Forschungsgruppe ORCOS
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Agglomeration Processes in Ageing Societies

WWTF (01.2008 − 06.2011), Project leader from TU: G. Tragler

Keywords: age structured systems, life cycle decisions, ageing populations, optimal control, economic geography, endogenous growth


Models of the New Economic Geography (NEG) show that dynamic variations in the local amount of productive factors can lead to agglomeration of the industrial activity in one region. From a methodological point of view, NEG models are genuinely dynamic models. For a long-term analysis, it is surprising that intertemporal optimality does not appear to be a core question and that, to our knowledge, the role of life-cycle decisions on consumption and savings and the role of ageing are not considered at all. In particular, most industrialized countries are subject to population ageing and individual patterns in consumption demand and labour productivity vary over the life cycle. In addition, we expect that the incentives to invest in existing products or in product innovation will be different in young and old societies.

We expect that these factors affect agglomeration processes. The first scientific challenge is to develop NEG models that incorporate elements of endogenous growth and intertemporal household decisions over the life cycle of an ageing population; thus to introduce a dynamic, age-structured optimization element into the NEG framework. The second scientific challenge is to study analytically the intertemporal optimal growth path for such an economy. Key research questions will be to choose the best way to incorporate elements of endogenous growth and life-cycle decisions into NEG models, to study the properties of the resulting growth path and to investigate the optimality of the growth path by comparing a centralised and decentralised version of our model framework.

Our model framework will allow to study the effect of population ageing on agglomeration processes. In particular, we aim at determining the role played by declining birth rates, by the change of productivity over the life-cycle and by a reduction of transport costs (i.e. by a deepening of integration) on regional policies. We will assess whether such changes in policy parameters will reduce the inefficiency/suboptimality of the growth path resulting in the (decentralised) NEG model; we thus assess whether these policy changes are welfare improving. We shall apply continuous time distributed optimal control models, structured along populations¿ age (McKendrick type) and along product variety. Such systems are described by first order partial differential equations (PDE), where the dynamics depends non-locally on the state and on control variables, the spatial domain and the boundary conditions may be endogenous. This type of models extends the so-called vintage capital PDE models, intensively investigated during the past decade, by allowing for endogenous product variety, endogenous obsolesce age, and involvement of labour with endogenous retirement age.

A substantial work is required to develop appropriate optimality conditions, conditions for stability of the optimal solution, and numerical methods and algorithms. The various steps require interdisciplinary expertise in economics, mathematics and demography as represented by the proposed research team with all partners located in Vienna. We expect that our analysis can improve the understanding of important socio-economic processes and can thus improve the basis for economic policy. At the same time, we expect to develop a flexible model structure that can be extended in several directions. In addition, we expect that the developed mathematical theory for distributed optimal control problems with dynamically controlled domain has potential applications in other problems of economics and management of renewable resources.