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Social security and risk sharing: the role of economic mobility across generations

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Abstract

How well does social security jointly insure lifetime earnings risk and longevity risk? We show that the answer to this fundamental question depends critically on the nature of economic mobility across generations. To show this result, we compare two economies. In our first economy, inheritances are uncorrelated with wage earnings, implying that an individual’s earnings are unrelated to the wages and asset holdings of their predecessors. In our second economy, there is no such economic mobility; instead, low-wage earners are stuck receiving small inheritances from their low-wage ancestral line, while high-wage earners enjoy large inheritances from their high-wage ancestral line. We make these comparisons in a variety of settings including both fixed and endogenous factor prices. Social security causes large welfare losses in the first economy but can generate large welfare gains in the second economy. Given the apparent limits to economic mobility in the USA, the welfare gains from collective risk sharing through social security are potentially large.

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Notes

  1. Although longevity risk can be insured using annuities, participation is low in private annuity markets and the market is characterized by asymmetric information and adverse selection [see Pashchenko (2013) for a discussion]. Similarly, there is no insurance market to protect against low-wage earnings over the life cycle.

  2. See Chetty and Hendren (2018a, b), Chetty et al. (2018a, b, 2020) for a discussion of the determinants of economic mobility.

  3. Hosseini (2015) studies the welfare effects on mandatory annuitization through social security in a model where private annuity markets do exist but suffer from adverse selection problems. We abstract from the adverse selection problem and instead assume annuity markets are closed and focus our attention on the issue of economic mobility.

  4. A number of studies examine the degree to which differential mortality by wage type offsets the level of redistribution that is otherwise implied by the progressive benefit earning rule (Coronado et al., 1999, 2002, 2011; Bishnu et al., 2019; Liebman, 2002; Goda et al., 2011; Gustman & Steinmeier, 2001), and a number of papers consider how this fact affects the desirability of different reform options (Pestieau & Racionero, 2016; Bommier et al., 2011; Sheshinski & Caliendo, 2020). We abstract from differential mortality considerations and focus directly on the role of intergenerational economic mobility in the study of risk sharing through social security.

  5. One implication of our analysis is that optimal reform policies would preserve the current benefit levels. A vast literature explores changes in Social Security taxes and benefits in response to changing demographics such as Coronado et al. (1999, 2002), De Nardi et al. (1999), Diamond and Orszag (2005), Bommier et al. (2011), İmrohoroğlu and Kitao (2012), Kitao (2014), Pestieau and Racionero (2016), Bagchi (2016, 2017), and McGrattan and Prescott (2017) among many others. A closely related literature focuses on social security privatization in response to aging demographics, such as Feldstein (1996), Huggett and Ventura (1999), Kotlikoff et al. (2007), Nishiyama and Smetters (2007), and Conesa and Garriga (2008).

  6. See Findley and Caliendo (2008) for a survey of behavioral models used to justify social security.

  7. We abstract from any timing uncertainty regarding the receipt of a bequest. Cottle Hunt and Caliendo (2021) find that social security is welfare enhancing if the timing of bequest income is risky.

  8. This is a little larger than the full employer and employee tax of 10.6% (the Old-Age and Survivors Insurance (OASI) tax rate since 1990).

  9. The marginal tax rates are 10%, 12%, 22%, 24%, and 32%. The standard deduction is $12,000 (normalized to 0.04673 for our wage distribution). The thresholds at which the marginal tax rate increases are $9,525, $38,700, $82,500, $157,500, and $200,000 (normalized to 0.037, 0.151, 0.321, 0.613, and 0.779 for our wage distribution). The sixth marginal income tax bin (37% for wages over $500,000) is excluded from our analysis, since our maximum calibrated wage \(w=1\) corresponds to a wage income of $256,800.

  10. Our baseline model follows the convention of a “timeless equilibrium” concept without a beginning or end of time. While this is a convenient modeling device, the timeless feature of the equilibrium makes the model intractable if one wants to go a step further and model specific bequest linkages between parents and children. The intractability arises because the size of the bequest from a given parent to child would depend on the entire history of bequests in that parent’s ancestral line. Nevertheless, we find it potentially useful to build a model with specific parent–child linkages when studying intentional bequests, because in doing so we are able to connect the bequest utility of Generation 1 to the utility that Generation 2 receives from the bequest through a tractable, dynamic-stochastic recursive problem.

  11. Otherwise the timing and magnitude of inheritance income received by Generation 2 are stochastic, and this is a rather complex problem that is studied elsewhere in the literature (Cottle Hunt & Caliendo, 2021). Here, we wish to side step this complexity to focus our attention on the mobility issue.

  12. There is some empirical support for less than perfect altruism. Laitner (2001) models altruism in a similar way to this section of our paper. In Laitner’s model, parents place a weight of \(\xi \) on their children’s utility (and \(\xi ^2\) on their grandchildren’s utility and so on recursively). He calibrates the model and finds \(\xi =0.83\) best matches US data.

  13. The literature has suggested several other motivations for bequests aside from altruism. Bequest can be the result of survival risk and incomplete insurance markets, as in our baseline model and in Hurd (1987, 1989), or Gokhale et al. (2001). Bequests can result from self-interested exchange with one’s heirs (Bernheim et al., 1985), as inter-generational risk sharing (Kotlikoff & Spivak, 1981), or parents might experience a “joy of giving” or “warm glow” (Altig et al., 2001; De Nardi, 2004).

  14. When \(\rho =0\), the interest rate is \(r=-0.016\) without social security and \(r=0.016\) with social security. When \(\rho =0.029\) the interest rate is \(r=0.01\) without social security and 0.044 with social security.

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Acknowledgments

We thank two anonymous referees and the editor for very helpful recommendations, as well as the participants from the 16th annual Liberal Arts Macroeconomics Conference, hosted by Pamona College in August 2020.

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  1. Lafayette College, Easton, USA

    Erin Cottle Hunt

  2. Utah State University, Logan, USA

    Frank N. Caliendo

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Cottle Hunt, E., Caliendo, F.N. Social security and risk sharing: the role of economic mobility across generations. Int Tax Public Finance 30, 1374–1407 (2023). https://doi.org/10.1007/s10797-022-09761-x

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