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Leadership delegation in rotten kid families

Abstract

In a family context with endogenous timing, multiple public goods, and alternative parental instruments, we show that the optimality of authority (leadership) delegation for the sequential-action game played by rotten kids and a parent depends crucially on the degree of heterogeneity in the kids’ preferences. For homogeneous kids, the rotten kid theorem—the situation in which rotten kids find it desirable to internalize all externalities that arise in the family setting—holds irrespective of the parental policy instrument, implying that it is optimal to delegate leadership to the kids. If the kids are heterogeneous, however, parental leadership yields a first best outcome if the kids are economically dependent and agree on the tradeoff between public goods. For economically independent kids, parental leadership is optimal if the degree of heterogeneity is sufficiently high. These findings provide us with empirically testable hypotheses and contribute to the debate regarding the social desirability of the ‘authoritative parenting style’.

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Notes

  1. Optimal timing in Stackelberg games have been investigated in the industrial organization literature. See, e.g., Gale-Or (1985), Dowrick (1986), Hamilton and Slutsky (1990), Pal (1998), and Amir and Stepanova (2006). Unlike these papers, we consider settings where the leader(s) and follower(s) control different types of actions and the players who contribute to public goods may have heterogeneous preferences.

  2. When considering parental leadership, we are not simply assuming that the parent can precommit to an action that immediately yields her most preferred outcome in the game played with her kid. Such a benefit of precommitment for the parent is present in the Samaritan’s dilemma (e.g., Buchanan (1975) and Faria and Arce (2018)). Gintis (2009) (see also Bruce and Waldman (1990)) models the Samaritan’s dilemma in a two-period setting where a kid saves part of her income in the first period and receives a transfer from her father in the second period. Her father has an altruistic feeling toward his daughter. He saves in the first period in order to give a transfer to his daughter in the second period. In this game the kid is the leader, and the parent is the follower. In equilibrium, the kid saves too little and her father has to make a large transfer. If the father can precommit to a transfer level, both he and her daughter would be better off. The Samaritan’s dilemma yields an inefficient allocation. See, e.g., Thompson (1980), Kotlikoff (1987) and Coate (1995) for further discussion of the Samaritan’s dilemma.

  3. See also Akai and Silva (2009) and Nagase and Silva (2000) for alternative scenarios where the rotten kid theorem holds.

  4. The rotten theorem also fails in models that consider leisure choice (e.g., Bergstrom (1989)), when individuals choose between present and future consumption (Lindbeck and Weibull (1988), Bruce and Waldman (1990)) and when families make discrete choices (Lundberg and Pollak (2003)). For good surveys on this topic, see Bergstrom (2008) and Lafferrere and Wolff (2006).

  5. See below for a technical justification of considering a family setting with multiple public goods.

  6. We are aware that these two polar cases do not capture all possible situations. There are situations where the kids earn some income, but are still economically dependent on their parents. For simplicity, we ignore these situations.

  7. Wagner (1965) suggests that leaders who recognize the potential for welfare improvements may undertake convincing actions that cause others to act collectively toward their mutual benefit without the need for punishment, pressure groups, or rent seeking. Kindleberger (1981) argues that hegemonic power is not necessary for successful leadership in providing international public goods. It is possible for groups of smaller nations to serve successfully as examples through initiatives concerning foreign aid, peacekeeping, etc. Arce (2001) provides several illustrations of the success of leading by example (see also the articles contained in Tuchman Matthews (1991)).

  8. Oliveira et al. (2005) investigates how one can produce cooperative behavior in an evolutionary game where the players are non-cooperative. The paper shows that leading by example is more likely to succeed the greater the degree of concavity (curvature) of the public benefit function. Leading by example is neutrally stable if this function has a sufficiently low degree of concavity.

  9. We use superscripts to denote functions.

  10. Our qualitative results regarding a comparison of outcomes in the settings where the kids are heterogeneous and economically independent do not depend on this assumption. As we show below, leadership by kids dominates parental leadership if the kids are nearly homogeneous and parental leadership dominates leadership by kids if the kids are sufficiently heterogeneous. A proof of this claim can be obtained from the authors upon request.

  11. Even if the restriction appears to be strong, it is important to notice that it permits several combinations of taste parameters. Consider, for example, a family with three kids, where the utilities of kids 1, 2 and 3 have the following taste parameters, respectively: (α1, β1) = (0.1, 0.3), (α2, β2) = (0.4, 0.2) and (α3, β3) = (0.7, 0.1). Letting χi ≡ (1 − αi − βi)/βi, we have χ1 = χ2 = χ3 = 2.

  12. We assume throughout that the parent does not have any income of her own when the kids are economically independent. Adding an extra source of income to the model does not change the qualitative results.

  13. See, e.g., Cornes and Silva (1999), Silva (2014) and Silva and Yamaguchi (2010).

  14. See https://economia.uol.com.br/reportagens-especiais/reforma-da-previdencia-o-que-muda-na-aposentadoria/index.htm#aposentadoria-por-invalidez?cmpid=copiaecola

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Acknowledgments

We would like to thank Stefano Barbieri, Jun-ichi Itaya, Chikara Yamaguchi, and two referees for comments that helped us to improve the paper. Any errors are our own.

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Correspondence to Emilson Caputo Delfino Silva.

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Faria, J.R., Silva, E.C.D. Leadership delegation in rotten kid families. J Popul Econ 33, 441–460 (2020). https://doi.org/10.1007/s00148-019-00755-4

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Keywords

  • Rotten kids
  • Public goods
  • Endogenous timing
  • Heterogeneous preferences
  • Economically dependent

JEL

  • D13
  • D61
  • D64
  • D78
  • H41