Abstract: Through an intergenerational overlapping model of endogenous economic growth, this paper examines the mechanism of intergenerational support mode within families in the benefit defined Pay As You Go pension system, so as to provide theoretical reference for the pillardesign of China's urban pension system. The results show that due to the intergenerational support mechanism of“filial piety to parents”and“raising children for the aged”existing in the families, the contribution rate out of the willingness of the working generation in the early stage of system construction is higher than the optimal contribution rate to promote output growth. However, the optimal contribution rate of the second generations is at a lower level. At the present contribution rate out of willingness of the insured members, further reducing the pension insurance contribution rate and establishing pension pillar with financed fund from outside of the premium-paying pension insurance system to solve the pension payment gap of the present retired generation can generate the Pareto improvement of pension scheme design, which will not only improve the efficiency of intergenerational redistribution, but also promote the growth of output. Therefore, it is suggested that financial funds at all levels should be used to establish a“zero pillar”of basic pension as the first layer of pension payment, on this basis, the construction of China's urban multi-level and multi pillar pension system can be promoted.

Key words: family intergenerational support, contribution rate out of willingness, pension pillar, dynamic consistency