The Geneva Papers on Risk and Insurance Theory, 23: 119–125 (1998) c 1998 The Geneva Association °

Pareto-Improving Social Security Reform PASCAL BELAN CREST, INSEE, Paris, France PHILIPPE MICHEL GREQAM, University of the Mediterranian, IUF and CORE PIERRE PESTIEAU [email protected] CREPP, Universit´e de Li`ege and CORE, Universit´e de Louvain; 7, Boulevard du Rectorat, Li`ege 4000, Belgium

Abstract It is generally accepted that moving from an unfunded to a funded social security system implies a welfare loss for the transition generation—that is, the generation that has to pay twice: first, saving for its own retirement and, second, contributing to the pensions of the then retired generation. This article shows that in a setting of endogenous growth with positive externality such a transition can be Pareto improving. But it argues also that social security reform is more a pretext than a requirement for internalizing such a positive externality. Key words:

1.

social security, privatization, overlapping generations model, endogenous growth

Introduction

The heavy reliance on pay-as-you-go schemes of pensions provision in a large number of countries has been justified during the decades of rapid growth in population and productivity. However, with the prospect of an unprecedented aging of the population combined with a decline in productivity growth, one has the feeling that increasing reliance on funded schemes would contribute to avoid an unsustainable pressure on public finance. Unfortunately, such a shift is known to have a short-run cost. The transition generation is indeed constrained to pay twice: first, for its own retirement through the funded scheme and, second, for the then retirees through the pay-as-you-go scheme.1 To avoid this double burden, we should have kept and invested the contributions paid when the pay-as-you-go scheme was introduced instead of transferring it to a generation of retirees who had not contributed to it. There is no such a thing as a free lunch and therefore any shift back to a funded scheme is generally deemed to be burdensome for the transition period. A number of authors agree with that view but they still think that the long-run welfare gains are so huge that a temporary loss is bearable.2 From a social welfare viewpoint or from a political economy one, shifting to a partially or fully funded social security system is presented as desirable or implementable. Others have argued that if pay-as-you go social security was strongly

120

PASCAL BELAN, PHILIPPE MICHEL AND PIERRE PESTIEAU

inefficient not only in terms of depressed savings but also of distortion in the laborconsumption choice, a funded scheme that would foster saving and diminish, if not suppress, allocative distortions, then the transition could be Pareto-improving (see Kotlikoff [1996]; Homburg [1990]; and Breyer and Straub [1993]). In this reasoning, it is assumed that a funded scheme is not redistributive and is perfectly individualized so that contributions to it are not anymore viewed as distortionary. In this article, we present an alternative argument for a Pareto-improving social security reform. We adopt an endogenous-growth approach whereby technological knowledge is embodied in the capital stock and exerts a positive externality on individual producers.3 As a consequence, the assumption of diminishing returns on capital is replaced with the assumption of constant returns. With this modification, shifting from pay-as-you-go social security to a funded scheme with a saving-fostering subsidy can make both transition and future generations better off. Based on the labor-market discussion, one does not really need to reform social security to increase efficiency. After all, as shown by Vald´ez-Prieto [1997] (see also Belan and Pestieau [1997]), pay-as-you-go and funded systems are equivalent as long as public debt is accordingly adjusted to keep intergenerational distribution constant. Yet if one wants to eliminate the intergenerational transfer implicit in pay-as-you-go, one can do it progressively by using the efficiency gains so obtained. The rest of this article is organized as follows. In the next section, we present an overlapping-generations model with pay-as-you-go social security and endogenous growth. In Section 3, pay-as-you-go social security is dropped and replaced by a funded scheme and this leads to Pareto improvement. Section 4 briefly concludes the article. 2.

The economy with a pay-as-you-go system

We use a standard two-overlapping-generations model with identical individuals.4 These live for two periods, supply one unit of labor in the first period, and retire in the second one. A constant payroll tax rate τ is imposed to finance retirement benefits.5 In any period, the number of young people is constant and normalized to one. An individual born in t consumes ct in period t and dt+1 in period t + 1, and derives utility: u t = u(ct , dt+1 ), where u is strictly concave and increasing in each of its two arguments. He faces the following budget constraints: ct + st = (1 − τ )wt dt+1 = Rt+1 st + pt+1 ,

(1) (2)

where wt is the wage rate, Rt+1 the gross interest rate, st saving, and pt+1 retirement benefits. Assuming there is no public borrowing, pay-as-you-go imposes the revenue costraint: pt+1 = τ wt+1 . Maximizing u t subject to (1) and (2), one derives optimal saving and the indirect utility as a function of first-period income, (1 − τ )wt , second-period income, pt+1 , and gross

PARETO-IMPROVING SOCIAL SECURITY REFORM

121

interest rate Rt+1 : st = s((1 − τ )wt , pt+1 , Rt+1 )

(3)

u t = v((1 − τ )wt , pt+1 , Rt+1 )

(4)

and

Both consumptions are assumed to be normal goods. Firms act competitively and use a CRS production function: Yt = F(K t , At L t ), with as arguments capital K t and efficient labor At L t . Productivity parameter At represents a positive spillover from the size of the aggregate capital stock to the productivity of workers in individual firms. In the interpretation suggested by Romer [1989], it is proportional to capital: At = a K t . It is taken as given at the firms level and leads to increasing returns for the economy as a whole. By normalization, labor force is equal to one. Assuming capital depreciation at rate µ per period, we have wt = ωK t

and

Rt = R,

where ω ≡ a F20 (1, a) and R ≡ F10 (1, a) + 1 − µ. In equilibrium, the demand of capital by firms equals the supply of capital by consumers— K t+1 = st —and thus pt+1 = τ wt+1 = τ ωst . So, with rational expectations, equilibrium saving satisfies st = s((1 − τ )wt , τ ωst , R). This brings us to the following proposition. Proposition 1: In an economy with a pay-as-you-go social security, saving and utility increase with the current wage wt . That is, defining st ≡ σ (wt ) and u t ≡ µ(wt ), one has σ 0 (wt ) > 0 and µ0 (wt ) > 0. Proof. Indeed, we have σ 0 (wt ) =

∂st (1−τ ) ∂((1−τ )wt )

1−τ ω ∂ p∂st

t+1

> 0. Further, the life-cycle income,

(1 − τ )wt + τ ωσ (wt )/R, and thus the utility level increase with wt as well.

2

The dynamic of capital stock is given by K t+1 = σ (wt ) = σ (ωK t ) for a given K 0 . With homothetic preferences, the saving function is linear in wt and the economy admits a constant growth rate. For further use, we introduce the following notation: ct ≡ c(wt ) = (1 − τ )wt − σ (wt ) and dt+1 ≡ d(wt ) = Rσ (wt ) + τ ωσ (wt ). 3.

Transition to a fully funded pension system

Assume that up to period t = −1, pay-as-you-go social security has been in use. In period 0, if it still applies, each worker pays τ w0 to finance p0 ; he expects to receives p1 = τ w1 . We

122

PASCAL BELAN, PHILIPPE MICHEL AND PIERRE PESTIEAU

have just seen that w1 depends on saving s0 ; in other words, in our setting, a generation is responsible for its own pension levels through its saving. Let us now introduce an alternative policy. Generation 0 is offered a subsidy on the return on its saving. This subsidy is paid in period 1 and financed by a tax on wage w1 . In return, with this reform, there is no more pay-as-you-go benefits—that is, p1 = 0. We will show that this reform improves the welfare of both generations 0 and 1. The reasoning is quite intuitive. Being offered a subsidy equal to τ ω (the pay-as-you-go return on payroll taxes), each member of generation 0 can be made better off. He will consume less in the first period, save more and consume more in the second period. This appears clearly on figure 1. A is the initial endowment with pay-as-you-go (w0 (1 − τ ), p1 ) and A0 is the initial endowment with the new policy (w0 (1 − τ ), 0). AD is the budget constraint under pay-asyou-go with a slope equal to R; A0 D 0 is the new budget constraint with a slope equal to R + τ ω. The old and the new optimal consumption choices are given by E and E 0 . One clearly sees that utility is higher in E 0 than in E and that saving has increased as a result of the reform. We still have to show that increased saving is enough to generate more disposable income for generation 1 and to finance the increase in second-period consumption for generation 0.

Figure 1.

PARETO-IMPROVING SOCIAL SECURITY REFORM

123

This is quite obvious as w10 = ωs00 > w1 where the primes denote the postreform values: a share (1 − τ ) of w10 is disposable income for generation 1 and the remaining share is the subsidy (τ ωs00 > τ ωs0 = p0 ). This pedestrian proof can be applied to all subsequent generations. Let us present it more formally. We introduce a per unit subsidy equal to τ ω. The problem now for any generation is to find the level of saving st that maximizes ϕ(st ) ≡ u((1 − τ )wt − st , (R + τ ω)st ).

(P)

Let us label this optimization program P; it leads to FOC: ϕ 0 (st ) ≡ −u 0c (ct , dt+1 ) + (R + τ ω)u 0d (ct , dt+1 ) = 0.

(5)

This implies the following indirect utility and saving functions: u t = v((1 − τ )wt , 0, R + τ ω) and st = s((1 − τ )wt , 0, R + τ ω). To formally prove that shifting from pay-as-you-go social security to individual saving with subsidy in period t is Pareto improving, we show that if after the reform the wage rate wt is at least as high as w¯ t , the wage rate prevailing before the reform, then the welfare of generation t increases as well as its level of saving. Proposition 2:

For any wt ≥ w¯ t ,

v((1 − τ )wt , 0, R + τ ω) > µ(wt ) ≥ µ(w¯ t ) s((1 − τ )wt , 0, R + τ ω) > σ (wt ) ≥ σ (w¯ t )

(6) (7)

Proof. As we showed in Proposition 1, µ and σ increase with wt , so µ(wt ) ≥ µ(w¯ t ) and σ (wt ) ≥ σ (w¯ t ). We note that the consumption vector chosen before the reform is feasible within the budget set of program (P): c(wt ) + σ (wt ) = (1 − τ )wt and d(wt ) = (R + τ ω)σ (wt ). Thus, for all wt , v((1 − τ )wt , 0, R + τ ω) ≥ µ(wt ); and the inequality is strict since the optimality condition of program (P) is not verified in the economy with a pay-as-you-go system. This establishes (6). It remains to show that saving increases too. First, we contrast (5) with ϕ 0 (σ (wt )) = τ ωu 0d (c(wt ), d(wt )) > 0 and note that ϕ 00 < 0 since u is strictly concave. Hence, s((1 − τ )wt , 0, R + τ ω) > σ (wt ). This proves (7). 2 4.

Conclusion

In this article, we have shown that, within an endogenous growth model a` la Romer, a Paretoimproving transition from unfunded to funded social security can be implemented in one

124

PASCAL BELAN, PHILIPPE MICHEL AND PIERRE PESTIEAU

generation. Actually, what we call funded social security is just regular saving benefitting from a subsidy paid by the working generation. One could naturally have adopted a slower transition process but clearly with less welfare improvement for both the current and the future generations. In the identical individuals setting adopted here, this would not be justified. One could object that what we have studied is a capital income-tax (subsidy) reform rather than a social security reform. This argument in fact holds for most of the reforms based on corrections for allocative distortions. We however believe that reforming social security toward a funded scheme can be an opportunity to make the tax system more efficient and that in return the efficiency gains implied by subsidizing saving can be used to progressively refund the “free lunch” supplied at the start of the pay-as-you-go scheme and contribute to intergenerational equity.

Acknowledgment We are grateful to two referees for helpful comments.

Notes 1. A number of authors have shown that in a setting of exogenous growth shifting from pay-as-you go to funding cannot be Pareto improving (see, e.g., Diamond [1965]; Breyer [1989]; Verbon [1989]; Peters [1991]. 2. See, e.g., the contributions in Feldstein [1996]. 3. This is the so-called AK model due to Romer [1986, 1989]. 4. Intragenerational redistribution effects are thus assumed away. 5. This tax is nondistortionary because labor supply is inelastic.

References BELAN, P. and PESTIEAU, P. [1997]: “Privatizing Social Security: A Critical Assessment.” Mimeo, CORE DP #9784. BREYER, F. [1989]: “On the Intergenerational Pareto Efficiency of Pay-as-You-Go Financed Pension Systems,” Journal of Institutional and Theoretical Economics, 145, 643–658. BREYER, F., and STRAUB, M. [1993]: “Welfare Effects of Unfunded Pension Systems When Labor Supply is Endogenous,” Journal of Public Economics, 50, 77–91. DIAMOND, P.A. [1965]: “National Debt in a Neoclassical Growth Model,” American Economic Review, 55, 1126–1150. FELDSTEIN, M. (Ed.) [1996]: Privatizing Social Security. Chicago: NBER, Chicago University Press. HOMBURG, S. [1990]: “The Efficiency of Unfunded Pension Schemes,” Journal of Institutional and Theoretical Economics, 146, 630–647. KOTLIKOFF, L. [1996]: “Simulating the Privatization of Social Security in General Equilibrium.” In Feldstein [1996]. PETERS, W. [1991]: “Public Pensions in Transition: An Optimal Policy Path,” Journal of Population Economics, 4, 155–175. ROMER, P.M. [1986]: “Increasing Returns and Long-Run Growth,” Journal of Political Economy, 94, 1002– 1037.

PARETO-IMPROVING SOCIAL SECURITY REFORM

125

ROMER, P.M. [1989]: “Capital Accumulation in the Theory of Long-Run Growth.” In Modern Business Cycles Theory, R. Barro (Ed.), Harvard University Press, Cambridge, MA. ´ VALDEZ-PRIETO, S. [1997]: “Financing a Pension Reform Towards Private Funded Pensions.” In The Economics of Pensions. Principles, Policies and International Experiences, S. Vald´ez-Prieto, Cambridge University Press, Cambridge. VERBON, H.A. [1989]: “Conversion Policies for Public Pensions Plans in a Small Open Economy.” In The Political Economy of Social Security, Bjorn Gustafsson and N. Anders Klevmarken (Eds.), Elsevier Science (North Holland).