The role of active aging in enhancing human capital accumulation: A pathway to economic growth

The Role of Active Aging in Enhancing Human Capital Accumulation: A Pathway to Economic growth M. M. Baldi, R. Coppier, E. Michetti Department of Economics and Law, University of Macerata, Macerata, Italy This work has been funded by the European Union - NextGenerationEU under the Italian Ministry of University and Research (MUR) National Innovation Ecosystem grant ECS00000041 - VITALITY - CUP D83C22000710005. I punti di vista e le opinioni espresse sono tuttavia solo quelli degli autori e non riflettono necessariamente quelli dell’Unione europea o della Commissione europea. N´e l’Unione europea n´e la Commissione europea possono essere ritenute responsabili per essi. https://www.safina-vitality.it/ SOCIN 2025 1/15 Two demographic trends Life expectancy is increasing Fall in fertility rate 2/15 An obvious consequence The natural consequence is that people are aging Active aging is a potential scenario consisting of: 1Work more for a more prosperous retirement 2Devote time to educating or rearing grandchildren The novelty: models based on these assumptions 3/15 Model I - Assumptions Overlapping generations model with three agents: the children, the adults and the elderly Homogeneous individuals in each generation Each individual lives for these three periods and then passes away Each individual: Receives education in the first period Works and rears children in the second period Retires in the third period The length of each period is normalized to 1 Time is discrete and denoted by t∈N The innovation: the old generation can spend time both to leisure and educate grandchildren. 4/15 Model I - Mathematical formulation We have to address the following maximization problem: max Ut(c1,t,c2,t+1,nt,et) = ln c1,t+ρ[ln c2,t+1 +θln(1 −µ)] + +βln ht+1 +λln nt s. t.: wtht=c1,t+st+nt(et+zwtht) c2,t+1 =rt+1st ht+1 =π(ht−1µ+ϕet)δ¯ h1−δ t. 5/15 Model II - Assumptions Same assumptions as for the previous model. But: This time the fraction of time grandparents devote to educate their grandchildren is endogenous and denoted by µt+1. The rest of their time, lt+1 is for leisuring. Different formula for grandchildren’s human capital. 6/15 Model III - Assumptions In this model: Grandparents either work at a reduced productivity or they rear grandchildren In this model, grandparents do not have any leisure time There is another equation for grandchildren’s human capital: ht+1 =π(ϵ+ϕet)δ¯ h1−δ t 7/15 Model IV - Assumptions In this model: Grandparents either leisure or they educate grandchildren The fraction of time grandparents educate their grandchildren is endogenous There is another equation for grandchildren’s human capital: ht+1 =πht−1 µt nt +ϕetδ ¯ h1−δ t 8/15 Model V - Assumptions In this model: There are just two generations: the adults and the elderly There is a survival probability to get old This probability depends on the amount of taxes the goverments devolves to public health 9/15