Labor income taxation and human capital accumulation

Journal of Public Economics 68 (1998) 291–302

Labor income taxation and human capital accumulation Shuanglin Lin* Department of Economics, University of Nebraska, Omaha, NE 68182 -0048 USA Received 31 January 1997; received in revised form 30 June 1997; accepted 12 August 1997

Abstract This paper provides alternative analytical results concerning the effect of labor income taxation on human capital accumulation. With the tax revenues being consumed by the government and savings being negatively related to the labor tax rate, an increase in the labor income tax rate reduces the incentive for human capital accumulation, and thus, decreases human capital. With tax revenues being consumed by government and savings being positively related to the labor tax rate, an increase in the tax rate increases the incentive for human capital accumulation and increases human capital. With the tax revenues being used to compensate the individuals who pay the taxes, an increase in the tax rate has no effect on human capital.  1998 Elsevier Science S.A. Keywords: Labor taxation; Allocation of tax revenues; Human capital JEL classification: H2; J2

1. Introduction The importance of human capital accumulation has been increasingly emphasized in economics.1 However, studies on the effects of government tax policies on *Tel.: (402) 554-2815; fax: (402) 554-3747; e-mail [email protected] 1 The analysis of human capital accumulation can be traced back to Adam Smith who considered all of the useful abilities acquired through education, study, or apprenticeship as capital and pointed out that investment in this type of capital is motivated by the expected rate of return [see Smith, 1937, The Wealth of Nations, edited by Edwin Cannan, pp. 265–266]. Studies emphasizing the importance of human capital include Schultz, 1961; Becker, 1964; Lucas, 1988. 0047-2727 / 98 / $19.00  1998 Elsevier Science S.A. All rights reserved. PII S0047-2727( 97 )00094-7

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human capital accumulation are still limited. This paper analyzes the effect of labor income taxation on human capital accumulation.2 The earlier contributions to the literature have found that labor income taxation may either have no effect or a positive effect on human capital accumulation. Boskin (1975) showed that, since labor income taxation reduces both the return and cost of human capital investment by the same proportion, it has no effect on human capital accumulation.3 In a two-period model, Eaton and Rosen (1980) showed that without uncertainty labor income taxation has no effect on human capital, but in the presence of uncertainty labor income taxation may increase human capital. Both Boskin (1975); Eaton and Rosen (1980) assumed that the tax revenues from labor income are consumed by the government and the real interest rate is fixed.4 This paper extends the literature by allowing the interest rate to be flexible and the tax revenues to be used for alternative purposes. An overlapping generations (OG) model will be employed.5 At any moment in time, there are two generations, the young generation and the old generation. The young generation can allocate their time for work (earning current income) or for human capital accumulation (earning future income). The old generation supplies human and physical capital. Human capital is affected by the youngster’s time allocated for human capital accumulation, the government spending on human capital production, and the parent generation’s human capital. The following policies concerning alternative uses of the tax revenues are considered: 1) tax revenues are rebated to the tax payers, and 2) the tax revenues are consumed by the government. To focus on the allocation of the tax revenues we assume that there is no uncertainty. The major results of the paper are as follows. With the tax revenues being used to compensate the individuals who pay the taxes, an increase in the tax rate has no effect on human capital. With the tax revenues being consumed by the government, an increase in the labor income tax rate will raise (lower) the real interest rate, lower (raise) the present discounted value of the future income, reduce (increase) time allocated toward education, and thus, decrease (increase) human capital if savings are negatively (positively) related to the tax rate. 2 Labor income amounts to more than seventy percent of national income and labor income tax rate is around forty percent [see Lucas, 1990, p. 307]. Thus, analyses of the effect of labor income taxation on human capital accumulation are clearly important. 3 See Boskin (1975) p. 188. Also see Rosen (1995) pp. 405–406 for a review of the literature. 4 Kotlikoff and Summers (1979) developed a dynamic model of overlapping generations with human capital accumulation. By assuming that the tax revenues are rebated to the same individuals who pay the taxes, they analyzed the burden of capital and labor income taxes with the second-period labor supply being flexible. 5 The OG model was introduced by Samuelson (1958). Diamond (1965), (1970) advanced the model by introducing capital. The model is firmly grounded in the consumer’s utility and the firm’s profit maximization, and has been widely used in analyzing government policies and intertemporal economic decisions. Recent examples of using the OG model in analyzing government policies include Auerbach and Kotlikoff, 1987; Ihori, 1991; Sibert, 1990; Buiter and Kletzer, 1993; Lin, 1994].

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Recent years have also seen significant contributions on the effect of income (both labor income and capital income) taxation on human capital accumulation and other variables in the infinitely-lived representative agent models. Lucas (1990) showed that income taxation lowers the return to human capital and reduces the incentive to accumulate human capital. Assuming that the tax revenues are consumed by government, King and Rebelo (1990); Rebelo (1991) demonstrated that an increase in the income tax rate decreases human capital accumulation and economic growth. Trostel (1993) simulated the effect of an income tax on human capital accumulation based on an infinitely-lived representative agent model. He found that a one percent increase in the income tax rate would cause the human capital stock to decline by 0.39 percent in the long run. He assumed that the change in the tax revenue lump-sum transferred back to the tax payer. As Heckman (1976) showed, capital income taxation and labor income taxation may have completely different effects on human capital accumulation.6 Thus, it is useful to analyze the effects of labor and capital income taxation on human capital accumulation separately. The rest of the paper is organized as follows. Section 2 presents the model and defines the steady-state equilibrium. Section 3 provides comparative steady-state analyses of the effects of labor income taxation on human capital accumulation. Section 4 concludes the paper.

2. The model There are two production sectors in the economy, one producing a physical good which can be consumed or invested, and the other producing human capital (units of effective labor). Each individual lives for two periods, working and accumulating human capital in the first period, and supplying human and physical capital in the second period. Individuals are identical within and across generations. In each period, N individuals are born, and the population does not grow. Each individual is endowed with one unit of labor in the first period, which can be allocated toward either the production of physical goods or the production of human capital. Government lives forever, collecting taxes to finance its spending and transfers. Let Ht 11 be human capital produced in period t and to be used in period t 1 1. Ht 11 is measured by units of effective labor and is owned by an individual in generation t (born in period t). The human capital each individual has in the second period of life is: Ht 11 5 G(h t , Ht , gt ) 5 (1 2 d )Ht 1 P(h t , gt ), 0 , d , 1 6

(1)

Heckman (1976) demonstrated a positive effect of physical capital taxation on human capital.

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where 0,h t ,1 is the time that each young person (born in period t) allocates to human capital production, Ht is the average level of the parent generation’s human capital (which is equal to each parent’s human capital since individuals are identical within a generation), gt is government spending on human capital production per young person (subsidies to education, research grants, etc.), and d is a constant.7 For simplicity, assume that the parent generation’s human capital affects the young generation’s human capital externally. Lucas (1988) emphasized human capital externalities by including human capital externalities in the production of physical goods. Part of the parent generation’s human capital may be passed to the young generation through many family and social activities. The young generation can accumulate more human capital through their investment in human capital. The evolution rule for human capital in Eq. (1) insures a steady-state solution for human capital. It can be seen that the human capital of the parent’s generation is positively related to the young generation’s human capital. Assume that ≠P(h t , gt ) / ≠h t .0, ≠P(h t , gt ) / ≠gt .0, ≠ 2 P(h t , gt ) / ≠h 2t ,0, and 2 ≠ P(h t , gt ) / ≠g 2t ,0.8 In this model both the young and the old supply labor and the labor supply by both the young and the old is endogenous. The young supply labor endowed and not used for human capital accumulation, and the old supply all human capital measured by effective labor. Total human capital produced in period t and to be supplied in period t 1 1 is NHt 11 . The amount of time allocated toward physical goods production by each individual in period t is 12h t . Total amount of labor supplied by generation t in period t is (12h t )N. The total amount of effective labor supplied by both generation t and generation t21 in period t, Ft , is: Ft 5 (1 2 h t )N 1 G(h t 21 , Ht 21 , gt21 )N 5 (1 2 h t )N 1 Ht N where G(h t 21 , Ht 21 , gt 21 )N is the amount of human capital supplied by generation t21 in period t. Recall that Ht 5G(h t 21 , Ht 21 , gt 21 ) [see Eq. (1)]. Letting Lt ;Ft /N, the effective labor supplied per young person in period t, we obtain: Lt 5 (1 2 h t ) 1 G(h t 21 , Ht 21 , gt 21 ). Let Kt be the physical capital owned by each person in generation t21 (born in period t21). The production function of the physical goods exhibits constant returns to scale in both physical capital and effective labor. The output per person in generation t, Yt , is given by: Yt 5F(Kt , Lt ). Letting y t 5 Yt /Lt , the output-labor ratio, we have: y t 5 f(k t ), f 9(k t ) . 0, f 0(k t ) , 0 7

(2)

In Kotlikoff and Summers (1979) human capital is produced by the time of the young generation only. 8 In Lucas (1988) human capital production exhibits constant returns to scale in the input of human capital.

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where k t 5Kt /Lt is the ratio of physical capital to effective labor. Assume that physical capital is fully depreciated after one period’s production. The main result of this paper will remain unchanged even if this assumption is relaxed. Factor markets are perfectly competitive, thus the rate of return to each factor is its marginal product, i.e. 1 1 r t 5 f 9(k t )

(3)

w t 5 f(k t ) 2 f 9(k t )k t

(4)

where 11r t is the rate of return on physical capital in period t, and w t is the rate of return to labor.9 Individuals are identical within and across generations. To obtain explicit solutions for savings and other endogenous variables and keep the model tractable, assume that the utility function is log–linear [as in Buiter and Kletzer (1993)]. The representative individual’s optimization problem is as follows: max u(c tt , c tt 11 ) 5 log(c tt ) 1 r log(c tt11 ) c tt 11 t t s.t. c t 1 ]]] 5 (1 2 h t )(1 2 p )w t 1 t t 2 l 1 1 r t 11 (1 2 p )G(h t , Ht , gt )w t 11 1 t tt 11 t t 1 ]]]]]]]]], c t , c t11 $ 0 1 1 r t 11

(5)

where c tt 1j is consumption in period t1j of an agent born in period t (called generation t), j50, 1; r ,1 is the (constant) pure rate of time preference; p is the tax rate on labor income; t tt and t tt 11 are transfers in the first and second period of life, respectively; and l stands for lump-sum taxes. Solving the agent’s maximization problem yields: 10 St 5 (1 2 h t )(1 2 p )w t 1 t tt 2 l 2 c tt (1 2 p )G(h t , Ht , gt )w t 11 1 t tt 11 r t 5 ]][(1 2 h t )(1 2 p )w t 1 t t 2 l] 2 ]]]]]]]]] 11r (1 1 r )(1 1 r t 11 ) (6) w t (1 1 r t 11 ) 5 w t 11 ≠G(h t , Ht , gt ) / ≠h t

(7)

where St represents savings in period t of an agent born in period t, which is the difference between the first-period income and the first-period consumption. It can be seen from Eq. (6) that ≠s t / ≠r t 11 .0. With the log-linear utility function as specified in Eq. (5), if there is no second-period income, then ≠s t / ≠r t 11 50. Thus, 9

If capital does not depreciate, it is better to use r t for the rate of return on capital. A detailed derivation is available from the author upon request.

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the use of the log-linear utility function, with second-period income, will not result in perfect inelasticity of savings with respect to the interest rate as it does usually.11 Eq. (7) implicitly determines the time spent on human capital accumulation, h t , which is chosen to maximize the present discounted value of lifetime income. The government finances its spending and transfers by collecting labor income taxes and a lump-sum tax. The government budget constraint is as follows: Gt 1 Zt 1 T tt 1 T tt 21 5 N(1 2 h t )p w t 1 NG(h t 21 , Ht 21 , gt 21 )p w t 1 Nl where Gt is government spending on human capital production, Zt is government consumption, T tt and T tt 21 are the transfers to the young and the old generations, respectively; N(12h t )p w t is the tax revenue from generation t, NG(h t 21 , Ht21 , gt 21 )w t p is the revenue from generation t21 (the old generation in period t), and Nl is lump-sum taxes (which can be used to approximate non-labor taxes). Dividing both sides of the above equation by N gives: gt 1 z t 1 t tt 1 t tt 21 5 p (1 2 h t )w t 1 p G(h t 21 , Ht 21 , gt 21 )w t 1 l

(8)

where gt ;Gt /N, z t 5Zt /N, t tt ;T tt /N, and t tt 21;T t t 21 /N. A competitive equilibrium for the economy is defined as a set of quantities hHt 11 , k t 11 , s t , r t , w t , h t , gt , t tt , t tt 21 j satisfying Eqs. (1), (3), (4), (7), (8), and t

(1 2 p )G(h t , Ht , gt )w t 11 1 t t 11 r t St 5 ]][(1 2 h t )(1 2 p )w t 1 t t 2 l] 2 ]]]]]]]]] 11r (1 1 r )(1 1 r t 11 ) 5 Kt11 . Dividing the above equation by Lt 11 and letting s t ;St /Lt11 yields: t

(1 2 p )G(h t , Ht , gt )w t11 1 t t 11 t (1 2 h t )(1 2 p )w t 1 t t 2 l 2 ]]]]]]]]] r (1 1 rt 11 ) r s t 5 ]] ]]]]]]]]]]]]]]]]] 11r (1 2 h t 11 ) 1 G(h t , Ht , gt ) 5 k t11 .

(9)

Recall that Lt 5(12h t )1G(h t 21 , Ht 21 , gt 21 ). Eq. (9) indicates that savings in the current period must be equal to the physical capital in the next period. In the steady-state equilibrium, all the endogenous variables are invariant over time, i.e. w t 11 5w t 5w, r t 11 5r t 5r, k t 11 5k t 5k, h t 11 5h t 5h, Ht11 5Ht 5H, t 1 t t 21 2 t t11 5t and s t 11 5s t 5s. The steady-state equilibrium can t11 5 t t 5 t , t t 11 5 t t be characterized by the following equations: H 5 G(h, H, g) 5 (1 2 d )H 1 P(h, g) 11

(10)

The assumption ≠s t / ≠r t 11 $0 is common in the literature [see, for example, Ihori, 1991; Lin, 1994].

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1 1 r 5 f 9(k)

(11)

w 5 f(k) 2 f 9(k)k

(12)

1 1 r 5 ≠G(h, H, g) / ≠h

(13)

g 1 z 1 t 1 1 t 2 5 (1 2 h)p w 1 G(h, H, g)wp 1 l

(14)

r (1 2 h)(1 2 p )w 1 t 1 2 l 2 [(1 2 p )G(h, H, g)w 1 t 2 ] /r (1 1 r) ]] ]]]]]]]]]]]]]]]]]] 5 k. 11r (1 2 h) 1 G(h, H, g) (15) Eqs. (10)–(15) are steady-state versions of Eqs. (1), (3), (4), (7)–(9), respectively.

3. Comparative steady-state analyses This section examines the effect of labor income taxation on human capital accumulation. The following tax policies concerning different uses of the tax revenues will be considered: a policy where the tax revenues are rebated to the tax payers (called ‘‘the compensated tax policy’’) and a policy where the tax revenues are consumed by the government (called ‘‘the tax-spend policy’’).

3.1. The compensated tax policy Under the compensated tax policy, the government taxes both the young and the old generations’ labor income, and then transfers the tax revenues back to individuals who pay the taxes. Thus, t 1 5(12h)p w, and t 2 5G(h, H, g)wp. Assume that government spending on human capital production, g, and government consumption, z, and lump-sum-taxes, l, are constant. Substituting t 1 5(12h)p w and t 2 5G(h, H, g)wp into Eq. (15) gives: (1 2 h)w 2 l 2 G(h, H, g)w /r (1 1 r) r ]]]]]]]]]] ]] 5 k. 11r (1 2 h) 1 G(h, H, g) Clearly, the labor income tax rate is absent from the above equation. It can also be seen that the labor income tax rate is absent from Eqs. (11)–(13) and g is constant in this case. Thus, dr / dp 50, which implies that dh / dp 50 and dG(h, H, g) / dp 50 [see Eqs. (13) and (10)]. The results can be summarized as follows: Proposition 1. With the tax revenues being transferred to the same individuals

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who pay the taxes, a change in the labor income tax rate has no effect on the real interest rate, and thus, has no effect on human capital accumulation. This result is consistent with the findings of Boskin (1975). Eaton and Rosen (1980) also derived a similar result in their model.12 Both Boskin (1975); Eaton and Rosen (1980) assumed that the tax revenues are consumed by the government. The intuition behind Proposition 1 is clear. In this case, total taxes (the costs to the tax payers) are equal to the total transfers (the total benefits to the tax payers) and the individual’s income and savings remain unchanged at the given interest rate. Since there is no pressure (upward or downward) on the capital market, the equilibrium real interest rate, and therefore, human capital will remain unaltered. Because the interest rate, the price of current goods in terms of future goods, remains unchanged, there is no substitution effect (substitution between current and future consumption or substitution between labor and accumulation of human capital). In the present model, the key to this neutrality result is that the tax revenue is rebated to the tax payer, a common assumption in the literature [see, for example, Diamond, 1970].

3.2. The tax-spend policy Under the tax-spend policy, the government taxes labor income of both young and old generations and then consumes all the tax revenues. Without loss of generality, assume that government spending on human capital is constant and equal to the lump-sum-taxes. Boskin (1975) analyzed a similar tax policy, but he focused on the case where the interest rate is exogenous. With the real interest rate being endogenous, we obtain the following proposition concerning the effect of labor taxation on human capital accumulation: Proposition 2. With the tax revenues being consumed by the government, an increase in the labor income tax rate will increase (decrease) the real interest rate, reduce ( increase) the time spent on human capital accumulation and reduce ( increase) the level of human capital if savings are negatively ( positively) related to the tax rate. Proof: We first examine the effect of labor income taxation on the real interest rate. Differentiating Eq. (15), with government spending on human capital production, g, transfers, t 1 and t 2 , and lump-sum taxes, l, being constant, yields:

12

See also Rosen (1995) for a discussion of the literature.

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t2 dh dw ≠G/≠h)w dh ≠G/≠H)w dH G(h, H, g) dw G(h, H, g)w 1 ]] 12p 2 ]w 1 (1 2 h) ] 2 ]] ] 2 ]] ] 2 ]] ] 1 ]]]] dr dr r (1 1 r) dr r (1 1 r) dr r (1 1 r) dr r (1 2 p ) r (1 1 r)2 ]] ]]]]]]]]]]]]]]]]]]]dr 11r (1 2 h) 1 G(h, H, g) G(h, H, g) 1 2 h 2 ]] r (1 1 r) r (1 2 p ) rw 2 ] ]]]]dp 2 ]] 1 1 r 1 2 h 1 G(h, H, g) 11r

F

GS

t2 ]] G(h, H, g)w 1 l2t dh ≠G dh ≠G dH 12p (1 2 h)w 2 ]] 2 ]]]] 2]1] ]1] ] 12p dr ≠h dr ≠H dr r (1 1 r) dk 3 ]]]]]]]]]]]]]]] dr 5 ]dr. 2 dr [(1 2 h) 1 G(h, H, g)] 1

D

(16)

Rearranging terms in Eq. (16) yields the effect of an increase in the labor income tax rate on the real interest rate: dr L ]5] dp V

(17)

where

r (1 2 h)w 2 G(h, H, g)w /r (1 1 r) L ; ]] ]]]]]]]]] 11r (1 2 h) 1 G(h, H, g) dk r (1 2 p ) V ; ] 2 ]] dr 11r

t2 dh dw (≠G/≠h)w dh (≠G/≠H)w dH G(h, H, g) dw G(h, H, g)w 1 ]] 12p 2 ]w 1 (1 2 h)] 2 ]] ] 2 ]] ] 2 ]] ] 1 ]]]] dr dr r (1 1 r) dr r (1 1 r) dr r (1 1 r) dr r (1 1 r)2 3 ]]]]]]]]]]]]]]]]]]] (1 2 h) 1 G(h, H, g)

F

GS

t2 l 2 t 1 G(h, H, g)w 1 ]] dh ≠G dh ≠G dH 12p (1 2 h)w 2 ]] 2 ]]]] 2]1] ]1] ] 12p dr ≠h dr ≠H dr r (1 2 p ) r (1 1 r) 1 ]] ]]]]]]]]]]]]]]] . 11r [(1 2 h) 1 G(h, H, g)] 2

D

The numerator is the change in savings, which can be either positive or negative. . The denominator is negative by the stability condition.13 Thus, dr / dp ] if 12h , . ]G(h, H, g) / r(11r). , Next, we examine the effect of labor income taxation on the human capital accumulation. Totally differentiating Eq. (13) and rearranging terms gives the effect of labor taxation on the time allocated towards human capital accumulation: 13

Detailed derivations of the stability condition are available from the author upon request. The stability condition simply requires that the quantity of excess funds demanded (investment minus savings) decreases as the interest rate increases, or the slope of the savings curve must be greater than the slope of the investment curve.

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dh / dp 5 d (dr / dp ) /(≠ 2 P / ≠h 2 ).

(18)

, . . Since ≠ 2 P / ≠h 2 ,0, dh / dp ]0 if dr / dp ]0 or 12h ]G(h, H, g) / r(11r). In the . , , steady state, H5P(h, g) /d [see Eq. (10)]. Differentiating H5P(h, g) /d with g being constant yields the effect of labor taxation on human capital: dH / dp 5 (1 /d )[≠P(h, g) / ≠h](dh / dp ). , Based on the assumption, ≠P(h, g) / ≠h.0, and the result in Eq. (18), dH / dp ]0 . , . if dh / dp ]0 or 12h ]G(h, H, g) /r (11r). Q.E.D. . , The intuition behind proposition 2 is as follows. When the labor income tax rate increases, savings may either decrease or increase, depending on the magnitude of the decrease in the first-period income and the first-period consumption. The first-period consumption depends on the lifetime income which is the sum of the first-period income, (12 p )(12h)w, the present discounted value of the secondperiod income, (12 p )G(h, H, g)w /(11r), and time preference, r. The composition of lifetime income does not affect consumption, but it does affect savings. If 12h.G(h, H, g) /r (11r), then the decrease in the first-period income will be larger than the decrease in the first-period consumption after the tax increase, and savings will decrease. If 12h,G(h, H, g) /r (11r), then the decrease in the first-period income will be smaller than the decrease in the first-period consumption after the tax increase, and savings will increase. If savings at the initial interest rate decreases after the tax increase, a shortage of funds at the initial interest rate will occur and the real interest rate will increase to clear the market.14 The increase in the real interest rate will reduce the present discounted value of future income, resulting in a decrease in the amount of time spent on accumulating human capital which will earn income in the future, and therefore, a decrease in human capital. If savings at the initial interest rate increases after the tax increase, a surplus of funds at the initial interest rate will occur and the real interest rate will decrease to clear the market. The decrease in the real interest rate will increase the present discounted value of future income, resulting in an increase in the amount of time allocated towards human capital production, and therefore, an increase in human capital. Under the fixed real interest rate, Boskin (1975); Eaton and Rosen (1980) showed that an increase in the labor income tax rate will not affect the human capital accumulation. The same result will be obtained in the present model if the interest rate is fixed. This can be seen by setting dr / dp 50 in Eq. (18). Thus, endogenizing the real interest rate alters the result from previous studies concerning the effect of labor income taxation on human capital accumulation. 14 Note that investment, which is equal to capital in the OG model, will be unaltered by the increase in the labor income tax rate at the initial interest rate. Of course, the equilibrium value of investment will be altered by the change in taxes.

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4. Concluding remarks In an overlapping generations model with alternative uses of labor tax revenues, this paper has analyzed the effect of labor income taxation on the individual’s incentive for human capital accumulation, and therefore, on the level of human capital. The major results are summarized in Propositions 1 and 2. It should be mentioned that, in this paper, labor and human capital are assumed to be perfectly substitutable and can be measured by effective labor. If labor and human capital are not perfect substitutes, labor, physical capital, as well as human capital will enter production function. With a flat tax on both labor income and human capital income, the result in Proposition 1 will remain unaltered and the result in Proposition 2 will hold with some additional assumptions. The present model may be extended in two interesting directions to further investigate the effect of labor income taxation on human capital accumulation. First, incorporate intergenerational aspects of human capital accumulation by assuming that the old generation invests on the young generation’s human capital free of charge, motivated by altruism. Second, introduce labor-education-leisure choice in the first period of life and labor-leisure choice in the second period of life by employing a more general utility function in which leisure is a variable. In both cases, the dynamic system will be characterized by higher-order difference equations.

Acknowledgements I am grateful to two anonymous referees and Sheng C. Hu for helpful comments.

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