Economic Growth and Fiscal Policy

Abstract

In the short-run macroeconomic model, investment is an important component of aggregate demand. Certainly, investment is a part of current effective demand. At the same time, it may increase production capacity by accumulating capital stock in the long run. This is an important function of public investment. It is also useful to investigate the impact of taxes on economic growth, since public investment is normally financed by taxes and an increase in taxes in the private sector depresses private investment. Thus, in this chapter, we investigate the supply-side effect of public investment and the impact of fiscal policy on long-run economic growth.

Appendices

Appendix A: Taxes on Capital Accumulation and Economic Growth

1.1 A1 Introduction

There are two types of capital from the viewpoint of origin; life cycle capital (capital accumulated from life cycle behavior) and transfer capital (capital derived from intergenerational transfers ). We observe a large amount of intergenerational transfers (educational investment and physical bequests ) in the real economy (see Kotlikoff and Summers 1981). Hence, it is important to analyze the effect on economic growth of taxation on two types of capital accumulation.

It is generally believed that an increase in capital income taxes (i.e., taxation on capital accumulation) reduces economic growth. It should be noted that the effect on capital accumulation is not necessarily the same as the effect on the rate of economic growth. In order to explore this point, models of endogenous growth that explicitly distinguish transfer capital from life cycle capital are useful.

There have been several attempts to consider endogenous growth by using a framework of overlapping generations . Jones and Manuelli (1990) showed that a redistributive policy financed by income tax can be used to induce positive growth. Azariadis and Drazen (1990) presented models of endogenous growth in which the accumulation of human capital is subject to externalities. Buiter and Kletzer (1993) investigated international productivity growth differentials by incorporating human capital accumulation.

Caballe (1995) showed that lump sum intergenerational transfer policies are ineffective when altruistic bequests are fully operative. He then investigated the effect of several fiscal policy experiments for bequest-constrained economies and unconstrained ones.

In this advanced study, we formulate the human capital accumulation process in a different way so as to obtain clearer results with respect to the degree of externality. Namely, this appendix incorporates three types of tax on capital (a tax on life cycle physical capital income, a tax on human capital income, and a tax on transfer physical capital or bequests) into an endogenous growth model with an altruistic bequest motive. The analytical results depend upon whether bequests are operative or not.

When bequests are not operative and the externality effect of human capital is small, the laissez-faire growth rate may well be too high. An increase in a tax on human capital income (a wage income tax) may raise the rate of economic growth, while an increase in a tax on life cycle physical capital income (an interest income tax) will reduce the growth rate. If bequests are operative, the laissez-faire growth rate is too low. A tax on life cycle capital income will not affect the growth rate, while an increase in taxes on transfer capital income (a wage income tax and a bequest tax) will reduce the growth rate.

This advanced study is organized as follows. Section A2 presents an overlapping -generations model of endogenous growth. Section A3 compares the competitive laissez-faire growth rate with the efficient one. Section A4 investigates the effect on economic growth of taxation on capital accumulation and considers how to attain the first best solution. Finally, Sect. A5 concludes the appendix.

1.2 A2 The Endogenous Growth Model

1.2.1 A2.1 Technology

A general feature of standard models of endogenous growth is the presence of constant or increasing returns in physical capital and human capital. Firms act competitively and use a constant-returns-to-scale technology.

$$ {Y}_t=A{K}_t^{1-\alpha }{H}_t^{\alpha } $$

(5.A1)

where Y is output, K is physical capital, and H is human capital. A is a productivity parameter which is taken here to be multiplicative and to capture the idea of endogenous growth in accordance with Rebelo (1991).

1.2.2 A2.2 The Three-Period Overlapping-Generations Model

In order to make the point clear, consider a three-period overlapping-generations model similar to those of Batina (1987), Jones and Manuelli (1990), Caballe (1995), and Buiter and Kletzer (1993). The number of households of each generation, n, is normalized to one. In period t − 1, when the household of generation t is young, the parent of generation t − 1 can choose to spend private resources other than time on human capital formation of her or his child, ${B}_{t-1}$, and physical savings (bequests) for her or his child, ${M}_{t-1}$.

The stock of human capital used by generation t during period t, H _t , is assumed to be a sum of a function of transfer input, ${B}_{t-1}$, and the average level of human capital achieved by the prior generation, ${\widehat{H}}_{t-1}$.

$$ {\widehat{H}}_t=\left(1-\delta \right){H}_t+{\overline{H}}_t $$

(5.A2)

where $\delta =1-\frac{1}{n}$. ${\overline{H}}_t$ is the ratio of the others’ human capital to the total number of people. n is the total number of individuals of each generation. The first term reflects the effect of the parent’s own human capital on the average human capital and the second term reflects the effect of the others’ human capital on the average level. When $n\to \infty$, the parent would not recognize the externality effect of her or his own capital, and hence the externality effect of human capital is perfect. When n = 1, she or he considers her or his own capital and the average level as equivalent; the externality effect is absent. Thus, δ may be regarded as the degree of externality. This extra term, ${\widehat{H}}_{t-1}$, embodies a similar kind of externality as in Romer (1986), and reflects the fact that production is a social activity.

Thus, we have

$$ {H}_t={\widehat{H}}_{t-1}+{B}_{t-1}. $$

(5.A3)

All human capital is inherited either genetically or through educational expenditure B by parents. The externality effect in the accumulation of human capital is not fully considered by parents when they decide how much to invest in their children’s education.

During middle age, the household choice of generation t concerns how much to consume, c ¹ _t ; to save for old age, s _t ; to save for her or his child, M _t ; and to spend on the human capital formation of her or his child, B _t . The entire endowment of labor time services in efficiency units H _t is supplied inelastically in the labor market. Thus, wage income h _t H _t is obtained where h _t is the wage rate. In the last period of life (“old age” or “retirement”), households do not work or educate themselves, and consume ${c}_{t+1}^2$.

The government imposes taxes on capital accumulation and tax revenue is returned as a lump sum transfer to the same generation. This is a standard assumption of the differential incidence . Otherwise, the tax policy would include the intergenerational redistribution effect such as debt issuance or unfunded social security.

Thus, the middle-age budget constraint is given by

$$ \begin{array}{l}{c}_t^1+{s}_t+{B}_t+{M}_t+{\theta}_B{h}_t{H}_t+{\theta}_M\left(1+{r}_t\right){M}_{t-1}=\\ {}\kern0.6em {h}_t{H}_t+\left(1+{r}_t\right){M}_{t-1}+{R}_t^1.\end{array} $$

(5.A4.1)

Substituting (5.A3) into (5.A4.1), we have

$$ \begin{array}{l}{c}_t^1+{s}_t+{M}_t+{H}_{t+1}+{\theta}_B{h}_t{H}_t+{\theta}_M\left(1+{r}_t\right){M}_{t-1}=\\ {}\kern0.36em \left({\widehat{H}}_t+{h}_t{H}_t\right)+\left(1+{r}_t\right){M}_{t-1}+{R}_t^1.\end{array} $$

(5.A4.1′)

The old-age budget constraint is given by

$$ {c}_{t+1}^2+\tau {r}_{t+1}{s}_t=\left(1+{r}_{t+1}\right){s}_t+{R}_{t+1}^2, $$

(5.A4.2)

where θ _B is a tax on income from human capital (a wage income tax), θ _M is a tax on physical bequests , τ is a tax on income from life cycle physical capital (an interest income tax), R ¹ _t is a lump sum transfer to the young in period t, and R ² _t is a lump sum transfer to the old in period t.

The government budget constraints with respect to generation t for the middle-age period t and the old-age period t +1 are given respectively by

$$ {R}_t^1={\theta}_B{h}_t{H}_t+{\theta}_M\left(1+{r}_t\right){M}_{t-1}\kern0.24em \mathrm{and} $$

(5.A5.1)

$$ {R}_{t+1}^2=\tau {r}_{t+1}{s}_t. $$

(5.A5.2)

Taxes on human capital accumulation are represented by taxes on wage income, θ _B h _t H _t . Note that from Eq. (5.A2), ${H}_t={\widehat{H}}_t$ holds in the aggregate economy.

The feasibility condition in the aggregate economy is given by

$$ {c}_t^1+{c}_t^2+{K}_{t+1}+{H}_{t+1}={Y}_t+{K}_t+{H}_t. $$

(5.A6)

Physical capital accumulation is given by

$$ {s}_t+{M}_t={K}_{t+1}. $$

(5.A7)

Recall that both life cycle saving and bequests provide funds for physical capital accumulation in the aggregate economy. Note also that human capital accumulation is given by Eqs. (5.A2) and (5.A3). The rates of return on the two types of capital are given respectively by

$$ r=\partial Y/\partial K=A\left(1-\alpha \right){k}^{-\alpha}\kern0.24em \mathrm{and} $$

(5.A8.1)

$$ h=\left(Y-rK\right)/H=\partial Y/\partial H=A\alpha {k}^{1-\alpha } $$

(5.A8.2)

where k = K/H is the physical capital/human capital ratio.

1.2.3 A2.3 The Altruistic Bequest Motive

An individual born at time t − 1 consumes c ¹ _t in period t and ${c}_{t+1}^2$ in period t + 1, and derives utility from her or his own consumption. Thus,

$$u_t=log{c}_t^1+\epsilon log{c}_{t+1}^2,0<\epsilon <1\text{.}$$

(5.A9)

Here, ε reflects the private preference of old-age consumption or life cycle savings. For simplicity, we assume a log-linear form throughout this appendix. The qualitative results would be the same in a more general functional form.

In the altruism model, the parent cares about the welfare of her or his offspring. The parent’s utility function is given by

$$ {U}_t={u}_t+\rho {U}_{t+1}= \log {c}_t^1+\varepsilon \log {c}_{t+1}^2+\rho {U}_{t+1}. $$

(5.A10)

0 <ρ< 1. ρ reflects the parent’s concern for the child’s well - being.

1.3 A3 Economic Growth and Efficiency

1.3.1 A3.1 The First Best Solution

We first analyze the growth path that would be chosen by a central planner who maximizes an intertemporal social welfare function . The objective of the planner at time t is the same as that of the altruistic individual, the “head of the family,” living at time t. Since the planner does not discriminate between H _t and Ĥ _t , the maximization problem faced by the planner is

$$ Max\kern0.24em {\displaystyle {\sum}_{t=0}^{\infty }{\rho}^t{u}_t}\ \mathrm{subject}\ \mathrm{t}\mathrm{o}\ \mathrm{E}\mathrm{q}.\ \left(5.\mathrm{A}6\right) $$

Solving c ² _t in Eq. (5.A6) and substituting the objective function, we obtain the following first-order conditions for the planner’s optimization problem by calculating the derivatives with respect to c ¹ _t , K _t , H _t , respectively.

$$ 1/{c}_t^1=\varepsilon \left(1+{r}_{t+1}\right)/{c}_{t+1}^2, $$

(5.A11.1)

$$ 1/{c}_t^1=\rho \left(1+{r}_{t+1}\right)/{c}_{t+1}^1,\kern0.24em \mathrm{and} $$

(5.A11.2)

$$ {r}_t={h}_t $$

(5.A11.3)

together with the transversality condition,

$$ { \lim}_{t\to \infty }{\rho}^t{K}_t/{c}_t^1=0. $$

(5.A11.4)

Equations (5.A11.1, 5.A11.2, 5.A11.3, and 5.A11.4) imply that the economy moves right from the first period on a path of balanced growth. The optimal growth rate, γ*, is given by

$$ \gamma *=\rho \left(1+r*\right) $$

(5.A12)

where r* is given by

$$ r*=h*=A\alpha k{*}^{1-\alpha },\kern0.48em \mathrm{and}\kern0.24em k*=\alpha /\left(1-\alpha \right). $$

(5.A13)

1.3.2 A3.2 Optimizing Behavior in the Market Economy

An individual born at time t solves the following problem of maximization. She or he chooses s_t, H_t+1, and M_t, given ${\overline{H}}_{t+1}$ in Eq. (5.A2). Substituting Eqs. (5.A2), (5.A4.1′), and (5.A4.2) into (5.A10), we have

$$ \begin{array}{ll}{U}_t=& \log \left[{\widehat{H}}_t+\left(1-{\theta}_B\right){h}_t{H}_t+\left(1-{\theta}_M\right)\left(1+{r}_t\right){M}_{t-1}-{H}_{t+1}-{s}_t-{M}_t+{R}_t^1\right]\hfill \\ {}& +\kern0.36em \varepsilon \log \left[\left(1+\left(1-\tau \right){r}_{t+1}\right){s}_t+{R}_{t+1}^2\right]+\rho \left\{ \log \right[\left(1-\delta \right){H}_{t+1}\hfill \\ {}& +{\overline{H}}_{t+1}+\left(1-{\theta}_B\right){h}_{t+1}{H}_{t+1}+\left(1-{\theta}_M\right)\left(1+{r}_{t+1}\right){M}_t\hfill \\ {}& -{H}_{t+2}-{s}_{t+1}-{M}_{t+1}+{R}_{t+1}^1\Big]+\varepsilon \log \left[\left(1+\left(1-\tau \right){r}_{t+2}\right){s}_{t+1}+{R}_{t+2}^2\right]\hfill \\ {}& +\rho {U}_{t+2}\Big\}\hfill \end{array} $$

(5.A14)

The optimality conditions with respect to s_t, H_t+1, and M_t are respectively

$$ 1/{c}_t^1=\left[1+\left(1-\tau \right){r}_{t+1}\right]\varepsilon /{c}_{t+1}^2, $$

(5.A15.1)

$$ 1/{c}_t^1=\rho \left[1-\delta +\left(1-{\theta}_B\right){h}_{t+1}\right]/{c}_{t+1}^1,\;\mathrm{and} $$

(5.A15.2)

$$ 1/{c}_t^1\ge \rho \left(1-{\theta}_M\right)\left(1+{r}_{t+1}\right)/{c}_{t+1}^1\kern0.24em \mathrm{with}\ \mathrm{equality}\ \mathrm{if}\ {\mathrm{M}}_{\mathrm{t}+1}>0. $$

(5.A15.3)

s cannot be zero; otherwise, c² would be zero, which is inconsistent with optimizing behavior. H cannot be zero either; otherwise, Y would be zero, which is inconsistent with optimizing behavior. However, M could become zero. If the private marginal return of educational investment is higher than the private marginal return of bequests at M = 0, intergenerational transfer is operated only in the form of human capital investment.

1.3.3 A3.3 The Circumstance in Which Physical Bequests Are Zero

Suppose the government does not levy any taxes: $\tau ={\theta}_B={\theta}_M=0.$ If 1 − δ + h > 1 + r at M = 0, we have the corner solution where bequests are zero. From Eqs. (5.A4.2) and (5.A15.1), we have

$$ s={c}^1\varepsilon . $$

(5.A16)

Substituting Eq. (5.A16) into Eq. (5.A4.1′), we have

$$ {H}_{t+1}+\left[\frac{1}{\varepsilon }+1\right]{s}_t=\left(1+{h}_t\right){H}_t. $$

(5.A17)

However, from Eq. (5.A15.2) we have in the steady state

$$ {H}_{t+1}=\rho \left(1-\delta +{h}_t\right){H}_t. $$

(5.A18)

Hence, considering Eqs. (5.A7), (5.A17), and (5.A18), the steady-state physical capital/human capital ratio $\widehat{k}$ is uniquely given as a solution of (5.A19). Thus,

$$ 1+\left(\frac{1}{\varepsilon }+1\right)k=\frac{1+h}{\left(1+h-\delta \right)\rho }. $$

(5.A19)

The left-hand side of Eq. (5.A19) increases with k, while the right-hand side of Eq. (5.A19) decreases with k. When ε increases, the left-hand side decreases, so that $\widehat{k}$ increases. When ρ decreases, the right-hand side increases, so that $\widehat{k}$ increases.

However, considering Eqs. (5.A8.1) and (5.A8.2), 1 − δ + h > 1 + r at M = 0 if and only if

$$ A\alpha {\widehat{k}}^{-\alpha}\left[\widehat{k}-\frac{1-\alpha }{\alpha}\right]>\updelta $$

(5.A20)

or

$$ \widehat{k}>\tilde{k},\kern0.48em where\kern0.24em \tilde{k}\kern0.24em satisfies\;A\alpha {k}^{-\alpha}\left[k-\frac{1-\alpha }{\alpha}\right]=\delta . $$

(5.A21)

When there are less incentives to leave bequests , we may well have the corner solution of M = 0. When ε is larger and ρ is smaller, inequality is more likely (see Eq. (5.A21)).

The laissez-faire growth rate is given by

$$ {\gamma}_{M=0}=\rho \left(1-\delta +A\alpha {\widehat{k}}^{1-\alpha}\right) $$

(5.A22)

where $\widehat{k}$ is given by Eq. (5.A19). An increase in the intragenerational preference for life cycle capital ε raises the physical capital/human capital ratio $\widehat{k}$, leading to a higher rate of return on human capital and higher economic growth. An increase in the intergenerational preference ρ has two effects. It stimulates intergenerational transfer from the old to the young, inducing high growth. However, it reduces $\widehat{k}$ and the rate of return on human capital, h, depressing economic growth.

Considering Eqs. (5.A19) and (5.A22), we have

$$ \frac{\partial \gamma }{\partial \rho }=\left(1+h-\delta \right)\frac{\left(1+h-\delta \right)\left[\left(1+h\right)\left(1-\rho \right)+\rho \delta -\left(1-\alpha \right)h\right]}{\delta \left(1-\alpha \right)h+\left[\left(1+h\right)\left(1-\rho \right)+\rho \delta \right]\left(1+h-\delta \right)}. $$

(5.A23)

Thus, if $\frac{1+\alpha h}{1+h-\delta }>\rho$, then $\frac{\partial \gamma }{\partial \rho }>0$ (and vice versa). In other words, if α and δ are high, it is likely that $\frac{\partial \gamma }{\partial \rho }>0$. However, it should be stressed that $\frac{\partial \gamma }{\partial \rho }<0$ is also possible. In the bequest- constrained economy, an increase in the parent’s concern for the child’s welfare does not necessarily raise the growth rate.

Since 1 – δ + h > 1 + r, h > r. Hence, r < r* = h* < h. It is possible that 1 − δ + h > 1 + h*. In such a circumstance, ${\gamma}_{M=0}>\gamma *$: The laissez-faire growth rate in the constrained equilibrium is too high. If the externality effect is absent (δ = 0), 1 + h > 1 + h*, the laissez-faire growth rate is always too high.

The laissez-faire economy may not attain the first best solution because of two reasons. First, the externality effect in the accumulation of human capital is not considered by the parent. This means that the competitive growth rate becomes too low. Second, M_t cannot be negative because there is no institutional mechanism to enforce such a liability on future generations. Human capital is too little and the marginal return of human capital is too high, which means that the competitive growth rate becomes too high. When δ is lower, it is more likely that the second effect predominates and the laissez-faire growth rate is too high.

1.3.4 A3.4 The Circumstance in Which Physical Bequests Are Operative

When M > 0, Eqs. (5.A15.2) and (5.A15.3) have equality. Hence, we have

$$ 1-\updelta +\mathrm{h}=1+\mathrm{r}. $$

(5.A24)

k is given by $\tilde{k}$, which is defined by the following equation:

$$ A\ \alpha {k}^{-\alpha}\left[k,-,\frac{1-\alpha }{\alpha}\right]=\delta $$

(5.A25)

Thus, the unconstrained growth rate is given by

$$ {\gamma}_{M>0}=\rho \left(1-\delta +A\alpha {\tilde{k}}^{1-\alpha}\right)=\rho \left[1+A\left(1-\alpha \right){\tilde{k}}^{-\alpha}\right]. $$

(5.A26)

From Eq. (5.A25), $\tilde{k}$ is independent of ρ or ε. Equation (5.A26) shows that the life cycle saving motive ε does not affect the growth rate, while an increase in the transfer-saving motive ρ definitely raises the growth rate.

Since h > h* and r < r*, we always have

$$ {\gamma}_{M>0}<\gamma *. $$

When physical bequests are operative, the competitive economy could be different from the first best solution only because of the externality effect of human capital . Thus, the laissez-faire growth rate is always too low.

1.4 A4 Taxes and Economic Growth

1.4.1 A4.1 The Constrained Economy

We now consider the effect of taxes on capital accumulation in the bequest -constrained economy of M = 0. When taxes are incorporated, Eq. (5.A19) may be rewritten as

$$ 1+\left\{\frac{1+r}{\varepsilon \left[1+\left(1-\tau \right)r\right]}+1\right\}k=\frac{1+h}{\left[1+\left(1-{\theta}_B\right)h-\delta \right]\rho }. $$

(5.A19′)

Considering Eq. (5.A8.1), it is easy to find that the right-hand side of (5.A19′) increases with k, while the left-hand side of (5.A19′) decreases with k. Hence, as in Sect. A3.3, the steady-state physical capital/human capital ratio $\widehat{k}$ is uniquely determined.

In this instance, Eq. (5.A22) may be rewritten as

$$ {\gamma}_{M=0}=\rho \left[1-\delta +\left(1-{\theta}_B\right)A\alpha {\widehat{k}}^{1-\alpha}\right]. $$

(5.A22′)

An increase in the tax on life cycle capital income (an increase in the interest income tax), τ, reduces $\widehat{k}$ and hence depresses the growth rate.

However, the effect of an increase in the tax on income from human capital (an increase in the wage income tax), θ_B, on the growth rate is ambiguous. It directly reduces the growth rate, while it indirectly raises the growth rate by increasing $\widehat{k}$ and h. Namely, an increase in the wage income tax raises the physical capital/human capital ratio, and hence increases h. If this indirect effect predominates, an increase in the wage income tax raises the growth rate.

Finally, let us consider how to attain the first best solution by using capital taxes. The optimal levels of τ and θ_B are given respectively by

$$ \uptau =0\kern0.24em \mathrm{and} $$

(5.A27)

$$ 1-\delta +\left(1-{\theta}_B\right)A\alpha {\left(\frac{\alpha }{1-\alpha}\right)}^{1-\alpha }=1+A\alpha {\left(\frac{\alpha }{1-\alpha}\right)}^{1-\alpha }. $$

(5.A28)

From Eq. (5.A28), the optimal level of θ_B is negative so long as δ > 0. Further, in order to attain $k*=\widehat{k}$, an additional lump sum intergenerational transfer from the young to the old, such as debt issuance or unfunded social security, is also needed. Such a policy can substitute for negative bequests.

1.4.2 A4.2 The Unconstrained Circumstance

When M > 0, Eqs. (5.A15.2) and (5.A15.3) have equality. Hence, we have

$$ 1-\delta +\left(1-{\theta}_B\right)h=\left(1-{\theta}_M\right)\left(1+r\right). $$

(5.A29)

In this circumstance, $\widehat{k}$ is given by Eq. (5.A29); hence, the growth rate is given by

$$ {\gamma}_{M>0}=\rho \left[1-\delta +\left(1-{\theta}_B\right)A\alpha {\widehat{k}}^{1-\alpha}\right]=\rho \left(1-{\theta}_M\right)\left[1+A\left(1-\alpha \right){\widehat{k}}^{-\alpha}\right]. $$

(5.A26′)

An increase in θ _B raises $\widehat{k}$ and reduces r. Hence, from the second equality of (5.A26′), it reduces the growth rate. An increase in θ _M reduces $\widehat{k}$ and h. Hence, from the first equality of (5.A26′), it also reduces the growth rate. In other words, an increase in any tax on transfer capital definitely reduces the growth rate when bequests are operative. Equation (5.A26′) is independent of τ; the tax rate on life cycle capital income does not affect the growth rate.

The optimal level of θ_B is given by Eq. (5.A28), which is the same as in the constrained circumstance. Note that θ_M = τ = 0 at the first best solution. In this instance, market failure comes only from the externality effect of human capital . A subsidy for human capital accumulation raises the growth rate and can attain the first best solution.

1.5 A5 Conclusion

This appendix has incorporated the altruistic bequest motive into an endogenous growth model of overlapping generations . We have shown that the impact on the growth rate of taxes on capital accumulation differs depending upon whether bequests are operative or not. When bequests are zero, an increase in a tax on human capital accumulation may not reduce the rate of economic growth, while an increase in a tax on life cycle physical capital reduces the growth rate. If bequests are operative, a tax on life cycle capital accumulation does not affect the growth rate, while an increase in any tax on transfer capital (educational investment or bequests) reduces the growth rate. Our analysis has explored the paradoxical possibility that taxes on capital accumulation may not reduce the rate of economic growth in several instances.

Finally, in the bequest-constrained economy, the laissez-faire growth rate may be too high if the externality effect is small. A subsidy for human capital accumulation and a lump sum transfer from the young to the old can attain the first best solution. In the unconstrained economy, market failure comes only from the externality effect of human capital. A subsidy for human capital accumulation raises the growth rate and can attain the first best solution.

Appendix B: The Supply-Side Effect of Public Investment in Japan

2.1 B1 Earlier Studies

In this case study, we examine the supply-side effect of public investment in Japan. Whether public capital provision is efficient in Japan is a crucial question from a normative perspective. Some empirical studies have analyzed the productivity of public capital in Japan. In the 1990s, Iwamoto (1990) and Mitsui and Ota (1995) calculated the marginal productivity of public capital based on the estimated production function. They concluded that the level of public capital was considerably low in Japan until the early 1980s.

Ihori and Kondo (1998) investigated the effect of public investment on private consumption by estimating the consumption function from 1955 to 1996. They found that in the 1960s, public investment had a significant impact on private consumption; however, this impact decreased after 1980. The evidence suggests that the total level of public capital was not considerably low in the 1990s. Ihori and Kondo (1998) and Ihori and Kondo (2001) found that the causality relationship between public works and private consumption was significant during the entire sample period (1957–1994). Moreover, this causality was strong, and the impulse response of private consumption to public works was substantial during 1958–1975. However, both causality and the impulse response reduced subsequently.

Thus, the aggregate level of public capital might have been sufficient or considerably high in the last part of 1958–1975. As shown in Asako et al. (1994), if the allocation of public works is appropriately revised, then it can stimulate macroeconomic activities and enhance economic welfare.

Ihori and Kondo (2001) investigated the efficacy of public works for the Japanese economy. They investigated the productivity of disaggregated public capital goods by estimating the productivity of income related to public capital, or labor income, based on the aggregate production function approach. While not definitive because of limited data availability, their results suggest that the allocation of public works was not optimal in Japan. Namely, there still existed large differences among the marginal productivity levels of the various types of public capital. The infrastructures for railways, telephone networks, and postal services were not large enough until the early 1990s. Thus, if public works spending was reallocated to projects in order to improve economic efficiency, it could have stimulated private consumption and enhanced economic welfare in Japan.

To sum up, the supply-side effect of public investment has decreased in recent years. The aforementioned studies commonly conclude that public capital was productive, but its productivity has declined in recent years. In addition, see Aso and Nakamoto (2008) for a similar conclusion.

2.2 B2 Recent Studies

Recently, Miyazaki (2004, 2014) surveyed studies on the productivity effect of public investment in several fields. Among others, Hayashi (2003) and Hatano (2006) estimated the productivity effect of road capital in the Kyushu area, considering the network properties of transportation capital. Further, Nakazato (2001, 2003), Miyazaki (2004, 2014), and Hayashi (2010) estimated the productivity of road capital and its effect on the economic growth of several regions by dividing regions in accordance with the prefectural per capita GDP. Miyazaki (2004, 2014) empirically examined the supply-side effect of transportation-related public capital using contemporary econometric methods. In particular, he analyzed the effect in two areas: the Tokyo metropolitan area and other rural areas .

Most studies on the productivity effect of public investment in various fields use three approaches: (i) the estimation of production function; (ii) the regression of growth convergence; and (iii) growth accounting. In Japan, several studies have used the first two approaches to show the productivity effect of transportation-related public investment.

Table 5.B1 summarizes the main empirical results so far in Japan. The standard econometric approach is to use the panel data for 47 prefectures.

Table 5.B1 Studies on the productivity effect of transportation-related public investment

Some researchers point out that road investment expenditure in a rural area has negative spillover effects on the area in that it results in a concentration of the population. This is because firms are induced to move from the rural area to the Tokyo metropolitan area and/or some core cities in other areas. Such movements cause and/or increase inequality among regions. Namely, the accumulation of road capital increases productivity in urban areas , which are characterized by high concentrations of industry, while it does not raise productivity in rural areas, which are characterized by low concentrations of industry. Productivity in some rural areas could even reduce because newly accumulated road capital facilitates the easy movement of firms and workers to urban areas. In order to verify this concern, it is necessary to investigate how transportation capital has affected productivity in areas with different income levels and industry concentrations.

For this purpose, Miyazaki (2014)estimated the following production function:

$$ \begin{array}{l} \log {Y}_{it}={D}_i+{D}_t+\alpha \log {N}_{it}+\beta \log {K}_{it}+{\gamma}_1 \log {G}_{it}\\ {}\kern2.04em +{\gamma}_2{D}_{tokyo} \log {G}_{it}+{u}_{it}\end{array} $$

where u _it represents a random term and D _tokyo represents a dummy variable that takes the value of 1 for the Tokyo metropolitan area (Tokyo, Kanagawa, Saitama, and Chiba) and 0 for others. Since Miyazaki (2014) found the productivity-enhancing effect of road capital only for downtown Tokyo, he added a second dummy variable to capture the effect of concentration in downtown Tokyo. His estimation is based on the difference generalized method of moments (GMM) method, presented by Arellano and Bover (1995). In order to develop a dynamic model, he incorporated the first difference lag with respect to variables by using two models: the autoregressive distributed lag (ADL) model and the state-dependent dynamic model. The former incorporates the first difference into dependent and independent variables, and one-period lagged variables of production inputs; the latter focuses on the dependent variables that include the lagged independent variables. The estimation results are as follows.

• 1. ADL model. For either the Tokyo metropolitan dummy or the Tokyo downtown dummy, the coefficient of the current road capital stock is significantly negative, while that of the one-period lagged road capital stock is significantly positive. Note that the effect of inputs on productivity has a lag in the ADL model. We can include the effect of the lagged variable as a proxy of the productivity effect. Thus, we can say that road construction in the Tokyo area has a significantly positive effect on the overall economy.

• 2. State-dependent model (1). If a dummy is used for the Tokyo metropolitan area, we do not obtain a significant result. However, if a dummy is used for the Tokyo area, we have a significantly positive effect, irrespective of the length of the lag periods.

• 3. State-dependent model (2). The coefficient of road capital γ ₁ becomes significantly negative if the three-moment lagged instrumental variable is used. However, we do not obtain any significant results if the two-moment lagged instrumental variable is used. This suggests that road construction may not necessarily stimulate aggregate demand in regions other than the Tokyo metropolitan area.

To sum up, Miyazaki (2014) confirmed a large productivity effect of road capital accumulation in the Tokyo metropolitan area, especially the downtown Tokyo area. However, he did not obtain a definite result for many rural areas. Thus , road capital accumulation may even contribute to stagnation in some rural areas.

2.3 B3 Public Investment Management

2.3.1 B3.1 Constraints in Japan

This section discusses public investment management reforms in Japan. There are several constraints to efficient and effective public investment management. First, it must be stressed that the social infrastructure was intensively constructed during the high-growth period in Japan. This infrastructure is assumed to be rapidly deteriorating because it is 30–50 years old.

For instance, a comparison of the social infrastructure that is more than 50 years old today with that in the next 20 years reveals that the demand for roads and bridges will surge from approximately 8 % to 53 %. In addition, the ratio for river management facilities, such as drainage pump stations and water gates, will rise from approximately 23 % to 60 %; for sewer lines, it will increase from approximately 2 % to 19 %; and for harbor quays, it will grow from approximately 5 % to 53 %.

The Ministry of Land, Infrastructure, Transport, and Tourism (MLIT) White Paper (2011) has estimated that the total renewal cost of infrastructure for the 50 years from 2011 to 2061 is approximately 190 trillion yen. However, looking at the present fiscal scenario of Japan, it is estimated that even a portion of the total renewal cost (approximately 30 trillion yen or 16 % of the entire amount) will be difficult to accomplish. Hence, it is more important to renew the existing public capital appropriately than to construct new projects. If the existing public capital is not appropriately maintained, managed, and renewed because of a lack of funds, the malfunction of the infrastructure could negatively affect the economy and people’s lives. Moreover, the possibility of accidents or disasters due to deterioration could become a serious concern over time.

Japan faces several social constraints regarding the renewal of public capital. An important constraint is demographic. Since Japan is an aging society, the aging population, combined with low birth rates, implies that the population will decrease considerably. Since the benefit of public capital depends heavily upon the number of people who may use it, population decline would reduce the benefit of public capital in the long run. Thus, in principle, it is undesirable to construct new public projects when the population is declining.

Japan also faces many environmental issues and energy constraints, particularly after the awful Fukushima nuclear power plant accident in 2011. Further, with the national finances in deficit, public funds for public investment must be limited. In order to implement proper infrastructure maintenance, management, and renewal measures so as to meet the various demands of the present era, the government needs to achieve effective and efficient facility operations and management in a planned manner through comprehensive and strategic management.

2.3.2 B3.2 Public Investment Management Reform

Under the above circumstances, it is important to estimate accurately the size of existing infrastructures and their degrees of deterioration and renewal costs. At the same time, it is necessary to acquire accurate information on the future demands of a society that has a declining and aging population. In order to achieve this, efficient and effective public investment management reforms are needed. These should include planned and effective maintenance, management, renewal, disposition, utilization, exploitation, consolidation, and privatization . In particular, the following options should be regarded as important in Japan.

• 1. Routine management must be emphasized to enhance efficiency in daily cleaning, maintenance, repairs, and so on.

• 2. Management must be based on a long-term perspective. Total cost reduction can be realized through preventive maintenance based on a long-term perspective (e.g., life extension projects).

• 3. A small number of useful projects must be preferred to a large number of unwanted/non-essential projects. Under the significant direction of a strategic infrastructural operation known as “selection and intensification,” we need to evaluate individual management strategies and introduce innovative approaches that are different from those in the past. In order to achieve this, we must introduce new advanced technology, and review existing regulations and programs, to attain more efficient infrastructure management.

• 4. The major infrastructure management method implemented so far includes that of the designated administrator system. This system was introduced recently by local governments to reduce the cost of maintaining existing public capital.

• 5. Privatization is also an effective tool for cost reduction. With regard to road management, four highway- related public corporations in Japan were privatized in 2005. These corporations are making efforts to secure debt repayment by implementing highway business activities through the three Nippon Expressway Companies (East, Central, and West Nippon Expressway Companies) and the Japan Expressway Holding and Debt Repayment Agency. They are also employing diverse service provisions through efficient operations by applying the expertise of the private sector. Regarding airport management, the New Kansai International Airport (fully owned by the state) was established on April 1, 2012 under the Act on Integrated and Efficient Establishment and Management of Kansai International Airport and Osaka International Airport as a Unit, enacted in May 2011. Osaka International Airport, which was controlled by the national government, has been operated together with Kansai International Airport under a new company (the New Kansai International Airport) as a single unit from July 1, 2012.

2.3.3 B3.3 Strengthening Wide-Ranging Coordination

Considering the issue of rapid aging in Japan, it is usually expect ed that the share of social welfare expenditures in national spending will increase rapidly each year, while the share of public works expenditures will decline. Hence, raising public funds to finance public investment expenditures is severely limited. However, while the financial constraints on the government’s budget are aggravating, the household and firm sectors still hold huge financial assets. The household sector holds financial assets worth 1700 trillion yen in 2016. Among others, people who are 60 years old or above hold the highest share of cash and bank deposits (60 %).

In order to achieve sustainable growth by enhancing the vitality of Japan’s regions despite the extremely tight fiscal situation, it is indispensable for Japan to utilize the funds of the private sector. In this sense, Public-Private Partnerships (PPPs) and Private Finance Initiatives (PFIs) are useful ways to promote public-private coordination. Namely, in addition to the projects executed by the national government, the subsidized projects of local public authorities, and local independent projects, all of which have constituted the major implementation methods of public works, the government must develop other methods such as PPPs and PFIs so that private funding, knowledge, and human resources in the private sector are utilized. PPP/PFI projects can mainly include comprehensive private consignment, the designated administrator system, the PFI method, and the concession system.

With the aim of expanding projects based on the PFI system, the MLIT has invited PPP projects from local public authorities and the private sector since 2011. The purpose is to develop a new PPP/PFI system and to promote the formation of specific projects. The targeted categories include the following three functions:

• 1. Pioneering PPP support projects;

• 2. The promotion of PPP projects; and

• 3. Encouraging PPP projects for earthquake disaster reconstruction.

A total of 144 applications have been collected.

Finally, it is also useful to develop business operators such as nonprofit organizations (NPOs) that engage in activities of public interest for a community. They can usually raise only a limited amount of money because they rely on official support and/or donations. Thus, more private funds should be allocated to NPO activities. It would be useful to have a “voluntary funds” scheme in which private funds can be utilized to provide services of a public nature.

As part of such a scheme, an entity called a “community fund” must be introduced to serve as a financial intermediary and coordinator for those companies and individuals who work for the community and those who want to provide financial assistance in some way. The purpose here is to raise funds from voluntary community citizens, corporations, local governments, and so on, and to invest these funds in business projects of public interest that can positively contribute to the community. By establishing such a “flow-of-funds” scheme through these private institutions, funds from a community will become available to use within that community.

To sum up, it is important to consider the following options.

• 1. Japan should promote various public capital accumulation and management operations such as the further selection a nd intensification of public works, rationalization, the consolidation of facilities, disposal, utilization, and exploitation to suit regional needs.

• 2. Japan should further utilize private funds, skills, and expertise in the public sector by promoting PPP , PFI , etc.

• 3. Japan should support and foster new public investment activities and a system of self-help and mutual assistance through the private sector by developing NPOs, etc.

2.3.4 B3.4 Cost-Benefit Analysis

Needless to say, the role of public works is to secure safety and comfort. It is also important to secure the efficiency and transparency of public investment projects. By improving pleasant living standards and preserving the natural environment, we can vitalize local communities and the overall economy in modern society. In order to improve the efficiency of public works, the government must launch and/or continue only those projects whose necessity is confirmed and discontinue those whose necessity has diminished or where progress is inadequate. It is also useful to disclose the evaluation methods and results to ensure the transparency of public works.

Regarding the methods of evaluation, the government should conduct comprehensive evaluations, including cost-effective analysis. It should thus check whether a new project deserves to be launched and decide whether an existing project should be continued or discontinued after considering all the relevant issues comprehensively. These evaluations should include those aspects of public works that are hard to express in monetary terms.

We may describe the workflow of project evaluation as follows. In the planning stage, policy targets must be clarified and several policy proposals must be compared and evaluated. In the evaluation stage, the necessity of a new project must be carefully evaluated to decide whether to launch the project. In the reevaluation stage, the necessity of a project should be reviewed to decide whether to continue or discontinue the project. In the ex-post evaluation stage, the effects, benefits, and environmental impacts of a project must be analyzed after its completion and, if necessary, appropriate measures and planning must be discussed for future projects.

There are some controversial arguments in Japan regarding evaluations in terms of benefit (B)/cost (C) ratio, B/C. In principle, government officers who carry out a project must understand that B/C is just one of the indices in the evaluation process. Evaluation should be comprehensive, taking into account many different factors beyond the standard B/C. The current B/C is incomplete because it fails to take into account factors relating to the environment and safety, among others.

However, many citizens believe that transparency regarding public investment projects has still a long way to go. People distrust the disclosed figures, suspecting some window dressing with political bias toward the overestimation of benefit, B. They conjecture that the calculations are made by government-friendly consultants. The natural belief of most voters in Japan is that accurate estimations of B/C should be at the center of all evaluations. Since efficiency matters the most, evaluations should begin with high B/C scores.

Thus, we have some serious concerns regarding the current evaluation system in Japan. Many voters still criticize public works regarding their necessity. They also find fault with the current evaluation system. Evaluation methods have two difficulties. The first is the limitation of accuracy. Evaluation requires an element of prediction; thus, inevitably, it involves a degree of error in the results. The second difficulty relates to the limitation of estimation technology. Some projects’ effects are not measurable. Even though some effects can be quantified, many cannot be expressed in monetary terms. Moreover, the use of evaluation results has two associated problems. First, it is unclear how evaluation results are related to decision-making. Although comprehensive evaluations are made, including cost-benefit analysis and much other data, it is hard to understand how such results are used in priority setting, budget allocation, and other decision-making in the actual political process. Second, it is important but hard to disclose all information on evaluations .

2.4 B4 Public Investment Management Reform

Finally, it is important to conduct microeconomic reforms to revamp public investment management drastically. Considering the Japanese government’s severe fiscal constraint coupled with rapid aging, public investment operations must be made more efficient. An important policy objective in Japan is to achieve an efficient government through public investment management reforms based on the principles “from public sector to private sector” and “from the state to the regions.”

In view of the severe fiscal situation in Japan, public investment projects that provide few benefits compared to the burden they impose are not sustainable. In order to ensure the efficiency of public spending, privatization and decentralization reforms are useful for bridging the gap between the benefits and the financial burdens. These reforms are necessary in order to reduce wasteful public projects.

As explained in Doi and Ihori (2009), the Japanese government introduced the Fiscal Investment and Loan Program (FILP) and privatized, merged, and abolished several state-owned companies. These steps are desirable, but only in the first phase of the structural reforms of public investment management. However, the reforms have not proceeded at a fast pace, owing to resistance from interest groups .

Further decisive efforts are needed to make the public sector, including public investment management, more efficient. Confidence in future public investment management should be enhanced by implementing structural reforms more fervently. A successful outcome of fiscal reorganization, including the reform of public investment management by utilizing private skills and funds, may increase the overall political support for the drastic fiscal reforms that the country needs today.

Through continued deficit reduction and a revamp of the public investment management system using macroeconomic and microeconomic measures, Japan can build an efficient and equit able public sector and bequeath to future generations strong public capital. This will enable future generations to achieve a dynamic economy and society, and improve their standards of living in an aging Japan .

Questions

• 5.1 Consider the simple growth model:

  $$ \begin{array}{l}\mathrm{S}=0.2\left(1-\mathrm{t}\right)\mathrm{Y}\\ {}\mathrm{Y}=0.3\mathrm{K}\end{array} $$

  If the tax rate t = 0.2, what is the growth rate?

• 5.2 Suppose an increase in the tax rate promotes capital accumulation and economic growth. How can you explain this positive relation?

• 5.3 Public capital is often not so productive compared with private capital. Explain why.