Abstract

Japan’s high saving rate relative to those of other industrial countries gives rise to the question of whether Japan is saving “too much.” This section utilizes the conditions on optimal steady-state saving behavior derived from neoclassical growth theory to examine whether Japan saves too much (or too little)—thus assessing the optimality of its national saving behavior.

Japan’s high saving rate relative to those of other industrial countries gives rise to the question of whether Japan is saving “too much.” This section utilizes the conditions on optimal steady-state saving behavior derived from neoclassical growth theory to examine whether Japan saves too much (or too little)—thus assessing the optimality of its national saving behavior.

The section is organized as follows: the first part provides a brief review of recent trends in Japanese saving behavior and a comparison with other major industrial countries; following an outline of three testable conditions derived from neoclassical growth theory for assessing the sufficiency of saving, the second part examines the empirical evidence for each of these approaches; the last part draws some conclusions from the analysis.

How Much Does Japan Save?

Saving behavior is important because it helps to determine the evolution of future consumption opportunities. As such, saving can be viewed as the portion of current income that allows a nation to raise its future consumption opportunities—that is, to raise its standard of living.

Japan’s postwar saving behavior can be viewed in this light. Saving has enabled Japan to increase its stock of assets rapidly (physical and financial as well as domestic and international), increase worker productivity, achieve rapid rates of economic growth, and raise its standard of living.

Recent Trends in National Saving

Chart 2-1 shows Japan’s national saving rate, both gross and net of depreciation, for the period 1975–93. Both of these measures indicate a negative trend through the first part of the 1980s, with levels in the early 1980s that are about 2 percentage points of GNP lower than those recorded at the beginning of the period. Since 1983, however, there has been a moderate increase in saving rates.

Chart 2-1.
Chart 2-1.

Gross and Net National Saving Rates

(In percent of GNP)

Sources: Japan, Economic Planning Agency (EPA), Annual Report on National Accounts (Tokyo, various issues); and IMF staff estimates.1 Includes public enterprise sector savings.

Gross saving in Japan declined from about 33 percent of GNP in 1975 to 30 percent in 1983, before recovering beginning in the mid-1980s. Preliminary data for 1993 suggest that gross saving rebounded to 33 percent of GNP. For net saving, the secular decline through 1983 is more marked (from 20 percent of GNP in 1976 to 16 percent of GNP by 1983) because of rapid rates of depreciation charges over the period. Chart 2-1 also shows disaggregated saving data. As can be seen, the upturn in the saving rate in the latter half of the 1980s was due primarily to an increase in general government saving.

Japanese Saving in an International Context

Table 2-1 and Chart 2-2 show Japanese gross saving in comparison with other major industrial countries for the most recent ten-year period. As can be seen, there are wide disparities in saving behavior across countries. Japan is clearly the highest saver among the major industrial countries, and by a large margin. The other countries are clustered in terms of their saving rates, with the United States and the United Kingdom at the low end of the spectrum.

Table 2-1.

Saving Rates of Major industrial Countries

(In percent of GNP)

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Source: IMF, World Economic Outlook (Washington, various issues).
Chart 2-2.
Chart 2-2.

Gross National Saving Rates of Major Industrial Countries

(In percent of GNP)

Source: IMF, World Economic Outlook (Washington, various issues).

How Much Should Japan Save?

The preceding indicates that Japan’s saving rate is high, both in absolute terms and relative to other countries. In saving, a country chooses to forgo current consumption in order to increase future consumption opportunities. Clearly, a balance must be struck between the costs of forgoing consumption today and the benefits of increased future consumption. Too little saving will be suboptimal in that a low level of capital formation will result in a low level of sustainable consumption. Too much saving, however, can also be suboptimal because present and future consumption opportunities are forgone in favor of building and maintaining the stock of capital.1

Neoclassical growth theory provides at least three separate, but interrelated, conditions by which to assess whether an appropriate balance between consumption and saving (investment) is struck—that is, whether a country is saving too much or too little.2 These are (1) the (modified) “golden-rule” criterion; (2) the dynamic efficiency condition; and (3) the marginal productivity approach.

Briefly, the golden-rule criterion allows an optimal saving rate to be calculated. If the actual saving rate is less than (greater than) the golden-rule saving rate, then a country is saving too little (too much) from the perspective of maximizing the level of sustainable consumption. In practice, the actual saving rate can be compared with a range of golden-rule saving rates, derived by varying the values of the key parameters (given uncertainties surrounding their exact values). The second condition, the dynamic efficiency criterion, compares profits with investment. So long as profits exceed investment, then capital (the sum of past saving decisions) has not been overaccumulated. The criterion is a variant of the commonly cited proposition that, at the golden rule, all profits are saved (that is, invested). The third criterion, the marginal productivity approach, suggests that capital has not been overaccumulated so long as the net marginal product of capital exceeds the growth rate of the economy or a relevant social discount rate. It is a variant of another commonly cited result of neoclassical growth theory: at the golden rule, the net marginal product of capital is equal to the steady-state growth rate.

“Golden Rule” of Accumulation

In neoclassical growth models, a commonly cited criterion for choosing among saving rates is the golden rule, which maximizes per capita consumption through time. The golden-rule criterion suggests that the highest sustainable level of per capita consumption is attained when the net rate of return on capital equals the sum of the population growth rate and the rate of technological progress. If allowance is made for time preference, then a modified golden-rule proposition emerges under which the welfare-maximizing steady-state path is characterized by the condition that the rate of return on capital minus the rate of pure time preference equals the sum of the population growth rate and the rate of technological progress. In the steady state, a saving rate above or below this welfare-maximizing rate will be suboptimal.3

The modified golden rule allows one to calculate the saving rate and the capital-output ratio that would be approached in the long run. Briefly, it can be shown that only two equations need to be parameterized to solve for the optimal steady-state capital-output ratio and saving rate:

K/Y=α/(δ+p+g+n)(21)S/Y=(n+g+δ)K/Y=α[(n+g+δ)/(p+n+g+δ)],(22)

where K, Y, S, α, δ, p, g, and n are the capital stock, output, saving, capital’s share of output, rate of depreciation, social rate of time preference, exogenous rate of technical progress, and growth rate of the labor force, respectively.4 Equation (2-1) defines the capital-output ratio consistent with the modified golden rule, and equation (2-2) defines the steady-state saving ratio. From equation (2-2), it is easy to see that if the pure rate of time preference (p) is zero, then the optimal steady-state saving rate is equal to capital’s share of output (α)—commonly interpreted in the literature as the proposition that, in the golden-rule steady state, all profits are saved (invested).

Parameter Values

To make the two equations above operational, it is necessary to evaluate the likely values of the parameters in the case of Japan.

Capital’s Share of Output (a). National accounts data in Japan suggest that capital’s share of national income is about 35 percent. Estimates based on an aggregate production function approach, however, indicate an even higher share (of about 40 percent).5 For analytical purposes, the work that follows will consider values of 0.35 and 0.40.

Rate of Depreciation (8). Rates of economic depreciation of 7 percent (low) and 9 percent (high) are considered. This range is based on the recent shift toward relatively shorter-lived assets (in part owing to increasing speeds of technological obsolescence) and takes into account the behavior of the capital goods deflator and the composition of investment (public, private fixed, and residential).

Rate of Technical Progress (g). Assuming that most “catch-up” effects have already occurred, the prospective exogenous rate of technical progress (multifactor productivity growth) is assumed to be about 1 percent a year.6 This value is consistent with the multifactor productivity growth rate embodied in estimates for potential output growth. A lower-bound value of 0.5 percent is also considered.

Growth Rate of the Labor Force (n). Although demographic projections for the total population and for the prime working-age group (aged 15-64) suggest very little growth, a modest rise in the labor force participation rate (especially for women, but also reflecting a gradual boost in the retirement age) is expected. Accordingly, a longrun rate of labor force growth of ½ of 1 percent is utilized.

A final issue that must be considered is the social rate of time preference.7 Unfortunately, the social rate of time preference is not an observable variable. Rather than assigning an arbitrary value, the approach adopted in this section is to provide a benchmark optimal saving rate and capital-output ratio on the assumption that the social rate of time preference is zero. The revealed social rate of time preference can then be deduced from the deviations of the actual from the optimal rate of saving.8

Implied and Actual Saving Rates

Table 2-2 provides illustrative calculations for the optimal saving rates and capital-output ratios implied by the ranges of parameter values outlined above. As can be seen, the golden-rule saving rates are 35 percent and 40 percent (equal, of course, to the assumed capital shares). The long-run capital-output ratios range between 3.3 and 5.0. These results provide a benchmark by which to judge the optimality of recent Japanese saving behavior. During the 1984–93 period, the gross national saving rate in Japan averaged 33 percent of GNP, with a high of 34 percent in 1991 and a low of 31 percent in 1984. In the same period, the capital-output ratio averaged 2.9, with a period-ending high of 3.2.9

Table 2-2.

Optimal Gross Saving Rates Under Alternative Parameter Values1

article image
Source: IMF staff calculations.

The calculations assume a labor force growth rate of ½ of 1 percent annually and a social rate of time preference of 0 percent.

In percent.

These figures suggest that Japan’s saving rate and capital-output ratio are currently both lower than the long-run steady-state rates implied by a modified golden rule under a range of reasonable parameter values. On this basis, Japan cannot be said to be oversaving. Indeed, the calculations suggest that Japan could increase its sustainable level of consumption by raising its saving rate by 2 percent of GNP, if capital’s share is 35 percent, and by 7 percent of GNP, if capital’s share is 40 percent. Note, however, that the deviation between actual and optimal saving rates would be consistent with a nonzero social rate of time preference. The deviation suggests that, with a capital share of 35 percent and allowing the other parameters to take on their range of values, the revealed social rate of time preference is about ½ of 1 percent. If the capital share is 40 percent (and, again, allowing the other parameters to take on their range of values), then the revealed social rate of time preference is 2 percent.

Dynamic Efficiency

An alternative approach to the question of saving behavior that is also derived from neoclassical growth models is the dynamic efficiency criterion. This criterion allows a judgment of whether an economy has overaccumulated capital—that is, oversaved—on the basis of easily observable economic variables. Moreover, while one is left, under the modified golden rule, with a plausible range of saving rates that can be deemed optimal, the dynamic efficiency criterion is a one-way test: it allows one to assess whether the current capital stock is too high—and thus, whether overaccumulation (oversaving) has occurred.

Conceptual Underpinnings

According to the literature on optimal economic growth, an economy is said to be dynamically efficient if it invests less than the return to capital. In the case of dynamic efficiency, the economy has not overaccumulated capital in the sense that the marginal product of capital exceeds the rate of growth of the economy. In the case of dynamic inefficiency, the reverse is true—implying that a “society would be reducing its consumption merely to support the growth of a capital stock which is so large that diminishing returns have robbed it of its capacity to support its own growth and leave a surplus for extra consumption” (Solow (1970, p. 28)). Thus, in a dynamically inefficient economy, it is possible for society to go on a consumption binge, thereby reducing the stock of (overaccumulated) capital. Thereafter, consumption per capita could be higher because resources do not have to be devoted to maintaining an inefficiently large capital stock.

More formally, the condition for an economy to be dynamically efficient can be derived from the steady-state relationship among consumption (C), output (Y), the capital stock (K), and the rate of economic growth (μ):

C=YμK.(23)

Equation (2-3) says that steady-state consumption is equal to steady-state output, less the proportion of output that must be invested each period for the capital stock to grow at the same rate as output.10 Differentiating equation (2-3) with respect to the capital stock gives

dC/dK=dY/dKμ=MPKμ.(24)

Equation (2-4) implies that steady-state consumption can be raised by increasing the capital stock as long as the marginal product of capital (MPK) exceeds the rate of economic growth. If this is the case, the economy is said to be dynamically efficient: it has not overaccumulated capital. But if the marginal product of capital is less than the rate of economic growth, more capital must be reinvested to maintain a constant capital-output ratio than capital produces at the margin. Consumption is thus reduced to maintain the capital stock at an inefficiently high level.11

A final step is needed to implement a test for dynamic efficiency. Multiplying both sides of equation (2-4) by the capital stock results in the following measurable condition for testing whether an economy is in the dynamically efficient region:

MPK(K)μ(K)=MPK(K)I0.(25)

That is, an economy is dynamically efficient if the return to capital exceeds investment.12 The intuition behind this result is straightforward: if the return to all past investments exceeds current investment, then part of the return is being consumed by society. The capital sector is contributing to consumption opportunities. If this were not the case, then society would never partake in the fruits of earlier sacrifices and would perpetually not only rein-vest all the returns from past investment, but also depress current consumption to further add to the capital stock: the capital sector is a drain on consumption opportunities.

Previous Findings

Abel, Mankiw, Summers, and Zeckhauser (1989; here-after, AMSZ) used equation (2-5) to test for dynamic efficiency in a cross section of countries, including Japan. In their approach, they showed that equation (2-5) holds if production technology exhibits constant returns to scale and there are no monopoly profits, so that capital earns a competitive return. Equation (2-5) also requires that a steady state has been achieved. As a result, less weight can and should be given to results pertaining to any individual year; rather, investment rates and returns to capital should be examined for longer (five-year or ten-year) periods (over which it can be assumed that the capital-output ratio is fairly constant). In addition, AMSZ noted that their analysis takes no account of investment in human capital and may be misleading in its treatment of the return to land.13 Finally, AMSZ ignored the role of public investment in assessing dynamic efficiency (see below).

In examining Japan for the period 1960–84, AMSZ found that the economy is dynamically efficient. The gross profit rate exceeded the investment rate throughout the period by an average of slightly more than 10 percentage points of GNP, although the difference between the rates shows a marked secular decline. In the early 1980s, the average difference falls to about8¼percent of GNP, compared with an average difference of 13¾ percentage points in the decade of the 1960s. AMSZ concluded that, despite Japan’s high rate of capital accumulation and tradition of low real interest rates, the criterion for dynamic efficiency is comfortably satisfied.

Recent Evidence

The latter part of the 1980s saw a remarkable boom in investment activity, and it is therefore relevant to revisit the question of dynamic efficiency in Japan. The following sections first examine dynamic efficiency along the lines of the AMSZ approach, but extending the results through 1992, and then expand the AMSZ results by considering two other large sources of capital accumulation in Japan: public and foreign investment.

Extending the AMSZ Results

Table 2-3 presents profit and investment rates for the private sector based on national accounts data from Japan’s Economic Planning Agency (EPA) for the period 1976–92.14 Profits are calculated as the sum of operating surpluses of the nonfinancial corporate sector, the financial sector, and the unincorporated nonfinancial enterprise sector, plus the capital consumption allowances of these sectors. The operating surplus of the unincorporated non-financial enterprise sector has been adjusted downward, since a large part of the operating surplus may actually reflect a return to labor.15 The adjustment factor used is 65 percent, on the assumption that the return to labor in this sector does not differ significantly from other estimates of labor’s share in income. The profit rate is the ratio of gross profits to GNP. The investment rate is the sum of gross fixed capital formation plus inventory accumulation in each of the sectors, relative to GNP.

Table 2-3.

Private Sector Dynamic Efficiency

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Sources: Japan, Economic Planning Agency (EPA), Annual Report on National Accounts (various issues); and IMF staff estimates.

The data indicate that Japan’s private sector has been dynamically efficient over the period (Chart 2-3, top panel). On average, over the 1976–92 period the profit rate exceeded the investment rate by 7.2 percentage points of GNP, with a minimum of 4.2 percent of GNP in 1976 and a maximum of 10.1 percent of GNP in 1986. For the decade ending in 1985, the average difference was 7.2 percent of GNP; and for the decade ending in 1992, the average difference was 7.9 percent of GNP.

Chart 2-3.
Chart 2-3.

Dynamic Efficiency

(In percent of GNP)

Sources: Japan, EPA, Annual Report on National Accounts (Tokyo, various issues); and IMF staff estimates.

Role of Public and Foreign Investment

A broader approach to the question of dynamic efficiency is provided by including public as well as foreign investment (saving).16 Foreign investment (defined as the current account balance less capital transfers) is included because it ultimately represents a claim on capital, even if such claims are not located domestically. Moreover, such investment (saving), whether located domestically or abroad, represents forgone consumption opportunities, a key issue in deciding whether overaccumulation is occurring. Finally, at a technical level, GNP includes factor incomes from abroad, and thus the return to capital calculated there from includes returns to domestic and foreign investment. Government investment is included for two reasons: it is as germane to the question of overaccumulation as private investment; and public investment may well be used by the Government to bring the economy closer to a golden rule. That is, it may well be used to supplement suboptimal private sector investment, brought about by the disincentive effects inherent in government tax and regulatory policies as well as higher than socially optimal rates of time preference in the private sector (see Evans (1992); Foley and Sidrauski (1971); and Atkinson and Sandmo (1980)).

Table 2-4 presents profit and investment rates for this exercise. After public and foreign investment were included, the test indicated that Japan has been dynamically efficient over the period. On average, the profit rate has exceeded the investment rate by 0.7 percentage points of GNP over the 1976–92 period. For the decade ending in 1985, the average difference was 0.8 percent of GNP; and for the decade ending in 1992, the average difference was 1.1 percent of GNP.

Table 2-4.

Aggregate Dynamic Efficiency

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Sources: Japan, EPA, Annual Report on National Accounts (various issues); and IMF staff estimates.

In examining the results, two features are apparent. First, the average difference, whether for the entire period or for the identified decades, is positive but small.17 Second, for some years of the period under investigation, the difference between the gross profit rate and the investment rate is negative. One possible interpretation of these features is that Japan, while dynamically efficient, may be close to an inefficient region. There are, however, a number of reasons, related in part to data and measurement issues, for questioning this interpretation.

Although the average difference between the gross profit rate and the investment rate is relatively small, it is probably substantially understated. The inclusion of public investment, which averaged 8 percent of GNP over the 1976–92 period, results in a bias toward dynamic inefficiency because national accounts data do not make an imputation for the flow of services yielded by the public capital stock, and hence the overall gross profit rate in the economy may well be understated.18 Moreover, the period under investigation includes subperiods of two major recessions (1976–78, when the economy was still in a recovery phase from the first oil shock; and 1991—92, the onset of the current recession). In general, cyclical conditions can adversely affect measures of dynamic efficiency—both because gross profits tend to fall and because declines in private investment may well be compensated by increases in countercyclical public investment expenditure measures. This consideration is particularly relevant for the two subperiods in which the difference between the gross profit rates and investment rates are negative. Finally, as noted earlier, because of the underlying steady-state assumption, that the measure of dynamic efficiency in any one year shows a negative difference cannot be taken as conclusive evidence of inefficiency. Rather, averages over longer periods are more germane. That cyclical conditions also influence the measure of dynamic efficiency bolsters the argument for looking at averages over five- or ten-year periods.

In summary, the results indicate that Japan is dynamically efficient; that is, it has not overaccumulated capital. This is true whether narrow (private sector) or broader concepts (including government capital and foreign investment) of accumulation are considered.

Marginal Productivity

A third approach to the question of over- or undersaving involves calculating the marginal productivity of capital, and comparing it either with a measure of the opportunity cost of savings or with the growth rate of the economy. The former comparison is really a cost-benefit approach (or deadweight loss approach),19 wherein a demand price (or marginal social benefit) is compared with a supply price (or opportunity cost variable). The latter comparison is related both to the golden rule and to dynamic efficiency.

Cost-Benefit Approach

The cost-benefit approach is a direct test of whether an economy is oversaving or not. If the marginal product of capital exceeds the opportunity cost of saving, then an incremental unit of saving will increase intertemporal consumption opportunities. The problem then becomes one of estimating the marginal product of capital and finding a measure of the opportunity cost of saving.

The marginal product of capital can be computed from national accounts data and a measure of the capital-output ratio. Assuming that aggregate output is governed by a Cobb-Douglas production function with constant returns to scale, gross profits as a share of output are equal to capital’s share of output:

(grossprofits/Y)=α=[f(k)(K)]/Y=r(K/Y).(26)

Dividing equation (2-6) by the capital-output ratio yields the marginal product of capital, r:

(grossprofits/Y)/(K/Y)=α/(K/Y)=f(k)=r.(27)

In turn, subtracting depreciation yields a net return to capital:

R=r-δ(2-8)

This (net-of-depreciation) return can be compared with a variable for the opportunity cost of saving.

As regards the opportunity cost of saving, various authors have considered alternative approaches. Some (for example, Harberger (1972) and Feldstein (1977)) adjusted the return to capital for corporate and personal taxes to find the net-of-tax return received by investors.20 The supply price of saving derived from this exercise is the market’s revelation of investors’ rate of time discount. Although such an approach is useful in measuring the deadweight loss associated with capital market distortions, it is less useful in addressing the issue of oversaving—since, by construction, the demand price will exceed the supply price. Others (for example, Feldstein (1977) and Boskin (1986)) have used cardinalist utility approaches to derive a theoretical supply price. Under these approaches, assumptions about the elasticity of marginal utility with respect to consumption and the marginal rate of substitution between consumption at different dates are made to derive a “planner’s” rate of time preference, which is a function of the rate of consumption growth. The planner’s rate of time preference can in turn be augmented to take into account individuals’ myopia and the probability of death in order to find the private rate of time preference. Either of these rates, depending on the situation, can then be compared with the return to capital to establish whether too much or too little saving is taking place.

The approach taken here is along lines of the latter approach: thus, so long as the calculated return to capital is greater than a range of values for the “planner’s” or social rate of time preference, oversaving cannot be said to have occurred. Table 2-5 presents data for alternative measures of the return to capital under alternative depreciation rates of 7 percent and 9 percent. The first measure is an estimate of the return to private capital; the second is the return to private and public capital. Again, because of cyclical and other influences, both annual and period averages are provided.

Table 2-5.

Return to Capital

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Sources: Japan, EPA, Annual Report on National Accounts (various issues); and IMF staff estimates.

As can be seen, the first measure averages 10 percent over the full period at the depreciation rate of 7 percent. If the higher rate of depreciation is used, the average is 8 percent. Thus, for values of the social rate of discount as high as even 2 percent, the data suggest that capital accumulation in Japan has not driven the stock of capital to the point that the return to capital is below the relevant opportunity cost. The second measure, although smaller, also exceeds reasonable values of the social rate of time preference. Again, recall that this measure may be biased downward because the national accounts make no imputation for the flow of services from the government capital stock. Indeed, all the caveats discussed in the section on dynamic efficiency apply equally to this measure.

Growth Rate Approach

The return to capital can also be compared with the real rate of economic growth, reflecting the standard result from growth theory that, at the golden rule, R = g.21 Thus, if R > g, then the capital stock has not reached its golden-rule level, and the economy cannot be said to have overaccumulated.22 For this reason, Table 2-5 also includes a column on the real rate of economic growth. The private sector return to capital exceeds the real rate of economic growth for both of the assumed rates of depreciation. For the aggregate economy, the return to capital exceeds the growth rate of the economy at a depreciation rate of 7 percent, but it is lower than the growth rate of the economy at a depreciation rate of 9 percent. Once again, the same caveats apply. Using a modified golden-rule result does not alter these findings for reasonable values of the social rate of time preference.23 In sum, comparing rates of return with growth rates of the economy suggests that the golden-rule level of capital stock is unlikely to have been exceeded.

Conclusions

This section has used conditions from neoclassical growth theory to investigate Japanese saving behavior. More specifically, three separate but interrelated tests were conducted to determine whether the flow of saving or the stock of accumulated capital could be deemed “excessive” from an economic viewpoint. The modified golden-rule criteria, although perhaps the weakest of the three tests (because of the uncertainty surrounding parameter values), suggests that Japan’s recent saving behavior and capital-output ratio are lower than those consistent with maximizing the level of sustainable consumption over the long run. Tests of dynamic efficiency indicated that for the period 1975–92 Japan has not overaccumulated capital. The result holds for both the private sector as well as the aggregate economy (that is, including public and foreign investment). A final test relating to the marginal productivity of capital showed that the net rates of return to capital have generally exceeded opportunity costs, unless the depreciation rate is assumed to be relatively high. Again, this was true both for the private sector and for the aggregate economy.

Still, it is important to recognize several caveats with respect to the work that has been presented. First, as regards the golden-rule approach, there is some uncertainty about the relevant parameter values. In addition, the social rate of time preference is an unobservable variable. Second, there may be a bias introduced in the tests for dynamic efficiency as well as those for the marginal productivity because national accounts data do not make an imputation for the service flows generated by public investment. Finally, to the extent that Japan is still in the process of capital deepening, technological catch-up, or even postwar reconstruction, the assumption that the economy is at or near a steady state may not be justified. Notwithstanding these caveats, the three sets of tests, whether looked at individually or together, suggest that neither Japan’s flow of saving nor its stock of accumulated capital can be considered excessive from the perspective of maximizing sustainable consumption.

References

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1

In such a circumstance, a society puts itself on a path toward capital saturation or overaccumulation, thereby driving the marginal product of capital toward zero.

2

In a neoclassical growth model, the economy converges to a steady-state balanced-growth path (with a constant capital-labor ratio, constant net rate of return to capital, and a constant rate of growth). The constant long-run rate of growth will equal the (exogenous) rate of population growth plus the (exogenous) pace of technological progress. Although the long-run rate of growth is not affected by the economy’s saving rate, the saving rate determines the steady-state capital-labor ratio as well as the level of consumption per capita. Thus, the “choice” of the saving rate has important implications for steady-state consumption opportunities. See Solow (1956), Hahn and Matthews (1964), Jones (1976), and Phelps (1961 and 1966) for an overview of neoclassical growth models and golden rules. Also, see Evans (1992) for a discussion of the neoclassical growth model and the adequacy of saving in the United States.

3

Note that, in the short run, a saving rate even higher than the longrun value implied by equation (2-2) below can be justified. This would be the case if the economy were approaching the steady state from below (that is, from a capital-output ratio lower than the long-run capital output). In such an instance, saving might be higher than the long-run rate in response to a rate of return on capital greater than the long-run rate. Saving would eventually fall to its long-run level as the marginal productivity of capital was driven to its long-run rate. In this regard, Christiano (1989) argued that trends in Japan’s saving behavior have been associated with efforts to rebuild the capital stock (and the attendant high rates of return to capital) after World War II.

4

See Evans (1992) for a full description of the methodology and a derivation of the conditions. This section draws heavily from this source.

5

See, for example, estimates of the aggregate production function in Japan (1993).

6

Alexander (1994) has noted that, for many sectors of the Japanese economy, significant productivity gaps exist between Japan and the United States, suggesting that either technological catch-up is not as yet complete (or that further capital deepening is necessary). An assumption of slightly higher multifactor productivity growth, however, has a minimal effect on the golden-rule saving rates calculated below, all other things held constant.

7

The social rate of time preference is intended to reflect a society’s evaluation of the relative desirability of consumption at different points in time. There is an extensive literature on the choice of the appropriate social rate of time preference, but the little agreement that has emerged suggests that the social rate of time preference is low, if not zero. See Jones (1976, Chapter 9) for a brief summary of the academic debate; see also Sen (1967) and Arrow and Lind (1970) for specific approaches to the issue.

8

The subsection on dynamic efficiency, below, provides an approach to the question of oversaving that is independent of the social rate of time preference.

9

Capital-output ratios are derived by cumulating real net investment flows (public, private fixed, residential, and inventory investment) and dividing by real GNP.

10

If the capital stock grows at a rate other than u, the capital-output ratio would be changing, thus violating the steady-state assumption. For simplicity, depreciation is ignored. It is, however, straightforward to generalize equation (2-3) by adding the depreciation rate to μ.

11

The golden-rule growth path is defined as the point where dC/dK = 0, or where the marginal product of capital equals the rate of economic growth. At this point, the associated capital-output ratio maximizes sustainable consumption. Such a point is consistent with an assumption of a zero rate of social time preference.

12

Phelps (1966) noted that, in a world of uncertainty, overaccumulation may be optimal, so that a reserve of capital could be consumed in the event of an earthquake, war, or other probabilistic phenomena. In this sense, a strict nonnegativity criterion might not be the appropriate test of dynamic efficiency.

13

To take human capital accumulation into account, it is necessary to add investment in human capital to the gross investment figure and to make an estimate of the proportion of wage compensation that is due to human capital formation. This proportion could then be added to the gross profit figure. Although this would be an interesting extension, it is beyond the scope of the present analysis.

For the treatment of land, AMSZ pointed out that part of the gross profit is a return to land, and that as a result the return to capital (the gross profit rate) may be overstated. They noted, however, that research in this area has not produced conclusive results (see AMSZ, p. 9).

14

AMSZ used data from the Organization for Economic Cooperation and Development (OECD) for their calculations.

15

Because the EPA’s national accounts data consolidate the house-hold sector with unincorporated nonfinancial enterprises and include the imputed rent for the flow of services from owner-occupied housing within the (consolidated) operating surplus, this amount is netted for purposes of calculating the wage component of the operating surplus. It is, however, included in the calculation of gross profits.

16

An alternative test, between the AMSZ approach and the one used here, was also considered: foreign investment (saving) was added to private gross fixed capital formation and inventory accumulation to arrive at a broader measure of private sector accumulation, and net property income from abroad was included in deriving the gross rate of profit—thereby providing an augmented test for private sector dynamic efficiency. The inclusion of these flows does not alter the basic conclusions on private sector dynamic efficiency.

17

In a policy sense, the size of the difference between the gross profit and investment rates is less germane when the difference is small. It is more relevant when the difference is large, since this may suggest that, although the economy is efficient in that it is not overaccumulating, it does not rule out that the economy may be underaccumulating.

18

Of course, part of the flow of services may indeed be captured, to the extent that public services are priced (toll roads, airport taxes) or to the extent that the flow of unpriced or underpriced services are captured in firms’ profitability or workers’ wages. The degree of complementarity among public capital, private capital, and labor inputs then becomes an issue. Still, to the extent that a large part of the service flow from public investment is not captured and imputed, the difference between gross profit and investment may be significantly biased downward—that is, away from dynamic efficiency.

19

That is, to the extent that the demand price differs from the supply price, the deadweight loss of the distortion (as well as the theoretical level of saving and investment in an undistorted market) can be calculated on the basis of estimated values for the interest elasticities of saving and investment.

20

Alternatively, the average net-of-tax return to savers can be compared directly with the net return to capital, attributing the difference to a tax wedge.

21

This can easily be seen in the derivation for the dynamic efficiency criteria above.

22

Note that a number of authors have compared the growth rate with the risk-free real interest rate, rather than with the net return to capital. In general they have found that the real risk-free rate is lower than the real growth rate, which would in turn suggest that capital overaccumulation has occurred. Other authors, however, note that the return on equities has substantially exceeded the real growth rate of the economy and that the test for capital overaccumulation based solely on the risk-free rate of return may not be sufficiently rigorous (see, for example, Blanchard and Fischer (1989) and Boskin (1986)).

23

Under a modified golden rule, if the rate of return to capital less the rate of time preference exceeds the growth rate of the economy, then the economy cannot be said to have overaccumulated.