Markovian Social Security in Unequal Societies

In this paper, we develop a dynamic politico-economic theory of social security to address two questions. First, how is social security sustained? Second, how does inequality affect the size of social security, and can the theoretical predictions be consistent with the observed puzzling relationships between inequality and the size of social security? As a stark framework, our model economy features the absence of altruism, commitment, reputation mechanism and electoral uncertainty. We characterize analytically a Markov perfect equilibrium and find that the joint between Markovian tax policy and tax distortion on private investment shapes an intertemporal policy rule linking taxes positively over time. The positive intertemporal tax linkage, by allowing current taxpayers to influence their own future social security benefit, provides the political support for social security. Moreover, we find that a larger wage inequality weakens the intertemporal tax linkage and, thus, reduces inter-generational redistributive benefit. This may lead to a smaller size of social security. Our theoretical predictions are in line with both time-series and cross-country correlations between inequality and social security