Abstract
In our model, the government operates a mandatory proportional (DC) pension system to substitute for the low life-cycle savings of the lower-paid myopic workers, while maintaining the incentives of the higher-paid far-sighted ones in contributing to the system. The introduction of an appropriate cap on pension contribution (or its base)—excluding the earnings above the cap from the contribution base—raises the optimal contribution rate, helping more the lower-paid myopic workers and reserving enough room for the saving of higher-paid far-sighted ones. The social welfare is almost independent of the cap in a relatively wide interval but the maximal welfare is higher than the capless welfare by 0.3–4.5 %.
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Notes
Recently, the US Social Security contribution rate is as low as 12.4 %, while in Italy it is as high as 34 %. There are a number of causes of this difference, e.g. the higher systemic dependency in Italy and the stronger redistribution in the US, see Disney (2004). Taking the average gross wage as unity, the cap is as low as 1.3 in Sweden and as high as 2.5 in the US, cf. also Table 1 in Valdés-Prieto and Schwarzhupt (2011). Lovell (2009) gives a useful dataset and analysis of the long and sometimes turbulent history of the US Social Security.
The lowered contribution rate for the self employed can be explained along this line, too, but in fact, it stems from the difficulties of auditing rather than paternalistic differentiation.
In Hungary, the former contribution rate is 10 % of the gross wage, while the latter is 24%. Until 2013, the uncapped contributions alone provided 6 % of the total pension contributions and gave 10 % of the de facto personal income tax. From 2013, there is no cap at all, decreasing the social welfare with respect to the maximum. At the same time, the weak progressivity of the system becomes stronger.
In the US, the progressivity of the Social Security disappears above the cap. In Great Britain of post-WWII the cap was set at the minimum wage, transforming the flat benefit system into a flat contribution one, see also Example 1 below.
One can also argue that their flexible labor supply is replaced by more efficient private saving in the present paper.
Studying lifetime income redistribution, Tenhunen and Tuomala (2010) connected the incomes and discount factors and compared the welfarist and the paternalistic social optima.
It would be interesting to see how our partial equilibrium result change in their general equilibrium model; for example, if the introduction of the cap raises savings, then the endogenous interest rate diminishes, weakening the advantage of the cap.
The use of various control characters may seem superfluously complicated but in fact this practice helps to understand the notations. For example, writing \(\bar w\) rather than an unrelated parameter, e.g. 𝜃 reminds the reader that it is related to wage w.
Using a Rawlsian social welfare function would defy the purpose of the study, rendering the socially optimal cap indeterminate and the corresponding contribution rate myopic (cf. (10) below)
Note that for zero contribution rate, the value of the cap is as irrelevant as for zero cap, the value of the contribution rate. Therefore \(V[\varepsilon ,\tau ,0]=V[\varepsilon ,0,\bar {w}]=V[\varepsilon ,0,0]\).
If we took into account that the socially optimal discount factor is less than one (e.g. labor disutility, reduced family size in old-age, etc., as postulated by Cremer et al. (2008)), then we could reduce the contribution rate further, even to 1/4.
We shall divide the interval [w m ,w Q ] into n = 100 subintervals such a way that the division points w i form a geometrical sequence. At integration, the representative points are the geometrical means of the subsequent points: w i + 1 = q w i and \(z_{i}=\sqrt {w_{i} w_{i+1}}\). The mass of the remaining infinite part is 1−F(w Q )=0.0001 with w Q =50 and the earning w K =100 represents the average highest wage.
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An earlier version of the present paper was published as a discussion paper, Simonovits (2012). I am indebted to N. Barr, Zs. Cseres-Gergely, G. Kézdi, J. Köllő, G. Kőrösi, M. C. Lovell, Th. Matheson (my discussant at the IIPF Congress in Dresden held in 2012), J. Pál and G. Varga for friendly comments. H. Fehr deserves a special acknowledgment for his steady contribution to developing this paper. I express my gratitude to anonymous referees, especially of the POJE’s; who greatly helped to improve the paper. This research has received generous financial support from OTKA K 81483.
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Simonovits, A. Socially optimal contribution rate and cap in a proportional (DC) pension system. Port Econ J 14, 45–63 (2015). https://doi.org/10.1007/s10258-015-0107-0
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DOI: https://doi.org/10.1007/s10258-015-0107-0