Abstract
This paper studies the optimal design of a pension system together with publicly provided individualized financial education. Agents can invest in both a risky and a non-risky asset and can either under- or over-estimate the expected return of the risky asset. We show that, under perfect information on the misperception biases, it is optimal for the government to impose a uniform level of pension contributions equal to the optimal level of investment in the riskless asset and a U-shaped level of mandatory education. Under asymmetric information, we show that the level of education is always distorted upward for agents with important misperception biases (who either under- or over-estimate financial returns), but can be distorted upward or downward for agents with mild misperception biases. Whether we end up in one or the other situation depends on the size of the public and private costs of education as well as on the shape of the distribution of the misperception biases in the economy.
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Notes
Financial education is formally defined as “the process by which financial consumers/investors improve their understanding of financial products, concepts and risks and, through information, instruction and/or objective advice, develop the skills and confidence to become more aware of financial risks and opportunities, to make informed choices, to know where to go for help, and to take other effective actions to improve their financial well-being” (OECD 2005).
Financial education can also be obtained through (voluntary) training on government platforms (see, for instance, in Canada, https://www.canada.ca/en/financial-consumer-agency/services/financial-literacy-programs.html).
In this respect, our model is relevant for agents who are able to save. It does not apply to agents whose income is so low that they live hand-to-mouth.
We come back on this point at the beginning of Section 4.2.
See also Dutta et al. (2000).
See also Spataro and Corsini (2017) who provide a unified framework for studying the impact of financial education on human capital acquisition and on capital market participation (i.e., through risky and riskless assets). In their case, the decision to acquire financial knowledge is a 0-1 decision and is only relevant for investing in the risky asset. Furthermore, in their paper, individuals are not myopic and the government does not intervene in the provision of financial education.
We assume no income heterogeneity to concentrate on the effects of misperception biases on the agents’ investment choices and on how the government should intervene to correct for this inefficiency, putting aside any income redistribution concern.
We could assume that the return of the risky asset in the bad state of nature is strictly positive. Relaxing this assumption would not qualitatively change our results.
This assumption allows to rule out income effects and to obtain clear comparative statics (in particular regarding the impact of education on saving decisions derived in Section 4.2).
An alternative way to model the misperception bias would be to assume that individuals have biased beliefs regarding investment returns, instead of misperceptions on the probability distribution of the returns. This approach would imply that the perceived marginal utilities of consumption in the good state of nature would be biased upwards or downwards, leading to an ambiguous overall impact of the misperception bias on investment levels in the risky asset.
The misperception level \(\alpha \) could be related to the initial level of financial education of the agent.
Throughout the paper, we assume that the second-order conditions of all maximization problems hold.
This is equivalent to the first pillar of the pension system.
At the end of this section, we discuss the case where pension contributions can be invested in the risky asset as well.
For ease of notation, we drop the arguments of the functions whenever this does not lead to ambiguity.
An alternative criterion would have consisted in assuming that the government is more risk averse than individuals themselves and would thus like to prevent ex post inequalities across states of nature and between individuals. We discuss in the Supplementary material how our results would change under this assumption.
If public funds were costly, the optimal contribution would be equal to zero, as the same (laissez-faire) welfare level could be attained either through B or b but at a smaller cost for the society in the latter case.
We have implicitly assumed here that individuals cannot borrow out of pension benefits. Assuming otherwise would only reinforce the case for mandatory financial education. Indeed, in our model, the only reason why people may borrow out of pension benefits would be to reallocate savings from the riskless to the risky asset. Hence, pessimistic agents would never borrow out of (riskless) pension benefits since they would prefer an even higher investment in the riskless asset. Only optimistic agents would borrow out of pension benefits to increase investments in the risky asset. This would undo the effect of the government’s intervention through the implementation of a pension system.
To prove this, we have derived a model where the government also chooses a level \(S(\alpha )\) of mandatory contributions in the risky asset. Computations are available upon request.
As Kezdi and Willis (2009) argue, it takes “effort, intelligence and motivation to acquire knowledge (..) and use it to make saving and portfolio decisions that will raise the individual’s or household’s level of expected utility.” As such, financial education is costly not only to governments but also to individuals, even in the absence of labour market opportunity costs (recall that, in our model, labor supply is fixed). Assuming \(p=0\) does not qualitatively change our conclusions both under symmetric and asymmetric information.
As before, due to the quasi-linearity of preferences, individual decisions do not depend on the level of \(T(\alpha )\).
It is straightforward to see that (16) evaluated at \(e=1\) is negative.
The thresholds are obtained such that (16) evaluated in \(\{e=0,\alpha =\alpha _1\}\) or in \(\{e=0,\alpha =\alpha _2\}\) is equal to zero.
When preferences are not CARA, we cannot obtain unambiguous results. Indeed, with CARA preferences, the bias \(\alpha \) affects investments in the risky and riskless assets only directly through \(\phi (\alpha ,e)\), but not indirectly through its impact on marginal utilities of consumption, \(u'(.)\).
We show in the Supplementary material that the assumption that \(db/d\alpha \) and \(\partial b/\partial \alpha \) have the same sign is equivalent to assuming that even with education, \(\phi (\alpha ,e(\alpha ))\) increases in \(\alpha \). The same is true for the assumption that \(ds/d\alpha \) and \(\partial s/\partial \alpha \) have the same sign.
Since the revelation principle applies in this context, we focus on a direct mechanism.
The cumulative density function \(F_\rho (\hat{\rho })=P(\rho \le \hat{\rho })=P(\alpha \pi \le \hat{\rho })=F(\rho /\pi )\). Differentiating this expression, we obtain that the density function of \(\rho \) is equal to \(f(\rho /\pi )/\pi \).
As we showed in the previous section, under full information, it is indeed optimal to set the same (first-best) level of mandatory contributions. To keep the model tractable and the results comparable with the ones from the previous sections, we limit the analysis to uniform benefits also in this section, even if they may be suboptimal under asymmetric information.
Under Assumption 1, the solution to the individual’s problem in the absence of pension contributions is always interior.
This is equivalent to a monotonicity constraint, which can replace second-order local incentive constraints. See the Supplementary material for further discussion.
Note that \(b^{FB}=b^{LF}(1)<b(\phi (\rho /\pi ,e),0,e)\) since \(\phi (\rho /\pi ,e)<1\) for pessimistic agents.
In Fig. 3, we implicitly assume that the distribution of \(e(\rho )\) is symmetric, which is not necessarily the case. A similar reasoning applies to the non-symmetric case.
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Acknowledgements
The authors would like to thank two anonymous referees and the Editor in charge, Grégory Ponthière, for their valuable comments. We further acknowledge valuable insights from participants at the L.-A. Gérard Varet Conference in Marseille (2022).
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Canta, C., Leroux, ML. Financial education as a complement to public pensions: the case of naive individuals. J Popul Econ 37, 69 (2024). https://doi.org/10.1007/s00148-024-01046-3
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DOI: https://doi.org/10.1007/s00148-024-01046-3