Abstract
The paper re-examines the idea that a family can be viewed as a community governed by a self-enforcing constitution, and extends existing results in two directions. First, it identifies the circumstances in which a constitution is renegotiation-proof. Second, it introduces parental altruism. The behavioural and policy implications are illustrated by showing the effects of public pensions and credit rationing. These implications are not much affected by whether altruism is assumed or not, but contrast sharply with those of more conventional models.
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Notes
If grown-up children give attention to elderly parents, \(m_{1}\) is the difference between the money that the agent gives each of her children, maybe in the form of bequest, and the money equivalent of the utility of the attention that she receives from each of them.
Nothing of substance changes if we assume, instead, that they face a positive credit ration, lower than the cost of a child.
In a seminal paper, Browning (1975) makes the point that, as children do not vote, the pension system produced by a direct democracy will be larger than the one which maximizes the lifetime utility of the representative agent. At the family level, that is the same as saying that \(z\) will be set at zero, and \(x\) at the highest level compatible with Nash equilibrium. The role of a constitution is to prevent just that.
The risk is that a child will be unwilling, or unable to pay her parent \(x\) in old age. The former would occur if a change in the economic environment (e.g., a rise in \(r\)) made the constitution unviable, the latter if the child died before reaching adulthood, or were too poor to pay her dues.
May, rather than will as in the model without altruism, because \(x\) reduces the altruistic component of the agent’s utility.
In a stationary environment, we shall then have that
Taking fertility as exogenous, and interpreting \(z\) as educational investment, Anderberg and Balestrino (2003) show that, if the Nash constraint is binding, the renegotiation-proof constitution is inefficient in the usual Pareto sense. Under their assumptions, this implies that investment in the children’s education, rather than the children’s current consumption, will be too low.
Given the (subjective) certainty framework, we are obviously talking of an unexpected change.
The implicit pension tax is defined as the difference, at the date of retirement, between the capitalized value of the contributions, and the expected value of the benefits; see Sinn (1990).
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Acknowledgements
This paper has benefited from comments by Daniele Fabbri and Annalisa Luporini and from constructive criticism by two anonymous referees. The remaining errors are the author’s responsibility.
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Cigno, A. A constitutional theory of the family. J Popul Econ 19, 259–283 (2006). https://doi.org/10.1007/s00148-006-0062-2
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DOI: https://doi.org/10.1007/s00148-006-0062-2
Keywords
- Families
- Self-enforcing constitutions
- Renegotiation-proofness
- Altruism
- Fertility
- Saving
- Transfers
- Attention
- Pensions
- Credit rationing