Abstract
We develop a two-period overlapping-generations model in which financial literacy, accumulated through parental investment and inherited ability, allows households to earn higher net returns only after a critical literacy threshold is reached. The model generates multiple steady states with a financial-literacy-induced poverty trap and yields a closed-form expression for the minimum policy effort needed to escape it. We then extend the framework to allow for dynastic heterogeneity in financial learning ability, which gives rise to the possibility of persistent polarization in returns across households. A simple calibration to the US economy suggests that a temporary public co-financing of about 7.88% of private financial education spending would suffice to permanently raise output by roughly 0.49% per year in the representative-agent benchmark, while heterogeneity amplifies the policy effort required to eliminate inequality or prevent long-run polarization.
Data Availability
No datasets were generated or analyzed during the current study.
Notes
In our analysis, the literacy threshold is treated as exogenous for tractability, but it may itself depend on institutional and technological features of the financial system. Greater financial complexity, weaker consumer protection, high participation costs, or the presence of large minimum-scale investment projects may raise the threshold. Conversely, financial regulation, digital access, default investment options, or compulsory financial education may lower it.
Since the intervention is temporary and designed only to move the economy across the literacy threshold, we abstract from distortionary taxation and government budget dynamics. A full welfare analysis with distortionary taxes is beyond the scope of the paper, thus our analysis aims only at measuring the minimum gross policy effort required to escape the low-literacy basin of attraction.
Since \(\eta _H > \eta _L\), in a polarized regime only type H can obtain high returns while type L needs to obtain low returns. Our parameter specification rules out the reverse polarized configuration.
Whenever the conditions of Proposition 2 are satisfied, the corresponding steady state is locally asymptotically stable. As in the representative-dynasty benchmark, stability follows from the monotonicity and concavity properties of the transition system. In regions of regime uniqueness, the admissible equilibrium attracts all nearby trajectories. When multiple regimes coexist, each admissible steady state is locally stable, and the literacy threshold defines a separatrix in the joint state space \((k_t, x_t^L, x_t^H)\) that partitions the basins of attraction.
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Appendices
Appendix A: Continuous return function
The results in the body of the paper are based on the assumption that the discontinuous piecewise literacy-adjusted factor function takes values \(R_L\) or \(R_H\) depending on whether financial literacy \(x_t\) lies below or above the threshold \(\tilde{x}\). Our main results hold true even if the return function is smooth, provided that it is continuous, increasing, bounded and S-shaped. Specifically, \(R:\mathbb {R}_{+}\rightarrow [R_L,R_H]\) is twice differentiable and satisfies: \(R(0)=R_L\ge 1\), with \(\lim _{x\rightarrow \infty } R(x)=R_H>R_L\); \(R^{\prime }(x)>0\) for all x; and there exists a unique inflection point \(\tilde{x}>0\) such that \(R^{\prime \prime }(x)>0\) for \(x< \tilde{x}\) and \(R^{\prime \prime }(x)<0\) for \(x>\tilde{x}\). In this case, the economic system becomes:
From Eq. 42, the stationary capital level conditional on literacy follows:
which substituted into Eq. 43 yields a fixed-point equation in literacy:
where \(\Theta \equiv \frac{\beta A(1-\alpha )}{1+\beta (1+\theta \delta )}\) and \( \Omega \equiv \chi ^{1/\delta }\! \left( \frac{\beta \theta \delta (1-\alpha )A}{ 1+\beta (1+\theta \delta )}\right) \!\Theta ^{\frac{\alpha }{1-\alpha }}\). Because R(x) is S-shaped, so is G(x) and thus provided that (i) \(G(0)0\), (ii) \(\max _x G^{\prime }(x)>1\), and (iii) \(G(x) R_L\) is generated by an increase in \(\varrho (\cdot )\) once literacy permits access to the superior project menu, rather than by a further increase in \(\varphi (\cdot )\).
This distinction matters for aggregation. Aggregating across identical households of a given type gives \(K_{t+1} = R_{t+1}(x_t)S_t\), so that in per-capita terms \(k_{t+1} = R_{t+1}(x_t)s_t\), exactly as in the main text. As in Greenwood and Jovanovic (1990), the fixed cost of information acquisition, not the number of available projects, is the binding constraint that literacy relaxes, so that additional aggregate capital in equilibrium reflects higher-productivity project selection rather than a zero-sum transfer from the projects held by less literate savers. This also implies that a larger share of the return gain accruing to literate savers need not come dollar-for-dollar out of intermediaries’ margins, since part of it reflects a real increase in the return on the marginal project funded, rather than a pure redistribution of intermediation profits.
We want to emphasize, however, that this decomposition is a theoretical device disciplining the interpretation of \(R_{t+1}(x_t)\), not an estimated object: we do not separately calibrate \(\varphi (\cdot )\) and \(\varrho (\cdot )\), and our empirical calibration of \(R_H/R_L\) in Section 3 is based on cross-sectional portfolio-return differentials (van Rooij et al. 2011) rather than on direct measurement of either channel in general equilibrium. In particular, in general equilibrium, broader financial literacy may compress the observed cross-sectional differential we use for calibration, as prices of the previously scarce higher-return projects adjust; the model requires only that higher literacy raises the efficiency with which savings are transformed into productive investment, not that the calibrated gap \(R_H - R_L\) would persist unchanged under universal literacy.
Appendix C: A calibration in low literacy environments
We now briefly compare the benchmark calibration based on stylized features of the US economy with an illustrative calibration intended to capture a lower financial literacy environment. Italy provides a natural comparison because, despite being a large advanced economy with developed financial institutions, it displays substantially lower financial literacy and lower stock market participation relative to the US (Guiso and Jappelli 2005; Klapper et al. 2015). The exercise is not intended as a full country-specific structural estimation, but rather as a sensitivity analysis illustrating how differences in literacy conditions may affect the model’s quantitative implications.
1.1 C.1 Homogeneous economy
To construct the Italian comparison, we keep the benchmark calibration’s macroeconomic parameters unchanged and modify only the productivity of financial literacy accumulation, \(\chi \). Specifically, we scale \(\chi \) proportionally to observed adult financial literacy rates, which are estimated at approximately \(57\%\) in the US and \(37\%\) in Italy (Klapper et al. 2015), thus we set \(\chi ^{IT}=\chi ^{US}\left( \frac{0.37}{0.57}\right) =11.56\).
This parametrization captures the idea that lower observed financial literacy may reflect a weaker environment for accumulating and intergenerationally transmitting financial knowledge. Such differences may arise from lower participation in financial markets, weaker financial education, stronger persistence of low-literacy conditions across generations, or lower exposure to sophisticated financial products.
Under this parametrization, the policy effort required to escape the low-literacy equilibrium increases substantially. In the benchmark US calibration, the minimum matching subsidy required to move the economy into the high-return basin of attraction is approximately \(7.88\%\). In Italy, the corresponding subsidy rises to roughly \(156\%\). While this magnitude should not be interpreted literally, it highlights an important implication of the model: once an economy is sufficiently far below the literacy threshold, the policy effort required to escape the low-literacy trap may increase nonlinearly. In this sense, the comparison illustrates how persistent differences in financial literacy may generate substantial divergence in long-run macroeconomic outcomes even across otherwise similar advanced economies.
From a policy perspective, the comparison suggests that preventive interventions aimed at avoiding persistent low-literacy regimes may be substantially less costly than ex-post attempts to reverse them. Early financial education, broader participation in capital markets, and institutional mechanisms favoring intergenerational transmission of financial knowledge may therefore have large long-run macroeconomic effects by reducing the likelihood that economies remain trapped in low-return equilibria.
1.2 C.2 Heterogeneous economy
We next extend the comparison to the heterogeneous economy. Consistently with the benchmark calibration, we interpret heterogeneity through differences in educational attainment and exposure to financial-learning opportunities rather than through intrinsic differences in financial-learning ability. Accordingly, we retain the benchmark ability parameters, \(\eta _L=0.77\) and \(\eta _H=1.30\), and instead modify population composition and literacy accumulation productivity. We retain the lower Italian literacy accumulation productivity, \(\chi ^{IT}=11.56\), and calibrate the population shares using educational attainment data. In the benchmark US calibration, the heterogeneous economy was motivated by the approximate split between individuals with at most high-school education and those with some college education or more. Italy, by contrast, displays substantially lower tertiary educational attainment, and specifically approximately \(28\%\) of Italians aged 25–34 possessed tertiary education in 2021 (OECD 2023). We therefore set \(\pi _H^{IT}=0.28\) and \(\pi _L^{IT}=0.72\). This calibration should not be interpreted as implying that education mechanically determines financial literacy, but rather as a parsimonious proxy for differences in financial learning opportunities, exposure to sophisticated financial decisions, and participation in higher return financial markets.
Under this parametrization, the aggregate participation-adjusted return factor in the polarized equilibrium becomes \(R_P^{IT} = \pi _L^{IT}R_L+\pi _H^{IT}R_H = 1.097\). The corresponding output ratio relative to the all-low equilibrium is therefore \(\frac{y_P^{IT}}{y_L} =( \frac{R_P^{IT}}{R_L})^{\frac{\alpha }{1-\alpha }} \simeq 1.047\), implying that the polarized Italian economy achieves an output level approximately \(4.7\%\) above the all-low regime. This is substantially smaller than the corresponding gain in the benchmark US calibration, where the polarized economy achieves an output level approximately \(8.2\%\) above the all-low regime.
The comparison highlights how lower financial literacy and lower financial inclusion may amplify the persistence of polarization. A larger share of dynasties operating below the literacy threshold reduces the average efficiency with which savings are transformed into productive capital and lowers the aggregate gains associated with partial access to high-return financial opportunities. In this sense, economies characterized by weaker financial inclusion may experience not only lower aggregate output and slower capital accumulation, but also stronger persistence of intergenerational financial inequality.
The policy implications are also stronger in the heterogeneous environment. Since a larger fraction of households remains below the literacy threshold, moderate interventions may be insufficient to eliminate polarization or generate widespread upward mobility. The Italian comparison therefore suggests that policies aimed at improving literacy may need to be broader and more persistent in economies where low-literacy dynasties constitute a large fraction of the population. Therefore, the exercise illustrates how differences in financial literacy conditions may translate into long-run divergence in both aggregate performance and inequality dynamics even among advanced economies with otherwise similar productive structures.
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Calcagno, R., Gori, L. & Marsiglio, S. Financial literacy, return on saving, and poverty traps. J Evol Econ 36, 67 (2026). https://doi.org/10.1007/s00191-026-00986-1
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DOI: https://doi.org/10.1007/s00191-026-00986-1