Most developed countries provide dedicated old-age savings programs with tax incentives. These programs are typically motivated by the argument that absent the fiscal incentives, people would not save enough for the old-age and thus face the risk of poverty in the last decades of their life. We verify this conjecture. We develop a model in which agents age and the subsequent generations of agents overlap. In this model economy, agents exhibit many types of bounded (incomplete) rationality, which prevents them from taking the old-age savings decisions such as a fully rational homo oeconomicus would take. We study their savings patterns. We then introduce a government-subsidized old-age saving instrument and study participation by incomplete agents as well as the changes in their savings behavior. Key finding of this report is that the government-subsidized old-age saving instruments may raise consumption of the incompletely rational agents, but not actually affect their wealth accumulated prior to the retirement. 

For the purpose of this report, we study how introducing a government subsidized old-age saving instrument with endogenous participation. Our instrument replicates the features of many such instruments around the world. First, the instrument provides full exemption from capital gains tax. Second, the participation is voluntary: the agents endogenously choose the age at which they choose to participate and in principle they may prefer not to enter the instrument at all. Third, the instrument is capped and the participation is binary that is when deciding about participation, the agents consider only two options: no participation (the contribution rate of 0%) and full participation (for a given contribution rate). Below, we summarize the key insights.

1. Fully rational agents change nothing in their behavior.
2. Agents with present bias and agents lacking financial literacy may afford smoother consumption paths, but the actual level of old-age wealth at retirement is the same regardless of the government subsidized old-age saving instrument. Hence, it remains below the levels for fully rational agents.
3. Introducing the instrument raises somewhat their stream of life-time income (e.g. from interest on assets), but is accompanied by reduced labor supply relative to the status quo of having no instrument.
4. Agents with hand-to-mouth behavior gain access to additional income, but at the expense of reducing their consumption in the working age. Generally, their consumption path is smoother.
5. Eventually, all types of agents choose to participate in the instrument, but agents with higher preference for present choose to join later in their lives. Bigger instruments (higher contribution rates) are characterized by participation later in life.
6. Taxes needed to finance this instrument reduce the gains from having access to this instrument at all. The more tax advantages the instrument offers, the bigger this negative effect is.
7. For the fully rational agents, the necessary rise in taxation results in negative felicity relative to status quo.
8. Participation is not a good measure of success of such programs. Fully rational agents participate even though introduction of such programs lower their welfare. The welfare loss is due to fiscal cost that is independent of their individual decision to participate, but rather by the participation decision of all the agents
9. For agents with incomplete rationality, felicity increases overall.  

• The report.
• The technical details (model derivation, calibration, full set of profiles, etc) are relegated to a background paper.
• Data (with documentation).