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Altruism, labor supply and redistributive neutrality

Abstract

This paper presents a model of familial altruism in which labor supply is chosen endogenously. The model is used to address the predictions of Ricardian Equivalence, both theoretical and empirical. It is argued that, to the extent that income variation in the data comes mostly from wage and effort changes, the empirical tests of neutrality are misspecified. Numerical estimates suggest that quantitatively important deviations from neutrality may be at work.

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Notes

  1. The immense literature on micro-models of family transfers has a very good survey in Laferrère and Wolff (2006), which also includes a section on empirical tests. Arrondel and Masson (2006) review the empirical evidence on transfers and compare it with the predictions of altruism, exchange and indirect reciprocity. Perhaps the most well-known empirical piece on the transfer derivative test is Altonji et al. (1997) but the examples are very numerous as can be seen in both surveys. The empirical literature on altruism is briefly discussed in Section 4.

  2. As the authors point out, this result is in line with theory: a higher wage raises the child’s opportunity cost of time and this effect counteracts the wealth effect also associated with the higher wage. The net effect is ambiguous from a theoretical point of view, thus not contradicted by an estimated coefficient not significantly different from zero.

  3. Using French panel data, Wolff (2006) finds no significant influence of parental transfers on the labor supply of their children.

  4. McGarry (2000) is another example where neutrality breaks down due to the informational content of different income observations. In her model, the child’s current income provides information regarding her future income. Different current income realizations therefore imply a shift in expectations regarding future income and this causes neutrality to fail.

  5. The restriction \(\lambda \in \left[ 0.5,1\right] \) arises naturally if we interpret the parent’s utility from consumption as

    $$ U\left( c_{p}\right) \equiv u\left( c_{p},1-e_{p}\right), $$

    with e p set to a constant (possibly zero). The values of λ now reflect a partially altruistic parent, one who loves himself more than his child. Though this is the utility representation we favor, the results would hold for any parental utility function \(U_{p}\left( \cdot \right) \) with the general properties outlined in the text.

  6. In the spirit of the Barro-Becker tradition, the effort-enlarged model presented here has all the decision making ability centralized in the parent. Since the child is selfish, it would be desirable to allow the child to select effort and to model the interaction between family members as a game. In Fernandes (2000), I model the interaction between parent and child as a noncooperative static game. It is shown that the unique Nash-equilibrium of that game replicates exactly the optimal parental choices of the current model. This is so since the parent cares for the child in a nondistortionary way: conditional on a transfer amount, parent and child would agree on the optimal amount of hours the child should work.

  7. Chami (1996) argues that, when the child’s effort is privately observed, the parent will be able to induce a higher level of effort from the child if he is able to precommit to a transfer amount as opposed to deciding on a transfer to the child after effort is undertaken. His result thus provides conditions under which Hirshleifer’s (1977) assertion that the parent must act after the child’s effort is implemented in order to prevent her from shirking—or acting “rotten”–is overturned; it is driven by the fact that the parent can no longer observe the child’s effort. In his (1998) piece, Chami again examines the implications of parental transfers and transfer regimes for the intensity of labor supply. The analysis considers a large number of alternative scenarios which include private information and/or merit goods. Chami does not address the question of interest here, namely the effect of private information on the properties of transfers regarding income redistribution and, further, how these results compare with empirical estimates. Gatti (1997) considers a model of bequests under private information and examines how different transfer regimes—related to the parents’ ability to commit—affect the utility of the parents.

  8. There is a technical reason for why the parent’s income is now stochastic. In Section 2, the income of parent and child was observed before the parental transfer was given or effort exerted. Comparing the parental transfer for different values of the family’s income was a straightforward experiment. In this section, the timing of moves—described below—prescribes the parent announcing a transfer menu of payments which are contingent on the future observations of I p and I c . If I p is drawn from a degenerate distribution, then the experiment of taking one dollar from the child’s income and adding it to the parent’s is not well-defined. In other words, the multiplier θ of the incentive compatibility constraint (9) would be a function of I p as opposed to a function of its distribution, as it is in the current case.

  9. If there is a nonlabor component in the child’s earnings, as it was the case in Section 2, it is assumed that the parent knows how much it totals.

  10. If the family of densities \(f\left( \cdot |e\right) \) satisfies the monotone likelihood property, then, for all \(I_{c}^{1}\geq I_{c}^{0}\) and e H  ≥ e L ,

    $$ \frac{f\left( I_{c}^{1}|e_{H}\right) }{f\left( I_{c}^{1}|e_{L}\right) }\geq \frac{f\left( I_{c}^{0}|e_{H}\right) }{f\left( I_{c}^{0}|e_{L}\right) }. $$
    (13)

    That is, the ratio of the probabilities that I c occurs under high and low effort is increasing in I c . The ratio of probabilities in the first-order condition, \(F\left( I_{c}\right) \), is the reciprocal of that in Eq. 13, and thus the monotone likelihood ratio property implies that \( F\left( \cdot \right) \) is decreasing in I c .

  11. Note that, from the first-order condition for transfers, Eq. 11, we know that the expression in square brackets in the denominator D is strictly positive when transfers are also strictly positive.

  12. See also the results in Jürges (1999).

  13. Other researchers, who also estimate transfer functions (for example McGarry and Schoeni (1995, 1997)) report—at least heuristically—that the implied difference in transfer derivatives falls far short of the neutrality benchmark.

  14. The model of Section 2 did not consider the choice of parental labor supply. By including the parent’s wage in the empirical Eq. 15, I am considering here the more realistic generalization of the model, with parents participating in the labor market and earning wage w p .

  15. Whether or not I c is small does not affect the substance of the results presented here, while simplifying the exposition.

  16. The actual estimate, without the assumption that I c is small, would be an weighted average of the coefficient presented in Eq. 19 and \( \partial T_{p}/\partial I_{c}\).

  17. Results are virtually insensitive to the choice of H.

  18. Empirical evidence directly targeted at the determinants of well-being and happiness, such as Schwarze and Winkelmann (2005) and Bruhin and Winkelmann (2009), has identified positive and significant effects of the well-being of the child on the parent’s. The estimates of the altruism parameter in Schwarze and Winkelmann would imply higher values for λ, in agreement with the indirect evidence uncovered in Bruhin and Winkelmann. The quantification under private information below considers higher λ values.

  19. It may appear surprising that the coefficient β 1 is increasing in λ, since the greater its value the more selfish the parent. The reason this is the case is the fact that, as λ increases, what is being kept constant is the combination of γ and ω values such that η e,w equals a target value of 0.1. If those were kept constant, β 1 would decrease with λ (and so would β 2).

  20. For negative values of η e,w , well-defined solutions are only found for negative values of α. Further, for these values of α, the range of λ values for for which solutions exist is usually very high, in particular significantly higher than the value of λ that would set the first-order condition of transfers at equality. For example, for α = − 1 and λ = 0.8, β 1 − b 2 equals 1.83. This difference declines as λ increases further. We find the admissible range of values for λ implausibly high and therefore disregard these cases.

  21. It is straightforward to show that \(F^{\prime }\left( I_{c}\right) <0\) obtains if μ c  < μ .

  22. Results were obtained using Matlab’s routine ‘fsolve’ and the code is available upon request. They were insensitive to initial conditions.

  23. Previous computations in this section found a value for μ c that solved instead

    $$ 0.13=\left( 1-\frac{u_{1}\left( c_{c},1-e_{H}\right) \theta U_{1}\left( c_{c}\right) F^{\prime }\left( I_{c}\right) }{D}\right) . $$
  24. The values obtained for β 1 do not vary with d and, as predicted by the model, that derivative is positive under all parameter configurations considered.

  25. Included in the prediction of altruism is the fact that consumption of individual households within the extended family linked by positive transfers should commove perfectly and individual income of a particular household should not have a differentiated effect on that household’s consumption relative to that of other households in the family. This is yet another face of the redistributive neutrality result. The first test of this prediction was carried out by Altonji et al. (1992).

  26. Villanueva conceptualizes the child’s household as having two earners, primary and secondary, and posits that the latter is the only one with an elastic labor supply. He assumes that parents can observe the earnings of both children but not the wages received by the secondary earner. Simulations of the model indicate that parental transfers will compensate a larger fraction of an income loss suffered by the primary earner compared to the secondary earner. He also tests empirically how parental transfers respond to the earnings of both earners and finds the same pattern in the data. Since the secondary earner is also—by assumption—the earner with greater labor supply wage elasticity, and his simulations under complete information show that parents also respond less to income losses of that earner, it is not clear how much of the differential response of transfers is due to private information or simply to hourly adjustment to wage changes.

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Acknowledgements

I am grateful to Robert E. Lucas, Jr., Fernando Alvarez, Gary S. Becker, Sherwin Rosen and Pedro Mira for comments, and also for valuable suggestions by two anonymous referees. Financial support from Banco de Portugal , Fundação para a Ciência e a Tecnologia and Fundación Ramón Areces is very gratefully acknowledged.

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Correspondence to Ana Fernandes.

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Responsible editor: Alessandro Cigno

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Fernandes, A. Altruism, labor supply and redistributive neutrality. J Popul Econ 24, 1443–1469 (2011). https://doi.org/10.1007/s00148-010-0317-9

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Keywords

  • Ricardian Equivalence
  • Endogenous labor supply
  • Private information

JEL Classification

  • D19
  • D64
  • D82