Social Security as Markov Equilibrium in OLG Models : Clarifications and New Insights

Forni (2005) is the first author to study the politico-economic sustainability of pay-as-you-go social security in the canonical 2-period OLG model that uses Cobb-Douglas production and logarithmic utility under Markovian voting strategies. This paper (1) shows that equilibria can only exist if the economy in absence of social security is dynamically inefficient, (2) derives the exact parametric conditions that lead to existence of equilibria, (3) shows that among all the admissible arbitrary constants that produce a Markov perfect equilibrium, the maximum constant in such set produces the only equilibrium that can solve dynamic inefficiency and produces a single steady state. Moreover, (4) the maximum constant has a closed form solution and (5) yields a social security tax rate that induces the golden rule of capital accumulation. Finally, (6) the paper shows that for any equilibrium using other admissible constants leads to 2 steady states: one that is dynamically-stable but dynamically-inefficient, and another one that is dynamically unstable but dynamically-efficient