering that parents with non-homothetic preferences derive utility only from children that survive to adulthood. This channel should be expected to be at work in the context of mortality affecting young adults rather than for child and infant mortality, because replacing children is easier than replacing adult offsprings.

Some complementary mechanisms might also reinforce this link. Most notably, delayed child birth can be related to increased education enrolments, see Bhrolchain and Beaujouan (2012), the higher labor force participation of women, see Bloom et al. (2009b), or the increase in capital endowments and consumption, see Lee and Mason (2010).

This has been pointed out already by Kalemli-Ozcan (2003) and Doepke (2005) for the precautionary demand motive for fertility. See also Soares (2005) for the analysis of the role of child mortality and adults longevity for the quantity–quality framework and Cervellati and Sunde (2014) for a more extensive more extensive discussion of this issue.

The effect of life expectancy on growth may also pass through other channels like, e.g., savings, dependency rates, or production of knowledge which are not investigated in this paper.

Their results also document that the different findings in the literature are not due to the different instrumentation strategies, but are largely due to the use of linear regression frameworks. The heterogeneity of effects implies that sample composition in terms of the relative number of countries before and after the transition is, however, crucial for estimates obtained with linear models.

The specification of preferences essentially follows Galor and Weil (2000), where the second component generates a link between generations that can be interpreted as a warm glow type of altruistic preferences. Given homothetic preferences, the optimal decisions are unaffected when assuming that utility depends on (planned) fertility rather than the number of surviving offspring or realized gross fertility. Also, it is implicitly assumed that individuals can perfectly smooth consumption as well as the utility from children over their lifetime, but crucially, they cannot perfectly substitute utility from their own consumption with utility derived from their offspring.

The simple formulation adopted here reflects a partial equilibrium setting with exogenous (and normalized) wages. This setting is consistent with the more general treatment in Cervellati and Sunde (2005, 2014), where investments in human capital depend on life expectancy, as well as on wages that are determined in general equilibrium, and where different types of human capital involve a different opportunity cost of raising children.

To ensure that parents with higher education have fewer children as the opportunity cost of fertility increases in the education investment, one can assume that \(\eta \gamma >x\left( 1-\gamma \right) \). This parametric restriction implies that the returns to investments in education are large enough to compensate for the increasing (opportunity) cost of raising children. In the literature the returns to education, here summarized by \(\eta \), have been related endogenously to skill-biased technological change, which would eventually make education profitable. In this paper we abstract from technological dynamics to concentrate on the main testable predictions. Also, notice that the acquisition of one’s own education would further reinforce the fertility reduction in a quantity–quality framework a laSoares (2005) if educated parents are more effective in producing educated (high quality) children.

In light of the literature, this is consistent with differential fertility across different education groups.

This mechanism would be at work before the demographic transition also if subsistence levels in consumption were considered, see, e.g., Galor and Weil (2000) or Croix and Licandro (2013).

Recall that the, GRR is the average number of daughters that would be born to the representative woman if she survived at least to the end of her reproductive life (given the age-specific fertility rate of each age). The TFR is similarly defined as the GRR but it refers to the average number of children (and not daughters). Abstracting from differences in birth rates between sexes, and since our model is asexual it holds that TFR = 2 \(\cdot \) GRR. Interpreting n to the be the planned GRR implies TFR \(=\) 2 \(\cdot \) GRR \(=\) 2 \(\cdot \) n.

The NRR is defined the same way as the GRR, but in addition to the age-specific fertility rates, it also accounts for the age-specific mortality rates.

In the theory presented in the previous section, we followed the typical assumptions in the long-run growth literature and abstracted from life cycle considerations and age-specific mortality rates, consistent with the conditions of a stable population model.

An alternative strategy would involve estimating the model on the pooled sample and allow the parameter \(\alpha \) to vary across pre-transitional and post-transitional countries. Compared to the estimation using split samples, this partial interaction approach would force the time effects to be the same across the two sub-samples, rather than allowing all parameters, even those not linked to life expectancy, to vary, as in the fully interacted model (with split samples). The analysis below presents results for the split sample estimation because it is more flexible.

See (Preston et al. (2001), pp. 158–159). In terms of population growth the only difference with respect to the predictions for \(\mathrm{{NRR}}_t\) derived above is that \(\lambda \equiv \lambda _1+\lambda _2>0\) may depend on both the long term component (reduced mortality in childbearing ages reflected by \(\lambda _1\)) and a temporary component (due to the higher survival of individuals at each point in time \(\lambda _2\)).

Age 25 is considered to concentrate attention to individuals with completed education. For robustness, the results have also been replicated with alternative measures such as the population share aged 15 and older without formal schooling, with qualitatively similar results that are available upon request.

Alternatively, we used average years of schooling of the entire population above 15, or average years of secondary schooling, with similar results. The effect of life expectancy might also affect the acquisition of human capital through channels alternative to formal schooling (like parents increasing the investment in quality at home, etc). However, the lack of comparable cross-panel data on alternative measures over a long period of time prevented us from investigating this possibility.

It should be noticed, however, that the measure of life expectancy at age 20 constitutes a very conservative and potentially overly restrictive measure for several reasons. First, the theoretical predictions are not restricted to life expectancy above the age of 20, but also apply to younger ages. Second, and most importantly, data availability is limited for life expectancy at later ages, and the data are of lower quality and inferior reliability. See also (Zhang and Zhang (2005), p. 53) for a discussion of this issue.

See also Acemoglu and Johnson (2007) for a discussion of this issue.

Ideally, one would take into account the exact time when the mortality reduction treatment is applied to a country and whether the country is pre-transitional or post-transitional at the time of treatment. In principle, the available data on fertility and realized mortality do allow for a fairly precise identification of the onset of the demographic transition within a range of about 10 years. However, the data on the predicted mortality instrument only contain country-specific information for the predicted change in mortality over the full period. See also the discussion on this issue in Cervellati and Sunde (2011).

To verify the second requirement we follow Reher (2004) and consider a country to be post-transitional if it has entered the falling trend in terms of the 5-year averages of crude birth rates by the year 1935. His definition of a sustained decline in fertility refers to the beginning of the first quinquennium after a peak, where fertility declines by at least 8 % over two quinquennia and never increases again to the levels of the original take-off point, ignoring one-time events (Reher 2004, p. 21). In robustness checks, we also considered the threshold of crude birth rates of 25/1,000 which, however, is more restrictive and fragile to short term fluctuations in birth rates like, e.g., the baby boom. Likewise, we also considered a less restrictive threshold of 35/1,000. All results are qualitatively identical.

In the case of Greece the problem is the lack of reliable data before 1950. Ireland and New Zealand display a very flat profile of crude birth rates around 30/1,000 after 1940 and a clear drop only in 1980 and 1960, respectively.

Robustness checks available upon request reveal qualitatively and quantitatively similar results when coding these countries as post-transitional.

We report +20 as reflecting the expected age at death to be comparable to life expectancy at birth.

Similar findings emerge when looking at the changes in the share of population with no schooling aged 15 and above. In this case the effect of life expectancy is positive and even slightly significant, although the effect is still substantially smaller in size than the effect obtained for post-transitional countries. This is to be expected since this measure further includes individuals aged 15–25 by 2000, which are the cohorts most likely affected by the reduction in fertility in countries that had not undergone the demographic transition by 1940, but underwent the fertility drop during the 1960s and 1970s. The results are available upon request.

Detailed results are available upon request.

Differently from education data this conjecture cannot be directly tested, however, since TFRs for the younger cohorts are not yet available.