Redistribution and Human Capital Investment

Transcription

1 Redistribution and Human Capital Investment Michal Horvath Aarti Singh August 208 Very preliminary: please do not quote Abstract We use a heterogeneous-agent framework to examine the impact of optimal redistributive policies on human capital investment. In a model in which physical capital is available as an alternative to investment in education we study the decisions of households that differ ex ante in wealth and ability, and in productivity ex post. Their choices are also shaped by the insurance and incentive effects of public policies. Policies that redistribute initial endowments, public provision of education and progressive income taxation providing a radical redistribution of income are shown to generate significant welfare gains and a reduction in inequality. A suitable combination of redistributive measures is consistent with significantly more human capital investment by the less wealthy, and in particular for those with higher ability. Keywords: heterogeneous agents; borrowing constraints; inequality; redistribution; progressive taxes; education; consumption tax. JEL codes: D30; E20; H20; H40; J22; J24. Corresponding author: Department of Economics and Related Studies, University of York; michal.horvath@york.ac.uk. School of Economics, University of Sydney; aarti.singh@sydney.edu.au. We are grateful for the financial support from the Australian Research Council grant DE (Singh) and the Worldwide Universities Network Research Mobility Programme. The usual disclaimers apply.

2 Introduction We develop a heterogeneous-agent framework to assess the conditions under which and the extent to which increased education investment can be a part of dynamics that lead to a reduction in income and wealth inequality. Our interest in this topic is motivated by empirical evidence that suggests borrowing constraints are important impediments to human capital investment for many. First, we know from the empirical literature that increasing returns to schooling have not resulted in higher college enrollment rates. For example, the wage premium was 43 percent in 980 and it rose to 8 percent in 2005 (Goldin and Katz 2008). However, the percentage of population between age completing an undergraduate degree only increased from 23% to 29% (Aud et. al. 202, ). Carneiro and Heckman (2003) also find that the college participation rates have stagnated. At the same time however, the enrollment gaps between students from different family income groups widened (Ellwood and Kane, 2000 and Kane, 2007). Borrowing constraints impacting the decision to invest in education are thought to be a part of the answer (see Belley and Lochner, 2007 for a survey). A related literature documents a positive correlation between a child s education attainment and their parents. Two possible reasons are (i) genetics, traits, and other factors that are inherited and (ii) parents with higher education invest more in their children s education because they have higher wealth. We examine the latter in this paper as we study the impact of credit market imperfections in skill investment. DeGregorio (996) provides evidence that borrowing constraints affect human capital accumulation in both OECD and developing countries. More youth in the US are borrowing constrained today than were in the early 980s (Belley and Lochner 2007; Lochner and Monge-Naranjo 2008, Lovenheim 2008). Belley and Lochner (2007) point out that college attendance rate is positively correlated with both ability and family income. But in recent years,

3 the rise in college attendance among the bottom half of the ability distribution has entirely come from higher income parents/households. According to Keane and Wolpin (IER 200), even though borrowing constraints are tight, relaxing them doesn t change school attendance but instead makes them consume more and work less. Johnson (203) reached similar conclusions and argues that tuition subsidies are necessary to increase education levels, especially among the average-ability students. The objective of this paper is, therefore, to evaluate the impact of relaxing borrowing constraints on investment. We also examine the effectiveness of alternative policies that are designed to reduce directly or indirectly inequality such as education subsidies and progressive income taxation. Our work provides a qualitative and quantitative assessment of the extent to which they are associated with more human capital investment, particularly by the less well-off. To conduct our analysis, we build a dynamic general equilibrium model with two assets, physical capital and human capital/education. We study the decisions of households that differ ex ante in wealth and ability, and in productivity ex post. Their endogenous choices of consumption, labor and investment in the two assets are impacted by the insurance and incentive effects of public policies. Our paper is closely related to Benabou (2002), Heathcote et al. (206) who study policy design in frameworks with idiosyncratic uncertainty and borrowing constraints. Crucially, in their frameworks, financial market imperfections affecting human capital investment are not considered: individual skill investment depends only on expected returns to the investment which is subject to uninsurable idiosyncratic risk. We formally consider the role of inherited wealth heterogeneity and limits to borrowing to fund human capital investment (and indeed consumption) in a way that resembles Galor and Zeira (993). Using first a two-period model, we find that policies that redistribute initial endowments, public provision of education and progressive income taxation providing a radical redistribution of income in a two-period context generate significant welfare gains and a reduction in inequality. A 2

4 FIGURE. DISTRIBUTION OF ABILITY Notes: The horizontal axis plots the percentile score from 0-99 upto 3 decimal points. Therefore is on the horizontal axis. The total number of observations is suitable combination of redistributive measures is consistent with significantly more education investment by the less wealthy, and in particular by those with higher ability. The rest of this paper is organized as follows: Section 2 presents some empirical evidence supporting our calibration of heterogeneity. Section 3 provides intuition using a 2 period case and presents some indicative numerical results from this case. Section 4, yet to be completed, will present the quantitative analysis from an infinite-horizon version of the model. Section 5 concludes. 2 Evidence of heterogeneity Following the micro empirical literature, we examine the evidence on skill/ability heterogeneity and family income at the age of 6. We use the ability mea- Empirical studies, such as.., argue that children of wealthy parents have better cognitive skills and do better in these tests. While we think that it is an important consideration, we abstract from it in this paper and assume that ability is exogenous and not correlated with initial endowment. 3

5 FIGURE 2. DISTRIBUTION OF INITIAL ENDOWMENT (a) Data (b) Lognormal distribution Notes: The left panel is the histogram of the data on gross household income from parent in 997. The right panel plots 4500 draws from a lognormal distribution with mean -.4 and variance.2. sure of individuals between the age 9-5 in NLYS97. 2 Figure plots this distribution. In our calibration we therefore assume that ability is uniformly distributed. For the initial endowment, we use the gross household income from parent, see Figure 2. The mean and variance of the fitted lognormal distribution are -.4 and.2. The quartiles (in 00,000 USD) of this distribution are the following: 0.07, 0.26, 0.55,.26. Typically in the cross-sectional distribution, the variance of log income at age 25 is 0.05 and by the end of the work life, say 55, it would have increased to , so an increase of about So to calibrate the shocks such that we get this fanning of the income distribution in the 2-period model, we specify the variance of the shock process as σ ω = Note that the formula used to construct the ability variable, ASVAB MATH VERBAL SCORE PCT, is similar to AFQT score generated for the NLSY79 by the department of defense, this score is generated by the NLS staff. The score is a composite derived from tests of arithmetic reasoning, word knowledge, paragraph comprehension, and numerical operations. 3 See Fig 5 in Heathcote, Perri and Violante (200). 4

6 In this case then the expected value of z i t =. lnz i t = ω i t, ω i.i.d.n( σ ω /2, σ ω ) () 3 A two-period model In this section we describe a simple 2 period problem to gain some insight into the decision problem. The agent lives for two periods where he/she makes the decision to acquire skills, save and consume final good and leisure. The government policy variables are the income tax rate τ, consumption tax rate θ, education subsidy a 0, a and lump-sum taxes and transfers. 3. Production In this economy, total output is produced according to an aggregate neoclassical production function F(K, H) where K is the stock of aggregate capital, K = k i, H is total efficiency units given by H = s i ( l i ). In this economy we assume that capital depreciates at an exogenous rate δ (0, ). The profits of the firm are therefore given by the following equation Π = K α H α wh R k K (2) where w is the wage rate per efficiency unit and R k is the rental rate of physical capital. Therefore the firm equates the marginal product to the rental prices to get: and since profits are zero in equilibrium R K = αk α H α = αy K, (3) w = ( α)k α H α = ( α)y H (4) 5

7 3.2 Agents problem An individual i with ability κ i and initial wealth W i chooses the vector {c0 i, ei 0, ci, li, ki } to solve the following maximization problem taking as given the government policy variables. U i = u(c0 i, ei 0 ; κi, W0 i) + βe 0u(c i, li ), (5) and the budget constraints in period 0 and period are ( + θ 0 )c i 0 + ( a 0)e i 0 + ki = Wi 0 + T 0, (6) ( + θ )c i = τ[zi si w( li ) + R kk i ] τ + k i ( δ) + T, (7) where the stochastic return to labor income, returns from both raw labor and returns to skill, is given by: lnz i t = ρlnz i t + ωi t, ω i.i.d.n( σ ω /2, σ ω ), (8) k i k, (9) and s i = (κi (e + ( + a )e i 0 ))γ (0) with e as basic skill level inherited and µ = α. Let the gross income, which includes returns to labor, skill and capital, at date be denoted by y i = zi si w( li ) + R kk i, then the first term of the right hand side of equation (7) simplifies to τy τ. Therefore the tax is on both capital and labor income. 4 4 Instead of assuming the shocks to be permanent, we assume that they are highly persistent. For a two period case set z = 0. But in the many period case, we will assume it to be very persistent. Since consumption of most households is completely insured against transitory shocks, we ignore these shocks in our specification. In addition we proxy a random walk permanent shock with the one which is highly persistent. If tracking these different histories turns out to be difficult, then we may have to simplify things. 6

8 The agent draws from an initial ability distribution κ i i.i.d.u(0, ) and an initial wealth distribution W0 i i.i.d.ln(.4,.2). The ability impacts skill investment via utility cost of acquiring skills, for higher ability this cost is lower, and it also impacts returns to skill investment via the production technology. Acquiring skill however needs resources e 0 therefore initial endowment impacts investment in skill. In our specification agents are borrowing constrained; they can consume, save and invest in skills based on their initial endowment only. The period 0 and period and + η u i o = ci σ c 0 (κ i ) ei η 0 σ c + η. () u i = ci σ c + A li σ l. (2) σ c σ l With this utility function, the intertemporal elasticity of substitution of consumption is /σ c and the intertemporal elasticity of substitution of leisure is /σ l. 5 The timing in the model is the following. At date 0, given the government policy and the agent s realization of ability and wealth, he/she decides how much to consume, save in a risk-free asset and how much to allocate to skill acquisition. In period, after knowing the realized value of the labor income shock, he decides how much labor to supply and how much to consume. The first order conditions for the agent s problem are the following, where the subscripts to the period utility function indicate the partial deriva- 5 In our analysis we could also consider how sensitive the optimal government policies are to these intertemporal elasticities. Also the dynamics seem to be different when we have the following preferences (c φ l φ ) φ2 /( φ2). For example for initial wealth greater than, both investment in skills and time spent working is increasing in κ. 7

9 tive with respect to the argument of the utility function: a 0 u + (c 0, e 0, κ) u 2 (c 0, e 0, κ) = β θ 0 Eu + (c, l )[( τ)τy θ τ y s s e 0 ], (3) u + (c 0, e 0, κ) = β Eu θ 0 + (c, l )[( τ)τy θ τ y + ( δ)], (4) k and Since Eu 2 (c, l ) = Eu + (c, l )[( τ)τy τ y θ ]. (5) ( l ) and y ( l ) = (zi s )w, (6) y s = z i γs w( l s e i ) ( + a ) 0 (e + ( + a )e 0 ), (7) we can rewrite the first order conditions as y k = R k, (8) a 0 + θ 0 u (c 0, e 0, κ) u 2 (c 0, e 0, κ) = β E[u + (c, l )[( τ)τy θ τ z i γs w( l i ) ( + a ) (e + ( + a )e 0 ) ]], (9) u + (c 0, e 0, κ) = β E[u θ 0 + (c, l )[( τ)τy θ τ R k + ( δ)], (20) and Eu 2 (c, l ) = + θ E[u (c, l )( τ)τy τ zi w s ]. (2) 8

10 TABLE 2. CALIBRATION OF THE MODEL Values Other values Description Source β Discount rate α 0.3 Share of physical capital in total output Benabou 2002 µ 0.7 Share of labor and skills in total output Benabou 2002 η , 2 Elasticity of skill investment with respect to return HSV 206 γ 0.4/0.75 γλ = [0, 4] explain Benabou 2002 σ c.458 inverse of intertemporal elasticity of substitution of consumption Pijoan-Mas 2006 σ l inverse of intertemporal elasticity of substitution of leisure Pijoan-Mas 2006 A weight on leisure target (-l) to /3 σ ω , 0.03 variance of permanent income shock HVY 20 AER Notes: The table reports the calibrated values of the parameters of the model. According to equation (9), at the optimal level of skill, the marginal cost of acquiring skills, the left hand side of the equation, equals the present value of future marginal benefit. In a many period problem, the left hand side of the equation will not change, however the right hand side will have an additional terms as the initial investment in skills gives return over an individual s working life-span. For simplicity we have not assumed depreciation or appreciation of skills via experience. The second equation, equation (20), at the optimal level of physical capital, the marginal cost of acquiring additional capital equals the marginal benefit. Combining the first two equations will however also give us the no arbitrage condition between the two assets. The third equation, equation (2), is the standard intra-temporal condition where at the optimal level of leisure, the marginal cost of giving up leisure equals the marginal benefit from extra consumption. Using this maximization problem of the agent and the calibrated parameters in Table 2, in this section we examine how the agents endogenous decisions, in particular skill acquisition and leisure, e 0 and l respectively change in economies that differ in terms of risk and borrowing constraints faced by these agents. Since each period is 25 years, capital depreciates fully so δ =. We calibrate e = 0.00 such that 5 percent of the GDP is allocated to skill acquisition. 9

11 3.3 A representative agent economy In this benchmark economy, we abstract from heterogeneity and assume that each individual inherits the mean level of ability, initial wealth and z=. The rate of return to the factor inputs in the production is given by equations (3) and (4). The factor inputs are simply the aggregate of the individual supply of these inputs. The no arbitrage condition between the two assets, skill investment and investing in physical capital, has to be satisfied in equilibrium. The resource constraint of this economy at each date is given by W 0 = Y = 0 0 c0 i di + k i di + 0 c i di ( δ) 0 0 e0 i di (22) k i di (23) Note that here in this 2 period example, K 0 = K 2 = 0. In this benchmark complete markets economy, the key endogenous variables are c 0 = 0.53, c 0 = 0.42, e 0 = 0.07 and l = Heterogeneity and optimal government policies In the case where agents are heterogeneous in terms of ability, initial wealth and idiosyncratic income risk, we examine optimal government policies. We follow Benabou (2002) and Heathcote, Storesletten and Violante (206) and define net tax revenues at income level y as, T y = y τy τ (24) where τ determines the progressivity of the tax system and τy τ i is the disposable income of individual i. In this formulation, if τ > 0 the tax is progressive, τ < 0, its regressive and if τ = 0 then its flat and equals τ. The optimization problem of the fiscal authority is the following: max τ U(κ, W 0, z) df κ df w0 df z 0

12 subject to the individual s budget constraints in period 0 and period, equations (6) and (7), utility functions, () and (2), and the government budget constraint. 3.5 Results from the two-period model In this subsection we present the results from the two-period version of the model to highlight the key mechanics of the model in place. The two period version with wealth heterogeneity is best thought of as a world with incomplete markets that generates heterogeneity in wealth and incomes. This simple model aims to capture the effects on individual choice as well as the aggregate consequences of inherited wealth disparities. To this simple model, we also the add innate differences in ability that are perfectly observable and idiosyncratic income risk. Overall, such an environment provides a simple yet realistic setting to think about education investment decisions at the individual level and the design of policies to correct for the consequences of market failures. We find that as we add a realistic degree of initial wealth heterogeneity, differences in ability and income risk in the context of a two-period model, welfare falls considerably. As Table 3 shows, at the aggregate level, the average consumption in both periods is lower, investment in education falls and people work more in period. At the same time, we see savings in the form of physical capital going up on aggregate. Note that the welfare calculation is based on the total utility of all the agents in the economy. The inherited level of wealth heterogeneity (with a Gini of 0.92) gets replicated in the disparity in the level of savings in physical capital in period 0, and also gross and net income (consumption) inequality in period. 6 In the absence of any policy intervention, inherited wealth heterogeneity causes individuals with moderate wealth levels (the "middle class") to invest in education. This is particularly true for higher ability individuals 6 The latter holds quantitatively because there is little conceptual difference between wealth and income in the two-period setting.

13 TABLE 3. AGGREGATE OUTCOMES WITH NO POLICY INTERVENTION RA Heterogeneity Wealth Wealth, ability Wealth, ability, income C E K C L Welfare Gini k Gini y and c Notes: The aggregate variables are denoted with capital letters. whose investment far exceeds the levels obtained in a representative-agent setting. Individuals in fact face a portfolio choice problem here, and the optimal allocation is such that the poorest and the richest individuals do not invest in education at all. We also see from Figure 3 that poorer agents end up working considerably more relative to the complete markets benchmark, while the richest enjoy more leisure, l, living off their savings (and hence do not invest in education in the first place). We also see that agents use labour supply as a way of insuring against idiosyncratic uncertainty, as they tend to work more in lower productivity states Simple policy strategies When it comes to policy, we find that progressive taxation in the spirit of HSV does little to address the adverse welfare consequences of the presence of wealth and ability heterogeneity. As seen in Table 4A, an optimized tax system operating in period (i.e. during the working life of our households) raises welfare only marginally, although it lowers net income inequality in period. Intuitively, the high level of marginal (and average) income tax in pe- 2

14 FIGURE 3. INDIVIDUAL CHOICES AND NO POLICY INTERVENTION 3

15 TABLE 4 A. OUTCOMES WITH WITH OPTIMIZED POLICY INTERVENTION RA no policy opt τ=0.56 opt a 0 =-0.04 opt T 0 =0.84 opt a =34.5 C E K C L Welfare Gini k Gini y Gini c Notes: The outcomes displayed are for a model with heterogeneity in wealth and ability, and idiosyncratic uncertainty. riod reduces returns to all kinds of investment. Education investment as well as investment into physical capital drops relative to an environment without policy intervention. By contrast, agents consume more in period 0. The policy also discourages work in period. Note that the implied optimal degree of progressivity here is very high with τ at 0.56 with an average tax rate of 46 percent. Figure 4 confirms these insights into the limits of addressing the welfare consequences of inherited heterogeneity through a progressive tax system. We have considered a range of alternative policies that may affect investment in education. First, a potential subsidy to education investment in period 0 actually turned out to be optimally a small tax. This presumably addresses the inefficiency arising from "overinvestment" by some of the groups in the population. The results in general barely differ from the scenario without policy intervention. Next, we considered a consumption-tax-financed lump sum payment to all households in period 0. Table 4A indicates that such a policy generates large welfare gains as well as a reduction in inequality in income and consumption in period. The tax rate under optimal policy exceeds 200 percent and the policy finances a lump-sum transfer equivalent to.25 4

16 FIGURE 4. INDIVIDUAL CHOICES WITH OPTIMIZED τ Note: The figure reports results for ability level 3. The results for other ability levels are similar. 5

17 times the average inherited wealth in the population. The high consumption tax rate discourages consumption and encourages investment in period 0. Investment into education as well as physical capital increase. In period, agents enjoy more leisure and consume a lot more at the same time. Low ability, poor households now invest into physical capital which supports their consumption in period, particularly in low productivity states (in which they do not work at all). "Middle class" low ability households do not invest into education at all but this is more than offset by the investment activity of the higher ability households so that overall investment in education almost doubles relative to an environment with no policy intervention. This is documented in Figures 5A and 5B. In Figure 6, we consider an alternative policy which is a subsidy (paid in period ) that raises the returns to education investment, and is financed by a proportional income/consumption tax in period. Under this scenario, a consumption tax of around 24 percent finances a considerable productivity boost for those who invest into education. At the same time the high consumption tax discourages savings in period 0 for those who would otherwise save (i.e. the wealthy). The policy does little to address inequality in the economy, yet it raises welfare. It lifts the period- net income of many middle-wealth households but at the same time, it gives a significant boost to the earnings and hence consumption of the very wealth through a general equilibrium effect on interest rates. This arises as the ratio between human and physical capital increases considerably in this economy Combining policies We also investigated how a suitable combination of measures can get the economy closer to the world with a representative agent in terms of welfare. Having demonstrated the potential for generating welfare improvement of a consumption tax-financed transfer in period 0 and a highly progressive tax schedule in period, we can show that a suitable combination 6

18 FIGURE 5A. INDIVIDUAL DECISION FUNCTIONS WITH OPTIMIZED T 0 Note: The figure reports results for ability level. 7

19 FIGURE 5B. INDIVIDUAL DECISION FUNCTIONS WITH OPTIMIZED T 0 Note: The figure reports results for ability level 3. 8

20 FIGURE 6. INDIVIDUAL DECISION FUNCTIONS WITH OPTIMIZED a Note: The figure reports results for ability level 3. 9

21 of such measures can get the economy, in terms of welfare, very close to a world with no heterogeneity. Table 4B shows that the optimal policy mix involves a large degree of redistribution on both periods. High consumption taxation in period and high average income taxation in period result in low aggregate consumption levels. Investment physical capital is double of what one would see in a representative agent framework. While investment in education is at the level of the representative agent framework, it is lower than in the case of a T 0 subsidy only given the high marginal income taxation in period. That high marginal rate also discourages work effort, and so the welfare improvement in period comes mainly from much higher leisure. Higher savings and higher productivity support consumption in period, albeit it is still significantly lower than in an economy with no heterogeneity or heterogeneity and no policy intervention. Figures 7A and 7B reveal that the optimal policy mix pushes low ability people out of the market for education and labour completely. Increased savings in physical capital by the poor and middle classes, together with income redistribution within period, ensures those groups register consumption gains relative to the world with heterogeneity and no policy intervention Widening the policy toolkit We also explored two policy options that are commonly considered to be effective in improving access to education investment. First, we allowed borrowing in period. The natural borrowing limit in this economy is low. Nevertheless, the framework allows us to evaluate the case when households are allow to borrow around the third of the amount the representative agent would spend on education. Optimizing households, however, engage in very little borrowing. Only the poorest low ability households borrow. Moreover, the borrowing goes mainly towards funding extra consumption in period 0. Overall, the policy delivers virtually no improvement relative to the no 20

22 FIGURE 7A. INDIVIDUAL DECISION FUNCTIONS WITH OPTIMIZED τ AND T 0 Note: The figure reports results for ability level. 2

23 FIGURE 7B. INDIVIDUAL DECISION FUNCTIONS WITH OPTIMIZED τ AND T 0 Note: The figure reports results for ability level 3. 22

24 TABLE 4 B. OUTCOMES WITH WITH OPTIMIZED POLICY COMBINATION RA no policy opt τ=0.74 & T 0 =.99 C E K C L Welfare Gini k Gini y Gini c Notes: The outcomes displayed are for a model with heterogeneity in wealth and ability, and idiosyncratic uncertainty. policy intervention case (see Table 4C). We also considered a special case in our model in which e 0 is not chosen by households but for them directly by the state which then funds the provision through a consumption tax. 7 Given that information is perfect, we allow the public authority to condition education provision both on wealth and ability. On aggregate, the policy actually delivers less investment into education than under no policy intervention. This is because the government would want the upper middle class higher ability households to invest into capital rather than education which they otherwise would choose to invest heavily into. At the same time, poorer households of all ability receive significant provision of e 0 which somewhat declines in ability. Poorer households then have higher human capital and consumption levels in period which allows them to work less and consume more across all states of nature but particularly in high productivity states. Very wealthy households receive education, as they do work, although very little, in some states of the world. Their education also has private utility 7 Equation (9) is then no longer an equilibrium condition and e 0 does not enter the household budget constraint. 23

25 TABLE 4 C. WIDENING THE TOOLBOX RA no policy mink =-0.03 public e 0 public e 0 and T 0 =.02 C E K C L Welfare Gini k Gini y Gini c Notes: The outcomes displayed are for a model with heterogeneity in wealth and ability, and idiosyncratic uncertainty. implications. Figures 8A and 8B display the individual decision functions under this policy scenario. There are also general equilibrium consequences of government policy. More investment in capital reduces return for the relatively well of, and also their consumption in period. Overall, the policy that levies a consumption tax of around percent generates welfare gains and reduces inequality in period roughly to the extent an unconditional transfer T 0 or progressive taxation would accomplish. On the other hand, like progressive taxation and unlike the policy of T 0, it does little to address the problem of low consumption in period 0. This suggests the policy could do well in combination with an unconditional transfer which is what happens as documented in the last column of Table 4C. 4 Quantitative evaluation In this section, we will present the results from the quantitative analysis using the infinite-horizon version of the model. INCOMPLETE..to be added 24

26 FIGURE 8A. INDIVIDUAL DECISION FUNCTIONS WITH PUBLICLY PROVIDED e 0 Note: The figure reports results for ability level. 25

27 FIGURE 8B. INDIVIDUAL DECISION FUNCTIONS WITH PUBLICLY PROVIDED e 0 Note: The figure reports results for ability level 3. 26

28 5 Conclusion We studied the interaction between education investment by optimizing households and public policies. We showed how wealth heterogeneity causes significant welfare losses. It widens disparities in consumption and leisure. It also causes that households at the bottom end of the wealth distribution do not invest in education while households in the uppermiddle interval of the wealth spectrum invest a lot given the high returns to human capital. Appropriate public policy intervention can bring welfare in such an economy with heterogeneous agents closer to the representative agent benchmark. Progressive taxation of income combined with tax-financed general redistribution of endowments raises welfare considerably. It achieves that partly by promoting education investment as a basis for higher incomes among the less wealthy. Public provision of education achieves similar outcomes particularly if coupled with tax-financed re-shuffle of endowments. 27

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