Skip to main content

Strategic altruistic transfers and rent seeking within the family

Abstract

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.

This is a preview of subscription content, access via your institution.

Notes

  1. 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. 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. 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. 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. 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. 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. 7.

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

  8. 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. 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. 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. 11.

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

  12. 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. 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. 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. 15.

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

  16. 16.

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

  17. 17.

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

  18. 18.

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

  19. 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. 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. 21.

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

  22. 22.

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

References

  1. Barro RJ (1974) Are government bonds net wealth? J Polit Econ 82:1095–1117

    Article  Google Scholar 

  2. Barro RJ (1996) Reflections on Ricardian equivalence. NBER Working Paper #5502, National Bureau of Economic Research

  3. Becker GS (1974) A theory of social interactions. J Polit Econ 82:1063–1093

    Article  Google Scholar 

  4. Becker GS (1981) A treatise on the family. Harvard University Press, Cambridge

    Google Scholar 

  5. Becker GS (1991) A treatise on the family. Enlarged Edition, Harvard University Press, Cambridge

    Google Scholar 

  6. Becker GS (1993) Nobel lecture: the economic way of looking at behavior. J Polit Econ 101:85–409

    Google Scholar 

  7. Becker GS, Barro RJ (1988) A reformation of the economic theory of fertility. Q J Econ 103:1–25

    Article  Google Scholar 

  8. Becker GS, Tomes N (1979) An equilibrium theory of the distribution of income and intergenerational mobility. J Polit Econ 87:1153–1189

    Article  Google Scholar 

  9. Becker GS, Tomes N (1986) Human capital and the rise and fall of families. J Labor Econ 4:S1–S39

    Article  Google Scholar 

  10. Bergstrom TC (1989) A fresh look at the rotten kid theorem—and other household mysteries. J Polit Econ 97:1138–1159

    Article  Google Scholar 

  11. Bergstrom TC (1996) Economics in a family way. J Econ Lit 34:1903–1934

    Google Scholar 

  12. Bernheim BD, Shleifer A, Summers L (1985) The strategic bequest motive. J Polit Econ 93:1045–1076

    Article  Google Scholar 

  13. Bommier A, Eckhardt S (1998) Parent–child coresidence and inter-sibling transfers in Indonesia. (Unpublished manuscript)

  14. Buchanan JM (1983) Rent seeking, noncompensated transfers, and laws of succession. J Law Econ 26:71–85

    Article  Google Scholar 

  15. Chami R (1996) King Lear’s dilemma: precommitment versus the last word. Econ Lett 52:171–176

    Article  Google Scholar 

  16. Chang Y-M (2007) Transfers and bequests: a portfolio analysis in a Nash game. Ann Finance 3:277–295

    Article  Google Scholar 

  17. Chang Y-M, Weisman DL (2005) Sibling rivalry and strategic parental transfers. South Econ J 71:821–836

    Article  Google Scholar 

  18. Chang Y-M, Potter J, Sanders S (2007a) The fate of disputed territories: an economic analysis. Def Peace Econ 18(2):183–200

    Article  Google Scholar 

  19. Chang Y-M, Potter J, Sanders S (2007b) War and peace: third-party intervention in conflict. Eur J Polit Econ 23(4):954–974

    Article  Google Scholar 

  20. Checkovich T, Stern S (2002) Shared caregiving responsibilities of adult siblings with elderly parents. J Human Resource 37(3):441–478

    Article  Google Scholar 

  21. Cox D (1987) Motives for private income transfers. J Polit Econ 95:508–546

    Article  Google Scholar 

  22. Cox D (2003) Private transfers within the family: mothers, fathers, sons and daughters. In: Munnell AH, Sundén A (eds) Death and dollars: the role of gifts and bequests in America. The Brookings Institution. Washington, DC, pp 167–197

    Google Scholar 

  23. Cox D, Rank MR (1992) Inter-vivos transfers and intergenerational exchange. Rev Econ Stat 74:305–314

    Article  Google Scholar 

  24. Engers M, Stern S (2002) Long-term care and family bargaining. Int Econ Rev 43:73–114

    Article  Google Scholar 

  25. Faith RL, Tollison RD (2001) Inheritance, equal division and rent seeking. Unpublished Manuscript, Department of Economics, Arizona State University

  26. Feinerman E, Seiler EJ (2002) Private transfers with incomplete information: a contribution to the ‘Altruism-exchange motivation for transfers’ debate. J Popul Econ 15:715–736

    Article  Google Scholar 

  27. Garfinkel M, Skaperdas S (2006) Economics of conflict: an overview. Manuscript, Department of Economics, University of California, Irvine

  28. Grossman HI (2004) Peace and war in territorial disputes. Manuscript, Department of Economics, Brown University

  29. Hiedemann B, Stern S (1999) Strategic play among family members when making long-term care decisions. J Econ Behav Organ 41(1):29–57

    Article  Google Scholar 

  30. Hirshleifer J (1977) Shakespeare versus Becker on altruism: the importance of having the last word. J Econ Lit 15:500–502

    Google Scholar 

  31. Hirshleifer J (1989) Conflict and rent-seeking success functions: ratio vs. difference models of relative success. Public Choice 63:101–112

    Article  Google Scholar 

  32. Konrad KA (2007) Strategy in contests—an introduction. Discussion Paper SP II 2007-01. Wissenschaftszentrum, Berlin

    Google Scholar 

  33. Konrad KA, Künemund H, Lommerud KE, Robledo J (2002) Geography of the family. Amer Econ Rev 92:981–998

    Article  Google Scholar 

  34. Kotlikoff LJ, Morris JN (1989) How much care do the aged receive from their children? In: Wise DA (ed) The economics of aging. University of Chicago Press, Chicago, pp 149–172

    Google Scholar 

  35. Laferrère A, Wolff F-C (2006) Microeconomic models of family transfers. In: Kolm S, Mercier-Ytier J (eds) Handbook on the economics of giving, reciprocity and altruism. Elsevier, North-Holland

    Google Scholar 

  36. Lazear EP, Rosen S (1981) Rank-order tournaments as optimum labor contracts. J Polit Econ 89:841–864

    Article  Google Scholar 

  37. Manski CF (2000) Economic analysis of social interactions. J Econ Perspect 14:115–136

    Article  Google Scholar 

  38. Pezzin LE, Schone BS (1997) The allocation of resources in intergenerational households: adult children and their elderly parents. Amer Econ Rev 87:460–464

    Google Scholar 

  39. Pezzin LE, Schone BS (1999) Intergenerational household formation, female labor supply and informal caregiving: a bargaining approach. J Human Resource 34:475–503

    Article  Google Scholar 

  40. Pezzin LE, Schone BS (2002) Intergenerational transfers of time and elderly living arrangements: a bargaining model of family decisions. Manuscript, Agency for Healthcare Research and Quality

  41. Pollak RA (1988) Tied transfers and paternalistic preferences. Amer Econ Rev 78(2):240–244

    Google Scholar 

  42. Schoeck H (1987) Envy: a theory of social behavior. Liberty Fund

  43. Schoeni RF (2003) Support networks within the family as a public good problem. PSC Research Report No. 03-545, Population Studies Center, University of Michigan

  44. Skaperdas S (1996) Contest success functions. Econ Theory 7:283–290

    Google Scholar 

  45. Sloan FA, Zhang HH, Whang J (2002) Upstream intergenerational transfers. South Econ J 69(2):363–380

    Article  Google Scholar 

  46. Stark O, Zhang J (2002) Counter-compensatory inter-vivos transfers and parental altruism: compatibility or orthogonality? J Econ Behav Organ 47:19–25

    Article  Google Scholar 

  47. Tomes N (1981) The family, inheritance and the intergenerational transmission of inequality. J Polit Econ 89:928–958

    Article  Google Scholar 

  48. Tullock G (1980) Efficient rent seeking. In: Buchanan JM, Tollison RD, Tullock G (eds) Toward a theory of rent-seeking society. Texas A&M University Press, College Station, pp 97–112

    Google Scholar 

  49. Victorio AG, Arnott R (1993) Wealth, bequest, and attention. Econ Lett 42(2–3):149–154

    Article  Google Scholar 

  50. Villanueva E (2001) Parental altruism under imperfect information: theory and evidence. Mimeographed, Universitat Pompeu Fabra

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yang-Ming Chang.

Additional information

Responsible editor: Alessandro Cigno

Appendix

Appendix

A-1.

Rewriting the time contribution equation in (15a) yields

$$\label{eq22}t^\ast =\frac{\left( {N-1} \right)\left( {y_p +S} \right)}{N^2\left( {w+\theta } \right)}-\frac{\left( {N-1} \right)}{N\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]}. $$
(22)

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

$$\label{eq23}\frac{\partial t^\ast }{\partial N}=\frac{\left( {N-2} \right)\left( {y_p +S} \right)}{N^3\left( {w+\theta } \right)}-\frac{\alpha _p \beta \left( {w+\theta } \right)-\gamma \left( {N-1} \right)^2}{N^2\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}. $$
(23)

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

$$\begin{array}{*{20}l}\label{eq24} \frac{\partial t^\ast }{\partial N}&\!=\!&\frac{\left( {N-2} \right)}{N^3\left( {w+\theta } \right)}\frac{N\left( {w+\theta } \right)}{\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]}-\frac{\alpha _p \beta \left( {w+\theta } \right)-\gamma \left( {N-1} \right)^2}{N^2[\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)]^2} \\\\ [4pt] &\!=\!&-\frac{\left( {N-1} \right)[\alpha _p \beta \left( {w+\theta } \right)-\gamma ]}{N^2\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}<0. \end{array}$$
(24)

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

$$\label{eq25} \frac{\partial t^\ast }{\partial w}=-\frac{\left( {N-1} \right)\left( {y_p +S} \right)}{N^2\left( {w+\theta } \right)^2}+\frac{\left( {N-1} \right)\alpha _p \beta }{N\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}. $$
(25)

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

$$\begin{array}{*{20}l}\label{eq26} \frac{\partial t^\ast }{\partial w}&\!=\!&-\frac{\left( {N\!-\!1} \right)}{N^2\left( {w\!+\!\theta } \right)^2}\frac{N\left( {w\!+\!\theta } \right)}{\left[ {\left( {N\!-\!1} \right)\gamma \!+\!\alpha _p \beta \left( {w\!+\!\theta } \right)} \right]}\!+\!\frac{\left( {N\!-\!1} \right)\alpha _p \beta }{N\left[ {\left( {N\!-\!1} \right)\gamma \!+\!\alpha _p \beta \left( {w\!+\!\theta } \right)} \right]^2}. \\ &\!=\!&-\frac{\left( {N-1} \right)^2\gamma }{N\left( {w+\theta } \right)\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}<0. \end{array}$$
(26)

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

$$\frac{\partial t^\ast }{\partial \theta }=-\frac{\left( {N-1} \right)^2\gamma }{N\left( {w+\theta } \right)\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}<0. $$
(27)

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

$$\begin{array}{*{20}c} \frac{\partial t^\ast }{\partial y_p }=\frac{\partial t^\ast }{\partial S}=\frac{\left( {N-1} \right)}{N^2\left( {w+\theta } \right)}\!>\!0\;\mbox{ and }\;\frac{\partial t^\ast }{\partial \alpha _p }=\frac{\left( {N-1} \right)\left( {w+\theta } \right)\beta }{N\left[ {\left( {N-1} \right)\gamma +\alpha _p \beta \left( {w+\theta } \right)} \right]^2}\!>\!0.\\ \end{array}$$
(28)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chang, YM. Strategic altruistic transfers and rent seeking within the family. J Popul Econ 22, 1081–1098 (2009). https://doi.org/10.1007/s00148-008-0200-0

Download citation

Keywords

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

JEL Classification

  • D1
  • C7