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Strategic altruistic transfers and rent seeking within the family


This paper examines the rent-seeking behavior of “selfish” children in competing for parental transfers. The paper extends Chang and Weisman (South Econ J 71:821–836, 2005), that focuses on compensated transfers, to allow for non-compensated transfers à la Buchanan (J Law Econ 26:71–85, 1983) and derives results for the case in which children’s time contributions as perceived by their parents are a merit good (e.g., service), pure waste (e.g., bugging), or a mix of both. For an increase in the proportion of time contributions that are pure waste, parents find it optimal to reduce the size of an overall transfer, thereby lowering the levels of wasteful rent-seeking activities by their children within the family.

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  1. There are some exceptions. Stark and Zhang (2002) consider inter-sibling interaction and show that a positive transfer–earnings relationship is counter-compensatory which, rather than being orthogonal to parental altruism, originates from such altruism. Engers and Stern (2002) examine long-term care and family bargaining. For empirical studies that examine issues related to inter-sibling interaction in providing long-term care to elderly parents and intra-family allocation of resources, see Bommier and Eckhardt (1998), Hiedemann and Stern (1999), Pezzin and Schone (1997, 1999, 2002), Checkovich and Stern (2002), and Schoeni (2003). I thank an anonymous referee for drawing my attention to these important contributions. The present paper departs from these contributions in some important aspects. This paper pays particular attention to (1) elements of conflict or non-cooperation in parental-children interactions, (2) differences in compensated and non-compensated transfers, and (3) issues related to socially desirable or undesirable rent seeking by children in a Nash game.

  2. I thank James Buchanan who, in a personal correspondence, links the sibling rivalry model of Chang and Weisman (2005) to his classic 1983 paper on non-compensated transfers and rules of succession, viewed from the perspective of rent seeking.

  3. Becker (1993, p. 398) remarks that “most parents believe that the best example of selfish beneficiaries and altruistic benefactors is selfish children with altruistic parents.” As in the family economics literature, children are assumed to be selfish in that they only care about the well-being of their own.

  4. Skaperdas (1996) presents axiomatic characterizations of various forms of contest success functions. The additive form of contest success function has been widely employed to examine various issues such as those on rent seeking and lobbying, tournaments and labor contracts, political conflict, war and peace, and sibling rivalry. See, e.g., Tullock (1980), Lazear and Rosen (1981), Hirshleifer (1989), Grossman (2004), Chang and Weisman (2005), Garfinkel and Skaperdas (2006), Chang et al. (2007a, b), and Chang (2007). Konrad (2007) presents a systematic review of applications in economics and other fields that use CSFs similar to those in Eq. 1.

  5. Hirshleifer (1977) argues the importance of parents’ “last word” in decision-making to discipline “rotten” kids as discussed by Becker (1974). Bergstrom (1989) further proposes the use of a two-stage, non-cooperative Nash game to deal with the “Rotten Kids Theorem” of Becker and to examine parental-children interactions. Manski (2000) points out that the use of non-cooperative game theory as a set of tools for the study of market and non-market interactions in microeconomics may be the “defining event of the late twentieth century” (p. 116).

  6. Alternative approaches include the use of a cooperative game or a bargaining game. Nevertheless, these two games generally require a well-defined mechanism for “contract” enforcement because there is no endogenously determined incentive mechanism to move to the cooperative outcome or the bargaining solution.

  7. We follow Cox (1987) and assume that there is a disutility to the selfish children when they spend time with their parents.

  8. I thank an anonymous referee for pointing out a non-negativity constraint concerning the child’s utility as discussed in Bernheim et al. (1985), Cox (1987), and Victorio and Arnott (1993). Parallel to the non-negativity constraint discussed in these studies, the present paper examines the “participation incentive constraint” for the existence of a money–services exchange.

  9. An additively separable utility function has been widely adopted to analyze various issues such as the “rise and fall of families” (Becker and Tomes 1979, 1986), the economic analysis of fertility (Becker and Barro 1988), residential choice of family members (Konrad et al. 2002), and sibling rivalry and parental transfers (Chang and Weisman 2005; Chang 2007). Laferrère and Wolff (2006) present a systematic review of studies that show alternative or more general forms of the utility functions of altruistic parents.

  10. We can incorporate γ into the contest success function in (1) and rewrite it to be \(P_i ={\gamma t_i } \mathord{\left/ {\vphantom {{\gamma t_i } {\left( {\gamma t_i +\gamma t_{-i} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\gamma t_i +\gamma t_{-i} } \right)},\) where γt i is that portion of child i’s time contribution which is valuable to the parents. The assumption of symmetry implies that we have the same CSF as that in (1).

  11. I thank an anonymous referee who suggests that a more general approach be developed to include the three possible cases.

  12. Defining post-transfer income as I, where I = y p M, the parents spend I on a composite good whose price is normalized to one.

  13. Becker (1974) was the first to introduce parental altruistic preferences into the analysis of family economics. Becker (1991, p. 279) further observes that because parents maximize their own utility subject to the family constraints, they may be labeled “selfish,” not altruistic, in terms of utility maximization. Pollak (1988) proposes the use of “paternalistic” preferences to replace altruistic preferences in analyzing parent–child relationships and tied transfers.

  14. Bergstrom (1996) presents an excellent review on the economics of the family and explains why, from the perspectives of economics and evolutionary biology, there is a downward transmission of resources from parents to their offspring.

  15. See A-1 in the Appendix for a detailed derivation of the derivatives.

  16. I thank an anonymous referee who suggests that policy implications of the model be addressed.

  17. Chang and Weisman (2005) do not examine policy implications of their model for government’s intergenerational income redistribution.

  18. See, e.g., Laferrère and Wolff (2006).

  19. Laferrère and Wolff (2006) present a systematic review of papers that lend a support to the Ricardian neutrality proposition (see their Table 4). These papers include Cox (1987), Chami (1996), Sloan et al. (2002), and Villanueva (2001).

  20. The theoretical model presented in the paper ignores the possibilities of inter-sibling coalition for acquiring more transfers from parents or inter-sibling transfers for providing caregiving to elderly parents. These are interesting and important topics for future research. This paper also abstracts from information asymmetry. See Feinerman and Seiler (2002) for an analysis of parental-children transfers when a parent does not have perfect information about the degree of her children’s selfishness. The authors show that both altruism and exchange are important motives under asymmetric information.

  21. See, e.g., Konrad (2007) for a thorough review of studies on strategy in contests and contest design.

  22. Cox (2003) indicates that “conflict ... might occupy a significant niche in the familial landscape” (p. 197).


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I am grateful to the editor, Alessandro Cigno, and two anonymous referees for very constructive suggestions and critical insights that led to substantial improvements in the paper. I thank James Buchanan for valuable comments in an email correspondence. I also thank Kyle Ross and Shane Sanders for helpful comments. All remaining errors are my own.

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Correspondence to Yang-Ming Chang.

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Rewriting the time contribution equation in (15a) yields

$$\label{eq22}t^\ast =\frac{\left( {N-1} \right)\left( {y_p +S} \right)}{N^2\left( {w+\theta } \right)}-\frac{\left( {N-1} \right)}{N\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]}. $$

Taking the partial derivative of t   in (22) with respect to N, we have

$$\label{eq23}\frac{\partial t^\ast }{\partial N}=\frac{\left( {N-2} \right)\left( {y_p +S} \right)}{N^3\left( {w+\theta } \right)}-\frac{\alpha _p \beta \left( {w+\theta } \right)-\gamma \left( {N-1} \right)^2}{N^2\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}. $$

Evaluating the derivative in (23) at the point where (y p  + S) satisfies the financial condition in (12) yields

$$\begin{array}{*{20}l}\label{eq24} \frac{\partial t^\ast }{\partial N}&\!=\!&\frac{\left( {N-2} \right)}{N^3\left( {w+\theta } \right)}\frac{N\left( {w+\theta } \right)}{\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]}-\frac{\alpha _p \beta \left( {w+\theta } \right)-\gamma \left( {N-1} \right)^2}{N^2[\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)]^2} \\\\ [4pt] &\!=\!&-\frac{\left( {N-1} \right)[\alpha _p \beta \left( {w+\theta } \right)-\gamma ]}{N^2\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}<0. \end{array}$$

Next, the partial derivative of t   in (22) with respect to w is

$$\label{eq25} \frac{\partial t^\ast }{\partial w}=-\frac{\left( {N-1} \right)\left( {y_p +S} \right)}{N^2\left( {w+\theta } \right)^2}+\frac{\left( {N-1} \right)\alpha _p \beta }{N\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}. $$

Evaluating the derivative in (25) at the point where (y p  + S) satisfies the financial condition in (12) yields

$$\begin{array}{*{20}l}\label{eq26} \frac{\partial t^\ast }{\partial w}&\!=\!&-\frac{\left( {N\!-\!1} \right)}{N^2\left( {w\!+\!\theta } \right)^2}\frac{N\left( {w\!+\!\theta } \right)}{\left[ {\left( {N\!-\!1} \right)\gamma \!+\!\alpha _p \beta \left( {w\!+\!\theta } \right)} \right]}\!+\!\frac{\left( {N\!-\!1} \right)\alpha _p \beta }{N\left[ {\left( {N\!-\!1} \right)\gamma \!+\!\alpha _p \beta \left( {w\!+\!\theta } \right)} \right]^2}. \\ &\!=\!&-\frac{\left( {N-1} \right)^2\gamma }{N\left( {w+\theta } \right)\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}<0. \end{array}$$

Similarly, the partial derivative of t   with respect to θ, when evaluating at the point where (y p  + S) satisfies condition (12), yields

$$\frac{\partial t^\ast }{\partial \theta }=-\frac{\left( {N-1} \right)^2\gamma }{N\left( {w+\theta } \right)\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}<0. $$

The partial derivatives of t  in (22) with respect to y p , S, and α p are given respectively as

$$\begin{array}{*{20}c} \frac{\partial t^\ast }{\partial y_p }=\frac{\partial t^\ast }{\partial S}=\frac{\left( {N-1} \right)}{N^2\left( {w+\theta } \right)}\!>\!0\;\mbox{ and }\;\frac{\partial t^\ast }{\partial \alpha _p }=\frac{\left( {N-1} \right)\left( {w+\theta } \right)\beta }{N\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}\!>\!0.\\ \end{array}$$

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Chang, YM. Strategic altruistic transfers and rent seeking within the family. J Popul Econ 22, 1081–1098 (2009).

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  • Strategic altruism
  • Parental transfers
  • Sibling rivalry
  • Rent seeking

JEL Classification

  • D1
  • C7