Life expectancy, schooling, and lifetime labor supply: theory and evidence revisited (Q2871448)

Really, ``the increase in life expectancy has been one of the most important demographic changes over the last two centuries''. The paper presents the results of theoretical, empirical, and formal studies on influence of the ``changes in age-specific mortality rates on optimal schooling and life-time labor supply''.NEWLINENEWLINEThe basis of the theoretical investigation is the model of Ben-Porath. Let \(p_t\) be the unconditional probability of being alive at age \(t\). The maximum age that can be reached, implicitly defined by \(p_{\overline{T}}=0\), is \(T\in (0,\infty)\), while life expectancy at birth is denoted by \(T\). Individuals maximize the expected lifetime utility: NEWLINE\[NEWLINE V=\sum\limits_{t=1}^{\overline{T}}\beta^{t-1}p_t[u(c_t)+v(l_t)], NEWLINE\]NEWLINE where \(u(\cdot)\) and \(v(\cdot)\) are increasing and concave functions of consumption \(c\) and leisure \(l\), respectively, and \(\beta\) is the subjective discount factor. Then the individual lifetime budget constraint, conditions for consumption, leisure at school, and leisure at work are defined. The costs and benefits of schooling are described by algebraical expressions. Particularly, the benefits of staying in school at age \(S\) (after \(S-1\) years of school) are given by the increase in lifetime earnings associated with the higher human capital, which is obtained in the last year at school, NEWLINE\[NEWLINE [y(\overline{s}(S))-y(\overline{s}(S-1))]\cdot\sum\limits_{t=S+1}^Rp_tb^{t-1}L_t(S). NEWLINE\]NEWLINE Following \textit{M. Hazan} [``Longevity and lifetime labor supply: evidence and implications'', Econometrica 77, No. 6, 1829--1863 (2009; \url{doi:10.3982/ECTA8107})], let the acronym ETWH designate a shorthand notation for the expected total (lifetime) hours of work, so the second component of the expected benefits from schooling: NEWLINE\[NEWLINE\text{ETWH}:=\sum\limits_{t=S+1}^Rp_tb^{t-1}L_t(S). NEWLINE\]NEWLINE From the theoretical analysis, the authors infer two implications, which are discussed before the presentation of their empirical relevance. The first is that ``a change in ETWH alone is neither a necessary nor a sufficient condition for observing an increase in relative benefits of schooling''. Really, one can be sure that a change in demographic or economic conditions is a more important factor in altering the costs and benefits of schooling.NEWLINENEWLINEThe second implication is that ``relative benefits of schooling increase the reductions in mortality at working ages, while higher longevity by itself may not matter''. The function due to Gompertz and Makeham that models mortality is well known:NEWLINENEWLINENEWLINE\[NEWLINE \mu(t)=A+Be^{\delta{t}},NEWLINE\]NEWLINENEWLINENEWLINEwhere \(A\) reflects the age-independent mortality rate, and \(B\) and \(\delta\) are parameters that describe the age-dependent mortality process. Considering the ``compensation law'' of mortality (Strehler and Mildvan, 1960): NEWLINE\[NEWLINE\ln{B}=\ln{M}-\delta{\overline{T}},NEWLINE\]NEWLINE where \(M\) and \(\overline{T}\) are invariant parameters, the authors introduce the term of rectangularization of the survival function. This means that ``the increase in life expectancy is mainly due to an increase in the survival probability during working ages, while survival rates at young ages and the maximum life-span are essentially unchanged''. In order to validate the thesis that the process of rectangularization is associated with an increase in benefits of schooling, the authors turn to empirical evidence. Leaving aside the description of two steps of the empirical analysis, namely, the investigations of the change in the age-specific survival functions of cohorts of U.S. men born between 1840--1930, and the historical changes of the different components of benefits and costs of schooling, we specify some interesting implications of the authors:NEWLINENEWLINEThe empirical results show that the estimates of the relative benefits from schooling have increased over time despite the reductions in lifetime labor supply;NEWLINENEWLINEA realistic shift in the survival function can lead to an increase in schooling and a reduction in lifetime labor hours.NEWLINENEWLINEIt is clear that the obtained results designate the directions for future studies in theoretical and empirical areas of very interesting and important problems of mathematical demography.