Infrastructure and the Optimal Level of Public Debt

Transcription

1 Infrastructure and the Optimal Level of Public Debt Santanu Chatterjee University of Georgia Felix Rioja Georgia State University February 29, 2016 John Gibson Georgia State University Abstract We examine the role played by government investment in infrastructure in determining the optimal quantity of public debt in a heterogeneous agent economy with incomplete markets. Calibrating our model to the key aggregate and distributional moments of the U.S. economy, we show that the inclusion of public investment in this framework significantly alters the level of optimal public debt. In fact, this optimal level is now negative, underscoring a previously ignored channel through which government spending can affect the precautionary savings motive at the individual level. We also show how changes in the composition of government spending generate trade-offs for the household: while public investment tends to reduce the precautionary savings motive, other types of public spending may work in the opposite direction. Our results also indicate that previous work in this area, by ignoring public investment, may have significantly over-estimated the optimal level of public debt for the United States. Finally, we show that an increase in public investment in infrastructure is associated with a reduction in wealth inequality. Keywords: Infrastructure, public investment, heterogenous agents, public debt, welfare. JEL Classification: E2, E6, H3, H4, H6 Department of Economics, University of Georgia, Athens, GA 30602, USA. Telephone: schatt@uga.edu Department of Economics, Georgia State University, Atlanta, GA 30303, USA. Telephone: jgibson25@gsu.edu Department of Economics, Georgia State University, Atlanta, GA 30303, USA. Telephone: frioja@gsu.edu 1

2 1 Introduction What is the optimal amount of public debt? This is an important question that has received a lot of attention recently, especially after the global financial crisis of In a traditional representative agent macro model, the quantity of public debt is irrelevant for private decision making, as long as the intertemporal budget constraint of the government satisfies the transversality condition, thereby ensuring that the government does not run a ponzi scheme against the private sector. However, in a context where households receive idiosyncratic shocks that cannot be perfectly insured, public debt can have important consequences for private investment and labor supply and, therefore, it can affect their precautionary savings motive. The seminal paper by Aiyagari and McGrattan (1998) started a literature studying this question finding that the optimal quantity of debt in the US was about two-thirds of GDP, which was very close to the actual share of US public debt in They also found that there were only small welfare gains to moving from the existing level of debt at the time to the optimum. Subsequent refinements to that framework by Floden (2001), Desbonnet and Weitzenblum (2011), and Rohrs and Winter (2015) have found that the optimum quantity of debt may actually be negative; or in other words, that positive public savings may be optimal. However, an important issue in this context is the role played by the government in influencing economic activity at the individual level. While the existing literature has only considered unproductive public expenditures like government consumption and transfers, little attention has been paid to another potential channel through which the government can influence resource allocation decisions, namely public investment. Public investment, by generating a stock of infrastructure such as roads, transportation and telecommunications networks, power, ports airports, etc., can have important consequences for the productivity of private factors like labor and capital, and also for a households precautionary motive for savings. A large body of literature has documented its importance, not only for an economy s productive capacity and long-run growth (Aschauer, 1989; Barro, 1990; Glomm 2

3 and Ravikumar, 1994), but also for the distribution of wealth (Chatterjee and Turnovsky, 2012; Gibson and Rioja, 2015a, 2015b; Klenert et al., 2016). The total public infrastructure stock in the US is sizable, at about 60% of GDP and, given the recent concerns about its maintenance and upgrading, its inclusion is essential in a model of optimal debt. This is the central objective of this paper. We study how the optimal quantity of public debt is affected by the presence of government spending on public infrastructure in a heterogeneous agent economy with incomplete markets. As in the previous literature, individuals in our model are subject to idiosyncratic shocks to their productivity that cannot be fully insured. Thus, they undertake precautionary saving in order to self-insure, with government debt reinforcing this motive by relaxing their borrowing constraint. In this scenario, we introduce a stock of public infrastructure that is complementary to private capital and labor supply in the production function. In incorporating public investment into the model, we take into account the distinction between investment in the provision of new public capital and maintenance expenditures on its existing stock. In addition, we also consider other types of government spending such as transfers and government consumption. In essence, we have a more careful description of the composition of government spending than the previous literature on this issue. We calibrate our baseline model with infrastructure investment and maintenance to be consistent with the key aggregate and distributional characteristics of the U.S. economy. We also consider a model specification where infrastructure has been removed. This allows us to compare our baseline model s results with a model more aligned with the current literature. Our results indicate that the inclusion of public infrastructure can fundamentally alter the optimal quantity of public debt for the United States. As mentioned above, the benchmark result from the work of Aiyagari and McGrattan (1998) is that the optimal share of public debt is about 67 percent of US GDP, with very little welfare gains from reducing debt from this level. However, in a model with public infrastructure, we find that the optimal level is actually a large surplus for the government, around 140 percent of GDP. In other words, 3

4 the inclusion of infrastructure implies that it is optimal for the government to have positive savings and be a net creditor to the private sector. Further, to address issues related to the underlying income shock process assumed by Aiyagari and McGrattan (1998), we adopt the more recent strategy of Castaneda et al. (2003) and Rohrs and Winter (2015) and use the 2007 Survey of Consumer Finances to calibrate the income process. The basic insight from this exercise is that the inclusion of public capital, and its associated benefits for the return on capital and labor, tend to reduce the precautionary savings motive for households, causing them to sell their claims on the government. We also consider changes in the composition of government spending in favor of more public investment, which can come about by either reducing public consumption or government transfers. Here, we show that the effects of the composition of government spending on the optimal quantity of public debt depends critically on two opposing effects: on the one hand, public capital, by reducing the precautionary savings motive, tends to reduce the optimal level of public debt, while on the other the resource withdrawal effects of a reduction in other categories of public expenditures tend to increase the precautionary motive. The net effect on the optimum depends on the relative strength of these opposing influences. Finally, we show that increasing infrastructure investment leads to a reduction in wealth inequality. This paper is related to a growing body of work that attempts to quantify the optimal level of public debt for the United States. For example, Floden (2001) finds that the positive optimal debt found in Aiyagari and McGrattan (1998) depends on whether government transfers are below their optimal level. Further, while Aiyagari and McGrattan (1998) and Floden (2001) find that deviations from the optimal level do not lead to significant changes in the level of welfare, Desbonnet and Weitzenblum (2012) study the transitional dynamics of the welfare effects of getting to the optimal debt level, and find sizable effects. More recently, Rohrs and Winters (2015) use a more careful calibration to the wealth and earnings distribution data for the U.S. and find that the optimal level of public debt is negative, at about 80 percent of GDP. While our results are qualitatively consistent with theirs, we 4

5 show that the inclusion of public investment implies a much larger quantity of public savings at the optimum, at about 140 percent of GDP and a much larger change in welfare from moving away from this optimum. This suggests that previous studies, by neglecting the role of infrastructure investment, may have significantly over-estimated the optimal quantity of public debt and under-estimated the welfare effects associated with deviating from this optimum for the United States. The rest of the paper is organized as follows. Section 2 describes the analytical framework. Section 3 describes the calibration and computational procedure. Section 4 discusses the quantification of the optimal level of debt, while Section 5 considers some policy experiments related to the composition of government spending. Finally, Section 6 concludes. 2 Analytical Framework We consider an economy populated by a continuum of infinitely-lived households. The key feature of these households is that they face incomplete markets, as in Aiyagari (1994), i.e., they are unable to purchase perfect insurance against the realization of an idiosyncratic labor productivity shock. Therefore, though all households are identical ex-ante, their inability to insure against the labor productivity shock makes them heterogeneous ex-post. There is a government in the economy which spends tax revenues on two types of public goods-a public consumption good and the economy s stock of public infrastructure which, in turn, generates productivity spillovers for private production. The government can also sell or purchase bonds, resulting in a government debt or credit balance. 5

6 2.1 Households Households in this economy choose their rate of consumption, c, and time allocation between labor and leisure to maximize a per-period utility function given by: U(c, l) = [ c η (1 l) 1 η] 1 σ 1 σ (1) where l denotes the allocation of the household s unit time endowment to labor supply. Households are identical ex-ante, but receive idiosyncratic shocks to their labor productivity, ε, at the beginning of each period. While agents cannot perfectly insure against these fluctuations, they can partially insure against them by accumulating a stock of assets, a, that pay out a market-determined interest rate, r. These assets are comprise of private capital, which the households rent to the representative firm in the economy, and holdings of the government bond, b, such that a household s portfolio is given by a = k + b. Therefore, the presence of incomplete markets generate a precautionary motive for savings, causing households to accumulate wealth during periods of high productivity, in order to compensate for periods where adverse productivity shocks are realized. Over time, this mechanism leads to an endogenous distribution of wealth across households. In maximizing their per-period utility (1), households are constrained by an intertemporal budget constraint c + a [1 + (1 τ) r] a + (1 τ) wlε + T (2) where a denotes the household s stock of wealth in the next period, τ represents the income tax rate, w is the real wage rate, and T represents a lumpsum transfer, received from the government. We assume that the household-specific productivity shock, ε, follows a Markov process with a transition matrix given by π (ε ε). The household s maximization problem 6

7 can then be written as: V (a, ε) = max c,l,a U (c, l) + β π (ε ε) V (a, ε ) (3) ε subject to the intertemporal budget constraint (2), along with the restriction that a Firms A representative firm in this economy produces a flow of final output using a standard neoclassical technology and three inputs, namely private capital, K, rented from all households, labor purchased from households, L, and the stock of public infrastructure, K G, provided by the government: Y = (ΩK G ) φ K α L 1 α, φ (0, 1), α (0, 1) (4) In the production function (4), Ω represents the efficiency of the economy s existing stock of public infrastructure, and the term ΩK G is the efficiency-adjusted stock of public capital. As we discuss below, the level of efficiency of the stock of public capital is determined by government spending on maintenance. The representative firm is competitive and, in maximizing its flow of profits, takes all market prices and the stock of public capital as exogenously given. The firm s problem can be written as: max K,L (ΩK G) φ K α L 1 α wl (r + δ K ) K (5) where δ K is the rate of depreciation of private capital. The optimality conditions for the firm s problem pins down the equilibrium real wage and return on capital: w = (1 α) (ΩK G ) φ ( K L ) α (5a) r = α (ΩK G ) φ ( K L ) α 1 δ K (5b) 7

8 2.3 Government The government raises revenues by levying a tax on household income, and spends on transfer payments, a public consumption good and investment in the economy s stock of public capital. The government can also issue or purchase instantaneous one-period bonds (which are held by households). The government s flow budget constraint can be written as: b = (1 + r) b + G C + G I + T (τwlε + ra) (6) where b is the stock of public debt, G C is spending on the public consumption good, and G I is spending on public investment. Total spending on public investment is composed of two parts: G I = G N + G M (7) where G N denotes investment in new public capital, and G M represents expenditures to maintain the existing stock of public capital. We assume that the government spends a fraction g I of the economy s final output on new public investment, such that G N = g I Y, g I (0, 1) (7a) In addition, the government spends a proportion g M of the economy s output on the maintenance of the existing stock of public capital. These maintenance expenditures serve a dual purpose: they enhance the efficiency of the public capital stock and also reduce its depreciation rate over time: Ω = f(g M ) = f(g M Y ), g M (0, 1) (7b) δ G = 1 g ς M, ς > 0 (7c) 8

9 where the parameter ς captures the sensitivity of the depreciation rate for public capital to public maintenance expenditures. In other words, as ς 0, public capital would depreciate fully each period. The stock of public capital evolves according to K G = g I Y + (1 δ G (g M ))K G (8) Combining (2) with (7), we can derive the economy s aggregate market-clearing condition: k = (1 + r) k + wlε c G C G I (9) 2.4 Equilibrium A stationary equilibrium in this economy is characterized by a value function v (a, ε), agentspecific decision rules a (a, ε), l (a, ε) and c (a, ε), a time-invariant joint distribution of individual states F (a, ε), factor prices w and r, government policy variables g I, g M, τ, G C, and T, and the following market clearing conditions Labor market: L = ɛl(a, ɛ)f(a, ɛ)da ɛ a Asset market: A = a (a, ɛ)f(a, ɛ)da = K + B ɛ a Goods market: Y = c(a, ɛ)f(a, ɛ)da + I + G C + G I ɛ a (10a) (10b) (10c) where f(a, ɛ) is the density function associated with the distribution of individual states F (a, ɛ), K and B denote the economy-wide aggregate stocks of private capital and public debt, respectively, and I is aggregate private investment, given by I = K (1 δ K )K (11) 9

10 An important aspect of our analysis is the measurement of economic welfare from an underlying menu of government policies. We follow Floden (2001) and Rohrs and Winter (2015) in defining aggregate welfare as Γ = ɛ a V (a, ε) df (a, ε) (12) The intertemporal welfare measure in (12) can be interpreted as the welfare level of the average individual in the economy. In reporting welfare changes in subsequent sections, we use a compensating variation measure, which quantifies the units of consumption that need to be transferred between two steady-states (say, generated by two different policies or shocks), such that the average individual is indifferent between these steady states. This leads to the following compensating variation measure for welfare changes: [ ɛ a Γ = V ] 1 (ã, ε) df 1 (ã, ε) 1 η(1 σ) ɛ V 1 (13) a 0 (ã, ε) df 0 (ã, ε) where the subscripts 0 and 1 refer to the baseline (pre-shock) and new (post-shock) steady states. As in Rohrs and Winter (2015), if Γ > 0, the average agent would prefer being at the new equilibrium without compensation for the change. On the other hand, if Γ < 0, then Γ units of consumption is required to make the agent indifferent between the two steady states. This then becomes a measure of welfare loss across the two steady states. 3 Calibration The model is calibrated to be consistent with the long-run moments for the U.S. economy. To understand better the role played by public infrastructure, we compare our benchmark specification with infrastructure to a specification where infrastructure has been removed. 10

11 For the specification without infrastructure, the production function is given by: Y = ΦK α L 1 α, Φ > 0, α (0, 1) (14) where Φ denotes an exogenously specified aggregate level of productivity for the production sector. In this specification, government spending entails only the public consumption good G C and transfers, T. Table 1 describes the calibration of the benchmark model specification with public infrastructure. We set the parameter σ in the utility function (1) to 1.5, which yields an intertemporal elasticity of substitution of about 0.67, within the range of estimated values reviewed by Guvenen (2006). The relative share of consumption in the utility function, η, is set to 0.33 to match the aggregate share of time allocated to work, which is about 30 percent. The rate of time preference, β, is set at 0.95 in order to match a steady-state interest rate (or return on capital) of 3.5 percent. In the production function (4), we set the share of capital, α, to its standard value of 0.3, while the efficiency of public infrastructure, Ω, is set to 1 in the baseline case, indicating that the U.S. is at the global growth frontier. In other words, any deviation of Ω below 1 would denote an efficiency level for public infrastructure that is below the frontier. The depreciation rate for private capital and infrastructure are set at 8.9 and 4.4 percent, respectively, to target an aggregate capital-output ratio of The output elasticity of public infrastructure is set at 0.14, consistent with the findings of Bom and Ligthart (2014). With respect to the government policy parameters, we set the public investment parameters g I and g M to 1.2 percent each, such that total public investment (including new investment and maintenance) equal 2.4 percent of GDP, which is consistent with corresponding estimates from the Congressional Budget Office. Government transfers, T, are set to 8.2 percent of GDP, following Trabandt and Uhlig (2011). Finally, government consumption expenditures are set to 19.3 percent of GDP, so that total government spending equals about 30 percent of GDP in the steady state, consistent with the corresponding 1 We define the aggregate capital-output ratio as: (K + K G )/Y 11

12 long-run average for the U.S. economy. We set the public debt-to-gdp ratio, B/Y, to equal 0.67, which is the optimal level computed by Aiyagari and McGrattan (1998), in their study of public debt in the United States. Following Rohrs and Winter (2015), we assume that households can borrow up to 30 percent of output produced in the steady state equilibrium. As Rohrs and Winter (2015) report, this borrowing limit matches the share of households with zero or negative financial assets in the 2007 Survey of Consumer Finances in the U.S. Finally, we allow the income tax rate, τ, to adjust to satisfy the government budget constraint (6). In the alternative model specification without public capital, as characterized by the production function (14), we set the TFP parameter, Φ, to ensure that this specification yields a productivity index that matches (ΩK G ) φ in the baseline specification with public capital; See eq. (4). We also set the public debt-gdp ratio to 0.67, as in our baseline specification. This enables us to isolate the role played by public infrastructure in influencing the optimal quantity of public debt. Since there is no government spending on infrastructure in this alternative specification, we increase the share of transfers to 10.6 percent of GDP, in order to target the aggregate share of government spending of 30 percent in our baseline model. In other words, while total government spending is identical across the two specifications, its internal composition is quite different. The question we ask here is: what are the optimum shares of public debt in these two specifications? 3.1 Income Shock Process The vector of productivity shocks (ε) and the corresponding transition matrix π are calibrated to ensure that the distribution of net financial assets (wealth) in our model is consistent with its counterpart in the 2007 Survey of Consumer Finances. Our approach follows previous work by Castaneda et al. (2003), Abraham and Carceles-Poverda (2010), and Rohrs and Winter (2015). Given that households in our model have a precautionary savings motive due to the realization of idiosyncratic shocks, we calculate net financial assets for households 12

13 by excluding longer term investments such as property, vehicles, business ownership, residential mortgages, and automobile loans. Table 2 shows the distribution of net financial assets from the 2007 SCF: the top 20 percent of households hold more than 90 percent of net financial assets, while the bottom 40 percent s share is about 10 percent. The wealth Gini coefficient for this distribution is 0.9, indicating a highly unequal distribution of wealth in the U.S. economy. We assume that the vector of productivity realizations is given by four productivity states: s = [ɛ 1, ɛ 2, ɛ 3, ɛ 4 ] Following Heer and Trede (2003), we normalize the average productivity across all four quartiles to one. Using the 2007 SCF data, we find the following for the vector of productivity shocks and the corresponding transition matrix: 2 s = [0.055, 0.551, 1.195, 7.351] π = Table 2 illustrates the distribution of wealth (net financial assets) implied by our model s calibration, for both the specifications with and without public capital. As can be seen, both model specifications do a good job in matching the wealth distribution in the data, especially for the top two and bottom quintiles. The implied wealth Gini for both specifications is around 0.81, consistent with the high level of inequality seen in the data. 2 In the current draft we simply set s and π based on Rohrs and Winter (2015) and find a strong match between the empirical wealth distribution and our model generated wealth distribution. We are currently in the process of updating our calibration to include income and wealth data from the 2013 SCF. 13

14 4 The Optimal Level of Public Debt In this section, we ask the following question: what is the optimal quantity of public debt for the U.S. economy? More specifically, how does the presence of government investment in public capital affect the optimal quantity of public debt? To examine this issue, Figure 1 compares the stationary steady-state equilibria for our two model specifications, namely with public capital (red line) and without (black line), as a function of the underlying share of public debt in GDP. As can be seen from Figure 1, the optimum quantity of public debt differs dramatically depending on the inclusion or exclusion of public capital in the model specification. The model without public capital is essentially similar to the one considered by Aiyagari and McGrattan (1998), modified by the income shock process as in Castaneda et al. (2003). Consistent with Aiyagari and McGrattan (1998), we find that the optimal level of public debt is about two-thirds of GDP which, in turn, is the historical long-run average for the U.S. economy. In sharp contrast, the model specification with public capital implies a very different level for the welfare-maximizing level of public debt: in this case, the optimal share of public debt is actually a surplus of about 140 percent of GDP. In other words, the provision of a productive public good like infrastructure leads to the government accumulating assets to maximize aggregate welfare, in sharp contrast to the case without public capital, where welfare maximization requires a stock of net liabilities (debt). This is an important result, suggesting that by not including infrastructure in the model specification, previous studies on this issue may have over-estimated the optimal level of public debt by a significant amount. Further, we also note that the welfare function implied by the model without public capital is very flat around the optimum, indicating that reducing public debt from this level does not lead to significant welfare gains for the economy. On the other hand, the welfare function for the model with public capital is much steeper around the optimum, indicating that the welfare loss from reducing the net public surplus from the optimum level is non-trivial. To understand better the contrast between the implications of the two model specifica- 14

15 tions, we focus on the steady-state comparison between the economy s key macroeconomic aggregates, such as output, hours worked, and private capital. As shown in Figure 1, the presence of public capital leads to a higher stock of private capital and aggregate hours worked relative to the model without public capital. As such, aggregate output is also higher. This happens because of the productivity-enhancing role of public capital: it raises both the marginal product of labor and capital, enabling the agent to increase the flow of final output. The higher output increases tax revenues for the government, thus enabling it to reduce its debt liabilities to the private sector. As the government reduces the level of public debt, it further crowds in private capital which, in turn, feeds back into higher output. This can be easily seen in Figure 1: the lower is public debt, the larger is the gap between the flow of aggregate output between the two model specifications. The higher output enables the agent to increase consumption, thereby increasing welfare. In other words, in the presence of public capital, the government can raise aggregate welfare by reducing the quantity of public debt. As Figure 1 shows, this leads the government to accumulate assets and run a surplus, until diminishing returns to public capital set in, leading to the optimum. The intuition behind the dramatically different levels of optimal public debt across the two specifications can be explained as follows. In the specification without public capital, the interpretation of the Aiyagari and McGrattan (1998) result holds: increasing public debt relaxes the borrowing constraint for households around the borrowing limit, allowing them to respond to their precautionary savings motive and accumulate assets (claims against the government). Further, positive levels of public debt, by crowding out private savings, skews the composition of aggregate savings towards claims against the government. Consequently, the optimal level of public debt is positive. By contrast, when the government provides a productive public good like infrastructure, it acts as a complement to private factors in the production function, thereby raising the return to private capital and labor. Consequently, this reduces the precautionary savings motive for households, allowing them to sell their claims on the government. This causes households to be net debtors and the government to 15

16 be a net creditor to the private sector at the optimum. From a distributional standpoint, the inclusion of public capital leads to a larger increase in hours worked than in private investment relative to the specification without public capital. As such, the gap in labor income (the real wage rate) between the two model specifications also tends to be larger the lower is the level of public debt. Facing idiosyncratic shocks, households in the model specification with public capital therefore tend to have more insurance from wage earnings and savings. This leads to a more equal distribution of wealth relative to that implied by the model without public capital. 5 Policy Experiments In this section we consider two counterfactual policy experiments, and then compare the steady-state outcomes as a function of the share of public debt. Specifically, we increase new investment in public capital, g I, from its baseline value by 1 percentage point. To satisfy the government budget constraint, we examine two financing scenarios, where the increase in g I is financed by (i) reducing government consumption, G C, and (ii) reducing transfers, T. In other words, we are interested in analyzing the consequences of a change in the composition of government spending in favor of public investment. Note that in doing so, we keep total government spending at its baseline level of approximately 30 percent of GDP. Figures 2 and 3 illustrate the steady-state changes from these two policies, respectively, with the black line representing the case of an increase in public investment and the red line denoting the baseline steady state equilibrium, corresponding to Table 1 and Figure Increase in Public Investment by Reducing Public Consumption Figure 2 illustrates the steady-state consequences of increasing government investment in public capital by diverting resources away from public consumption. At the outset, given 16

17 that government consumption enters the government budget constraint as a lump-sum expenditure, its reduction in favor of more public investment has a level effect on the economy. Aggregate output, capital stock, and the real wage rate are higher, as the higher public capital stock increases the productivity of the private factors. Aggregate hours do not change much from this policy, mainly because the lower government consumption tends to crowd in private investment, reducing the marginal utility of wealth, and causing the agent to reduce labor supply. On the other hand, the higher level of government investment tends to raise labor supply by raising the marginal product of labor. In equilibrium, these two effects tend to offset each other. Further, the lower is the share of public debt, the more equal is the distribution of wealth from an increase in public investment. In terms of the welfare consequences of this policy as a function of public debt, we see that the optimum share of debt is still a surplus as in our baseline case, and remains more or less unaffected by this change in the composition of government spending. The intuition here is that the reduction in government consumption is an aggregate withdrawal of resources, and therefore does not affect the individual household s precautionary savings motive. As a result, the household has no incentive to change its net asset position, relative to the government. However, the fact that the lower level of government consumption leads to a higher level of government investment and its associated productivity benefits, leads to a larger welfare gain at the optimum. 5.2 Increase in Public Investment by Reducing Transfers Figure 3 plots the steady-state responses for an increase in public investment that is financed by a reduction in government transfers to households. The aggregate effects are similar to those in Figure 2, with output, capital, and the real wage being higher with the increase in government investment. Aggregate hours worked now increases, in contrast to the previous case. This is because a reduction of transfers to households represents a resource withdrawal effect at the individual level, which increases the marginal utility of wealth, leading the 17

18 household to increase labor supply. This is further reinforced by the higher return on labor generated by the increase in public investment. Interestingly, the increase in public investment financed by a reduction in transfers implies a welfare-maximizing level of public debt that is higher than that obtained in our baseline scenario. In other words, increasing public investment from the baseline case requires the government to lower its net surplus in order to maximize aggregate welfare. This happens because of two offsetting effects on the household s precautionary savings motive: on the one hand, the higher level of public investment reduces the precautionary savings motive for households, causing them to sell their claims on the government. On the other, the reduction in transfers is a resource withdrawal from households, and this increases their precautionary savings motive, causing them to accumulate more claims on the government. Over all, the second effect dominates the first, leading to a decline in the public surplus at the welfare-maximizing point. For the distribution of wealth, we find that the higher level of public investment tends to lower wealth inequality, with this effect becoming stronger the lower the share of public debt. 6 Conclusions In this paper, we have revisited an important policy issue that has recently received a lot of attention, namely the optimal share of public debt in an economy populated by heterogeneous agents. Previous studies, starting with the seminal work of Aiyagari and McGrattan (1998), have shown that this optimal share is positive, at least for the United States, possibly around two-thirds of GDP. More recent work has focused on the underlying income process that is used to calibrate these models to the data, showing that the Aiyagari-McGrattan result is indeed sensitive to the income process. One important issue this literature has neglected is the role of public investment in the context of heterogeneous agent models. Arguably, public investment, by generating productivity benefits for private capital and labor, can help reduce the precautionary savings motive in these models where households face idiosyncratic shocks 18

19 and incomplete insurance markets. On the other hand, how this investment is financed by the government can work in the opposite direction. This trade-off can have important consequences for the optimal quantity of public debt in the economy. By embedding public investment (and the stock of public capital it generates) into a standard heterogeneous agent economy with imperfect markets, we attempt to bridge an important gap in this literature. We calibrate the model to match the key aggregate and distributional moments of the United States, while also modeling carefully the composition of government spending. Here, we consider two types of public investment, on new public goods as well as maintenance of the existing stock of public capital. In addition, our model also incorporates government consumption and transfers. To understand better how our model relates to the previous literature, we compare our baseline specification to one without public capital. Further, we also adopt an income shock process used in the recent literature to avoid issues of robustness. Our results indicate that the inclusion of public capital fundamentally changes the optimal quantity of public debt for the U.S. economy. In fact, the optimal debt is now a surplus, indicating that aggregate welfare maximization requires the government to be a net lender to the private sector. We further investigate this result by examining changes in the composition of government spending. Specifically, we consider two cases where public investment increases, but via appropriate reductions in (i) government consumption and (ii) transfers. We find that an increase in public investment financed by a reduction in government consumption does not alter much the optimum quantity of public debt. On the other hand, diverting resources away from transfers into new public investment lowers the welfaremaximizing public surplus. These results are mainly driven by the trade-offs generated by a change in the composition of government spending for the household s precautionary savings motive. In summary, our paper contributes to the existing literature on the optimal quantity of public debt in two important ways. First, we show that previous studies, by neglecting the role of public investment and infrastructure, may have significantly over-estimated the 19

20 optimum quantity of debt. In fact, in the presence of public capital, this optimum quantity is a surplus. Second, we show how changes in the composition of government spending affects this optimal quantity, by generating trade-offs for the precautionary savings motive for households who face idiosyncratic shocks. Needless to say, there are several related issues that we do not yet consider, such as the internal composition of public spending between new investment and maintenance, transitional dynamics, and a richer tax structure that differentiates the tax rates on capital and labor income. These are important issues that we hope to address in future research. 20

21 Table 1: Model Parameters Parameter Value Target α Capital s Income Share β Rental Rate of Approximately 3.5% δ K Private Plus Public Capital-Output Ratio δ G Private Plus Public Capital-Output Ratio σ Std. Arrow-Pratt CRRA η Average Labor Supply in Steady State φ Elasticity of Y w.r.t Infrastructure g I Infrastructure Investment-GDP Ratio g M Infrastructure Maintenance-GDP Ratio Ω Efficiency of U.S. Infrastructure Table 2: Baseline Model vs. Data Aggregate Variables Wealth Distribution Data a Baseline Without KG Data b Baseline Without KG Interest Rate Q G C /Y Ratio Q T /Y Ratio Q C/Y Ratio Q K/Y Ratio Q a While we calibrate our model to target G C /Y, T /Y, and K/Y, we do not target C/Y. model s fit to the data in this dimension is an additional demonstration of its quality. Therefore, our b Wealth distribution data for the U.S. at the quintile level was taken from Rohrs and Winters (2015). 21

22 Table 3: Compare Model Specifications Baseline Without K G Add 1% to K G (T) Add 1% to K G (G) Government Budget Allocation g M g I G C T τ Aggregate Effects K G K N Y w r Distributional Effects Q Q Q Q Q

23 Figure 1: Model With K G Versus Model Without K G 23

24 Figure 2: Increase K G Investment and Reduce G by 1% of Output 24

25 Figure 3: Increase K G Investment and Reduce T by 1% of Output 25

26 References Abraham, A. & Carceles-Poverda, E., 2010, Endogenous Trading Constraints with Incomplete Asset Markets, Journal of Economic Theory, 145(3): Aiyagari, R. & McGrattan, E., 1998, The Optimum Quantity of Debt, Journal of Monetary Economics, 42: Aschauer D., 1989, Does Public Capital Crowd Out Private Capital? Journal of Monetary Economics, 24(2): Barro R., 1990, Government Spending in a Simple Model of Endogenous Growth, Journal of Political Economy, 98(5): S Bom P. R. & Ligthart J. E., 2014, What Have we Learned from Three Decades of Research on the Productivity of Public Capital? Journal of Economic Surveys, 28(5): Castaneda, A., Diaz-Giminenez, J., & Rios-Rull, J, 2003, Accounting for the U.S. Earnings and Wealth Inequality, Journal of Political Economy, 111(4): Chatterjee, S. & Turnovsky, S., 2012, Infrastructure and Inequality, European Economic Review, 56(8): Desbonnet, A., & Weitzenblum, T., 2012), Why Do Governments End Up with Debt? Short?Run Effects Matter. Economic inquiry, 50(4), Floden, M., 2001, The Effectiveness of Government Debt and Transfers as Insurance, Journal of Monetary Economics, 48: Gibson J., & Rioja, F., Public Infrastructure Maintenance and the Distribution of Wealth, Working paper.. Gibson J., & Rioja, F., A Bridge to Equality?: Aggregate and Distributional Effects of Investing in Infrastructure, Working paper. Glomm, G., & Ravikumar, B., Public Investment in Infrastructure in a Simply Growth Model, Journal of Economic Dynamics and Control, 18(6): Guvenen, F., 2006, Reconciling conflicting evidence on the elasticity of intertemporal substitution: A macroeconomic perspective. Journal of Monetary Economics, 53(7), Heer, B. & Trede, M., 2003, Efficiency and Distribution Effects of a Revenue-Neutral Income Tax Reform, Journal of Macroeconomics, 25: Klenert, D., Mattauch, L., Edenhofer, O., & Lessmann, K. 2014, Infrastructure and Inequality: Insights from Incorporating Key Economic Facts about Household Heterogeneity, CESifo Working Paper Series 4714, CESifo Group Munich. 26

27 Rohrs, S., & Winter, C., 2016, Reducing Government Debt in the Presence of Inequality, Working Paper. Trabandt, M., & Uhlig, H., 2011, The Laffer curve revisited. Journal of Monetary Economics, 58(4),