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Is there any gain from social security privatization?
China Economic Review 22 (2011) 278–289
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China Economic Review
Is there any gain from social security privatization? Shiyu LI a,1, Shuanglin LIN b,c,⁎ a b c
School of Finance, Renmin University of China, 100872, China School of Economics, Peking University, Beijing, 100871, China Department of Economics, College of Business Administration, University of Nebraska, Omaha, NE 68182
a r t i c l e
i n f o
Article history: Received 8 November 2010 Received in revised form 24 January 2011 Accepted 28 January 2011 Available online 4 February 2011 JEL classification: E6 H3 O53 Keywords: Social security reforms PAYG system Funded system Overlapping generations model
a b s t r a c t Increasing calls for a social security reform of switching from the pay-as-you-go (PAYG) system to a funded system has been seen in recent decades. This paper examines the effect of this reform on capital accumulation and the welfare of each generation. Three methods are used to finance the pension debt, government debt financing, tax financing, and government asset financing. With government debt or tax financing, the market equilibrium remains unchanged and all generations are as well off in the new system as in the PAYG system. Thus, switching from the PAYG system to a funded system is neutral. With government asset financing, the interest rate will decrease, private capital will increase, but the total output may either increase or decrease. The welfare effect is also ambiguous in general, depending on the rate of return of government assets. With plausible parameters, our simulation shows that the reform will lower the interest rate, increase private capital, and lower government capital in the short run, but raise government capital and increase output in the long run. Published by Elsevier Inc.
1. Introduction The pay-as-you-go (PAYG) social security system has been established in many countries for quite some time. Samuelson (1958) showed that, the PAYG system permits a windfall benefit to current retirees, with the social security payment to the current young deferred to the future generation, and an introduction of the PAYG social security system is a Pareto improvement. Recent decades, social security reforms have become a heated debated topic among academics and policy-makers. A prominent suggestion is to switch from the current PAYG social security system to a funded social security system with the establishment of personal social security accounts, often called social security privatization. This paper analyzes the gains from this type of social security reform by taking into consideration various ways to finance the social security debt to the current old generation. A number of studies have demonstrated the advantages of a switch from the PAYG system to a funded system. Feldstein (1995) used a partial equilibrium framework to examine whether privatizing social security (i.e., a switch from the PAYG system to a funded system) would raise welfare. He shows that a debt-financed transition from the PAYG system to a funded system would raise economic welfare if three conditions are met: (1) the marginal product of capital exceeds the rate of economic growth; (2) the marginal product of capital exceeds the appropriate consumption discount rate; and (3) the rate of economic growth is positive.2 These conditions are likely to be satisfied. However, he recognized that a majority of the adult population alive at the ⁎ Corresponding author at: Department of Economics, College of Business Administration, University of Nebraska, Omaha, NE 68182, United States. Tel.: +86 10 6276 0620, +1 402 554 2815; fax: +86 10 8252 4675, +1 402 554 2853. E-mail addresses: [email protected], [email protected], [email protected] (S. Lin). 1 Tel.: +86 10 6274 2511. 2 A debt financed transition means that the transition from an unfunded social security system to a funded social security system that does not reduce the benefits of existing retirees would, however, require substituting explicit government debt for the equally large implicit debt of the unfunded social security system. 1043-951X/$ – see front matter. Published by Elsevier Inc. doi:10.1016/j.chieco.2011.01.005
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time of the privatization might be worse off. Feldstein (1998) provided two alternatives, immediate transition by issuing “recognition bonds” or a gradual transition by collecting taxes. The first method substitutes new government bonds for the existing implicit claims of retirees and current employees. With the second method, employees during the transition period must pay payroll taxes to support the existing retirees and, at the same time, must accumulate assets for their own retirement. With both methods, the first few generations alive during the transition period will be worse off and the future generations will be better off. Kotlikoff (1996) used a general equilibrium model to simulate the effects of social security privatization and showed that a switch to an alternative tax base, such as from a progressive income tax to a consumption tax, may generate significant efficiency gains. Prior studies have also shown that in order to pay the implicit pension debt in the transition process, some generations have to be worse off to make others better off. Breyer (1989) argued that when the PAYG system is replaced by a funded system, it is generally impossible to compensate the pensioners in the transition generation without making at least one later generation worse off. By assuming agents within a generation are different, Brunner (1996) showed that a Pareto-improving transition to a funded system is not possible because any instrument applied to the financing of pensions in the transition period involves intragenerational redistribution. Murphy and Welch (1998) suggested that one way to complete the transition is to cut benefits instead of raising taxes. Sinn (1997, 2000) argued that there is nothing to be gained from a transition to a funded system in general, but he suggested privatization of the pension system for those not willing to have children. By assuming endogenous fertility, Groezen, Leers, and Meijdam (2003) and Hirazawa and Yakita (2009) examined social security payroll tax in a small open economy with exogenous interest rate and showed that, with a child allowance scheme or a child care market, it is possible to have Pareto improvement by a PAYG payroll tax cut. Recent years have seen increasing interest in China's social security reforms. Feldstein (1999) proposed that China should move from a PAYG defined benefit system to a funded defined contribution system. In his opinion, in the PAYG system, the rate of return depends on the growth rate of aggregate real wages. According to the World Bank estimation, wages in China will grow at approximately 7% or less per year. However, in the funded system, the rate of return depends on the marginal product of industrial capital, which was estimated at 17% in China (Chow, 1993), or with a conservative estimation of 12%. In this case, $1 saved at age 45 grows up to $7.6 at age 75 in the PAYG system, while $1 will grow up to $29.95 in the funded system.3 Therefore, the funded system can provide the same level of benefits with a savings rate equal to only one fourth of the rate of tax required in the PAYG system. However, he did not consider the social security payment to the current old generation. Lin (2008) argued that with only about 25% of employees involved in the current PAYG social security system, China should switch to a funded social security system immediately.4 This paper examines the effects of a switch from the PAYG system to a funded system by considering the implicit pension debt repayment and by allowing existing generations as well off in the new system as in the PAYG system. An overlapping generations model is utilized. Three methods are used to finance the pension debt to the current old generation: government debt financing, tax financing, and government asset financing. With government debt or tax financing, the market equilibrium remains unchanged, and all the generations are as well off in the new system as in the PAYG system. Thus, the social security reform is neutral. With government asset financing, the interest rate will decrease and private capital stock will increase, but the total output may either increase or decrease, while the welfare effect is ambiguous in general. With plausible parameters, our simulations show that the reform will lower the interest rate, increase private capital, and lower government capital in the short run, but raise government capital and increase the output level in the long run. The paper contributes not only to issues concerning China social security reforms, but also to the theoretical literature on social security reforms in general. The paper proceeds as follows. Section 2 introduces the model with a PAYG social security system. Section 3 analyzes the effects of switching from the PAYG system to a funded system with various ways of financing social security debt. Section 4 provides concluding remarks. 2. The model There are many individuals and firms in the economy. Individuals are identical within and across generations. The population of generation t + 1 in period t + 1 Lt + 1 is (n is constant): Lt + 1 = (1 + n)Lt.5 The government lives forever, running a social security system and managing government capital. 2.1. The firm The economy produces one good, which can be either consumed or invested. Output is produced by identical competitive firms using a constant-returns-to-scale production technology. There are three inputs in the production: private capital, government capital, and labor. Specifically, the production function is as follows: α
β
1−α−β
Yt = Kt Gt ðAt Lt Þ 3
ð2:1Þ
The detailed calculation is as follows: (1.07)30 = 7.6122 and (1.12)30 = 29.9599. Using the Computable General Equilibrium model Wang, Xu, Wang, and Zhai (2001) found that China's current PAYG system with a notional personal social security account is not sustainable. 5 The main result of this paper will remain unchanged even if we introduce endogenous fertility. The details are available on request. 4
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where Kt is the stock of private capital in period t; Gt is the stock of government capital in period t; At is the productivity parameter, γ = Δ At/At (Δ A t = At + 1 − At) is the growth rate of productivity. Letting yt = Yt/AtLt, the output-effective labor ratio, we have: yt = f ðkt ; gt Þ;
fk N 0; fg N 0; fkk b 0; and fg g b 0
ð2:2Þ
where kt = Kt/AtLt, is the private capital–effective labor ratio and gt = Gt/AtLt is the government capital–effective labor ratio. Assume that both private capital and government capital are fully depreciated after one period's production. Factor markets are perfectly competitive, and thus, the rate of return to each factor is its marginal product. Let 1 + rt be the rate of return on private capital in period t, let 1 + ht be the rate of return on government capital in period t, and let wt be the rate of return to effective labor.6 1 + rt =
∂Yt β α−1 = α gt kt ∂Kt
ð2:3Þ
1 + ht =
∂Yt β−1 α = βg t k t ∂Gt
ð2:4Þ
∂Yt α β = ð1−α−βÞk t g t ∂ðAt Lt Þ
ð2:5Þ
wt =
Let Wt be each individual's total wage income, and ΔWt/Wt be the growth rate of the wage rate. We have: Wt =
∂Yt = At w t ; ∂Lt
ΔWt ΔAt Δwt = + Wt At wt
ð2:6Þ
2.2. The consumer Each individual lives for two periods, working and saving in the first period, and consuming savings and interest income in the second period. The representative individual faces the following utility maximizing problem: t t Max u = ut ct ; ct
+ 1
t
s:t:ct ≤ð1−πÞAt wt −st −τt t ct +1 ≤st 1 + rt +1 + vt +1 t
t
ct ; ct +1 ≥ 0; t = 0; 1; 2… where ctt+j is consumption in period t + j of an agent born in period t (called generation t), j = 0, 1; π is the tax rate on labor income or the payroll tax rate; πAtwt is the social security tax or contribution to personal social security account; vt + 1 is the social security benefits that old people receive in the period of t + 1; st represents private savings in period t of an agent born in period t, which is the difference between the first-period disposable income and the first-period consumption; and τt is the tax collected at period t. The utility function is twice differentiable and strictly quasi-concave. The marginal utility is positive but diminishing. Combining the above two budget constraints, we have: t
ct +
t
ct +1 vt +1 ≤ ð1−πÞAt wt −τt + : 1 + rt +1 1 + rt +1
ð2:7Þ
To obtain explicit solutions for savings and other endogenous variables and to keep the model tractable, assume that the utility function is log-linear: u(ctt, ctt + 1) = ln(ctt) + ρ ln(ctt + 1), where ρ b 1 is the (constant) pure rate of time preference or discount factor. Solving the agent's maximization problem yields: t
ct =
t
ð1−πÞAt wt −τt + vt +1 = 1 + rt +1 ð1 + ρÞ
ct +1 =
# " ρ 1 + rt +1 vt +1 ð1−πÞAt wt −τt + ð1 + ρÞ 1 + rt +1
ð2:8Þ ð2:9Þ
6 This is different from other literature, like Barro (1990), Futagami, Morita, and Shibata (1993), Yakita (2008), which assumed that government capital is provided to the household-producer without user charges. Here, government capital as an input yields returns. In China, the government owns a large stock of capital in state-owned enterprises that yields returns to its owner.
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st =
ρ½At wt ð1−πÞ−τt vt +1 − 1+ρ ð1 + ρÞ 1 + rt +1
281
ð2:10Þ
Eqs. (2.8)–(2.10) show the optimal first- and second-period consumption and optimal savings. 2.3. The government The government faces the following constraints: Gt +1 = ð1 + ht ÞGt ; Bt + ð1 + rt ÞDt = πAt wt Lt + τt Lt + Dt +1
ð2:11Þ
where the first equation is government capital budget and the second one is social security budget, Gt + 1 is the government capital at the beginning of period t + 1; 1 + ht is the rate of return to government capital; (1 + ht)Gt is the total return to government capital; Bt is the social security expenditure, i.e., the total amount that government must pay to all retirees living in period t (or born in period t − 1); Dt is the government debt issued in period t; and πAtwtLt + τtLt is the total tax revenue. Dividing both sides of Eq. (2.11) by AtLt yields: ð1 + nÞð1 + γÞgt +1 = ð1 + ht Þgt ;
Bt τ + ð1 + rt Þdt = πwt + t + ð1 + nÞð1 + γÞdt +1 At Lt At
ð2:12Þ
where dt = Dt/AtLt and gt = Gt/AtLt. 2.4. The equilibrium A competitive equilibrium for the economy is a set of sequences {rt, ht, wt, ctt, ctt + 1, st, gt, kt} satisfying Eqs. (2.3)–(2.5), (2.8)– (2.10), (2.12), and ( ) ρ½At wt ð1−πÞ−τt vt +1 − Kt +1 + Dt +1 = St = Lt st = Lt ð2:13Þ 1+ρ ð1 + ρÞ 1 + rt +1 where Kt + 1 is the private capital to be used in period t + 1, St is the total savings at the end of period t, and Dt + 1 is the government debt issued in period t + 1. Dividing both sides by labor in period t, AtLt yields: ρ½wt ð1−πÞ−τt = At vt +1 − ð1 + nÞð1 + γÞ kt +1 + dt +1 = 1+ρ At ð1 + ρÞ 1 + rt +1 Recall that
ð2:14Þ
L t +1 At +1 = 1 + n and = ð1 + γÞ. Lt At
2.5. The PAYG social security system In the PAYG system, social security is financed by a payroll tax. An individual only needs to pay the payroll tax, πAtwt, and does not pay any additional tax (i.e.,τt = 0). The contribution made by all young individuals at time t,LtπAtwt, are used directly to pay social security benefit,Bt, to the old generation, where Bt = Lt − 1vt. Also, government does not issue debt (i.e.,Dt = 0). The social security budget constraint is as follows: Bt = Lt−1 vt = Lt πAt wt ; or vt = ð1 + nÞπAt wt
ð2:15Þ
Inserting τt = 0 and Eq. (2.15) into consumer's budget constraint Eq. (2.7), consumption Eqs. (2.8) and (2.9), saving Eq. (2.10), government budget Eq. (2.11), and the private capital market equilibrium condition Eq. (2.13), we have: t
ct + t
ct = t
t
ct +1 ð1 + nÞπAt +1 wt +1 ≤ð1−πÞAt wt + 1 + rt +1 1 + rt +1 ð1−πÞAt wt + πAt
ct +1 =
+ 1 wt +1 ð1
+ nÞ = 1 + rt +1
ð1 + ρÞ # " ρ 1 + rt +1 πAt + 1 wt +1 ð1 + nÞ ð1−πÞAt wt + ð1 + ρÞ 1 + rt +1
ð2:16Þ ð2:17Þ
ð2:18Þ
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st =
ρAt wt ð1−πÞ πAt +1 wt +1 ð1 + nÞ − 1+ρ ð1 + ρÞ 1 + rt +1
ð2:19Þ
Gt +1 = ð1 + ht ÞGt
Kt +1 = Lst = Lt
ð2:20Þ
! ρAt wt ð1−πÞ πAt +1 wt +1 ð1 + nÞ − 1+ρ ð1 + ρÞ 1 + rt +1
ð2:21Þ
3. A switch from the PAYG system to a funded system Assume that government decides to switch from the PAYG system to a fully funded system in which people are required to save in the first period of life and receive the principle and interest in the second period of life. Specifically, assume that in the first period, instead of paying social security tax, πAtwt, an individual needs to contribute the same amount, πAtwt, to his/her personal social security account, as well as paying a per capita tax τt. The amount of tax, τt, is defined as the discounted value of the difference between the pension benefit under the funded system and the benefit under the PAYG system. With this tax, the individual will be as well off as under the PAYG system. Specifically, τt =
πAt wt 1 + rt +1 −πAt +1 wt +1 ð1 + nÞ 1 + rt +1
=
πAt w 1 + rt +1 −wt +1 ð1 + nÞð1 + γÞ 1 + rt +1 t
ð3:1Þ
where πAtwt(1 + rt + 1) is the pension benefit under the funded system and 1 + rt + 1 is the rate of return from contribution to funded system, while πAt + 1wt + 1(1 + n) is the pension benefit under the PAYG system and (1 + γ)(1 + n)wt + 1/wt is the rate of return from contribution to the PAYG system. τt may be positive, zero, or negative depending on the rate of return from contribution to PAYG system and funded system. When the population growth rate and the productivity growth rate are low, τt tends to be positive, while for high population growth and productivity growth the tax (rate) may be negative. However, as in Feldstein (1999), we assume that the rate of return from contributions to a funded system is greater than the rate of return from contributions to a PAYG system, i.e., (1 + γ)(1 + n)wt + 1/wt b 1 + rt + 1 and hence τt is positive.7 In the second period, individuals receive benefit from personal social security account, (1 + rt + 1)πAtwt. Replacing vt + 1 by (1 + rt + 1)πAtwt and substituting Eq. (3.1) into the consumer's budget constraint Eq. (2.7), we have: t
ct +
ctt+1 ð1 + nÞπAt +1 wt +1 ≤ At wt −τt = ð1−πÞAt wt + : 1 + rt +1 1 + rt +1
Since the extra pension benefit in the funded system is taken away as a tax by the government to pay for the current generation's social security benefit, the individual's budget constraint is the same as Eq. (2.16) under the PAYG system. Solving the agent's maximization problem yields: t
ct =
t
ð1−πÞAt wt + πAt +1 wt +1 ð1 + nÞ = 1 + rt +1 ð1 + ρÞ
ct +1 =
st =
# " ρ 1 + rt +1 πAt +1 wt +1 ð1 + nÞ ð1−πÞAt wt + ð1 + ρÞ 1 + rt +1
ρAt wt ð1−πÞ ρπAt +1 wt +1 ð1 + nÞ −πAt wt : + 1+ρ ð1 + ρÞ 1 + rt +1
ð3:2Þ
ð3:3Þ
ð3:4Þ
It can be seen that Eq. (3.2) in the funded system is equivalent to Eq. (2.17) under the PAYG system, while Eq. (3.3) is equivalent to Eq. (2.18). However, Eqs. (3.4) and (2.19) are different, i.e., private savings are different in the funded system and the PAYG system. Savings affect the interest rate, the wage rate, and therefore, individuals' consumptions. Savings will be different under different methods of social security debt financing. We will consider three different ways of financing the implicit social security debt, debt financing, tax financing, and government asset financing, and examine savings and capital accumulation under various methods of social security debt financing.
7
If wt + 1 = wt, the condition becomes (1 + γ)(1 + n) b 1 + rt + 1.
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3.1. Debt financing Assume that starting from period 1 the government decides to reform the social security system and issues government bonds, D1, to finance the implicit social security debt (the social security benefits to the old generation), which is equal to B1 = L1A1πw1. In the meantime, the government starts to collect lump-sum tax from the young generation and future generations to pay off the debt. Let V1t denote taxes that the government collects from generation t, discounted to period 1. The amount of taxes paid by generation t equals τt L t. The present value (discounted to period 1) of taxes paid by generation t is as follows:
t
V1 =
t−1
τt L t
∏ 1 + rj+1
=
j=1
πAt wt 1 + rt +1 −πAt +1 wt +1 ð1 + nÞ L1 ð1 + nÞt−1 t−1 1 + rt +1 ∏ 1 + rj+1 j=1
ð3:5Þ
πAt wt ð1 + nÞt−1 L1 πAt +1 wt +1 ð1 + nÞt L1 ; j = 1; 2; …; t−1: = − t t−1 ∏ 1 + rj+1 ∏ 1 + rj+1 j=1
j=1
τ L
2 2 For example, if t = 1, then V11 = τ1L1 and if t = 2, then V12 = 1 + r2 . We assume that it takes N generations to pay off the implicit social security debt, i.e., the present value of lump-sum tax collected from N generations should be equal to the debt. Mathematically,
N
t
D1 = B1 = L1 A1 πw1 = ∑ V1 :
ð3:6Þ
t =1
During the transition period (N periods), government collects lump-sum tax to pay the debt. When the lump-sum tax collected from the young and future generations can pay off the debt, the transition period ends and government stops collecting lump-sum tax. How many generations will it take to pay off the debt, or how long will the transition time last? By summing up V1t from generation 1 to generation N we obtain the present value of total taxes paid by these N N
generations, ∑ V1t . We find that the second term of V1t can be cancelled out by the first term of V1t + 1 when adding them up. That t =1
is, N
t
∑ V1 = L1 πA1 w1 −L1 π
t =1
AN+1 wN+1 ð1 + nÞN ð1 + γÞN ð1 + nÞN = L πA w −L πA w 1 1 1 1 1 N+1 : N N ∏ 1 + rj+1 ∏ 1 + rj+1 j=1
ð3:7Þ
j=1
Substituting Eq. (3.7) into Eq. (3.6), we find, to satisfy Eq. (3.6), the following equation must be hold: L1 πA1 wN +1
ð1 + γÞN ð1 + nÞN = 0: N ∏ 1 + rj+1
ð3:8Þ
j=1
Now, in order to satisfy Eq. (3.8), how large should N be? As we assume earlier, [(1 + γ)(1 + n)]/(1 + rt + 1) b 1. Thus, we have ½ð1 + γÞð1 + nÞN =0 N N→∞ ∏ 1 + rj+1 lim
j=1
or
lim L1 πA1 wN +1
N→∞
½ð1 + γÞð1 + nÞN = 0: N ∏ 1 + rj+1 j=1
That is to say, to satisfy Eq. (3.8), N needs to approach infinity, or it takes infinite generations to pay off the implicit pension debt at the current tax system. Thus, every generation must pay taxes to finance the implicit social security debt, and their after-tax social security benefit is equivalent to that under the PAYG system. The debt will not be redeemed forever in order to avoid the welfare losses.
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What about capital accumulation? With the establishment of a personal social security account, the total savings, St, is the forced social security savings, πAtwtLt, plus the private savings, Ltst. When government issues bonds to finance implicit debt, the market equilibrium condition becomes: Kt +1 + Dt +1 = St = Lt st + πAt wt Lt " # ρAt wt ð1−πÞ ρπAt +1 wt +1 ð1 + nÞ −πAt wt + πAt wt Lt + = Lt 1+ρ ð1 + ρÞ 1 + rt +1 " # ρAt wt ð1−πÞ ρπAt +1 wt +1 ð1 + nÞ : + = Lt 1+ρ ð1 + ρÞ 1 + rt +1
ð3:9Þ
Government debt in the beginning of period t + 1 is as follows:8 Dt +1 = πAt wt Lt −τt Lt :
Substituting the above equation into the market equilibrium condition (3.9) and rearranging terms yield: ( Kt +1 = St −Dt +1 = Lt
) ρA t wt ð1−πÞ πAt +1 wt +1 ð1 + nÞ : − 1+ρ ð1 + ρÞ 1 + rt +1
It can be seen that capital market equilibrium condition is the same as that under the PAYG system Eq. (2.21). Therefore, with debt financing, a switch from the PAYG system to a funded system does not affect the equilibrium in capital market, i.e., it does not affect the market demand and supply and the equilibrium interest rate. On the consumption side, as we showed in Eqs. (3.2) and (3.3), as long as government keeps collecting lump-sum tax, an individual's consumption functions will be the same as those under the PAYG system. Therefore, with the interest rate and the wage rate being the same under the two systems, consumption in the funded system is the same as in the PAYG system. No generation, either the current or the future, will be better off or worse off with the social security reform. 3.2. Tax financing We now consider the case where the government financing the payment to the current old generation by collecting taxes from the young generation. To focus on tax financing, assume that government does not issue debt, i.e., Dt = 0. Assume that the government requires the young generation to save for their own retirement and collects taxes from them to keep them as well off as under the PAYG system. As we mentioned above, the lump-sum tax τtis defined as the discounted value of the difference between the pension benefit under the funded system and the pension benefit under the PAYG system, denoted by Eq. (3.1). In the new system, tax revenues collected are τtLt. Therefore, individual's budget constraint in the funded system is exactly the same as in the PAYG system, and hence, the solutions to the agent's maximization problem remain unchanged, i.e., both young and old generation's consumption functions will be the same as Eqs. (3.2) and (3.3), which are equivalent to , the consumption functions under the PAYG system [see Eqs. (2.17) and (2.18)]. We now examine total savings in the funded system with tax financing. In the funded system, since the contributions paid by young individuals at time t are put into a personal social security account to accrue interest instead of paying directly to the current old generation, the social security budget is different from that in the PAYG system.9 Let Zt − 1 denote government's social security savings in period t − 1, which equals social security revenue minus social security expenditure in period t − 1. In period t, government social security revenue includes taxes, τtLt, private pension contribution, πAtwtLt, and principal and interest of last period's social security savings, (1 + rt)Zt − 1. We now try to figure out government social security savings in each period, Zt. In period 1, total social security revenue is taxes, τ1L1, plus personal social security contribution, πA1w1L1 (paid by the young generation in period 1); while social security expenditure is pension benefit paid to the old generation in period 1, πA1w1L1. Social security savings in period 1, Z1, is social security revenue minus social security expenditure, which equals τ1L1. In period 2, social security revenue is τ2L2 + πA2w2L2 +(1+ r2)τ1L1, social security expenditure is πA1w1L1(1+ r2), which is the social security benefit the old receive under the new funded system, and it can be shown
8 At the beginning of period 2, government debt is πA1w1L1− τ1L1; at the beginning of period 3, government debt balance is (πA1w1L1− τ1L1)(1 + r2)− τ2L2 = πA2w2L2 − τ2L2, and so forth. We can calculate that government debt at the beginning of period t + 1 is πAtwtLt-τtLt. 9 As we showed in Eq. (2.15) in the PAYG system, social security revenue equals social security expenditure and hence social security saving is zero.
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that social security savings, Z2, is τ2L2. In general, for t =2, 3, …, social security revenue is τtLt + πAtwtLt +(1 +rt)τt − 1Lt − 1, social security expenditure is πAt − 1wt − 1Lt − 1(1 +rt), and social security saving is Zt = τtLt.10 The detailed derivation is as follows: Zt = ½τt L t + πAt wt Lt + ð1 + rt Þτt−1 Lt−1 −½πAt−1 wt−1 Lt−1 ð1 + rt Þ = τt L t + πAt wt Lt + ð1 + rt Þ
πAt−1 wt−1 ð1 + rt Þ−πAt wt ð1 + nÞ L t−1 −πAt−1 wt−1 Lt−1 ð1 + rt Þ 1 + rt
= τt L t + πAt wt Lt + πAt−1 wt−1 ð1 + rt ÞLt−1 −πAt wt ð1 + nÞLt−1 −πAt−1 wt−1 Lt−1 ð1 + rt Þ = τt L t + πAt wt Lt −πAt wt ð1 + nÞLt−1 = τt L t :
In period t, social security saving (Z t =τt L t) is far less than individual's contribution (πAtwtLt), and therefore, the system with tax financing is a funded system with notional personal account, i.e., pension paid to the old generation in period t (πAt − 1wt − 1Lt − 1(1+rt)) will use up the young generation's contributions (πA t wt L t) plus last period's social security savings and interest ((1+rt)zt − 1). If future generations stop paying taxes, the pension benefit underfunded system, (1+rt + 1)πAtwt, cannot be sustained. Thus, future generations need to pay taxes forever. The capital market equilibrium condition is as follows: " # ρAt wt ð1−πÞ ρπA t +1 wt +1 ð1 + nÞ −πAt wt + τt Lt + 1+ρ ð1 + ρÞ 1 + rt +1 ! ρAt wt ð1−πÞ πAt +1 wt +1 ð1 + nÞ − 1+ρ ð1 + ρÞ 1 + rt +1
Kt +1 = St = L t st + τt L t = Lt = Lt
ð3:10Þ
where Kt + 1 is the private capital to be used in period t + 1, St is total savings at the end of period t, Ltst is the private savings of generation t at the end of period t, and τtLt is government social security savings in period t. Comparing Eqs. (2.21) and (3.10), we find that the capital market equilibrium condition in the funded system is the same as that in the PAYG system. The decrease in private savings is exactly equal to the government social security savings, and the total savings remain unchanged. Thus, the equilibrium interest rate and the wage rate will be the same as that under the PAYG system. With the same consumption functions and the same interest rate and the wage rate, the consumption will be exactly the same. No generation will be better off or worse off with the social security reform. Thus, the switch from the PAYG system with tax financing is neutral, i.e., it does not affect the market equilibrium. 3.3. Government asset financing Unlike many other market economies, the Chinese economy evolved from a centrally planned system, and the government has a huge amount of state-owned assets. The asset of the state-owned enterprises was 13,437 billion yuan, or 44% of GDP in 2008.11 Huizinga and Nielsen (2001) argued that managers of public activities may lack the incentives to fully exploit the production potential of the activities. In addition, Boardman and Vining (1989) showed that after controlling for a wide variety of factors, large industrial mixed and state-owned enterprises perform substantially worse than similar private companies. We now consider the case where the government finances the implicit pension debt by selling government assets. Specifically, the government pays the social security benefit to the current old by selling government capital. The contribution made by the young in period t,πAtwt, is put into a personal account; and the rate of return on πAtwt is the same as private savings, st, and is equal to 1 + rt + 1. In this case, implicit pension debt is paid off in period 1 by government capital. Current and future generations can enjoy the higher pension return from funded system and without worrying about the pension debt. Replacing vt + 1 by (1 + rt + 1)πAtwt and setting τt = 0 in the consumer's budget constraint Eq. (2.7), consumption Eqs. (2.8) and (2.9), and saving Eq. (2.10), we have: t
ct +1 ≤ At wt 1 + rt +1 A t wt t ct = ð1 + ρÞ t
ct +
t
ct +1 =
ρ 1 + rt +1 At wt ð1 + ρÞ
ð3:11Þ ð3:12Þ
ð3:13Þ
10 Recall that τt is defined by Eq. (3.1), which guarantees generations under the funded system as well off as under the PAYG system. The tax (rate) is essential to obtain social security savings equal to Zt = τtLt. If τt takes other values, equation Zt = τtLt may not hold. 11 China Ministry of Finance, Finance Yearbook of China, China's Fiscal Press (1996–2009).
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Table 1 Initial values of exogenous variables and parameters. Variables
Definition
Value
ρ α β γ π n N T Population
Constant pure rate of time preference Private capital's share in production Public capital's share in production Productivity growth rate Tax rate on labor income or the payroll tax rate Population Growth rate Number of periods in lifetime Simulation period Initial population
0.56 0.3121 0.1 0.54 0.15 0.1556 2 15 50
Note: a: The share of total capital in GDP is calculated based on the data from Hsueh and Li (1999), China National Bureau of Statistics, China Statistical Yearbook (2009). b: China National Bureau of Statistics, 2009, China Statistical Yearbook shows that the household saving rate is 36%. ρ is calibrated according to the saving rate. c: For productivity growth rate: (1 + .015) 29 − 1 = 0.54. d: For population growth rate: (1 + .005)29 − 1 = 0.1556. We also conduct a sensitivity analysis. With a lower n, say n = 0, the results remain unchanged qualitatively.
st =
ρAt wt −πAt wt : 1+ρ
ð3:14Þ
In this system, government decreases government capital and contributes X1 = πA1w1L1 into a social security account in period 1. In period 1, the social security revenue is πA1w1L1 + X1, social security expenditure is πA1w1L1, and the social security savings are πA1w1L1; in period 2, the social security revenue is πA1w1L1(1 + r2) + πA2w2L2, social security expenditure is πA1w1L1(1 + r2), and the social security savings are πA2w2L2; in period t + 1, the social security revenue is πAtwtLt((1 + rt+1) + πAt+1wt+1Lt + 1, social security expenditure is πAtwtLt(1 + rt + 1), and the social security savings are πAt+1wt + 1Lt+1.
Fig. 1. Effects of social security reforms on private and public capital, the interest rate, and output.
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Fig. 2. Remaining lifetime utility of generation t.
When private capital market clears,
ρAt wt −πAt wt 1+ρ
Kt +1 = St = Lt st + πAt wt Lt = Lt
+ πAt wt Lt = Lt
ρAt wt 1+ρ
ð3:15Þ
where Kt + 1 is the private capital to be used in period t + 1, St is total saving at the end of period t,Ltst is the private savings of generation t at the end of period t, and πAtwtLt is social security saving in period t. Clearly, after the government uses its capital to pay for the social security benefit of the current old generation, total savings will increase (comparing Eqs. (2.21) and (3.15)). This will result in an increase in private capital stock, a decrease in the interest rate, and an increase in the wage rate. Government capital stock will decrease as a portion of it is used for social security payment. In period 1, government contributes X1 to the social security account and government capital becomes: G 2 = ð1 + h1 ÞG1 −X1 and G t +1 = ð1 + ht ÞGt ; t = 2; 3; …
ð3:16Þ
Under the new social security system with government asset financing, in period 2 private capital increases, while government capital decreases. Subtracting Eq. (2.21) from Eq. (3.15), we can calculate how much capital increased in the funded system in period 2, denoting by ΔK2. ΔK2 = L1
ρA1 w1 ρA1 w1 ð1−πÞ πA2 w2 ð1 + nÞ ρX1 πA2 w2 ð1 + nÞ − −L1 = + L1 1+ρ ð1 + ρÞð1 + r2 Þ ð1 + ρÞð1 + r2 Þ 1+ρ 1+ρ
h
ρA1 w
ρA w ð1−πÞ
π A w ð1 + nÞ
i
1 1 − ð1 +2 ρ2Þð1 + r2 Þ is total savings (capital) in the where L1 1 + ρ1 is total savings (capital) in the funded system and L1 1 + ρ PAYG system. Recall that the production function is Yt = KtαGtβ(AtLt)1 − α − β. The output in the second period becomes:
α
β
1−α−β
Y2 = ðK2 + ΔK2 Þ ðG2 −X1 Þ ðA2 L2 Þ
:
Differentiating Eq. (3.17) with respect to X1 gives:
dY2 ρ α−1 dK2 β α β−1 dG2 1−α−β = αðK2 + ΔK2 Þ + ðG2 −X1 Þ + βðK2 + ΔK2 Þ ðG2 −X1 Þ −1 ðA2 L2 Þ ⋛0 1+ρ dX1 dX1 dX1
ð3:17Þ
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dK
Since dX2 1
iff or or
or
= 0 and
dG2 = 0, the above equations can be simplified as follows: dX1
ρ ðG2 −X1 Þβ −βðK2 + ΔK2 Þα ðG2 −X1 Þβ−1 ⋛0 1+ρ ρ −1 −1 −βðG2 −X1 Þ ⋛0 αðK2 + ΔK2 Þ 1+ρ ρ K + ΔK2 αρ K + ΔK2 −β 2 −β 2 ⋛0 or ⋛0 α 1+ρ 1+ρ G2 −X1 G2 −X1 αðK2 + ΔK2 Þα−1
X1 ⋚
αρG2 −βð1 + ρÞK2 −βð1 + ρÞL1 ρðα + βÞ
πA2 w2 ð1 + nÞ ð1 + ρÞð1 + r2 Þ
:
It can be seen that if α and G2 are sufficiently large, or β and K2 are sufficiently small, output increases; otherwise, output decreases. Consumption depends on the interest rate and the wage rate, as well as other parameters. With an increase in the wage rate and a decrease in the interest rate, the impact on consumption is ambiguous. We now examine the effects of the social security reform on private capital, interest rate, government capital, output, and welfare through simulation analyses. We calibrate this model economy to the behavior of China to weigh the gains and losses from the transition. The calibrated parameters are summarized in Table 1. Fig. 1 illustrates the effects of a switch from the PAYG system to the funded system on private capital accumulation, government capital accumulation, the interest rate, and the output. For convenience, we define the ratio of capital under the funded system to capital under PAYG system as kˆt , and we define rˆt , gˆ t and Yˆ t in a similar way. Since at the beginning of period 1, k1 and g1 are the same under both systems, i.e., kˆ1 = 1, rˆ1 = 1, gˆ 1 = 1 and Yˆ 1 = 1. Fig. 1A shows the change in private capital. It can be seen that private capital–effective labor ratio increases after transferring from the PAYG system to the funded system. Around steady state, private capital–effective labor ratio in the funded system is 165% as much as that in the PAYG system. The funded system has a higher capital accumulation than the PAYG system. The interest rate or the rate of return to private capital decreases after transferring to a funded system, as shown in Fig. 1B. Fig. 1C shows the evolvement of government capital. Government capital is lower in the funded system than in the PAYG system at the beginning of the reform since government uses its capital to pay for pension debt. However, the amount of government capital will be higher in the funded system than that in the PAYG system from fourth period, and becomes 19% higher in the steady state. The evolvement of output is displayed in Fig. 1D. In the funded system, output is 10% lower than that in the PAYG system in period 2. However, after that the output has a sustainable increase: 5% higher in period 3, 13% higher in period 4, and 19% higher around steady state. Fig. 2 shows the impact of the transition from the PAYG system to the funded system on the utilities (welfare) of the current and the future generations. The horizontal axis indicates the time period in which the various generations were born, and the vertical axis shows the change of utility level. For example, a value of 1.05 means that the generation's remaining lifetime utility under the funded system is 5% higher than it would have been in the PAYG system. To be precise, the percent change in utility is measured as a consumption equivalent (See Kotlikoff (1996)). Specifically, let ut = ln(ctt) + ρ ln(ctt + 1) denote utility level in the PAYG system and u˜ t = ln c˜tt + ρln c˜tt+1 denote utility level in the funded system. Think about how much consumption should be increased or decreased in order to make people in the PAYG system achieve the same utility level as people in the funded system. Define λt satisfying the following equation: t t t t u˜ t = ln λ t ct + ρ ln λt ct +1 = ð1 + ρÞln λ t + ln ct + ρ ln ct +1 = ð1 + ρÞln λt + ut : Solving the above equation, we obtain the value of λt. If λt N 1 (or λt b 1), it means that consumption should be increased (or decreased) by λt − 1 (or 1 − λt) in order to make people in the PAYG system achieve the same utility level as people in the funded system. Fig. 2 provides the value of λt. The first two generations have a lifetime utility loss of 7% and 8%, respectively. The following generations have a utility gain: 4% for third generation, 10% for fourth generation, and 13% for fifth generation. The percentage of utility gain keeps increasing until tenth generation, which stays at 15% afterwards. The intuition is clear: during the transition private capital increases and the interest rate decreases. However, the wage rate in period 1 is the same in both systems. Thus, the current young generation will see a decrease in interest income from their savings when they get old, resulting in a utility loss for the old generation.12
12 For a country with a lower private saving rate, the loss of interest income by the old generation may be offset by the higher return from a personal account. In that case, no generation becomes worse off.
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4. Concluding remarks This paper has examined the effects of a switch from the current PAYG system to a funded system by taking into consideration the implicit pension debt caused by such a transition. Three methods are used to finance the implicit pension debt: debt financing, tax financing, and government asset financing. It shows that with debt or tax financing, the social security reform is neutral, i.e., the market equilibrium remains unchanged, and all generations are as well off in the new system as in the PAYG system. With government asset financing, the interest rate decreases, private capital increases, but the total output may either increase or decrease; the welfare effect is also ambiguous in general, depending on the rate of return on government assets. With plausible parameters, our simulation shows that the reform lowers the interest rate, increases private capital, and lowers government capital in the short run, but raises government capital and increases output levels in the long run. It is clear that the establishment of the PAYG social security system is essentially a transfer of wealth from the current young generation to the current old generation, and a transfer of burden of pension payment to future generations. If the population does not decrease, there will be no crisis of pension payment. If the population declines, a social security payment crisis may occur. If a country does not have a social security system, it is better to establish a fully funded system, instead of a PAYG system, to avoid a social security payment crisis due to population aging. If the PAYG system has been established, that is the initial old generation has already used up the windfall funds from the initial young generation, then privatization of a social security system may not bring any gain unless some generations suffer losses. However, social security reforms may result in efficiency gains. For example, if government capital is too large and the government capital share of income is small, a switch from the PAYG system to a funded system by using government capital to pay the implicit social security debt will improve productivity and result in welfare gains. However, gains can be reaped without relying on the social security reforms, i.e., other reforms can reap the efficiency gains also. Acknowledgments The authors thank an anonymous referee and Editor Belton Flesher for their helpful comments. The authors also thank Laurence Kotlikoff for his helpful suggestions. Part of the research was completed while Shiyu Li was a visiting scholar at Boston University. References Barro, R. J. (1990). Government spending in a simple model of endogenous growth. The Journal of Political Economy, 98, 103−126. Boardman, A. E., & Vining, A. R. (1989). Ownership and performance in competitive environments: a comparison of the performance of private, mixed, and stateowned enterprises. Journal of Law and Economics, 32, 1−33. 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. Brunner, J. K. (1996). Transition from a pay-as-you-go to a fully funded pension system: the case of differing individuals and intragenerational fairness. Journal of Public Economics, 60, 131−146. China Ministry of Finance (1996–2009). Finance Yearbook of China. China's Fiscal Press. China National Bureau of Statistics (2009). China Statistical Yearbook. Beijing: China Statistics Press. Chow, G. C. (1993). Capital formation and economic growth in China. Quarterly Journal of Economics, 108, 809−842. Feldstein, M. (1995). Would privatizing social security raise economic welfare? NBER working paper, 5281, National Bureau of Economic Research. Feldstein, M. (1998). A new era of social security. The Public Interest, 130, 102−125. Feldstein, M. (1999). Social security pension reform in China. China Economic Review, 10, 99−107. Futagami, K., Morita, Y., & Shibata, A. (1993). Dynamic analysis of an endogenous growth model with government capital. The Scandinavian Journal of Economics, 95, 607−625. Groezen, B., Leers, T., & Meijdam, L. (2003). Social security and endogenous fertility: Pensions and child allowances as Siamese twins. Journal of Public Economics, 87, 233−251. Hirazawa, M., & Yakita, A. (2009). Fertility, child care outside the home, and PAYG social security. Journal of Population Economics, 22, 565−583. Hsueh, T., & Li, Q. (1999). China's national income, 1952–1995. Westview Press. Huizinga, H., & Nielsen, S. B. (2001). Privatization, public investment, and capital income taxation. Journal of Public Economics, 82, 399−414. Kotlikoff, L. J. (1996). Privatization of social security: How it works and why it matters. Tax Policy and the Economy, 10, 1−31. Lin, S. (2008). Forced savings, social safety net, and family support: A new old-age security system for China. The Chinese Economy, 41, 10−44. Murphy, K., & Welch, F. (1998). Perspectives on the social security crisis and proposed solutions. The American Economic Review, 88, 142−150. Samuelson, P. A. (1958). An exact consumption-loan model of interest with or without the social contrivance of money. The Journal of Political Economy, 6, 467−482. Sinn, H. (1997). The value of children and immigrants in a pay-as-you-go pension system: A proposal for a partial transition to a funded system. NBER working paper, 6229. Sinn, H. (2000). Why a funded pension system is useful and why it is not useful. International Tax and Public Finance, 7, 389−410. Wang, Y., Xu, D., Wang, Z., & Zhai, F. (2001). Implicit pension debt, transition cost, options, and impact of china's pension reform: A computable general equilibrium analysis. World Bank Policy Research Working Paper, 2555. Yakita, A. (2008). Sustainability of government debt, government capital formation, and endogenous growth in an overlapping generations setting. Journal of Public Economics, 92, 897−914.
Contents lists available at ScienceDirect
China Economic Review
Is there any gain from social security privatization? Shiyu LI a,1, Shuanglin LIN b,c,⁎ a b c
School of Finance, Renmin University of China, 100872, China School of Economics, Peking University, Beijing, 100871, China Department of Economics, College of Business Administration, University of Nebraska, Omaha, NE 68182
a r t i c l e
i n f o
Article history: Received 8 November 2010 Received in revised form 24 January 2011 Accepted 28 January 2011 Available online 4 February 2011 JEL classification: E6 H3 O53 Keywords: Social security reforms PAYG system Funded system Overlapping generations model
a b s t r a c t Increasing calls for a social security reform of switching from the pay-as-you-go (PAYG) system to a funded system has been seen in recent decades. This paper examines the effect of this reform on capital accumulation and the welfare of each generation. Three methods are used to finance the pension debt, government debt financing, tax financing, and government asset financing. With government debt or tax financing, the market equilibrium remains unchanged and all generations are as well off in the new system as in the PAYG system. Thus, switching from the PAYG system to a funded system is neutral. With government asset financing, the interest rate will decrease, private capital will increase, but the total output may either increase or decrease. The welfare effect is also ambiguous in general, depending on the rate of return of government assets. With plausible parameters, our simulation shows that the reform will lower the interest rate, increase private capital, and lower government capital in the short run, but raise government capital and increase output in the long run. Published by Elsevier Inc.
1. Introduction The pay-as-you-go (PAYG) social security system has been established in many countries for quite some time. Samuelson (1958) showed that, the PAYG system permits a windfall benefit to current retirees, with the social security payment to the current young deferred to the future generation, and an introduction of the PAYG social security system is a Pareto improvement. Recent decades, social security reforms have become a heated debated topic among academics and policy-makers. A prominent suggestion is to switch from the current PAYG social security system to a funded social security system with the establishment of personal social security accounts, often called social security privatization. This paper analyzes the gains from this type of social security reform by taking into consideration various ways to finance the social security debt to the current old generation. A number of studies have demonstrated the advantages of a switch from the PAYG system to a funded system. Feldstein (1995) used a partial equilibrium framework to examine whether privatizing social security (i.e., a switch from the PAYG system to a funded system) would raise welfare. He shows that a debt-financed transition from the PAYG system to a funded system would raise economic welfare if three conditions are met: (1) the marginal product of capital exceeds the rate of economic growth; (2) the marginal product of capital exceeds the appropriate consumption discount rate; and (3) the rate of economic growth is positive.2 These conditions are likely to be satisfied. However, he recognized that a majority of the adult population alive at the ⁎ Corresponding author at: Department of Economics, College of Business Administration, University of Nebraska, Omaha, NE 68182, United States. Tel.: +86 10 6276 0620, +1 402 554 2815; fax: +86 10 8252 4675, +1 402 554 2853. E-mail addresses: [email protected], [email protected], [email protected] (S. Lin). 1 Tel.: +86 10 6274 2511. 2 A debt financed transition means that the transition from an unfunded social security system to a funded social security system that does not reduce the benefits of existing retirees would, however, require substituting explicit government debt for the equally large implicit debt of the unfunded social security system. 1043-951X/$ – see front matter. Published by Elsevier Inc. doi:10.1016/j.chieco.2011.01.005
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time of the privatization might be worse off. Feldstein (1998) provided two alternatives, immediate transition by issuing “recognition bonds” or a gradual transition by collecting taxes. The first method substitutes new government bonds for the existing implicit claims of retirees and current employees. With the second method, employees during the transition period must pay payroll taxes to support the existing retirees and, at the same time, must accumulate assets for their own retirement. With both methods, the first few generations alive during the transition period will be worse off and the future generations will be better off. Kotlikoff (1996) used a general equilibrium model to simulate the effects of social security privatization and showed that a switch to an alternative tax base, such as from a progressive income tax to a consumption tax, may generate significant efficiency gains. Prior studies have also shown that in order to pay the implicit pension debt in the transition process, some generations have to be worse off to make others better off. Breyer (1989) argued that when the PAYG system is replaced by a funded system, it is generally impossible to compensate the pensioners in the transition generation without making at least one later generation worse off. By assuming agents within a generation are different, Brunner (1996) showed that a Pareto-improving transition to a funded system is not possible because any instrument applied to the financing of pensions in the transition period involves intragenerational redistribution. Murphy and Welch (1998) suggested that one way to complete the transition is to cut benefits instead of raising taxes. Sinn (1997, 2000) argued that there is nothing to be gained from a transition to a funded system in general, but he suggested privatization of the pension system for those not willing to have children. By assuming endogenous fertility, Groezen, Leers, and Meijdam (2003) and Hirazawa and Yakita (2009) examined social security payroll tax in a small open economy with exogenous interest rate and showed that, with a child allowance scheme or a child care market, it is possible to have Pareto improvement by a PAYG payroll tax cut. Recent years have seen increasing interest in China's social security reforms. Feldstein (1999) proposed that China should move from a PAYG defined benefit system to a funded defined contribution system. In his opinion, in the PAYG system, the rate of return depends on the growth rate of aggregate real wages. According to the World Bank estimation, wages in China will grow at approximately 7% or less per year. However, in the funded system, the rate of return depends on the marginal product of industrial capital, which was estimated at 17% in China (Chow, 1993), or with a conservative estimation of 12%. In this case, $1 saved at age 45 grows up to $7.6 at age 75 in the PAYG system, while $1 will grow up to $29.95 in the funded system.3 Therefore, the funded system can provide the same level of benefits with a savings rate equal to only one fourth of the rate of tax required in the PAYG system. However, he did not consider the social security payment to the current old generation. Lin (2008) argued that with only about 25% of employees involved in the current PAYG social security system, China should switch to a funded social security system immediately.4 This paper examines the effects of a switch from the PAYG system to a funded system by considering the implicit pension debt repayment and by allowing existing generations as well off in the new system as in the PAYG system. An overlapping generations model is utilized. Three methods are used to finance the pension debt to the current old generation: government debt financing, tax financing, and government asset financing. With government debt or tax financing, the market equilibrium remains unchanged, and all the generations are as well off in the new system as in the PAYG system. Thus, the social security reform is neutral. With government asset financing, the interest rate will decrease and private capital stock will increase, but the total output may either increase or decrease, while the welfare effect is ambiguous in general. With plausible parameters, our simulations show that the reform will lower the interest rate, increase private capital, and lower government capital in the short run, but raise government capital and increase the output level in the long run. The paper contributes not only to issues concerning China social security reforms, but also to the theoretical literature on social security reforms in general. The paper proceeds as follows. Section 2 introduces the model with a PAYG social security system. Section 3 analyzes the effects of switching from the PAYG system to a funded system with various ways of financing social security debt. Section 4 provides concluding remarks. 2. The model There are many individuals and firms in the economy. Individuals are identical within and across generations. The population of generation t + 1 in period t + 1 Lt + 1 is (n is constant): Lt + 1 = (1 + n)Lt.5 The government lives forever, running a social security system and managing government capital. 2.1. The firm The economy produces one good, which can be either consumed or invested. Output is produced by identical competitive firms using a constant-returns-to-scale production technology. There are three inputs in the production: private capital, government capital, and labor. Specifically, the production function is as follows: α
β
1−α−β
Yt = Kt Gt ðAt Lt Þ 3
ð2:1Þ
The detailed calculation is as follows: (1.07)30 = 7.6122 and (1.12)30 = 29.9599. Using the Computable General Equilibrium model Wang, Xu, Wang, and Zhai (2001) found that China's current PAYG system with a notional personal social security account is not sustainable. 5 The main result of this paper will remain unchanged even if we introduce endogenous fertility. The details are available on request. 4
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where Kt is the stock of private capital in period t; Gt is the stock of government capital in period t; At is the productivity parameter, γ = Δ At/At (Δ A t = At + 1 − At) is the growth rate of productivity. Letting yt = Yt/AtLt, the output-effective labor ratio, we have: yt = f ðkt ; gt Þ;
fk N 0; fg N 0; fkk b 0; and fg g b 0
ð2:2Þ
where kt = Kt/AtLt, is the private capital–effective labor ratio and gt = Gt/AtLt is the government capital–effective labor ratio. Assume that both private capital and government capital are fully depreciated after one period's production. Factor markets are perfectly competitive, and thus, the rate of return to each factor is its marginal product. Let 1 + rt be the rate of return on private capital in period t, let 1 + ht be the rate of return on government capital in period t, and let wt be the rate of return to effective labor.6 1 + rt =
∂Yt β α−1 = α gt kt ∂Kt
ð2:3Þ
1 + ht =
∂Yt β−1 α = βg t k t ∂Gt
ð2:4Þ
∂Yt α β = ð1−α−βÞk t g t ∂ðAt Lt Þ
ð2:5Þ
wt =
Let Wt be each individual's total wage income, and ΔWt/Wt be the growth rate of the wage rate. We have: Wt =
∂Yt = At w t ; ∂Lt
ΔWt ΔAt Δwt = + Wt At wt
ð2:6Þ
2.2. The consumer Each individual lives for two periods, working and saving in the first period, and consuming savings and interest income in the second period. The representative individual faces the following utility maximizing problem: t t Max u = ut ct ; ct
+ 1
t
s:t:ct ≤ð1−πÞAt wt −st −τt t ct +1 ≤st 1 + rt +1 + vt +1 t
t
ct ; ct +1 ≥ 0; t = 0; 1; 2… where ctt+j is consumption in period t + j of an agent born in period t (called generation t), j = 0, 1; π is the tax rate on labor income or the payroll tax rate; πAtwt is the social security tax or contribution to personal social security account; vt + 1 is the social security benefits that old people receive in the period of t + 1; st represents private savings in period t of an agent born in period t, which is the difference between the first-period disposable income and the first-period consumption; and τt is the tax collected at period t. The utility function is twice differentiable and strictly quasi-concave. The marginal utility is positive but diminishing. Combining the above two budget constraints, we have: t
ct +
t
ct +1 vt +1 ≤ ð1−πÞAt wt −τt + : 1 + rt +1 1 + rt +1
ð2:7Þ
To obtain explicit solutions for savings and other endogenous variables and to keep the model tractable, assume that the utility function is log-linear: u(ctt, ctt + 1) = ln(ctt) + ρ ln(ctt + 1), where ρ b 1 is the (constant) pure rate of time preference or discount factor. Solving the agent's maximization problem yields: t
ct =
t
ð1−πÞAt wt −τt + vt +1 = 1 + rt +1 ð1 + ρÞ
ct +1 =
# " ρ 1 + rt +1 vt +1 ð1−πÞAt wt −τt + ð1 + ρÞ 1 + rt +1
ð2:8Þ ð2:9Þ
6 This is different from other literature, like Barro (1990), Futagami, Morita, and Shibata (1993), Yakita (2008), which assumed that government capital is provided to the household-producer without user charges. Here, government capital as an input yields returns. In China, the government owns a large stock of capital in state-owned enterprises that yields returns to its owner.
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st =
ρ½At wt ð1−πÞ−τt vt +1 − 1+ρ ð1 + ρÞ 1 + rt +1
281
ð2:10Þ
Eqs. (2.8)–(2.10) show the optimal first- and second-period consumption and optimal savings. 2.3. The government The government faces the following constraints: Gt +1 = ð1 + ht ÞGt ; Bt + ð1 + rt ÞDt = πAt wt Lt + τt Lt + Dt +1
ð2:11Þ
where the first equation is government capital budget and the second one is social security budget, Gt + 1 is the government capital at the beginning of period t + 1; 1 + ht is the rate of return to government capital; (1 + ht)Gt is the total return to government capital; Bt is the social security expenditure, i.e., the total amount that government must pay to all retirees living in period t (or born in period t − 1); Dt is the government debt issued in period t; and πAtwtLt + τtLt is the total tax revenue. Dividing both sides of Eq. (2.11) by AtLt yields: ð1 + nÞð1 + γÞgt +1 = ð1 + ht Þgt ;
Bt τ + ð1 + rt Þdt = πwt + t + ð1 + nÞð1 + γÞdt +1 At Lt At
ð2:12Þ
where dt = Dt/AtLt and gt = Gt/AtLt. 2.4. The equilibrium A competitive equilibrium for the economy is a set of sequences {rt, ht, wt, ctt, ctt + 1, st, gt, kt} satisfying Eqs. (2.3)–(2.5), (2.8)– (2.10), (2.12), and ( ) ρ½At wt ð1−πÞ−τt vt +1 − Kt +1 + Dt +1 = St = Lt st = Lt ð2:13Þ 1+ρ ð1 + ρÞ 1 + rt +1 where Kt + 1 is the private capital to be used in period t + 1, St is the total savings at the end of period t, and Dt + 1 is the government debt issued in period t + 1. Dividing both sides by labor in period t, AtLt yields: ρ½wt ð1−πÞ−τt = At vt +1 − ð1 + nÞð1 + γÞ kt +1 + dt +1 = 1+ρ At ð1 + ρÞ 1 + rt +1 Recall that
ð2:14Þ
L t +1 At +1 = 1 + n and = ð1 + γÞ. Lt At
2.5. The PAYG social security system In the PAYG system, social security is financed by a payroll tax. An individual only needs to pay the payroll tax, πAtwt, and does not pay any additional tax (i.e.,τt = 0). The contribution made by all young individuals at time t,LtπAtwt, are used directly to pay social security benefit,Bt, to the old generation, where Bt = Lt − 1vt. Also, government does not issue debt (i.e.,Dt = 0). The social security budget constraint is as follows: Bt = Lt−1 vt = Lt πAt wt ; or vt = ð1 + nÞπAt wt
ð2:15Þ
Inserting τt = 0 and Eq. (2.15) into consumer's budget constraint Eq. (2.7), consumption Eqs. (2.8) and (2.9), saving Eq. (2.10), government budget Eq. (2.11), and the private capital market equilibrium condition Eq. (2.13), we have: t
ct + t
ct = t
t
ct +1 ð1 + nÞπAt +1 wt +1 ≤ð1−πÞAt wt + 1 + rt +1 1 + rt +1 ð1−πÞAt wt + πAt
ct +1 =
+ 1 wt +1 ð1
+ nÞ = 1 + rt +1
ð1 + ρÞ # " ρ 1 + rt +1 πAt + 1 wt +1 ð1 + nÞ ð1−πÞAt wt + ð1 + ρÞ 1 + rt +1
ð2:16Þ ð2:17Þ
ð2:18Þ
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st =
ρAt wt ð1−πÞ πAt +1 wt +1 ð1 + nÞ − 1+ρ ð1 + ρÞ 1 + rt +1
ð2:19Þ
Gt +1 = ð1 + ht ÞGt
Kt +1 = Lst = Lt
ð2:20Þ
! ρAt wt ð1−πÞ πAt +1 wt +1 ð1 + nÞ − 1+ρ ð1 + ρÞ 1 + rt +1
ð2:21Þ
3. A switch from the PAYG system to a funded system Assume that government decides to switch from the PAYG system to a fully funded system in which people are required to save in the first period of life and receive the principle and interest in the second period of life. Specifically, assume that in the first period, instead of paying social security tax, πAtwt, an individual needs to contribute the same amount, πAtwt, to his/her personal social security account, as well as paying a per capita tax τt. The amount of tax, τt, is defined as the discounted value of the difference between the pension benefit under the funded system and the benefit under the PAYG system. With this tax, the individual will be as well off as under the PAYG system. Specifically, τt =
πAt wt 1 + rt +1 −πAt +1 wt +1 ð1 + nÞ 1 + rt +1
=
πAt w 1 + rt +1 −wt +1 ð1 + nÞð1 + γÞ 1 + rt +1 t
ð3:1Þ
where πAtwt(1 + rt + 1) is the pension benefit under the funded system and 1 + rt + 1 is the rate of return from contribution to funded system, while πAt + 1wt + 1(1 + n) is the pension benefit under the PAYG system and (1 + γ)(1 + n)wt + 1/wt is the rate of return from contribution to the PAYG system. τt may be positive, zero, or negative depending on the rate of return from contribution to PAYG system and funded system. When the population growth rate and the productivity growth rate are low, τt tends to be positive, while for high population growth and productivity growth the tax (rate) may be negative. However, as in Feldstein (1999), we assume that the rate of return from contributions to a funded system is greater than the rate of return from contributions to a PAYG system, i.e., (1 + γ)(1 + n)wt + 1/wt b 1 + rt + 1 and hence τt is positive.7 In the second period, individuals receive benefit from personal social security account, (1 + rt + 1)πAtwt. Replacing vt + 1 by (1 + rt + 1)πAtwt and substituting Eq. (3.1) into the consumer's budget constraint Eq. (2.7), we have: t
ct +
ctt+1 ð1 + nÞπAt +1 wt +1 ≤ At wt −τt = ð1−πÞAt wt + : 1 + rt +1 1 + rt +1
Since the extra pension benefit in the funded system is taken away as a tax by the government to pay for the current generation's social security benefit, the individual's budget constraint is the same as Eq. (2.16) under the PAYG system. Solving the agent's maximization problem yields: t
ct =
t
ð1−πÞAt wt + πAt +1 wt +1 ð1 + nÞ = 1 + rt +1 ð1 + ρÞ
ct +1 =
st =
# " ρ 1 + rt +1 πAt +1 wt +1 ð1 + nÞ ð1−πÞAt wt + ð1 + ρÞ 1 + rt +1
ρAt wt ð1−πÞ ρπAt +1 wt +1 ð1 + nÞ −πAt wt : + 1+ρ ð1 + ρÞ 1 + rt +1
ð3:2Þ
ð3:3Þ
ð3:4Þ
It can be seen that Eq. (3.2) in the funded system is equivalent to Eq. (2.17) under the PAYG system, while Eq. (3.3) is equivalent to Eq. (2.18). However, Eqs. (3.4) and (2.19) are different, i.e., private savings are different in the funded system and the PAYG system. Savings affect the interest rate, the wage rate, and therefore, individuals' consumptions. Savings will be different under different methods of social security debt financing. We will consider three different ways of financing the implicit social security debt, debt financing, tax financing, and government asset financing, and examine savings and capital accumulation under various methods of social security debt financing.
7
If wt + 1 = wt, the condition becomes (1 + γ)(1 + n) b 1 + rt + 1.
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3.1. Debt financing Assume that starting from period 1 the government decides to reform the social security system and issues government bonds, D1, to finance the implicit social security debt (the social security benefits to the old generation), which is equal to B1 = L1A1πw1. In the meantime, the government starts to collect lump-sum tax from the young generation and future generations to pay off the debt. Let V1t denote taxes that the government collects from generation t, discounted to period 1. The amount of taxes paid by generation t equals τt L t. The present value (discounted to period 1) of taxes paid by generation t is as follows:
t
V1 =
t−1
τt L t
∏ 1 + rj+1
=
j=1
πAt wt 1 + rt +1 −πAt +1 wt +1 ð1 + nÞ L1 ð1 + nÞt−1 t−1 1 + rt +1 ∏ 1 + rj+1 j=1
ð3:5Þ
πAt wt ð1 + nÞt−1 L1 πAt +1 wt +1 ð1 + nÞt L1 ; j = 1; 2; …; t−1: = − t t−1 ∏ 1 + rj+1 ∏ 1 + rj+1 j=1
j=1
τ L
2 2 For example, if t = 1, then V11 = τ1L1 and if t = 2, then V12 = 1 + r2 . We assume that it takes N generations to pay off the implicit social security debt, i.e., the present value of lump-sum tax collected from N generations should be equal to the debt. Mathematically,
N
t
D1 = B1 = L1 A1 πw1 = ∑ V1 :
ð3:6Þ
t =1
During the transition period (N periods), government collects lump-sum tax to pay the debt. When the lump-sum tax collected from the young and future generations can pay off the debt, the transition period ends and government stops collecting lump-sum tax. How many generations will it take to pay off the debt, or how long will the transition time last? By summing up V1t from generation 1 to generation N we obtain the present value of total taxes paid by these N N
generations, ∑ V1t . We find that the second term of V1t can be cancelled out by the first term of V1t + 1 when adding them up. That t =1
is, N
t
∑ V1 = L1 πA1 w1 −L1 π
t =1
AN+1 wN+1 ð1 + nÞN ð1 + γÞN ð1 + nÞN = L πA w −L πA w 1 1 1 1 1 N+1 : N N ∏ 1 + rj+1 ∏ 1 + rj+1 j=1
ð3:7Þ
j=1
Substituting Eq. (3.7) into Eq. (3.6), we find, to satisfy Eq. (3.6), the following equation must be hold: L1 πA1 wN +1
ð1 + γÞN ð1 + nÞN = 0: N ∏ 1 + rj+1
ð3:8Þ
j=1
Now, in order to satisfy Eq. (3.8), how large should N be? As we assume earlier, [(1 + γ)(1 + n)]/(1 + rt + 1) b 1. Thus, we have ½ð1 + γÞð1 + nÞN =0 N N→∞ ∏ 1 + rj+1 lim
j=1
or
lim L1 πA1 wN +1
N→∞
½ð1 + γÞð1 + nÞN = 0: N ∏ 1 + rj+1 j=1
That is to say, to satisfy Eq. (3.8), N needs to approach infinity, or it takes infinite generations to pay off the implicit pension debt at the current tax system. Thus, every generation must pay taxes to finance the implicit social security debt, and their after-tax social security benefit is equivalent to that under the PAYG system. The debt will not be redeemed forever in order to avoid the welfare losses.
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What about capital accumulation? With the establishment of a personal social security account, the total savings, St, is the forced social security savings, πAtwtLt, plus the private savings, Ltst. When government issues bonds to finance implicit debt, the market equilibrium condition becomes: Kt +1 + Dt +1 = St = Lt st + πAt wt Lt " # ρAt wt ð1−πÞ ρπAt +1 wt +1 ð1 + nÞ −πAt wt + πAt wt Lt + = Lt 1+ρ ð1 + ρÞ 1 + rt +1 " # ρAt wt ð1−πÞ ρπAt +1 wt +1 ð1 + nÞ : + = Lt 1+ρ ð1 + ρÞ 1 + rt +1
ð3:9Þ
Government debt in the beginning of period t + 1 is as follows:8 Dt +1 = πAt wt Lt −τt Lt :
Substituting the above equation into the market equilibrium condition (3.9) and rearranging terms yield: ( Kt +1 = St −Dt +1 = Lt
) ρA t wt ð1−πÞ πAt +1 wt +1 ð1 + nÞ : − 1+ρ ð1 + ρÞ 1 + rt +1
It can be seen that capital market equilibrium condition is the same as that under the PAYG system Eq. (2.21). Therefore, with debt financing, a switch from the PAYG system to a funded system does not affect the equilibrium in capital market, i.e., it does not affect the market demand and supply and the equilibrium interest rate. On the consumption side, as we showed in Eqs. (3.2) and (3.3), as long as government keeps collecting lump-sum tax, an individual's consumption functions will be the same as those under the PAYG system. Therefore, with the interest rate and the wage rate being the same under the two systems, consumption in the funded system is the same as in the PAYG system. No generation, either the current or the future, will be better off or worse off with the social security reform. 3.2. Tax financing We now consider the case where the government financing the payment to the current old generation by collecting taxes from the young generation. To focus on tax financing, assume that government does not issue debt, i.e., Dt = 0. Assume that the government requires the young generation to save for their own retirement and collects taxes from them to keep them as well off as under the PAYG system. As we mentioned above, the lump-sum tax τtis defined as the discounted value of the difference between the pension benefit under the funded system and the pension benefit under the PAYG system, denoted by Eq. (3.1). In the new system, tax revenues collected are τtLt. Therefore, individual's budget constraint in the funded system is exactly the same as in the PAYG system, and hence, the solutions to the agent's maximization problem remain unchanged, i.e., both young and old generation's consumption functions will be the same as Eqs. (3.2) and (3.3), which are equivalent to , the consumption functions under the PAYG system [see Eqs. (2.17) and (2.18)]. We now examine total savings in the funded system with tax financing. In the funded system, since the contributions paid by young individuals at time t are put into a personal social security account to accrue interest instead of paying directly to the current old generation, the social security budget is different from that in the PAYG system.9 Let Zt − 1 denote government's social security savings in period t − 1, which equals social security revenue minus social security expenditure in period t − 1. In period t, government social security revenue includes taxes, τtLt, private pension contribution, πAtwtLt, and principal and interest of last period's social security savings, (1 + rt)Zt − 1. We now try to figure out government social security savings in each period, Zt. In period 1, total social security revenue is taxes, τ1L1, plus personal social security contribution, πA1w1L1 (paid by the young generation in period 1); while social security expenditure is pension benefit paid to the old generation in period 1, πA1w1L1. Social security savings in period 1, Z1, is social security revenue minus social security expenditure, which equals τ1L1. In period 2, social security revenue is τ2L2 + πA2w2L2 +(1+ r2)τ1L1, social security expenditure is πA1w1L1(1+ r2), which is the social security benefit the old receive under the new funded system, and it can be shown
8 At the beginning of period 2, government debt is πA1w1L1− τ1L1; at the beginning of period 3, government debt balance is (πA1w1L1− τ1L1)(1 + r2)− τ2L2 = πA2w2L2 − τ2L2, and so forth. We can calculate that government debt at the beginning of period t + 1 is πAtwtLt-τtLt. 9 As we showed in Eq. (2.15) in the PAYG system, social security revenue equals social security expenditure and hence social security saving is zero.
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that social security savings, Z2, is τ2L2. In general, for t =2, 3, …, social security revenue is τtLt + πAtwtLt +(1 +rt)τt − 1Lt − 1, social security expenditure is πAt − 1wt − 1Lt − 1(1 +rt), and social security saving is Zt = τtLt.10 The detailed derivation is as follows: Zt = ½τt L t + πAt wt Lt + ð1 + rt Þτt−1 Lt−1 −½πAt−1 wt−1 Lt−1 ð1 + rt Þ = τt L t + πAt wt Lt + ð1 + rt Þ
πAt−1 wt−1 ð1 + rt Þ−πAt wt ð1 + nÞ L t−1 −πAt−1 wt−1 Lt−1 ð1 + rt Þ 1 + rt
= τt L t + πAt wt Lt + πAt−1 wt−1 ð1 + rt ÞLt−1 −πAt wt ð1 + nÞLt−1 −πAt−1 wt−1 Lt−1 ð1 + rt Þ = τt L t + πAt wt Lt −πAt wt ð1 + nÞLt−1 = τt L t :
In period t, social security saving (Z t =τt L t) is far less than individual's contribution (πAtwtLt), and therefore, the system with tax financing is a funded system with notional personal account, i.e., pension paid to the old generation in period t (πAt − 1wt − 1Lt − 1(1+rt)) will use up the young generation's contributions (πA t wt L t) plus last period's social security savings and interest ((1+rt)zt − 1). If future generations stop paying taxes, the pension benefit underfunded system, (1+rt + 1)πAtwt, cannot be sustained. Thus, future generations need to pay taxes forever. The capital market equilibrium condition is as follows: " # ρAt wt ð1−πÞ ρπA t +1 wt +1 ð1 + nÞ −πAt wt + τt Lt + 1+ρ ð1 + ρÞ 1 + rt +1 ! ρAt wt ð1−πÞ πAt +1 wt +1 ð1 + nÞ − 1+ρ ð1 + ρÞ 1 + rt +1
Kt +1 = St = L t st + τt L t = Lt = Lt
ð3:10Þ
where Kt + 1 is the private capital to be used in period t + 1, St is total savings at the end of period t, Ltst is the private savings of generation t at the end of period t, and τtLt is government social security savings in period t. Comparing Eqs. (2.21) and (3.10), we find that the capital market equilibrium condition in the funded system is the same as that in the PAYG system. The decrease in private savings is exactly equal to the government social security savings, and the total savings remain unchanged. Thus, the equilibrium interest rate and the wage rate will be the same as that under the PAYG system. With the same consumption functions and the same interest rate and the wage rate, the consumption will be exactly the same. No generation will be better off or worse off with the social security reform. Thus, the switch from the PAYG system with tax financing is neutral, i.e., it does not affect the market equilibrium. 3.3. Government asset financing Unlike many other market economies, the Chinese economy evolved from a centrally planned system, and the government has a huge amount of state-owned assets. The asset of the state-owned enterprises was 13,437 billion yuan, or 44% of GDP in 2008.11 Huizinga and Nielsen (2001) argued that managers of public activities may lack the incentives to fully exploit the production potential of the activities. In addition, Boardman and Vining (1989) showed that after controlling for a wide variety of factors, large industrial mixed and state-owned enterprises perform substantially worse than similar private companies. We now consider the case where the government finances the implicit pension debt by selling government assets. Specifically, the government pays the social security benefit to the current old by selling government capital. The contribution made by the young in period t,πAtwt, is put into a personal account; and the rate of return on πAtwt is the same as private savings, st, and is equal to 1 + rt + 1. In this case, implicit pension debt is paid off in period 1 by government capital. Current and future generations can enjoy the higher pension return from funded system and without worrying about the pension debt. Replacing vt + 1 by (1 + rt + 1)πAtwt and setting τt = 0 in the consumer's budget constraint Eq. (2.7), consumption Eqs. (2.8) and (2.9), and saving Eq. (2.10), we have: t
ct +1 ≤ At wt 1 + rt +1 A t wt t ct = ð1 + ρÞ t
ct +
t
ct +1 =
ρ 1 + rt +1 At wt ð1 + ρÞ
ð3:11Þ ð3:12Þ
ð3:13Þ
10 Recall that τt is defined by Eq. (3.1), which guarantees generations under the funded system as well off as under the PAYG system. The tax (rate) is essential to obtain social security savings equal to Zt = τtLt. If τt takes other values, equation Zt = τtLt may not hold. 11 China Ministry of Finance, Finance Yearbook of China, China's Fiscal Press (1996–2009).
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Table 1 Initial values of exogenous variables and parameters. Variables
Definition
Value
ρ α β γ π n N T Population
Constant pure rate of time preference Private capital's share in production Public capital's share in production Productivity growth rate Tax rate on labor income or the payroll tax rate Population Growth rate Number of periods in lifetime Simulation period Initial population
0.56 0.3121 0.1 0.54 0.15 0.1556 2 15 50
Note: a: The share of total capital in GDP is calculated based on the data from Hsueh and Li (1999), China National Bureau of Statistics, China Statistical Yearbook (2009). b: China National Bureau of Statistics, 2009, China Statistical Yearbook shows that the household saving rate is 36%. ρ is calibrated according to the saving rate. c: For productivity growth rate: (1 + .015) 29 − 1 = 0.54. d: For population growth rate: (1 + .005)29 − 1 = 0.1556. We also conduct a sensitivity analysis. With a lower n, say n = 0, the results remain unchanged qualitatively.
st =
ρAt wt −πAt wt : 1+ρ
ð3:14Þ
In this system, government decreases government capital and contributes X1 = πA1w1L1 into a social security account in period 1. In period 1, the social security revenue is πA1w1L1 + X1, social security expenditure is πA1w1L1, and the social security savings are πA1w1L1; in period 2, the social security revenue is πA1w1L1(1 + r2) + πA2w2L2, social security expenditure is πA1w1L1(1 + r2), and the social security savings are πA2w2L2; in period t + 1, the social security revenue is πAtwtLt((1 + rt+1) + πAt+1wt+1Lt + 1, social security expenditure is πAtwtLt(1 + rt + 1), and the social security savings are πAt+1wt + 1Lt+1.
Fig. 1. Effects of social security reforms on private and public capital, the interest rate, and output.
S. Li, S. Lin / China Economic Review 22 (2011) 278–289
287
Fig. 2. Remaining lifetime utility of generation t.
When private capital market clears,
ρAt wt −πAt wt 1+ρ
Kt +1 = St = Lt st + πAt wt Lt = Lt
+ πAt wt Lt = Lt
ρAt wt 1+ρ
ð3:15Þ
where Kt + 1 is the private capital to be used in period t + 1, St is total saving at the end of period t,Ltst is the private savings of generation t at the end of period t, and πAtwtLt is social security saving in period t. Clearly, after the government uses its capital to pay for the social security benefit of the current old generation, total savings will increase (comparing Eqs. (2.21) and (3.15)). This will result in an increase in private capital stock, a decrease in the interest rate, and an increase in the wage rate. Government capital stock will decrease as a portion of it is used for social security payment. In period 1, government contributes X1 to the social security account and government capital becomes: G 2 = ð1 + h1 ÞG1 −X1 and G t +1 = ð1 + ht ÞGt ; t = 2; 3; …
ð3:16Þ
Under the new social security system with government asset financing, in period 2 private capital increases, while government capital decreases. Subtracting Eq. (2.21) from Eq. (3.15), we can calculate how much capital increased in the funded system in period 2, denoting by ΔK2. ΔK2 = L1
ρA1 w1 ρA1 w1 ð1−πÞ πA2 w2 ð1 + nÞ ρX1 πA2 w2 ð1 + nÞ − −L1 = + L1 1+ρ ð1 + ρÞð1 + r2 Þ ð1 + ρÞð1 + r2 Þ 1+ρ 1+ρ
h
ρA1 w
ρA w ð1−πÞ
π A w ð1 + nÞ
i
1 1 − ð1 +2 ρ2Þð1 + r2 Þ is total savings (capital) in the where L1 1 + ρ1 is total savings (capital) in the funded system and L1 1 + ρ PAYG system. Recall that the production function is Yt = KtαGtβ(AtLt)1 − α − β. The output in the second period becomes:
α
β
1−α−β
Y2 = ðK2 + ΔK2 Þ ðG2 −X1 Þ ðA2 L2 Þ
:
Differentiating Eq. (3.17) with respect to X1 gives:
dY2 ρ α−1 dK2 β α β−1 dG2 1−α−β = αðK2 + ΔK2 Þ + ðG2 −X1 Þ + βðK2 + ΔK2 Þ ðG2 −X1 Þ −1 ðA2 L2 Þ ⋛0 1+ρ dX1 dX1 dX1
ð3:17Þ
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dK
Since dX2 1
iff or or
or
= 0 and
dG2 = 0, the above equations can be simplified as follows: dX1
ρ ðG2 −X1 Þβ −βðK2 + ΔK2 Þα ðG2 −X1 Þβ−1 ⋛0 1+ρ ρ −1 −1 −βðG2 −X1 Þ ⋛0 αðK2 + ΔK2 Þ 1+ρ ρ K + ΔK2 αρ K + ΔK2 −β 2 −β 2 ⋛0 or ⋛0 α 1+ρ 1+ρ G2 −X1 G2 −X1 αðK2 + ΔK2 Þα−1
X1 ⋚
αρG2 −βð1 + ρÞK2 −βð1 + ρÞL1 ρðα + βÞ
πA2 w2 ð1 + nÞ ð1 + ρÞð1 + r2 Þ
:
It can be seen that if α and G2 are sufficiently large, or β and K2 are sufficiently small, output increases; otherwise, output decreases. Consumption depends on the interest rate and the wage rate, as well as other parameters. With an increase in the wage rate and a decrease in the interest rate, the impact on consumption is ambiguous. We now examine the effects of the social security reform on private capital, interest rate, government capital, output, and welfare through simulation analyses. We calibrate this model economy to the behavior of China to weigh the gains and losses from the transition. The calibrated parameters are summarized in Table 1. Fig. 1 illustrates the effects of a switch from the PAYG system to the funded system on private capital accumulation, government capital accumulation, the interest rate, and the output. For convenience, we define the ratio of capital under the funded system to capital under PAYG system as kˆt , and we define rˆt , gˆ t and Yˆ t in a similar way. Since at the beginning of period 1, k1 and g1 are the same under both systems, i.e., kˆ1 = 1, rˆ1 = 1, gˆ 1 = 1 and Yˆ 1 = 1. Fig. 1A shows the change in private capital. It can be seen that private capital–effective labor ratio increases after transferring from the PAYG system to the funded system. Around steady state, private capital–effective labor ratio in the funded system is 165% as much as that in the PAYG system. The funded system has a higher capital accumulation than the PAYG system. The interest rate or the rate of return to private capital decreases after transferring to a funded system, as shown in Fig. 1B. Fig. 1C shows the evolvement of government capital. Government capital is lower in the funded system than in the PAYG system at the beginning of the reform since government uses its capital to pay for pension debt. However, the amount of government capital will be higher in the funded system than that in the PAYG system from fourth period, and becomes 19% higher in the steady state. The evolvement of output is displayed in Fig. 1D. In the funded system, output is 10% lower than that in the PAYG system in period 2. However, after that the output has a sustainable increase: 5% higher in period 3, 13% higher in period 4, and 19% higher around steady state. Fig. 2 shows the impact of the transition from the PAYG system to the funded system on the utilities (welfare) of the current and the future generations. The horizontal axis indicates the time period in which the various generations were born, and the vertical axis shows the change of utility level. For example, a value of 1.05 means that the generation's remaining lifetime utility under the funded system is 5% higher than it would have been in the PAYG system. To be precise, the percent change in utility is measured as a consumption equivalent (See Kotlikoff (1996)). Specifically, let ut = ln(ctt) + ρ ln(ctt + 1) denote utility level in the PAYG system and u˜ t = ln c˜tt + ρln c˜tt+1 denote utility level in the funded system. Think about how much consumption should be increased or decreased in order to make people in the PAYG system achieve the same utility level as people in the funded system. Define λt satisfying the following equation: t t t t u˜ t = ln λ t ct + ρ ln λt ct +1 = ð1 + ρÞln λ t + ln ct + ρ ln ct +1 = ð1 + ρÞln λt + ut : Solving the above equation, we obtain the value of λt. If λt N 1 (or λt b 1), it means that consumption should be increased (or decreased) by λt − 1 (or 1 − λt) in order to make people in the PAYG system achieve the same utility level as people in the funded system. Fig. 2 provides the value of λt. The first two generations have a lifetime utility loss of 7% and 8%, respectively. The following generations have a utility gain: 4% for third generation, 10% for fourth generation, and 13% for fifth generation. The percentage of utility gain keeps increasing until tenth generation, which stays at 15% afterwards. The intuition is clear: during the transition private capital increases and the interest rate decreases. However, the wage rate in period 1 is the same in both systems. Thus, the current young generation will see a decrease in interest income from their savings when they get old, resulting in a utility loss for the old generation.12
12 For a country with a lower private saving rate, the loss of interest income by the old generation may be offset by the higher return from a personal account. In that case, no generation becomes worse off.
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4. Concluding remarks This paper has examined the effects of a switch from the current PAYG system to a funded system by taking into consideration the implicit pension debt caused by such a transition. Three methods are used to finance the implicit pension debt: debt financing, tax financing, and government asset financing. It shows that with debt or tax financing, the social security reform is neutral, i.e., the market equilibrium remains unchanged, and all generations are as well off in the new system as in the PAYG system. With government asset financing, the interest rate decreases, private capital increases, but the total output may either increase or decrease; the welfare effect is also ambiguous in general, depending on the rate of return on government assets. With plausible parameters, our simulation shows that the reform lowers the interest rate, increases private capital, and lowers government capital in the short run, but raises government capital and increases output levels in the long run. It is clear that the establishment of the PAYG social security system is essentially a transfer of wealth from the current young generation to the current old generation, and a transfer of burden of pension payment to future generations. If the population does not decrease, there will be no crisis of pension payment. If the population declines, a social security payment crisis may occur. If a country does not have a social security system, it is better to establish a fully funded system, instead of a PAYG system, to avoid a social security payment crisis due to population aging. If the PAYG system has been established, that is the initial old generation has already used up the windfall funds from the initial young generation, then privatization of a social security system may not bring any gain unless some generations suffer losses. However, social security reforms may result in efficiency gains. For example, if government capital is too large and the government capital share of income is small, a switch from the PAYG system to a funded system by using government capital to pay the implicit social security debt will improve productivity and result in welfare gains. However, gains can be reaped without relying on the social security reforms, i.e., other reforms can reap the efficiency gains also. Acknowledgments The authors thank an anonymous referee and Editor Belton Flesher for their helpful comments. The authors also thank Laurence Kotlikoff for his helpful suggestions. 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