Title Tough love and intergenerational altruism Sub Title Author Bhatt, Vipul(Ogaki, Masao) 大垣, 昌夫 Publisher Keio Economic Society, Keio University Publication year 2011 Jtitle Keio Economic Society discussion paper series Vol.11, No.2 (2011. ) JaLC DOI Abstract This paper 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 low consumption at a young age leads to a higher discount factor later in life. Second, the parent evaluates the child's lifetime utility with a constant high discount factor. The tough love model predicts that transfers from the parent will fall when the child's discount factor falls. This is in contrast with the standard altruism model, which predicts that transfers from parents are independent of exogenous changes in the child's discount factor. Notes Genre Technical Report URL https://koara.lib.keio.ac.jp/xoonips/modules/xoonips/detail.php?koara_id=AA10715850-0000110 2-0001 慶應義塾大学学術情報リポジトリ(KOARA)に掲載されているコンテンツの著作権は、それぞれの著作者、学会または出版社/発行者に帰属し、その権利は著作権法によって 保護されています。引用にあたっては、著作権法を遵守してご利用ください。 The copyrights of content available on the KeiO Associated Repository of Academic resources (KOARA) belong to the respective authors, academic societies, or publishers/issuers, and these rights are protected by the Japanese Copyright Act. When quoting the content, please follow the Japanese copyright act. Powered by TCPDF (www.tcpdf.org) KESDP No. 11-2 Tough Love and Intergenerational Altruism Vipul Bhatt and Masao Ogaki Tough Love and Intergenerational Altruism∗ Vipul Bhatt† and Masao Ogaki‡ Abstract This paper 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’sdiscountfactorisendogenouslydetermined,solowconsumptionatayoungageleadsto ahigherdiscountfactorlaterinlife. Second,theparentevaluatesthechild’slifetimeutilitywith a constant high discount factor. The tough love model predicts that transfers from the parent will fall when the child’s discount factor falls. This is in contrast with the standard altruism model, whichpredictsthattransfersfromparentsareindependentofexogenouschangesinthe child’s discount factor. 1 Introduction How different generations are connected to each other is an important economic issue with implications for individual economic behavior such as savings, investment in human capi- ∗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 andsessionparticipantsatthe2008NorthAmericanSummerEconometricSociety,MidwestEconomics,and Midwest Macroeconomics Meetings; Aoyama Gakuin, Doshisha, Fukuoka, Hiroshima, Hitotsubashi, Keio, Kobe, Kyoto, Nagoya, Nihon, Ohio State, Osaka, Osaka Prefecture, Waseda, Yale Universities; and the University of Tokyo for comments. †Assistant Professor, Department of Economics, James Madison University. ‡Professor, Department of Economics, Keio University. tal, and bequests, which in turn affect aggregate savings and growth. These interactions are also important from a policy perspective since they determine how families respond to public policies aimed at redistributing resources among family members. A commonly used paradigm to study such linkages is the standard altruism model proposed by Becker (1974) and Barro (1974) in which the current generation derives utility from its own consumption and the utility level attainable by its descendant(s). Using this framework, Barro found that there will be no net wealth effect of a change in government debt. A striking prediction of the standard altruism model is that when the child becomes impatient, transfers from the parent to the child do not change when the child is borrowing constrained (as we show in section 3). This implication of the model is not consistent with recent empirical evidence on pecuniary and non-pecuniary parental punishments (see Bhatt (2011), Hao et al (2008), and Weinberg (2001) for empirical evidence). For example, imagine that a child befriends a group of impatient children and suddenly becomes impatient because of their influence. As a result, the child starts to spend more time playing with the new friendsandlesstimestudying. Intheworstcases,thechildstartstosmoke,drink,orconsume illegal drugs (see Ida and Goto (2009) for empirical evidence that shows the association of low discount factors and smoking). At least some parents are likely to respond by imposing pecuniary punishments, such as reducing allowances, or non-pecuniary punishments, such as grounding. Another feature of the standard altruism model is that it precludes parents from directly influencing their children’s time preferences. However, there is empirical evidence that parents attempt to shape their children’s economic behavior and attitudes, including time preferences, as reviewed below. In many recent theoretical contributions, preferences of children are not exogenous, but are shaped by the attitudes and actions of their parents and other role models. For example, in the literature on cultural transmission of preferences, Bisin and Verdier (2001) proposed a general model with endogenous cultural transmission mechanisms wherein parents take actions to affect children’s traits, which as a special case 2 can correspond to time preferences. In some other models, even though parents do not take actions with the deliberate intention of affecting their children’s preferences, they end up doingsoindirectly. Forexample,Fernandezetal(2004)usedadynamicmodelwheremothers who work play an important role in the transmission of attitudes favoring the participation of women in the labor force to their sons. We will further discuss this issue by presenting empirical evidence for the parents’ role in children’s endogenous preference formation in the next section. The main contribution of this paper is to propose a new theoretical model of parent–child interaction that incorporates a mechanism through which parents can affect their children’s time preference formation. We develop a tough love model of intergenerational altruism, in which the parent is purely altruistic to the child, but exhibit tough love: he allows the child to suffer in the short run with the intent of helping her in the long run. The main prediction of our tough love altruism model is that transfers from the parent will fall when the child’s discount factor falls exogenously. This is in sharp contrast to the prediction of the standard altruism model where the parent does not respond to such a change in the child’s discount factor. An interpretation of this result is that parents with the tough love motive use pecuniary incentives to mold their children’s time preferences. Since exogenous changes in the child’s discount factor that make her impatient are likely to cause behavior that calls for parents’ corrective actions, the prediction of the tough love altruism model is more consistent with the empirical evidence on parental punishments, as well as with the role of parents in shaping children’s preferences as compared with that of the standard altruism model. In the simple setting of a three-period economy with a single parent and single child with perfect information and borrowing constraints, we model parental tough love by combining two ideas that have been studied in the literature in various contexts. First, the child’s discount factor is endogenously determined, so low consumption at a young age leads to a 3 higher discount factor later in life. This is based on the endogenous discount factor models of Uzawa (1968), except that the change in the discount factor is immediate in Uzawa’s formulation, whereas a spoiled child with high consumption progressively grows impatient in our formulation.1 Second, the parent evaluates the child’s lifetime utility with a constant discount factor that is higher than that of the child. Since the parent is the social planner in our simple model, this feature is related to recent models in which the discount factor of the social planner is higher than that of the agents.2 In our model, these two features lead the parent to exhibit tough love behavior in which he takes into account the influence of income transfers to the child based on the latter’s discount factor. An argument for the plausibility of endogenous discounting can be found in Becker and Mulligan(1997). Theymodelanindividualwhosediscountfactordependsontheremoteness or vividness of imagined future pleasures. Becker and Mulligan’s model involves investment in human capital to increase the vividness of imagination. For the direction of the effect of wealth on the discount factor, this argument can be used to support both Fisher’s conjecture that poor people are less patient (see Fisher 1930, p.72 for details) and Uzawa’s (1968) hypothesis that poor people are more patient. Because richer people tend to invest more, their model typically implies that poorer people are less patient. On the other hand, if a child experiences low consumption, it should be easier for the child to imagine future misery more vividly. This argument implies that a child who experiences low consumption will tend to grow more patient. The child may experience low consumption either because the parent is poor or because the parent is concerned about spoiling the child. In our review of empirical evidence in the next section, we find mixed evidence for both directions, which seems to imply that both of these forces are working in practice. For the purpose of our paper, we abstract from the human capital aspect and adopt the formulation that a child 1Recent theoretical models that adopt the Uzawa-type formulation include Schmitt-Groh´e and Uribe (2003) and Choi et al (2008). 2SeeCaplinandLeahy(2004),FarhiandWerning(2007),Phelan(2006),andSleetandYeltekin(2005,2007). 4 who is spoiled by high consumption in childhood grows to be less patient.3 Turning to the plausibility of the parent using a higher discount factor than the child, an extreme case is a parent with a newborn baby. When the baby is born, it is very impatient and cries for food all the time but the parent does not give in to this persistent demand. This is likely because the parent evaluates the baby’s utility over its lifetime with a higher discount factor as compared with the baby’s very low discount factor. We think that it is likely that many parents continue to evaluate their children’s lifetime utility when they are no longer babies. Mischel’s (1961) results, which we mention in the next section, are consistent with our view. Parents may continue to do this until their children learn to be as patient as them. As a model of parental punishments, our model is related to Weinberg’s (2001) model.4 He develops a static incentive model based on asymmetric information, whereas our model is dynamic without any uncertainty. The parent in Weinberg’s model does not affect the child’s preferences, whereas the parent in our model takes actions with explicit intent to affect the child’s discount factor. In this paper, we are emphasizing the role of the parent in molding the time preference of the child. In this regard, our model is closely related to those of Akabayshi (2006) and Doepke and Zilibotti (2008). In these models also, the parent takes actions in order to influence the child’s discount factor. In Akabayashi’s model, the child has endogenous discounting, and the parent evaluates the child’s lifetime utility with a fixed dis- count factor. Together with asymmetric information about the child’s ability, Akabayashi’s model can explain abusive repeated punishments by parents under certain parameter con- figurations. In Doepke and Zilibotti’s model, the parent uses the child’s discount factor to 3This paper 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. 4In a recent work, Slav´ik and Wiseman (2009) have also proposed a model of tough love. These authors emphasizethemoralhazardproblemfacedbyparentsinordertoconstructamodelwithadynamicinsurance strategy that involves providing greater inter vivos transfers to poor children and dividing bequests equally. Their model does not involve endogenous time discounting. 5 evaluate the child’s lifetime utility. They use their model of occupational choice to account for a number of observations about the British Industrial Revolution. The main difference from our model is that these authors adopt a Becker-Mulligan formulation of endogenous discounting so that children become more patient when their human capital is higher. In contrast, we adopt an Uzawa-type formulation for our model. The remainder of the paper is organized as follows. Section 2 reviews the empirical evidence related to the key assumptions and implications of the tough love altruism model. Section 3 explains the structure and main findings of our model with only a consumption good, and contrasts the implications of the model with those of the standard altruism model. Section 4 proposes two alternative models of altruism in order to show that both features discussed above (the endogenous discount factor of the child and the parent’s evaluation of the child’s lifetime utility with a high constant discount factor) are necessary in order for transfers to decrease when a child exogenously becomes impatient. Section 5 introduces leisure in the tough love altruism model with the objective of studying how parental transfers are affected by endogenous changes in the child’s income caused by (exogenous) changes in her discount factor. Section 6 concludes. 2 A Review of Empirical Evidence In this section, we review the empirical evidence related to the key assumptions and impli- cations of the tough love altruism model. Endogenous discounting is an important assumption of our tough love model and we first review the existing empirical evidence for this assumption. In the literature, there are two competing hypotheses that allow for endogenous discount factor by linking patience to wealth. First is Fisher’s hypothesis that the rich are more likely to be patient, and second is the Uzawa’s hypothesis that implies the discount factor is decreasing in wealth. 6 Becker and Mulligan (1997) cite empirical evidence for endogenous discounting consistent with the Fisher hypothesis. Similarly, using the Panel Study of Income Dynamics (PSID), Lawrance (1991) employed the Euler equation approach to estimate the endogenous discount factor model and found evidence in favor of the discount factor increasing in wealth. However, one has to be careful in evaluating the empirical evidence for endogenous dis- counting because of two problems. First, we have the endogeneity problem in that patient people with high discount factors tend to accumulate financial and human wealth. Thus, we may find that rich people have higher discount factors than poor people even when the dis- count factor of an individual is decreasing in wealth as in Uzawa’s model.5 The endogeneity problem mentioned above is addressed in Ikeda, Ohtake, and Tsutsui (2005). In their paper, they found that without accounting for the possible endogeneity between discount factors and wealth, the discount factor appears to be an increasing function of income/wealth. Af- ter taking into account the endogeneity problem, they find evidence in favor of the discount factor decreasing in wealth.6 Another way to control for the endogeneity problem is to give different levels of consumption to the subjects before an experiment to see which subjects are more patient. Implementing this idea with human subjects is difficult, so rats were used instead. The results were in favor of the view that the discount factor is decreasing in wealth as reported in Kagel et al (1995, Ch. 7, Section 3). The second problem in evaluating empirical evidence for endogenous discounting is that endogenous discounting and wealth-varying intertemporal elasticity of substitution (IES) can have similar implications in growing economies, and may be hard to distinguish from 5This 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(howpersistentistheeffectofinitialendowmentsonoutcomes),andstatedependence(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). 6They control the endogeneity problem by analyzing how the discount factor changes with the size of a prize obtained in another experiment. 7 one another (Atkeson and Ogaki (1996)). Hence, although the Lawrance (1991) estimation method based on the instrumental variable approach could potentially resolve the endogene- ity problem, she did not allow the IES to vary with wealth. Ogaki and Atkeson (1997) allow both the IES and the discount factor to vary with wealth for a panel data of households in Indian villages. They find evidence in favor of the view that the discount factor is constant and that the IES is increasing in wealth. It is possible that the discount factor is decreasing in wealth for richer households, but Lawrence found the opposite result by not allowing the IES to change. Ogawa (1993) argues that empirical results from Japanese aggregate data are consistent with a combination of Fisher’s and Uzawa’s hypotheses. Overall, we think that the empirical evidence is consistent with the view that reality is best described by a combination of the two hypotheses. In our view, a child who experiences low consumption will grow to be more patient because he/she can more vividly imagine future misery. At the same time, a wealthier parent is more likely to invest in the child’s human capital to help the child see the future more vividly. In this paper, we aim to develop a simple model that captures our intuition of tough love, which is that a parent allows suffering so that the child can learn to be more patient. Such a model will imply that transfers decrease when the child exogenously becomes impatient. For this purpose, we will assume that low childhood consumption leads to more patience (higher discount factor) in adulthood and will abstract from the human capital nature of endogenous discounting. The tough love model presented in this paper hypothesizes a strong parental role in shaping child behavior and preferences. The main prediction of the model is that parents with tough love motives will provide lower childhood consumption to their children in order toinfluencetheirdiscountfactor. Ideally, wewouldliketopresentevidenceforsuchaparent- child interaction in data. However, to our knowledge, there is no existing study that seeks to answer this question directly. This is partially a consequence of lack of data (survey or experimental) on parental motives, childhood consumption, and discount factor of parents 8