Fully rational agents respond to old-age savings incentives with complete crowing out, hence any effects of such incentives stem from second order general equilibrium adjustments. However, agents facing constraints in obtaining optimal savings profiles experience also first order effects, i.e. substantial changes to the lifetime profiles of assets accumulation. We develop a fully fledged overlapping generations model with intra-cohort heterogeneity. In addition to fully rational agents, each generation has also agents with other types of preferences. In this economy we introduce a variety of tax incentivized old-age savings schemes with endogenous participation. We analyze macroeconomic and welfare effects of such instruments.

Our study provides several novel results. First, introducing incomplete rationality to macroeconomic setups addresses some issues related to the match between the models and the observational data, but ushers new issues. Namely, agents with incomplete rationality as discussed in our study may deliver wealth profiles closer to observational data. However, that comes at the expense of consumption and labor supply profiles which are seldom observed. Second, while fully rational agents demonstrate effectively complete crowding out, they are the key beneficiaries of instruments addressing savings shortages among incompletely rational agents. In fact, fully rational agents raise their consumption profiles already when young, whereas the other types of agents only observe gains after retirement. In essence, general equilibrium gains do not compensate individual direct decline of consumption for incompletely rational agents. This counter-intuitive redistribution raises doubts over fairness of such instruments, even if welfare accounting shows large positive effects for incompletely rational agents and small losses for fully rational agents. Third, we document the stark contrast between the direct and general equilibrium effects across the types of agents, in particular in economy where fully rational agents are not a majority.

We also provide policy implications. While the most prevalent are tax incentives at the contribution and accumulation stage (partial or full tax exemptions or even subsidies for contributions for capital income gains), such instruments are relatively less effective than exemptions in the old age, at deacumulation stage. Effectively, general equilibrium effects of ETT and TET instruments are sufficient to make agents endogenously choose participation for majority of their working life-time. This implies that subsidies are excessive fiscal cost and exemptions do not need to be nearly as generous. Meanwhile, instruments of TTE nature are fiscally not costly (their costs are delayed into the future, whereas the benefits of greater capital accumulation emerge instantaneously).