Abstract
This chapter develops and studies a tough love model of intergenerational altruism. We model tough love by modifying the Barro-Becker standard altruism model in two ways. First, the child’s discount factor is endogenously determined, so lower childhood consumption leads to a higher discount factor later in life. Second, the parent evaluates the child’s lifetime utility with a constant high discount factor. Our model predicts that parental transfers will fall when the child’s discount factor falls. This is in contrast with the standard altruism model, which predicts that parental transfers are independent of exogenous changes in the child’s discount factor.
The original article first appeared in the International Economic Review 53, 791–814, 2012. A newly written addendum has been added to this book chapter.
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Notes
- 1.
- 2.
- 3.
This chapter focuses on the parent’s role in preference formation. A related work is Mulligan (1998) on the altruistic preference formation of the parent toward the child.
- 4.
In a recent work, Slav́ik and Wiseman (2009, Tough love for lazy kids: dynamic insurance and equal bequests, unpublished manuscript) have also proposed a model of tough love. These authors emphasize the moral hazard problem faced by parents in order to construct a model with a dynamic insurance strategy that involves providing greater inter vivos transfers to poor children and dividing bequests equally. Their model does not involve endogenous time discounting.
- 5.
This issue is related to the literature on the importance of initial endowments on subsequent outcomes of a dynamic process (Heckman 1981, 1991). As suggested by Heckman, it is important to distinguish between heterogeneity (how persistent is the effect of initial endowments on outcomes), and state dependence (whether subsequent experiences attenuate or accentuate the effect of initial endowments). It is possible that a raw correlation between wealth and consumption growth reflects a causal influence of wealth on consumption growth (state dependence), or the fact that individuals differ in time preferences and more patient people accumulate more wealth (heterogeneity).
- 6.
They control the endogeneity problem by analyzing how the discount factor changes with the size of a prize obtained in another experiment.
- 7.
Baumrind (1966) identified three modes of parental control. The first mode is permissive, where parents act as a resource for their children and do not actively involve themselves in shaping the current and future behavior of the child. The second mode is authoritarian, where the parent uses a set standard of conduct that is theologically or religiously motivated and tries to shape and control the child’s behavior with overt use of power. The third mode is authoritative, where the parent actively involves himself/herself in shaping the child’s behavior and attitudes and uses reasoning and discipline to ensure a well-rounded long-term development of the child. The parent affirms the child’s current behavior, separating right from wrong, and also sets standards for the child’s future behavior.
- 8.
For expositional ease, we begin by making the simplifying assumption that these three periods are of equal duration. Note that results presented in this section as well as in Sect. 4 are robust to varying durations for the three periods. Further, in Sect. 5 we relax this assumption and study the model with varying durations for childhood, work, and retirement.
- 9.
Given the timing of our model, this implies that transfers, T, are made only in period 1. Further, we assume that transfers are made from the parent to the child and there are no reverse transfers.
- 10.
In this simple consumption good economy, we view consumption as a composite good that may include leisure activities such as TV time, video game time etc. In Sect. 5, we extend this basic setup and introduce leisure as a second good.
- 11.
u(.) is continuously differentiable with a nonzero Jacobian.
- 12.
Note that changes in the parent’s own discount factor will affect transfers. However, here we are imagining a sudden change in social norms that affects only the child’s discount factor with no effect on the parent’s discount factor.
- 13.
The discussion presented here postulates a model of parental tough love in the context of a single generation. An interesting extension is to model tough love in a dynastic framework exemplified in the context of the standard altruism model by Barro (1974). In such a model, the child will be a repeater in the dynamic process and will pass on the discount factor she inherited from her tough love parent to her own offspring. We are investigating the implications of such a framework for tough love altruism in a separate paper that is a work in progress (Bhatt et al. 2011).
- 14.
It can be easily shown that
$$\displaystyle\begin{array}{rcl} \frac{\partial C_{2}^{{\ast}}} {\partial \beta _{0}} <0\;\ \frac{\partial C_{2}^{{\ast}}} {\partial T}> 0& & {}\\ \end{array}$$ - 15.
Note that since \(\frac{\partial T^{{\ast}}} {\partial \beta _{0}}\) is strictly positive for β p = β 3, k , we have a positive relationship between T ∗ and β 0 even when β p < β 3, k , as long as the difference is small in magnitude.
- 16.
Our simulation results are robust to alternative parametric specifications of the utility function and also to a wide range of model parameter values.
- 17.
We have chosen our parameter values to be consistent with consensus estimates reported in the literature. When such estimates are not available, we have used the optimality conditions of our model and used micro data to approximate the parameter values. For σ, we are using a value of 1.5, which implies an elasticity of intertemporal substitution of around 0.67. In the literature, many studies have used micro data and have estimated this parameter to be between 0.4 and 0.7 (see Hall 2009; Ogaki and Reinhart 1998). For deriving a value for η, given our parametric specification and under the assumption that β p and β k are approximately close to each other, from the parent’s first-order condition we obtain:
$$\displaystyle{\frac{C_{p}^{-\sigma }} {C_{1}^{-\sigma }} = \frac{1-\eta } {\eta }.}$$We used σ = 1. 5 and data from the Consumer Expenditure Survey (CEX) on per capita annual consumption expenditure for individuals aged 25 or below to approximate C 1. We used per capita annual consumption expenditure for individuals aged 65 or above to approximate C p . Then, the above optimality condition η = 0. 66. Finally, for parameter a, we assumed a value of 0.02, although we also tried alternative values of 0.01 and 0.04 and found that the results are robust to these alternative values for parameter a.
- 18.
We have also studied the version of our model where we add the bequest motive for the parent. We find that the main result of the paper remains qualitatively unchanged. Consistent with our intuition of parental tough love, the parent with a tough love motive respond to a fall in his child’s discount factor by reducing transfers and increasing bequests. In contrast, the parent in the standard altruism model increase transfers and decrease bequests in response to a fall in the child’s discount factor.
- 19.
For brevity, we have not provided proofs for the redistributive neutrality property for all the models presented in this chapter. These analytical results are available from the authors upon request.
- 20.
Using data from the Health and Retirement Survey (HRS), McGarry (1999) found a positive relationship between the recipient’s permanent income and the amount of transfers. However, this study uses education of the respondent as a proxy for the permanent income, which may be missing important aspects of permanent income. Further, when estimating the relationship between the recipient’s permanent income and amount of transfers, McGarry (1999) did not adjust the parent’s permanent income in order to keep family permanent income constant. We believe that the Altonji et al. (1997) result is more robust as they used better measures of permanent incomes of the parent and the child and also controlled for family permanent income when evaluating the relationship between recipients’ permanent income and their transfers.
- 21.
For simplicity, we abstract from the child’s early life in which he does not face the work–leisure choice.
- 22.
Cunha et al. (2006) present a survey of empirical evidence that later interventions in adolescent years can affect noncognitive skills such as patience, self-control, temperament, time preferences, etc., while these interventions cannot affect cognitive skills.
- 23.
We thank an anonymous referee for bringing this point to our notice as a potential future work.
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Acknowledgements
We thank Shinsuke Ikeda for his initial collaboration, Dean Lillard for comments and discussions from the initial stage of this research, three anonymous referees, Fumio Hayashi, Nobuhiro Kiyotaki; and seminar and session participants at the 2008 North American Summer Econometric Society, Midwest Economics, and Midwest Macroeconomics Meetings; Aoyama Gakuin, Baskent, Bilkent, Doshisha, Fukuoka, Hiroshima, Hitotsubashi, Keio, Kobe, Koc, Kyoto, Nagoya, Nihon, Ohio State, Osaka, Osaka Prefecture, Sabanci, Waseda, Yale Universities; and the Universities of Cyprus and Tokyo for comments. This research of Masao Ogaki was partially supported by Grants-in-Aid for Scientific Research from Japan Society for the Promotion of Science.
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Appendices
Appendices
1.1 A Proof for Proposition 1
In this section of the appendix we provide an analytical proof of our main result specified in Eq. (2.13):
We start the derivation of the above result by noting that the parent accounts for C 2 ∗ when maximizing utility by choosing transfers, T. From the first-order condition for the parent’s problem described in Eqs. (2.10) and (2.11), we obtain:
where T ∗ denotes optimal parental transfers, \(V ^{{\prime}}(.) = \frac{\partial V (.)} {\partial T}\), and \(u^{{\prime}}(.) = \frac{\partial u(.)} {\partial T}.\)
Now consider an exogenous change in the child’s discount factor (β k ) captured by a change in β 0. From the parent’s first-order condition described above we obtain:
where:
Given concavity of V(.) and u(.), we know that A > 0. Hence:
Then \(\frac{\partial T^{{\ast}}} {\partial \beta _{0}}> 0\) if and only if:
Now using the first-order condition for the child’s problem, we can rewrite the above condition as follows.
It is straightforward to show that the LHS of the above expression is given by:
Since \(\frac{\partial C_{2}^{{\ast}}} {\partial T}> 0\) and u ′(. ) > 0, the above expression is strictly positive if and only if:
This establishes our claim in Eq. (2.14). Now, given positive marginal utility, concavity of u(. ), and \(\frac{\partial C_{2}^{{\ast}}} {\partial \beta _{0}} <0\), the sufficient conditions for the above expression to be strictly positive are:
-
(i)
β p ≥ β 3, k and
-
(ii)
\(\frac{\partial ^{2}C_{2}^{{\ast}}} {\partial \beta _{0}\partial T} \leq 0\).
1.2 A Proof for Proposition 2
In this section we show that \(\frac{\partial ^{2}C_{2}^{{\ast}}} {\partial \beta _{0}\partial T} \leq 0\) will depend on the convexity of the marginal utility (as captured by the positive third derivative of the utility function) and the impatience level of the child.
We start our derivation with the partial derivative of the optimal second period consumption with respect to parental transfers:
where
Differentiating with respect to β 0
where
and
Since, D is always positive, the sign of \(\frac{\partial ^{2}C_{2}^{{\ast}}} {\partial \beta _{0}\partial T}\) depends on the sign of N. Now, the sign of N will be the same as the sign of:
If the above expression is negative then N < 0.
Hence, the condition for N < 0 is:
The above condition holds if,
-
(i)
\(u^{{\prime\prime\prime}}(.) \geq 0\) and
-
(ii)
\(\beta _{3,k}\ R\ G \leq 1\),
where
1.3 Power Utility Function
In this section of the appendix we use the power utility function to interpret the following condition:
where
We assume that the period utility function is given by:
Using the above specification of the utility function, from the child’s optimization problem, we get:
Hence, for the power utility case we get:
Using the above expression for G we can rewrite the inequality of interest as:
Rearranging, we get the following condition:
Addendum: Recent Developments
This addendum has been newly written for this book chapter.
Two directions of research that are closely related to the tough love model have been developing since the working paper version (Bhatt and Ogaki 2008) of this chapter was published. One direction is for normative economics and the other is for positive economics. The first direction is to add an element of virtue ethics to welfarism that has been the basis of normative economics. The second direction is to empirically evaluate the tough love model.
In Bhatt et al. (2014), we proposed an approach of normative economics for models with endogenous preferences that adds an element of virtue ethics to the traditional formulation based on the Bergson-Samuelson social welfare function (SWF). Our approach is based on the moral evaluation function (MEF) that evaluates different endogenous preferences in terms of moral virtue and on the social objective function (SOF), which is a function of SWF and MEF in order to express a balanced value judgment. This is in a sense a response to Sandel’s (2013) call to introduce more value judgment into economics based on his ideas of political philosophy explained for wide audience in Sandel (2009, 2012). In the same issue of the Journal of Economic Perspectives as in Sandel (2013) and Bruni and Sugden (2013) argued that neoclassical economics has already incorporated virtue ethics if we think about market virtues. Our approach can incorporate market virtues, but can also incorporate other virtues such as altruism toward a disabled stranger as shown in Bhatt et al. (2014). In Bhatt and Ogaki (2014, Rational addiction and optimal taxation: a reexamination based on the social objective function, unpublished), we applied our approach to the rational addiction model. If a society finds that preferences with drug addiction caused by past drug consumption is less virtuous, preferences affected by drug addiction are less virtuous than preferences that are not.
For the purpose of illustrating our approach by an example, Bhatt et al. (2013) applies it to a version of Bhatt and Ogaki’s tough love model. In this version, the original model is extended by bequest and bequest tax. In the model, the parent thinks that he should not spoil the child so that the child will grow to be patient, but is tempted to spoil the child because he enjoys watching his child having higher childhood utility. With a bequest motive, the parent can use the money saved by lowering childhood transfers in order to increase his bequest given to the child after she grows up. In this version of the model, the government has a policy tool of the bequest tax rate that can be used to influence the optimizing behaviors of the parent and the child. When the bequest tax rate is higher, the parent is more tempted to spoil the child because the money he saves by giving less transfers to the child will be taxed away when he gives the bequest.
If our informal discussions with many economists give a good guidance, many economists seem to think that moral value ethics is not desirable for public policy evaluations because they do not want the government to influence people’s preferences. However, in our model, the government does influence the child’s preferences as long as the bequest tax rate is not zero. The optimum tax rate is positive when the SWF is maximized. On the other hand, the optimum tax rate is zero when the SOF is maximized with α = 0. 3. Thus, introducing moral virtue ethics may result in a policy that does not affect people’s preferences. This illustrates that introduction of moral virtue ethics does not necessarily mean that the government starts to influence people’s preferences. Because any government policy may be influencing people’s preferences even when the government does not intentionally do so, it seems important to examine how each policy is influencing people’s preferences and think about how desirable such influences are for the society.
This line of thoughts leads us to the second direction of research. In order to examine whether or not any policy is influencing people’s preferences, we need empirical work on models with endogenous preferences in which such policy can affect preferences. For the tough love model with the bequest tax rate, there already exit some empirical work. A starting point of any model with endogenous time discounting is that genetic factors do not completely determine time discounting. Using a unique data set of twins in Japan, Hirata et al. (2010) found empirical evidence in favor of this.
Kubota et al. (2013) examined how parents’ tendencies for tough love behavior depend on various measures of time discounting for parents’ own lending and borrowing over different time horizons. Using the Osaka University Global COE survey data for Japan and the United States, they found evidence that is consistent with the tough love model. They also found one empirical puzzle that proportionately more U.S. parents show tough love to young children before the school age than Japanese parents even after controlling for time discounting and other economic and demographic factors. The is especially puzzling because more patient parents tend to show tough love, and Japanese parents are estimated by Kubota et al. (2013) to be more patient than U.S. parents.
Kubota et al. (2013, Time discounting and intergenerational altruism, unpublished) examined a possible solution to this puzzle is cultural differences between the two countries. They used a framework in anthropology that a worldview is behind each culture. Using the Osaka University Global COE survey data for Japan and the United States, they found that differences in the distributions of the confidence in worldview beliefs can explain a substantial portion of the international differences in the parental attitudes.
Akabayashi et al. (2014) reported evidence that is more consistent with the tough love model than with the standard Barro-Becker model from experiments with parent-child pairs. In their time preference experiments, each parent-child pair makes individual and joint decisions about how much and when the child receives a payment (e.g., 1,000 yen now versus 1,001 yen in 2 months). The Barro-Becker model in which the parent does not know the child’s time discount rate predicts that the only reason for the parent to make a different decision from the child when s/he makes an individual decision is the lack of knowledge about the child’s time discount factor. Hence the joint decision is predicted to be the same as the child’s individual decision. However, they find that about half of the pairs do not follow this prediction.
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Bhatt, V., Ogaki, M. (2016). Tough Love and Intergenerational Altruism. In: Ikeda, S., Kato, H., Ohtake, F., Tsutsui, Y. (eds) Behavioral Interactions, Markets, and Economic Dynamics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55501-8_2
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