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Pension Participation: Do Parents Transmit Time Preference?

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Abstract

A wide range of economic and health behaviors are influenced by individuals’ attitudes toward the future—including investments in human capital, health capital and financial capital. Intergenerational correlations in such behaviors suggest an important role the family may play in transmitting time preferences to children. This article presents a model of parental investment in future-oriented capital, where parents shape their children’s time preference rates. The research identifies a dual role for a parent’s time preference rate in the process of shaping the offspring’s attitude toward the future, and discusses paths through which parents may socialize children to be patient. The model’s implications are studied by investigating the parent–child correlation in pension participation using data from the Panel Study of Income Dynamics

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Notes

  1. We are not the first to argue that parents may desire to influence their children's attitudes toward the future. Doepke and Zilibotti (2005) present a theoretical model that illustrates conditions under which one can expect to observe a connection between parents' discount rates and their offspring's during adulthood.

  2. The Becker–Mulligan model has this price fixed at 1 for all individuals.

  3. Alternatively, if one conceptualizes future-oriented capital as something a family purchases in the marketplace, one can expect costs to be lower for parents who are already patient themselves because these parents might have better knowledge about products that make the future more salient. Becker and Mulligan (1997) argue future-oriented capital can be purchased in markets.

  4. Research on parental modeling of behavior abounds in the psychology literature. For example, Mischel et al. (1989) write about the importance of "an early family environment in which self-imposed delay is encouraged and modeled" in their discussion of delay of gratification in children (Mischel et al. 1989, p. 936).

  5. One exception is a paper by Lusardi (2003) in which the effect of siblings on planning for retirement was examined.

  6. Note that the problem (3)–(4) is the adult child’s maximization problem from the point of view of a parent who cares only about her immediate offspring, but not about grandchildren and subsequent generations.

  7. While related, the terms “discount factor” and “discount rate” are not synonymous. The phrase “discount rate” or “rate of time preference” describes the parameter that is often compared to the market rate of interest. Hence the rate of time preference is the “d” term in the denominator of an expression such as β ≡ 1/(1 + d), while β is the discount factor.

  8. There also may be an inherited propensity to intertemporal choices. Studies of smoking have shown genetic patterns that predict who will smoke and who is unable to quit (Uhl et al. 2007).

  9. These assumptions make the return to investing in future-oriented capital positive, and they stipulate that the child discount factor rises at a decreasing rate in s. The assumptions are similar to those made by Becker and Mulligan (1997) in their model showing how an individual might shape her own preferences.

  10. \( - \pi^{\prime}(\beta) \cdot \left\{\cdot \right\} \) is negative because \( \pi^{\prime}(\beta) < 0 \) and the expression in the brackets is also negative.

  11. It is important to note that a corner solution with the parent choosing zero investment in future-oriented capital of the child cannot be ruled out. This situation is possible, for example, when the relative price of future-oriented capital investment facing the parent is prohibitively high. In such scenario, the corner solution should disproportionately occur among parents with low patience since they are likely to have high π. Furthermore, at the lower end of the discount factor distribution we may observe that while β is increasing the optimal investment in future-oriented capital remains zero, giving a range of β values over which \( {\frac{{d\tilde{\beta}}}{d\beta}} = 0 \). For the empirical strategy we employ, which is described in section four, the cases with corner solutions will bias the estimates of the intergenerational association in time preference toward zero.

  12. The question asked is, “In planning your saving and spending, which of the time periods listed is most important to you?” Response categories are (1) the next few months, (2) the next year, (3) the next few years, (4) the next 5–10 years, and (5) longer than 10 years. (This is variable ×3008 in the dataset.).

  13. Here, having a long time horizon is defined as having a planning horizon that is at least five years long. We get similar results—qualitatively--when we define long horizon as including only those whose time horizons are in the SCF’s 10 years or longer category.

  14. This analysis and the regressions are done using a sample of households with heads age 42–60 in 2004. This age restriction makes the age group comparable to the baby boom age group used in the next few sections of the paper.

  15. We use the phrase "pension participation decision" to indicate whether an individual participates in a pension plan. Pension coverage comes from either choosing to participate in a defined contribution (DC) plan, for companies whose coverage takes that form; or by selecting a job that comes with defined benefit (DB) coverage, for employers with this type of plan. Additionally, some individuals obtain coverage by choosing to establish an individual retirement account (IRA plan).

  16. By convention the PSID collects data on the head and the spouse for couples who are legally married, and for the two unmarried partners in the case of couples that are co-habitating but not legally married.

  17. Results in Table 3 are based on the entire unrestricted by age sample of working heads and wives.

  18. Some readers also may find the estimated effects of race and marital status to be of interest. Table 3 shows that being black raises a household’s probability of having a pension when other characteristics are controlled for. This is consistent with the job selection literature (see Chiteji et al. 2006 for example). Black families may be more likely to seek out “good” jobs when all other characteristics of the job are comparable. Accordingly, the racial disadvantage seen in other domains—in lower rates of bank account ownership or lower rates of stock market participation, for example—does not appear to be present for pension participation. For marital status, the positive and statistically significant effect found on pensions (using the DB measure) also is consistent with the existing literature. Empirical research shows that marriage is correlated with greater wealth, higher pension wealth, and greater family resources more generally (Wolff 2007; Keister 2000).

  19. Because the PSID did not ask workers whether they had pension coverage in early waves of the survey (prior to 1999), data on pension coverage for the father generation is inferred from actual receipt of pension income during retirement.

  20. In the PSID receipt of pension income as a separate question has been asked since 1993. From 1984 to 1993 receipt of pension income was asked in combination with receipt of annuities and other retirement pay.

  21. The PSID family id mapping system (FIMS) software that makes it possible to construct age-comparable pension measures has obvious applications to other forms of intergenerational analysis. For example, when attempting to study the correlation between earnings of fathers and sons, it is important to have each father–son pair at a similar point in the lifecycle when one measures the incomes of the two different generations, but it is equally important to have life cycle point comparability within generations in order to measure the association correctly.

  22. The other real estate variable does not include main home ownership.

  23. The weak significance is due in part to rather small sample size of 800. For comparison, the only other significant variable in the regression is father’s education which is similarly significant at 10% level.

  24. For each individual occupation and industry were assigned based on the most frequently reported occupation and industry.

  25. In our dataset four occupation groups, such as laborers, farmers/farm laborers, service workers and private household workers, and five industries, such as agriculture, construction, trade, business/repair service and entertainment, have less then 50% chance of pension receipt being reported.

  26. See McKernan and Sherraden (2008) and Sanders and Porterfield (2010) for example. Additionally, see Fry et al. (2008) for discussion of similar programs outside the United States.

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Authors and Affiliations

  1. Institute for Social Research, University of Michigan, 426 Thompson Street, Ann Arbor, MI, 48104, USA

    Elena Gouskova

  2. Department of Economics, Skidmore College, 815 N. Broadway, Saratoga Springs, NY, 12866, USA

    Ngina Chiteji

  3. Institute for Social Research, University of Michigan, 426 Thompson Street, Ann Arbor, MI, 48104, USA

    Frank Stafford

  4. Department of Economics, University of Michigan, Ann Arbor, MI, USA

    Frank Stafford

Authors
  1. Elena Gouskova
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  2. Ngina Chiteji
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  3. Frank Stafford
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Corresponding author

Correspondence to Elena Gouskova.

Appendix

Appendix

Conditions for Concavity of the Value Function

V(s) is the value function resulting from maximization of child’s utility:

$$ {\text{Max}}U(\tilde{c}_{1},\tilde{c}_{2},s) = u(\tilde{c}_{1}) + \tilde{\beta}(s) \cdot u(\tilde{c}_{2})\,{\text{subject to}}\,\tilde{c}_{1} + \tilde{c}_{2} \le \tilde{A} $$

Let \( (\tilde{c}_{1}^{*} (s),\tilde{c}_{2}^{*} (s)) \) be the solution.

By the envelope theorem,

$$ {\frac{dV}{ds}}(s) = \tilde{\beta}^{\prime}(s) \cdot u(\tilde{c}_{2}^{*} (s)) > 0 $$

The second derivative:

$$ {\frac{{d^{2} V}}{{ds^{2}}}}(s) = \tilde{\beta}^{\prime\prime}(s) \cdot u(\tilde{c}_{2}^{*} (s)) + \tilde{\beta}^{\prime}(s) \cdot u^{\prime}(\tilde{c}_{2}^{*} (s)) \cdot \tilde{c}_{2}^{*\prime} (s) $$

The first term in the above expression is negative, and the second term is positive. So for the value function to be concave the following condition must hold

$$ - \tilde{\beta}^{\prime\prime}(s) \cdot u(\tilde{c}_{2}^{*} (s)) \ge \tilde{\beta}^{\prime}(s) \cdot u^{\prime}(\tilde{c}_{2}^{*} (s)) \cdot \tilde{c}_{2}^{*\prime} (s) $$

i.e. \( \tilde{\beta}(s) \) should be sufficiently concave.

Derivation of Eq. 5

First order conditions for problem (1)–(2) are

  1. (i)

    \( u^{\prime}(c_{1}) - \beta \cdot u^{\prime}(c_{2}) = 0 \)

  2. (ii)

    \( u^{\prime}(c_{1}) - {\frac{{V^{\prime}(s)}}{\pi (\beta)}} = 0 \)

  3. (iii)

    \( A - c_{1} - c_{2} - \pi (\beta) \cdot s = 0 \)

We totally differentiate the three equations with respect to the endogenous variables c 1, c 2, s and the exogenous parameter β:

$$ u^{\prime\prime}(c_{1})dc_{1} - \beta \cdot u^{\prime\prime}(c_{2})dc_{2} - u^{\prime}(c_{2})d\beta = 0 $$
$$ u^{\prime\prime}(c_{1})dc_{1} -{\frac{\text{V}^{\prime\prime}(s)}{\pi (\beta)}} ds -{\frac{\pi^{\prime}(\beta)\text{V}^{\prime}(s)}{\pi^{2} (\beta)}}d\beta = 0 $$
$$ dc_{1} + dc_{2} + \pi (\beta)ds + s \cdot \pi^{\prime}(\beta)d\beta = 0 $$

Then solving this system of equations for \( {\raise0.7ex\hbox{${ds}$} \!\mathord{\left/{\vphantom {{ds} {d\beta}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${d\beta}$}} \) we get (5)

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Gouskova, E., Chiteji, N. & Stafford, F. Pension Participation: Do Parents Transmit Time Preference?. J Fam Econ Iss 31, 138–150 (2010). https://doi.org/10.1007/s10834-010-9181-8

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