We study macroeconomic and welfare effects of old-age savings incentives (OAS incentives). Fully rational agents respond to OAS incentives with complete crowding out, hence any effects of such incentives stem from second order general equilibrium adjustments. Meanwhile, agents with incomplete rationality face constraints in obtaining optimal savings profiles, and thus experience also first order effects in presence of OAS incentives. We develop an overlapping generations model with intra-cohort behavioral heterogeneity. In addition to fully rational agents, each generation has also agents with variety of incompletely rational preferences. In this economy we introduce tax incentivized old-age savings schemes with endogenous participation.