Social Security Rules, Labor Supply and Human Capital Formation

Transcription

1 Social Security Rules, Labor Supply and Human Capital Formation Morten I. Lau y Centre for Economic and Business Research Panu Poutvaara z Centre for Economic and Business Research May2,2002 Abstract Our objective is to illustrate how di erent social security systems may a ect lifelong educational decisions, retirement and welfare. We integrate human capital formation and retirement decisions into a computable life cycle model. The model is calibrated to a non-actuarial Beveridgean system. It generates a plausible allocation of time over the life cycle and provides one explanation for the existence and persistence of wage di erentials over the life cycle. We analyze steady state equilibrium e ects of replacing the initial social security system with an actuarial Beveridgean system, a non-actuarial Bismarckian system and an actuarial Bismarckian system, respectively. Keywords: social security, education, labor supply, computable general equilibrium models JEL Code: C68, H55, I21, J22 This paper was written while Poutvaara was employed rst by the Department of Economics at the University of Helsinki and then by the Government Institute for Economic Research. Part of the paper was written while Poutvaara visited the Center for Economic Studies (CES) in Munich. Their hospitality is gratefully acknowledged. Earlier versions of the paper have been presented at CES and the 57th International Institute of Public Finance Congress in Linz, August 27-30, We are grateful for insightful comments and suggestions from Peter Birch Sorensen, Anders Sorensen, and seminar participants at CES. We acknowledge nancial support from the Danish Ministry of Economic and Business A airs and from the Yrjö Jahnsson Foundation. None of our employers are responsible for our conclusions. y Corresponding author: Morten I. Lau, Centre for Economic and Business Research, Langelinie Alle 17, DK-2100 Copenhagen, Denmark. mol@cebr.dk. z Address: Panu Poutvaara, Centre for Economic and Business Research, Langelinie Alle 17, DK-2100 Copenhagen, Denmark. pp@cebr.dk 1

2 1 Introduction European countries and the United States have experienced a signi cant decrease in old age labor force participation rates during the last four decades. It is not plausible to explain increased retirement by worse health conditions, since life expectancy has increased at the same time. Boskin (1977) argues that the reduced labor force participation rates are caused by the development of social security systems, and his view is supported by Gruber and Wise (1999) who nd a strong correspondence between social security provisions and early retirement in Western Europe, the United States and Japan. In particular, early retirement is widespread in countries with high implicit tax penalties on wage earnings after qualifying for social security. Declining labor force participation rates combined with rapid population aging threaten the nancial viability of unfunded pay-asyou-go social security systems in almost every industrialized country. To avoid drastic increases in social security tax rates or reduced bene t levels, the ratio of workers to pensioners and the growth rate in labor productivity must increase in the a ected countries. Equity concerns reduce the possibilities for radical changes in the funding of social security systems, and we are instead concerned with economic incentive e ects of various social security systems with a constant payroll tax rate in relation to after-tax wage income. Since the empirical evidence suggests that reduced labor force participation rates are caused by adverse incentive e ects of past social security reforms, we can expect that the 1

3 early retirement problem to a great extent can be solved by reforms that operate in opposite directions. Unfortunately, we do not have su cient knowledge of the economic impacts of social security rules on human capital investment, retirement and production to allow a thorough evaluation of various policy alternatives. Social security systems can be classi ed into Beveridgean systems with decreasing replacement ratios and Bismarckian systems with constant replacement ratios across income levels. Social security bene ts are based on the judged need of the old in the Beveridgean system, whereas they can be interpreted as postponed wage income in the Bismarckian tradition. The United Kingdom and the Netherlands are examples of Beveridgean systems, while France, Germany and Italy follow the Bismarckian tradition (Casamatta et al., 2000). Another crucial issue is actuarial adjustment or the lack of it. Börsch-Supan (2000) suggests that retirement before age 60 would be reduced by more than a third in Germany if the social security system is reformed and made actuarially fair. To account for these two dimensions, we analyze and compare four di erent social security systems: (i) a non-actuarial Beveridgean system, (ii) an actuarial Beveridgean system, (iii) a non-actuarial Bismarckian system, and (iv) an actuarial Bismarckian system. Our objective is to illustrate how di erent social security systems may affect lifelong educational decisions, retirement and welfare. We integrate human capital formation and retirement decisions into a computable life cycle model. The presence of life cycle time allocation decisions and endogenous human capi- 2

4 tal formation provides one explanation for the existence and persistence of wage di erentials over the life cycle. Accounting for di erences in productivity over the life cycle is crucial to evaluate the nancial viability and welfare e ects of alternative social security systems. We compare the economic e ects of these various alternatives and choose the non-actuarial Beveridgean system as benchmark. Our framework is based on the life cycle model with endogenous human capital formation and retirement presented by Lau (2000). We modify and extend that model by introducing alternative unfunded social security systems. Public expenditures are nanced by wage taxes in each system, whereas social security bene ts are nanced by a separate payroll tax. The allocation of time over the life cycle in our framework is di erent from other studies based on computable life cycle models with endogenous human capital formation. In particular, the point in time at which the individual retires is endogenous in our model. Time is divided between work and human capital investment during the rst part of the life cycle and between work and leisure during the second part. Existing numerical models do not specify the point in time at which the individual retires, and the retirement curve is more prolonged and less steep compared to our framework. These studies evaluate the e ects of replacing a comprehensive at income tax system with progressive wage income taxation and proportional capital income taxation (Heckman et alii, 1998) or taxation based on consumption (Perroni, 1995). We are concerned about retirement and human capital investment decisions and evaluate how these decisions 3

5 are a ected by alternative social security rules. We follow Heckman (1976) and assume that the level of human capital depends on time devoted to education. The opportunity cost of human capital investment is thus determined by the lost after-tax wage income, which is a good approximation of degree studies in European countries where public education is widespread. This representation of human capital formation may also describe on-the-job training in general skills, since workers to some extent pay for the accumulation of general skills through lower wages during the training period (Becker, 1964). Lau and Poutvaara (2001), on the other hand, keep the duration of education constant and focus on tax distortions related to non-deductible tuition fees. They nd that actuarial adjustment and a positive link between contributions and bene ts in social security systems postpone retirement and encourage human capital investment. However, the productivity pro le is constant over the life cycle, and there is no physical capital in that model. We include both physical and human capital formation in this analysis. Our model generates a reasonable approximation of the estimated average labor supply curve over the life cycle in McGratten and Rogerson (1998). Human capital formation is concentrated in the beginning of the life cycle and is gradually phased out. Non-actuarial systems encourage retirement after the entitlement age, while the individual supply of labor is reduced more gradually during the second part of the life cycle under actuarial systems. We nd that both actuarial adjustment and linking social security bene ts to wage history have positive 4

6 e ects on aggregate production and welfare. The paper is organized as follows. Section 2 describes the individual intertemporal optimization problem in an economy with non-actuarial Beveridgean bene ts. Section 3 presents the calibration and the initial steady state equilibrium. Three alternative social security systems are introduced in Section 4, and income and welfare e ects are subsequently described in Section 5. Finally, Section 6 concludes. 2 Economy with Non-Actuarial Beveridgean Bene ts We present an overlapping generations model in which individuals divide their time between labor supply, human capital investment and leisure. There is perfect foresight in the model, and individuals maximize lifetime utility subject to an intertemporal budget constraint. Labor income taxes are collected to satisfy a given revenue requirement, while social security bene ts are nanced by a separate payroll tax. There is no actuarial adjustment in the benchmark social security system, and we assume that retirement bene ts are paid to retired individuals after a given entitlement age. Retirement is e ectively subsidized since the private cost of retirement is driven below the net wage, which is a common feature of social security systems in most industrialized countries. 5

7 The analysis is based on a steady state equilibrium, and the model represents a closed economy where the production technology combines labor services and physical capital. Perfect competition prevails in each market, and all agents consider output and factor prices as given. All agents are identical within and across generations, and the size of each cohort is normalized at unity. We assume that individuals begin their active life at age 18 and die at age 77. The size of each cohort is constant and normalized at 1, which implies that the size of the population is equal to 60. Including human capital formation in a life cycle model provides one way of explaining the existence of wage di erentials over the life cycle. Individuals can invest in human capital or invest in nancial assets. Investment in human capital is costly and speci c to each individual, and it is therefore concentrated at the beginning of the life cycle and ends when retirement sets in. Human capital depreciates at a constant rate, and the wage rate per unit of work e ort thus declines after the agents reduce their human capital investment. 2.1 Intertemporal Optimization In each period of the life cycle, individuals divide time between work, q, training, s, and leisure, v. The economic lifespan of each individual consists of 60 periods, each period representing one year, and the periods are indexed from 0 to 59. Total use of time in each period cannot exceed the time endowment, and the 6

8 following constraint on time applies: v t + q t + s t e; (1) where e is the constant endowment of time in each period. The time endowment denotes hours available to work, training and leisure, and it is therefore interpreted as the normal length of a work week, say 40 hours. Gross investment in human capital is determined by training, and the stock of human capital evolves according to the following law of motion: h t+1 =(1 ± H ) h t + s t ; (2) where h t is the individual human capital stock in period t, ± H istherateof depreciation with respect to human capital, and measures the elasticity of new human capital with respect to training, where 0 < 1. The initial stock of human capital, h 0, is positive and the economic agents thus possess some productive skills without training e ort. The e ective supply of labor services is found by multiplying the individual s productivity by time devoted to work: l t = h t q t ; (3) where l t is the individual supply of labor services, and measures the elasticity 7

9 of productivity with respect to human capital. We assume that 0 < <1, implying diminishing marginal productivity of human capital. The individual maximization problem is based on an explicit representation of the utility function: U = 59X t=0 "Ã! # 1 (1 + ½) t c (1 ) t + v t ¹ vt 2 ; (4) 1 where c t is the consumption of goods in period t, v t is the demand for leisure in period t, ½ istherateoftimepreference, is the inverse of the intertemporal elasticity of substitution, ¾, and 2¹ re ects the rate at which the marginal utility of leisure is reduced as the amount of leisure increases. The speci cation of the instantaneous utility function implies that individuals smoothe consumption across the life cycle, whereas leisure is not necessarily consumed in every period. Contrary to popular constant elasticity of substitution formulations of the utility function, the additively separable utility function allows the point in time at which the individual begins to retire to be endogenous. Retirement begins when the individual starts to demand a positive amount of leisure. Demanding a positive amount of leisure means that less time than the normal work week is devoted to work and human capital formation. The quadratic utility function with respect to leisure allows us to capture two labor market features. First active labor market participation is phased out at old age. Investment in human capital is concentrated in the beginning of the 8

10 life cycle and ends when retirement sets in. Human capital depreciates at a constant rate, and the opportunity cost to leisure thus declines during the last part of the life cycle when investment in human capital is low or absent. Second, the model captures the idea that people typically require a higher marginal wage compensation when leisure time is scarce. 1 Individuals are born without nancial wealth, and they can save and borrow without liquidity constraints at the market interest rate, r. The lifetime budget constraint states that the present value of lifetime expenditures on consumption cannot exceed the present value of lifetime wage income and retirement bene ts: 59X t=0 W (1 + r) t l t + 59X t=45 1 (1 + r) t! v t 59X t=0 1 (1 + r) t c t; (5) where W is the net return to labor services, and! is the retirement subsidy. In this example, we assume that individuals are eligible for retirement bene ts at age 63. The price of the consumption good is chosen as numeraire and normalized at unity. Each individual maximizes the present value of lifetime utility, U, subject to the time endowment constraint, the law of motion with respect to human capital, and the intertemporal budget constraint. 1 Lau (2000) applies a homothetic Cobb-Douglas speci cation of labor services and a linear speci cation of leisure in the instantaneous utility function to achieve a similar allocation of time over the life cycle. The disadvantage of that approach is that labor productivity at late stages in the life cycle may increase if the work e ort is su ciently small. We avoid that problem with the present speci cation. 9

11 2.2 General Equilibrium Given the assumption that all individuals are identical, it is a simple task to derive the aggregate supply of labor services to the labor market and consumption in the steady state. Since the size of each cohort is constant and equal to one, the aggregate supply of labor services is equal to the sum of the supply of labor services over the life cycle for the representative individual: L = 59X t=0 l t ; (6) where L is the aggregate supply of labor services in steady state. The production of nal goods combines labor services and physical capital, and the technology is represented by a Cobb-Douglas speci cation: Y = K Á L (1 Á) ; (7) where Y is aggregate output, K is the aggregate stock of physical capital, and Á is the value share of physical capital. Each producer of goods maximizes pro ts subject to the production technology, and the rst order conditions imply that the marginal product of the particular factor input is equal to the producer price of that factor input. The capital stock in period t is equal to the capital stock at the beginning of the previous period less depreciation plus investment in the previous period. 10

12 The capital stock is constant in the steady state, and gross investment in physical capitalisthusgivenby: I = ± K K; (8) where I is gross investment in physical capital, and ± K is the rate of depreciation with respect to physical capital. Aggregate output is either invested or consumed by individuals and the public sector, and the market clearing condition for goods is: Y = C + I + G; (9) where C is aggregate private demand for consumption goods, and G is public demand for goods. The government operates with two dynamic budget constraints: one constraint on social security expenditures and another constraint on other public expenditures. Both budgets are balanced in each period, and the constraint with respect to social security is: s W L = 59X t=45! v t ; (10) where s is the social security tax rate. The social security tax payment is de ned in relation to after-tax wage income. The left-hand side is equal to the social 11

13 security tax revenue, and the right-hand side is equal to social security payments to entitled generations. The budget constraint with respect to the supply of other public goods and services is: l W L = G; (11) where l is the tax rate on labor income. The tax rate on labor income is also de ned in relation to the after-tax wage income Welfare E ects We use the equivalent variation measure to assess private welfare e ects of the social security reform. This measure is derived as the percentage change in lifetime earnings (in base year prices) necessary to yield the welfare level reached in the new steady state. More formally, private welfare is determined by: U(E 0 (1 + Â);r 0 ;w 0 )=U(E 1 ;r 1 ;w 1 ); (12) where E is the net present value of lifetime income, and the subscripts 0 and 1 denote the initial and the new steady state, respectively. The parameter  measures the change in private welfare between the two steady states. This welfare measure can be compared across di erent steady states and is applicable 2 The corresponding net tax rates are determined by s =(1 + l + s ) and l =(1 + l + s ). 12

14 for changes of any size and not only di erential approximations. 3 Calibration We specify the parameter values according to two criteria. Whenever possible, we use values that correspond closely to what we observe in developed Western economies. For parameters that cannot be chosen in that way, like the weight parameter for leisure in the quadratic utility function, we choose values such that the average individual labor supply pro le resembles the estimated average individual labor supply pro le (measured in hours worked) for recent generations in McGratten and Rogerson (1998). Table 1 presents our choice of parameter values that represents the initial steady state. The following standard parameter values are applied in the baseline scenario. Capital income accounts for 30.0 percent of GDP and labor income accounts for 70.0 percent of GDP, which implies that the labor-capital income ratio is equal to 2.3. The level of investment is equal to 20.0 percent of GDP, given a net interest rate of 5 percent and a 10 percent depreciation rate with respect to physical capital. To achieve a su ciently high private saving rate, we assume thattherateoftimepreferenceisequalto3.6percent. Thisishighcomparedto the numerical analyses by Auerbach and Kotliko (1987) and Perroni (1995), for example, but empirical studies by Warner and Pleeter (2001) and Harrison et alii (2002) suggest that the rate of time preference may be considerably higher. We 13

15 assume that the intertemporal elasticity of substitution is equal to 0.667, which is within the range from 0.5 to 1 that is applied in most studies. The tax revenue from the labor income tax in the initial steady state is equal to 18.1 percent of GDP, and the tax revenue from the social security tax is equal to 9.9 percent of GDP. These revenues are achieved by a 43.0 percent gross labor income tax rate and a 23.6 percent gross social security tax rate, respectively. The combined gross tax rate on labor income is 66.6 percent, which corresponds to a 40.0 percent combined net tax rate on labor income. These revenue requirements and the average tax rate on labor income closely resemble tax systems in most industrialized countries. [insert TABLE 1] Figure 1 illustrates the allocation of time over the life cycle for the representative agent in the initial steady state. Time is allocated between training and work during the rst 35 years of the individual s active life. The individual begins to retire from the labor market when he/she is 53 years old, and time is mainly divided between work and leisure during the last 25 years of the life cycle; investment in human capital is reduced signi cantly after retirement begins. We assume that agents are eligible for social security at age 63. The subsidy to retirement has a signi cant impact on retirement from this age and individuals retire completely from the labor market. Time spent on work increases sharply during the rst ve years of the life cycle. It then stays constant for approximately 30 years and begins to fall when the individual begins to retire from the 14

16 labor market. [insert FIGURE 1] Investment in human capital is costly and speci c to each individual, and it is concentrated in the beginning of the life cycle. The marginal product of human capital investment falls with the level of training, and the buildup of human capital is thus spread over several periods. Figure 2 shows that labor productivity in the rst period of the life cycle is normalized at unity, and it increases during the rst 10 years of the life cycle. The level of labor productivity is maintained during the next 20 years and falls when the individual begins to retire from the labor market. Human capital depreciates by a constant rate, and the wage rate per unit of work e ort is falling during the second half of the life cycle. [insert FIGURE 2] 4 Three Alternative Social Security Systems We next analyze the economic e ects of three alternative social security systems: actuarial Beveridgean bene ts, non-actuarial Bismarckian bene ts and actuarial Bismarckian bene ts. Actuarial adjustment can be expected to yield more ef- cient labor supply decisions over the life cycle, because non-actuarial systems subsidize retirement and reduce the supply of labor after the entitlement age. Bismarckian systems introduce an intertemporal distortion in the supply of la- 15

17 bor since social security bene ts depend on wage income before and not after the entitlement age. On the other hand, the private return to labor before the entitlement age is closer to the market return, and the Bismarckian system may therefore reduce the distortion due to the labor income tax. To evaluate the combined e ect of these opposite forces and compare alternative social security rules, the calibrated parameter values are kept unchanged across the three scenarios. The social security tax rate as a share of net wage income is kept constant, and the tax rate on net wage income is determined endogenously to balance the public budget Actuarial Beveridgean Bene ts Under the actuarial Beveridgean bene t system, the individual intertemporal budget constraint changes to: 59X t=0 W (1 + r) t l t + 59X t= X (1 + r) 1 t (1 + r) c t; (13) t t=0 where is the constant social security payment per period to individuals above the entitlement age. The government budget constraint with respect to the social 3 We use GAMS/MPSGE to solve the model numerically. Rutherford (1995, 1999) documents this modeling system and software. The code we use is available upon request. 16

18 security system accordingly changes to: s W L = 59X t=45 ; (14) where the left-hand side is the social security tax revenue, and the right-hand side is the aggregate social security payment to current old generations. Figure 3 shows that the retirement rate after the entitlement age is reduced when the Beveridgean system is made actuarially fair. Retirement is e ectively subsidized under the former system, and the private opportunity cost of retirement increases when the actuarial bene t system is introduced. The social security reform has a positive impact on the aggregate supply of labor services, and the gross tax rate on labor income is reduced from 43.0 percent to 41.7 percent in accordance with the public budget constraint. The increased supply of labor at the end of the life cycle and the lower tax rate on wage income yield positive income e ects, and the degree of retirement increases before the entitlement age. [insert FIGURE 3] Figure 4 illustrates that the overall impact on human capital investment is marginal. The two social security systems have no direct incentive e ects on human capital investment, but individuals shift part of the labor supply from more productive periods before the entitlement age to less productive periods after the entitlement age when the non-actuarial Beveridgean bene t system is replaced by an actuarial bene t system. These changes in the supply of labor 17

19 a ect the return to human capital investment, and training accordingly increases late in the life cycle. Hence, the social security reform has a signi cant impact on the allocation of time during the second part of the life cycle and marginal e ects on time allocation decisions during the rst part. [insert FIGURE 4] 4.2 Non-actuarial Bismarckian Bene ts The non-actuarial Bismarckian bene t system includes a link between social security contributions and bene ts, where bene ts after the entitlement age depend linearly on the wage income before that age. The individual budget constraint is determined by: 59X t=0 W (1 + r) t l t + 59X t=45 1 (1 + r) t à v t 59X t=0 1 (1 + r) t c t; (15) where à is the income dependent subsidy to retirement after the entitlement age. The social security bene t stream is equal to a fraction of the net present value of net wage income before the entitlement age: à = z 44X t=0 W (1 + r) t l t; (16) where the fraction z>0 is given to all individuals and determined by the government in accordance with the public budget constraint. The parameter z measures 18

20 the responsiveness of social security bene ts to past earnings. The government budget constraint with respect to the social security system changes to: s W L = 59X t=45 Ã v t ; (17) where the left-hand side is the social security tax revenue, and the right-hand side is the aggregate social security payment to current old generations. The responsiveness parameter z is determined by the government budget constraint and (16) taken together. Figure 5 reveals that retirement is postponed when the non-actuarial Beveridgean system is replaced by the non-actuarial Bismarckian system. The income dependency with respect to social security contributions and bene ts provides an incentive to increase the supply of labor before the entitlement age in order to secure higher bene ts during retirement. [insert FIGURE 5] The link between social security contributions and bene ts has a positive, but small impact on human capital investment. This e ect is driven by two mechanisms. First, the rate of return to human capital increases for a given number of hours worked when retirement bene ts depend on past wage income, which creates an incentive to accumulate more human capital. Second, the return to human capital increases when retirement is postponed. Figure 6 shows that 19

21 these two e ects increase human capital investment late in the life cycle, while training during the earlier years is unchanged. [insert FIGURE 6] 4.3 Actuarial Bismarckian Bene ts Under the actuarial Bismarckian bene t system, the individual intertemporal budget constraint changes to: 59X t=0 W (1 + r) t l t + 59X t= X (1 + r) ¼ 1 t (1 + r) c t; (18) t t=0 where ¼ is the social security payment per period to individuals after the entitlement age. The social security bene t depends on wage income history during the period before the entitlement age and is determined by: ¼ = x 44X t=0 W (1 + r) t l t; (19) where x is a positive number, which is determined by the government in accordance with the public budget constraint. This speci cation implies that the social security payment per period during the o cial retirement period is a constant fraction of the net present value of after-tax wage income before the entitlement age. The government budget constraint with respect to the social security system 20

22 changes to: s W L = 59X t=45 ¼; (20) where the left-hand side is the social security tax revenue, and the right-hand side is the aggregate social security payment to current old generations. The responsiveness parameter x is determined by this constraint and the above link between contributions and bene ts (19). Figure 7 shows that retirement is postponed when the actuarial Beveridgean system is replaced by the actuarial Bismarckian system. The social security reform increases the return to labor services during the period before the entitlement age, and the degree of retirement before the o cial retirement age falls. The positive impact on the supply of labor services implies that the gross tax rate on labor income is reduced from 43.0 percent to 40.5 percent. Although the tax rate on labor income falls, retirement after the entitlement age is marginally higher compared to the Beveridgean system due to the positive income e ect in previous periods. [insert FIGURE 7] Human capital investment increases when the constant retirement bene ts depend on wage income history compared to a similar social security system without such dependency. Postponing retirement increases the amortization period for human capital investment and leads to more training. Figure 8 shows 21

23 that training increases late in the life cycle and is not a ected in the earlier years. [insert FIGURE 8] 5 Income and Welfare Comparisons Replacing the non-actuarial Beveridgean system with an actuarial Beveridgean system has positive e ects in the long run on income and private consumption. The rst column in Table 2 shows that GDP increases by 1.2 percent and private consumption increases by 1.7 percent compared to the initial steady state equilibrium. Removing the subsidy to retirement has a positive impact on the supply of labor services, and the capital intensity falls despite an increase in private saving. The increased labor-capital ratio implies that the gross return to physical capital goes up while the gross return to labor services falls. The increase in private consumption leads to a positive welfare e ect, and welfare increases by 0.7 percent. Although the steady state re ects the long-run position of the economy, the positive welfare e ect may come at the expense of earlier generations. The only way to evaluate this inter-generational redistribution is to examine the dynamic transition from the initial steady state to the nal steady state. [insert TABLE 2] The second column in Table 2 shows that GDP increases by 1.2 percent and private consumption increases by 1.7 percent when the non-actuarial Beveridgean system is replaced by a non-actuarial Bismarckian system. The link between 22

24 social security contributions and bene ts increases the return to labor services before the entitlement age, and the aggregate supply of labor increases. Although retirement is postponed compared to the initial steady state equilibrium, private saving increases in the long run. The gross return to labor services falls, but the reduced tax rate on wage income implies that the net return to labor services increases. The results indicate that welfare increases by 0.7 percent. Finally, the move to the actuarial Bismarckian system is a combination of the two previous reforms. The last column in Table 2 shows that GDP increases by 2.3 percent and private consumption increases by 3.3 percent after the reform is introduced. The labor-capital ratio goes up, and the gross return to physical capital increases by 0.9 percent, while the gross return to labor services falls by 0.4 percent. Each of the two previous reforms lead to higher welfare, and the combined reform has a positive impact on welfare as well. Welfare increases by 1.4 percent in the nal steady state equilibrium, which is twice the e ect compared to each of the two previous reforms. The three social security reforms have positive e ects on economic activity, and we next derive and compare contributions to income from physical capital and labor services across the di erent scenarios. Table 3 shows that the increase in labor services accounts for most of the 1.16 percent increase in GDP when the nonactuarial Beveridgean system is replaced by the actuarial Beveridgean system; the increase in labor services accounts for 0.99 percentage points of the increase in 23

25 GDP, while the increase in physical capital accounts for 0.17 percentage points. 4 Going into further detail, the results suggest that the changes in human capital investment have a small positive impact on economic growth, and the positive growth rate in labor services is thus explained by the increased work e ort after the entitlement age. [insert TABLE 3] Economic activity increases by 1.23 percentage points when the non-actuarial Beveridgean system is replaced by the non-actuarial Bismarckian system. The reform has a positive impact on labor income before the entitlement age, and private saving increases. The impact on physical capital is slightly higher compared to the previous reform, and the increase in physical capital accounts for 0.25 percentage points of the increase in GDP. The increase in labor services thus accounts for 0.98 percentage points, which primarily is due to the increase in work e ort before the entitlement age. The link between social security contributions and bene ts increases the return to human capital investment before the entitlement age, and changes in human capital investment account for 0.16 percentage points of the higher economic activity, while increased work e ort accounts for 0.82 percentage points. 4 Contributions to the increase in steady-state output from physical capital and labor services are determined by: lny = Á lnk +(1 Á) lnl. Having derived the growth rate in aggregate labor services, the contribution to the increase in steady-state output from labor services across generations is derived = P i (l i =l i. Finally, the contribution to the increase in steady-state output from changes in human capital and work e ort across generations is determined by: lnl i = lnh i + lnq i. 24

26 The actuarial Bismarckian system combines features from the two previous reforms, and GDP increases by 2.28 percent when this system is introduced. An increase in labor services explains 1.87 percentage points of the increase in GDP, while a greater accumulation of physical capital accounts for 0.41 percentage points. Most of the increase in labor services is due to the di erent retirement pattern, and the increased work e ort during the second half of the life cycle explains 1.67 percentage points of the contribution to economic growth from labor services. To gain insight about the behavior of the model, it is useful to consider the welfare e ects of the same social security reforms when the elasticity of new human capital with respect to time is changed. The marginal product of training in the production of new human capital is diminishing when <1, andhuman capital investment falls early in the life cycle and increases later in the life cycle when the elasticity of new human capital with respect to time is reduced. These changes in the labor productivity pro le subsequently imply that individuals retire earlier, but the degree of retirement falls late in the life cycle. 5 Having changed one parameter value, it is necessary to adjust another parameter value to arrive at approximately the same initial steady state equilibrium. We keep the social security tax rate constant and adjust the subsidy to retirement. The upper part of Table 4 shows that the welfare results are robust to simultaneous changes 5 The results are reversed if the elasticity of new human capital with respect to training is increased. 25

27 in the elasticity of new human capital with respect to time and the subsidy to retirement. Actuarial adjustment and linking bene ts to contributions increase welfare. [insert TABLE 4] We next change the elasticity of labor services with respect to human capital and adjust the social security tax rate. A higher elasticity of labor services with respect to human capital leads to more investment in human capital and retirement is postponed. The social security tax rate is accordingly reduced to arrive at approximately the same initial steady state equilibrium. Reducing the cost of investment in human capital tends to increase the welfare gain from each of the three social security reforms. However, the combined marginal tax rate on labor income is reduced, and the lower part of Table 4 shows that the welfare gain from each of the three reforms is reduced. Finally, the qualitative results are robust to changes in the tax rate on labor income, and the three social security reforms lead to positive welfare e ects even when the tax rate on labor income is zero. 6 Conclusions We analyze and compare human capital formation, labor supply and retirement behavior under four di erent social security bene t rules. Individuals divide their time between human capital investment, work e ort and leisure in each 26

28 period over the life cycle, and the model is calibrated to a non-actuarial Beveridgean system in the initial steady state equilibrium. The presence of life cycle time allocation decisions and endogenous human capital formation provides one explanation for the existence and persistence of wage di erentials over the life cycle. Human capital investment is costly and speci c to each individual, and it is therefore concentrated in the beginning of the life cycle and ends when the individual begins to retire from the labor market. Hence, the individual stock of human capital increases until the age of 30, remains constant until the age of 50 and begins to fall when retirement sets in. Individuals are eligible for social security at age 63, and the subsidy to retirement has a signi cant impact on retirement from this age. The social security system in the initial steady state equilibrium is compared with an actuarial Beveridgean system, a non-actuarial Bismarckian system and an actuarial Bismarckian system, respectively. The type of the social security system has signi cant e ects on the allocation of time during the second part of the life cycle and marginal e ects on time allocation decisions during the rst part. Retirement is signi cantly reduced after the entitlement age when actuarial adjustment is introduced. This result is well in line with the empirical results by Börsch-Supan (2000), who estimates that early retirement in Germany may be reduced by one third if the social security system is made actuarially fair. The two Bismarckian systems include a link between social security contributions and bene ts, where bene ts after the entitlement age depend linearly on wage income 27

29 before that age. A switch from a Beveridgean system to a Bismarckian system implies that retirement is postponed by roughly a year before the entitlement age. The e ect of income dependency on retirement is smaller than that of actuarial adjustment. Social security rules a ect human capital investment when individuals are between 45 and 60 years of age. Moving from a Beveridgean system to a Bismarckian system increases human capital investment late in the life cycle, while training during the earlier years is unchanged. The impact of actuarial adjustment on training is positive, but small. Acturial adjustment has no direct incentive e ects on human capital investment, but individuals shift part of the labor supply from more productive periods before the entitlement age to less productive periods after the entitlement age. These changes in the supply of labor a ect the return to human capital investment, and training accordingly increases late in the life cycle and is marginally reduced before retirement begins. The analysis is based on a stylized model, and the speci c quantitative results should not be taken too literally. Our model does not capture intra-generational income e ects, and redistributional motives may imply that the link between social security contributions and bene ts is undesirable from a utilitarian perspective. Moreover, uncertainty with respect to personal health conditions suggests that actuarial adjustment should not be complete. As a nal caveat, dynamic transition is not examined in the model. Although the steady state equilibrium re ects the long-run position of the economy, future generations may bene t 28

30 from a reform because earlier generations su ered. The only way to consider this inter-generational redistribution is to examine the dynamic transition from the initial to the nal steady state equilibrium. References [1] Auerbach, Alan J. and Laurence J. Kotliko, Dynamic Fiscal Policy (Cambridge, UK: Cambridge University Press, 1987). [2] Becker, Gary S., Human Capital (NBER General Series, number 80, 1964). [3] Boskin, Michael J., Social Security and Retirement Decisions, Economic Inquiry, 15, 1977, [4] Börsch-Supan, Axel, Incentive e ects of social security on labor force participation, Journal of Public Economics, 78(1-2), October 2000, [5] Casamatta, Georges, Helmuth Cremer and Pierre Pestieau, The Political Economy of Social Security, Scandinavian Journal of Economics, 102 (3), 2000, [6] Gruber, Jonathan and David A. Wise, Introduction and Summary, in J. Gruber and D. A. Wise (eds.) Social Security and Retirement Around the World (Chicago, IL: Chicago University Press, 1999). 29

31 [7] Harrison, Glenn W., Morten I. Lau and Melonie B. Williams, Estimating Individual Discount Rates in Denmark: A Field Experiment, forthcoming in American Economic Review, [8] Heckman, James J., A Life Cycle Model of Earnings, Learning and Consumption, Journal of Political Economy, 84, 1976, S11-S44. [9]Heckman,JamesJ.,LanceLochnerandChristopherTaber, TaxPolicy and Human Capital Formation, Working Paper 6462, National Bureau of Economic Research, [10] Lau, Morten I., Assessing Tax Reforms When Human Capital is Endogenous, in G. W. Harrison, S. H. J. Jensen, L. H. Pedersen and T. F. Rutherford (eds.), Using Dynamic General Equilibrium Models for Policy Analysis (Amsterdam: North Holland, 2000). [11] Lau, Morten I. and Panu Poutvaara, Social Security Incentives and Human Capital Investment, CESifo Working Paper No. 438, Center for Economic Studies, University of Munich, [12] McGratten, Ellen R. and Richard Rogerson, Changes in Hours Worked Since 1950, Quarterly Review, Winter 1998, Federal Reserve Bank of Minneapolis. 30

32 [13] Perroni, Carlo, Assessing the Dynamic E ciency Gains of Tax Reform when Human Capital is Endogenous, International Economic Review, 36(4), 1995, [14] Pogue, T. F. and L. G. Sgontz, Social Security and Investment in Human Capital, National Tax Journal, 30(2), June 1977, [15] Rutherford, Thomas F., Extensions of GAMS for Complementarity Problems Arising in Applied Economics, Journal of Economic Dynamics and Control, 19, 1995, [16] Rutherford, Thomas F., Applied General Equilibrium Modeling with MPSGE as a GAMS Subsystem: An Overview of Modeling Framework and Syntax, Computational Economics, 14, 1999, [17] Warner, John T. and Saul Pleeter, The Personal Discount Rate: Evidence from Military Downsizing Programs, American Economic Review, 91(1), March 2001,

33 Table 1. Parameter values, tax rates and factor prices in the initial steady state equilibrium. Parameter values: ρ Time preference rate σ Intertemporal elasticity of substitution µ Weight parameter in quadratic utility function wrt. leisure η Elasticity of human capital wrt. training δ H Depreciation rate for human capital β Elasticity of labor services wrt. human capital φ Value share of physical capital in production of goods δ K Depreciation rate for physical capital h 0 Initial human capital stock e Endowment of time in each period Tax rates: τ l Gross tax rate on labor income τ s Social security tax rate ω Subsidy to retirement Factor prices: r Annual interest rate w Wage rate after tax 1.000

34 Table 2. Income and welfare effects across social security systems (percentage change from initial steady state equilibrium). Actuarial Non-actuarial Actuarial Beveridgean Bismarckian Bismarckian GDP Private consumption Physical capital stock Labor services Rental price of capital Return to labor services before tax Welfare (equivalent variation) Table 3. Contributions to income across social security systems (percentage change from initial steady state equilibrium). Actuarial Non-actuarial Actuarial Beveridgean Bismarckian Bismarckian GDP Physical capital Labor services Work effort Human capital

35 Table 4. Sensitivity analysis (percentage change from initial steady state equilibrium). Elasticity of new human capital wrt. training time Retirement subsidy Equivalent variation (percent) Actuarial Beveridgean system Non-actuarial Bismarckian system Actuarial Bismarckian system Elasticity of labor services wrt. human capital Social security tax rate (percent) Equivalent variation (percent) Actuarial Beveridgean system Non-actuarial Bismarckian system Actuarial Bismarckian system

36 Figure 1. Allocation of time over the life cycle Work effort Training Retirement Age Figure 2. Labor productivity over the life cycle Labor productivity Age

37 Figure 3. Individual retirement across Beveridgean systems Non-actuarial Beveridgean system 40 Actuarial Beveridgean system Age Figure 4. Individual training across Beveridgean systems Non-actuarial Beveridgean system Actuarial Beveridgean system Age

38 Figure 5. Individual retirement across non-actuarial systems Non-actuarial Beveridgean system 40 Non-actuarial Bismarckian system Age Figure 6. Individual training across non-actuarial systems Non-actuarial Beveridgean System Non-actuarial Bismarckian system Age

39 Figure 7. Individual retirement across actuarial systems Actuarial Beveridgean system 40 Actuarial Bismarckian system Age Figure 8. Individual training across actuarial systems Actuarial Beveridgean system Actuarial Bismarckian system Age