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International Tax and Public Finance

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09-10-2019

Myopia, education, and social security

Authors: Frank N. Caliendo, T. Scott Findley

Published in: International Tax and Public Finance | Issue 3/2020

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Abstract

A potential role of social security is to protect individuals who have accumulated little or no assets for retirement. Yet, this type of social safety net could reduce human capital formation by making the life-cycle financial rewards from education less attractive. For example, social security tax rates are correlated negatively with tertiary educational attainment across OECD countries. We construct a continuous-time overlapping-generations model with endogenous school duration that can account for this correlation, and we use the model to compute the social security tax rate that maximizes steady-state social welfare in general equilibrium. Social security in the model provides protection for retirees who arrive at retirement with no assets, and it can also redistribute wealth toward those with low earnings, but the program distorts the level of human and physical capital accumulation. In the presence of these characteristics, the social security tax rate that maximizes steady-state welfare is approximately 10%, which is about half of the average rate of 21% across the OECD. This result is robust to whether the social security program is redistributive or earnings based.

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Among other possibilities, social security might also provide longevity insurance when annuity markets are missing. Other such roles are not the focus of this study.

Multiple surveys establish a rather robust fact about saving behavior in the USA: approximately 20-30% of households never save for retirement and are completely reliant on Social Security to finance their retirement needs. These surveys include the Health and Retirement Study, Social Security Administration data, Panel Study of Income Dynamics, and the Retirement Confidence Survey. See Huang and Caliendo (2011) for a review of this evidence and related evidence, as well as the many references therein.

While we focus on a general-equilibrium interpretation of Fig. 1, there are also microeconomic reasons for why social security taxation might lead to lower educational attainment (see Jacobs 2009). In other words, while our model captures a viable channel through which social security might affect educational attainment, other potential channels could exist as well. For instance, social security taxation might reduce the rewards from acquiring more education by reducing the after-tax skill premium. And depending on the way benefits are structured, it might further reduce the rewards from education by incentivizing early retirement and hence reducing the length of the earning period. These are potentially important effects that we abstract from in our analysis. In addition, there are other possible explanations for the correlation in Fig. 1 wherein the causality might go the other way. One could imagine a country where average education is low and where this group forms a powerful voting block that advocates for a generous (and redistributive) social security program.

Equilibrium objects differ across alternative steady-state competitive equilibria when searching to identify the one in which social welfare is maximized in the tax rate.

The average tax rate of 21% across the OECD is close to the social security tax rate that maximizes steady-state welfare in the case where the social welfare function is of the Rawlsian or Maximin form.

Cremer et al. (2008) compute the degree of redistribution toward individuals with low earnings that maximizes a weighted aggregation of lifetime utilities in partial equilibrium, when there are exogenous differences in worker productivity. We compute the degree of redistribution that maximizes steady-state social welfare, and a key feature of our model is that heterogeneity in productivity arises endogenously.

The welfare function that is optimized by searching over different values of the social security tax rate often varies throughout this literature. In the partial-equilibrium studies, the social welfare function is lifetime utility. In the general-equilibrium studies with representative agents, the welfare function is steady-state lifetime utility. And lastly, in the general-equilibrium studies with heterogeneous agents, the welfare function is most often a weighted aggregation of steady-state lifetime utilities across the heterogenous characteristics of individuals.

Although the mechanics of the model in our study relate most closely to those of Wallenius (2013) and Ortiz (2014), because both have calibrated general-equilibrium models, there are many other studies that also examine the effect of various institutional features of social security on labor force participation in old age. Examples include Diamond and Gruber (1997), Gruber and Wise (1998), Samwick (1998), Börsch-Supan (2000), Coile et al. (2002), Cremer and Pestieau (2003), Gustman and Steinmeier (2005), Coile and Gruber (2007), Cigno (2008), Liebman et al. (2009), and Mastrobuoni (2009), to name just a few. All of these studies focus on exit from the labor force, whereas we focus on entrance into the labor force.

For convenience, we assume that there is no private tuition cost to acquiring tertiary education. This is a reasonable first approximation given that 75% of tertiary education spending is publicly subsidized on average in OECD countries (Jacobs 2009).

The microeconomic part of our model is a special case of the model in Jacobs (2009), obtained by abstracting from hours worked, retirement choice, and by setting the subsidy rate on direct education costs to 100%. These features are of course important, but abstracting from them allows us to demonstrate the predictive power of our simple model via the general-equilibrium mechanism.

Institutional details (e.g., eligibility age, whether collection of benefits is allowed while working, and rewards for delayed claiming) vary across the OECD. Ortiz (2014) examines differences in institutional details in accounting for variation in retirement across OECD countries. See also Caliendo and Gahramanov (2013).

While actual retirement from the labor force need not coincide with the social security eligibility age in general (indeed, some countries show somewhat large discrepancies between the two), retirement and eligibility are very nearly synchronized on average across the OECD. The former is 63.5, and the latter is 63.6.

This includes public subsidies to households for living costs and public subsidies to private entities.

The OECD measures what is referred to as “school expectancy,” which is the average or expected number of years of tertiary education.

To be precise, the analytical solutions for some of the variables are not defined when $\rho =0$, so we use $\rho =0.0001$ as a proxy instead.

Jacobs (2009) offers three additional microeconomic reasons as to why high social security taxes (or high labor taxes of any kind) might lead endogenously to low levels of educational attainment. First, high taxes might make the direct education costs (tuition) high relative to the rewards for obtaining an education (after-tax wage income). Second, high taxes might lead to greater demand for leisure during the working period, which discourages educational attainment since utilization of the extra human capital is low anyway. And third, high taxes might lead to early retirement, which in turn might also reduce the incentive to get an education.

We can illustrate this effect a little more formally as follows. After defining the total discounted income flow as a function of school duration,

$$\begin{aligned} D(S)\equiv \int _{S}^{T}\exp [-rt](1-\theta -\tau ){\bar{e}}(S)w\ \mathrm{d}t+\int _{T}^{ {\bar{T}}}\exp [-rt]b(S)\mathrm{d}t, \end{aligned}$$

we note that the financial effect of an additional year in school, evaluated at $S=0$ to reduce clutter and without loss of generality, is

$$\begin{aligned} D^{\prime }(0)=-(1-\theta -\tau ){\bar{e}}(0)w+\int _{0}^{T}\exp [-rt](1-\theta -\tau ){\bar{e}}^{\prime }(0)w\ \mathrm{d}t+\int _{T}^{{\bar{T}}}\exp [-rt]b^{\prime }(0)\mathrm{d}t. \end{aligned}$$

Note that the net financial gain from attending the first year of school, $ D^{\prime }(0)$, is reduced by an increase in the interest rate: the foregone earnings associated with attending a year of school (1st term) become relatively large as the gains from schooling through the skill premium (2nd term) and any increase in social security benefits (3rd term) are reduced by an increase in the interest rate.

The OASI tax rate of 10.6% in the US social security program is also very close to the model-generated optimal value.

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Title: Myopia, education, and social security
Authors: Frank N. Caliendo
T. Scott Findley
Publication date: 09-10-2019
Publisher: Springer US
Published in: International Tax and Public Finance / Issue 3/2020
Print ISSN: 0927-5940
Electronic ISSN: 1573-6970
DOI: https://doi.org/10.1007/s10797-019-09569-2

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