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The political economy of derived pension rights

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Abstract

Derived pension rights (including survivor benefits and spousal compensations for one-earner couples) exist in most Social Security systems but with variable generosity. They are mainly viewed as a means to alleviate poverty among older women living alone. The purpose of this paper is to explain how they can emerge from a political economy process when Social Security is a combination of Bismarckian and Beveridgean pillars. We find that the pension system should be contributive but with a positive level of derived rights. We also show that such a system encourages stay-at-home wives, thus revealing an unpleasant trade-off between female labor participation and poverty alleviation.

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Notes

  1. In general, pension systems include both Bismarckian and Beveridgean elements.

  2. In France, in 2006, derived pension rights were estimated to represent 14% of total Social Security expenditure (see “Les comptes de la protection nationale”, DREES, 2007, Bourgeois et al. 2009). In Belgium, figures are even larger: for the same year, spousal benefits plus the survival benefits amounted to 29% of the private sector pension expenditures (see Office National des Pensions, “Statistique annuelle des bénéficiaires de prestations”, 2009).

  3. These figures are taken from Choi (2006).

  4. In the case of France, see for example, Bonnet and Hourriez (2009a, 2009b).

  5. For simplicity, we consider only heterosexual couples and we assume away the possibility of divorce.

  6. Assuming the existence of single individuals would certainly make the model more realistic but at the cost of increased complexity as in such a case, we would also have to take into account that the marriage decision may be endogenous and may depend on our fiscal instruments. This is on our research agenda.

  7. For good surveys, see Galasso and Profeta (2002) and de Walque (2005).

  8. In our model, lifetime is certain and agents are perfectly rationals. Thus, the objective of the pension system is to redistribute resources between agents with different incomes but not to insure them against the risk of living long.

  9. For instance, in France the pay gap between men and women is around 20% while women have on average a life expectancy at 60 which is around 20% higher than that of men (see www.insee.fr).

  10. This assumption is made for simplicity. Adding also single individuals would not change our conclusions. In a subsequent work, we plan to make marriage endogenous in the same way as wife’s labor participation is made here endogenous.

  11. The papers of Mare (1991), Pencavel (1998) and Qian (1998) find strong evidence of perfect assortative mating with respect to education. Education can be regarded as a good proxy for income.

  12. We could have as well assumed that k<0, that is, the second earner would always prefer to go working rather than taking care of the house. This would lead to more two-breadwinner couples at the laissez-faire. We also assumed that k is independent of the couple’s productivity.

  13. This is at odds with a number of alternative household models, ranging from bargaining to non-cooperative models. This would complicate the model and this would not change the main messages of our paper.

  14. Many countries like France, Belgium and Japan offer such benefits.

  15. Under our assumption that r=n=0, this system can equally be viewed as being PAYG or Fully Funded.

  16. To see this, we combine (5) and (6) with the government revenue constraint made explicit in Sect. 2.3 and we obtain:

    $$( 1-\gamma ) \tau E[ \omega _{m}l_{m}+\omega _{f}l_{f}]=( \pi _{m}+\pi _{f}) b,$$

    where E[.] is the expectation operator. Hence γ=1 leads to b=0.

  17. On the opposite, women from two-breadwinner couples do not receive a survivor benefit, as they benefit from their own pension entitlements.

  18. Note however, that it may be the case that the solution is never interior and that for any \(w\in [ \underline{w},\bar{w}] \), V c1(w,t,b,g)<V c2(w,t,b) so that the society comprises only two-breadwinner couples and \(\hat{w}( t,b,g) arrow \underline{w}\). On the other hand (for instance, if k is extremely high), it may be the case that for any \(w\in [ \underline{w},\bar{w}] \), V c1(w,t,b,g)>V c2(w,t,b) so that every couple is a one-breadwinner couple and \(\hat{w}( t,b,g) arrow \bar{w}\).

  19. Alternatively, we could have assumed that the social planner still controls the division between one- and two-breadwinner couples. Since this is different from what we have at the majority-voting equilibrium, we did not retain this specification.

  20. Given our quasi-linear utility functions, without this transformation, there is no need for redistribution.

  21. Replacing for (10), it can be shown that the expression in parentheses in the denominator is always positive.

  22. The way we proceed may not be the unique one. For instance, we could have as well assumed that the level of derived rights, g, is decided at the constitutional level while the flat benefit, b, is decided by majority voting. We could also have assumed sequential voting. This is left for future work.

  23. Our analysis can be extended to the case of a continuous distribution of productivity. However, it would be more technical and less intuitive without bringing additional results.

  24. In the numerical section, we verify that this is still the case after the introduction of a pension system.

  25. The threshold \(\hat{w}\) disappears because of the discrete distribution of productivity. Here, this is equivalent to assuming that type-w 2 is either a one- or a two-breadwinner couple, which also changes the form of the government budget constraint.

  26. A corner solution is never possible. Using the Jensen’s inequality and our assumptions on the distribution of productivity, it is always the case that \(w_{2}\leq E( w) <\sqrt{Ew^{2}}<\sqrt{\frac{Ew^{2}+p_{3}\alpha ^{2}w_{3}^{2}}{p_{1}+p_{2}}}\), which makes impossible to have ∂V c1(w 2,t,b,g(t,b))/∂t<0. Thus, one always has t c1>0.

  27. Equation (16) has two solutions. We retain the lowest t c2(b) as it implies less labor distortions.

  28. The single-crossing condition defined by Gans and Smart (1996) is effectively satisfied in our framework, even though we have two subgroups in the population. The marginal rate of substitution between t and g is monotonically decreasing in w for one-breadwinner couples and two-breadwinner couples always prefer zero derived rights. This guarantees that a political equilibrium exists under pure majority rule and that the Condorcet winner is the preferred tax rate of the median productivity individual.

  29. Indeed, d(b+g c1(b))/db=−p 3(1+β)/(p 1+p 2)<0.

  30. In the laissez-faire, for 0.08≤k≤5.12, type-1 agents are one-breadwinner and type-3 agents are two-breadwinner couples.

  31. The interval for b is such that \(b\in [0,[ Ew^{2}+\alpha ^{2}(p_{2}w_{2}^{2}+p_{3}w_{3}^{2}) ] /[ 4(1+(p_{2}+p_{3}) \beta ) ] ]\) where the upper-bound corresponds to the peak of the Laffer curve and is equal to 0.387 under our assumptions.

  32. In unreported simulations, we checked that our results are invariant to the level of w 1.

  33. At k=0, for any b, the median couple is always a two-breadwinner couple as \(\min \hat{k}( b) =\hat{k}( 0) =0.001\). In that case, it is optimal to set b ∗ so as to maximize the income of the poorest couple. Yet, this result is not robust as w 1-couples would now prefer to be two-breadwinner couples.

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Acknowledgements

We would like to thank Yvonne Adema, Carole Bonnet and Erik Schokkaert as well as an anonymous referee for helpful comments.

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Authors and Affiliations

  1. Département des Sciences Économiques, ESG UQAM, C.P. 8888, Succ. Centre-ville, Montréal, H3C 3P8, QC, Canada

    M.-L. Leroux

  2. CORE, Université Catholique de Louvain, 34 Voie du Roman Pays, B1348, Louvain la Neuve, Belgium

    M.-L. Leroux

  3. CESifo, Munich, Germany

    M.-L. Leroux

  4. CREPP, CORE, PSE and CEPR, University of Liege, Liege, France

    P. Pestieau

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  1. M.-L. Leroux
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Correspondence to M.-L. Leroux.

Appendix A: Second-best solution

Appendix A: Second-best solution

The Lagrangian of problem (C) has the following expression:

with λ the Lagrange multiplier associated with the resource constraint and \(\hat{w}( t,b,g) \) being defined by (10). First-order conditions are

(U)
(V)
(W)

For simplicity, we drop the arguments in the expressions of indirect utility functions and set \(V_{w}^{c1}\equiv V^{c1}( w,t,b,g) \) and \(V_{w}^{c2}\equiv V^{c2}( w,t,b) \). By definition of \(\hat{w}( t,b,g) \), one has that \(\varPsi ( V_{\hat{w}(t,b,g) }^{c1}) -\varPsi ( V_{\hat{w}( t,b,g)}^{c2}) =0\) and \(d\hat{w}\,( t,b,g) /dg=-d\hat{w}\,(t,b,g) /db\). Adding (22) and (23), we obtain, after some rearrangements, that

$$\int_{\underline{w}}^{\hat{w}( t,b,g) }\varPsi ^{\prime }\bigl(V_{w}^{c1}\bigr) f( w)\, dw+\int_{\hat{w}( t,b,g) }^{\bar{w}}\varPsi ^{\prime }\bigl( V_{w}^{c2}\bigr) f( w)\, dw=\lambda.$$

Inserting this expression into (21) and rearranging terms,

This yields

where

$$E\omega ^{2}=\int_{\underline{w}}^{\hat{w}( t,b,g) }w^{2}f(w)\, dw+\bigl( 1+\alpha ^{2}\bigr) \int_{\hat{w}( t,b,g) }^{\bar{w}}w^{2}f( w)\, dw$$

is the average square wage and \(\mathit{cov}( \varPsi ^{\prime }(V_{w}^{ci}) ,\omega ^{2}) \) is the covariance between marginal social utility and couples’ income. This yields (15).

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Leroux, ML., Pestieau, P. The political economy of derived pension rights. Int Tax Public Finance 19, 753–776 (2012). https://doi.org/10.1007/s10797-011-9205-9

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