Abstract

Demographic projections for coming decades indicate that, of the major industrial countries, Japan will experience the most rapid increase in the share of the elderly in the total population.1 This demographic shift is expected to cause pressures on the financing of the social security system and slower growth in the labor force and in potential output. Many observers also believe that a consequence of the transition to a more elderly population will be a reduction in the private saving rate, based on the view that retired households save less than those of working age. Such a decline would reduce the flow of saving to both Japan and overseas economies, implying a reduction in domestic investment or the external surplus, or both.

Demographic projections for coming decades indicate that, of the major industrial countries, Japan will experience the most rapid increase in the share of the elderly in the total population.1 This demographic shift is expected to cause pressures on the financing of the social security system and slower growth in the labor force and in potential output. Many observers also believe that a consequence of the transition to a more elderly population will be a reduction in the private saving rate, based on the view that retired households save less than those of working age. Such a decline would reduce the flow of saving to both Japan and overseas economies, implying a reduction in domestic investment or the external surplus, or both.

The view that the transition to a more elderly population will reduce the aggregate saving rate is controversial, however. Broadly speaking, there are two schools of thought on the issue of saving and demographics. The first, associated with the life-cycle model of household behavior, views saving as being motivated by the desire of households to smooth lifetime consumption in the face of uneven income flows. The saving rate of the workingage population is positive, whereas that of the retired population is negative. An increase in the ratio of the retired population to the working-age population thus lowers the aggregate saving rate. The second view follows from evidence suggesting that the saving rate of the elderly is not significantly lower than that of the overall population, a phenomenon that is sometimes attributed to the existence of an altruistic bequest motive for saving. An inference drawn from the apparent similarity of saving rates of different age groups is that a shift toward a more elderly population will have little effect on the aggregate saving rate.

This section first reviews the literature on demographics and saving, with a focus on the Japanese experience. As shown in the next part, the aggregate evidence on saving and demographic structure for Japan and other countries appears to be consistent with the life-cycle model. Some studies using household data, however, seem to contradict predictions of the life-cycle model. In the third part, the household data for Japan are re-examined. These data show that retired households in Japan do, in fact, dissave; the rate of dissaving is magnified when income is adjusted for social security benefits. Indeed, it appears that an inappropriate treatment of social security and pension income is a flaw in many household-level studies, both for Japan and other countries. The fourth part presents simulation results, based on a life-cycle model, that suggest that Japan’s private saving rate will decline significantly as a result of demographic factors. The last part summarizes the results.

Previous Studies on Demographics and Saving

Evidence Supporting the Life-Cycle Model

Much work has been done on the ability of the life-cycle model to explain aggregate saving.2 As discussed above, an important prediction of the model is that a shift in the demographic structure toward a higher ratio of elderly households to working-age households will reduce the aggregate saving rate. In addition, life-cycle models that include a period of youth preceding working life predict that the aggregate saving rate will be negatively related to the population share of the young. Another prediction of the life-cycle model is that saving during working life will depend on expected income from sources other than household saving during retirement. For instance, income in the form of benefits from fully funded private pension plans is likely to reduce saving by working-age households, excluding contributions to pension plans. Unfunded public pension plans also tend to reduce household saving in a life-cycle model, al-though the exact impact is complicated by the implicit rate of return households expect to realize on their contributions and the possible earnings-testing of benefits.3

Evidence based on aggregate data typically supports the predictions of the life-cycle model regarding demographics and saving, as indicated by the results shown in Table 4-1. Most of the studies have been based on cross-section data for OECD countries, while others have used time-series data for Japan only or have pooled cross-section and time-series data for several industrial countries. The methodology typically has involved regressing the saving rate on variables that capture the demographic structure of the population and other factors. The demographic structure is summarized by the ratios of the elderly and the young to the population of working age—that is, the elderly and youth dependency ratios.

Table 4-1.

Summary of Studies on Demographics and Saving

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Note: Lines 1, 2, and 3 are cited in Heller (1989); line 5 is from Graham's equation 1 in Table 2; line 6 is from Koskela and Viren's equation (6) in Table 1; lines 7 and 10 are cited in Horioka (1991); line 9 is a simulated effect based on 1980 values; line 11 is the simulated post–1980 impact. Figures in parentheses are estimated t-statistics.

Ratio of population aged 0–19 to population aged 20–64.

Ratio of population over 64 to population aged 20–64, except line 8 is ratio to total population.

Pooled data for the seven major industrial countries and the small industrial countries.

In most cases, the demographic effects are both statistically and economically significant. The impact of a change in the elderly dependency ratio typically exceeds that of the youth dependency ratio: an unweighted average of the estimation results indicates that a 1 percentage point rise in the elderly ratio lowers the saving rate by

0.86 percentage point, whereas the same increase in the youth dependency ratio lowers the saving rate by 0.61 percentage point. Effects of this magnitude imply a large change in the aggregate saving rate in response to projected shifts in Japan’s demographic structure. Specifically, the elderly dependency ratio is projected to rise by over 20 percentage points from the first half of the 1990s to 2020. In the absence of changes in other factors that affect saving, these results would suggest a reduction in the household saving rate of over 15 percentage points.4

Fewer studies have examined the impact of social security on private saving in Japan. Using aggregate time-series data from the period 1966–83, Shibuya (1987) found a significant negative effect from the social security replacement ratio. Yamada, Yamada, and Liu (1990) also found a significant effect of social security retirement benefits on both the saving and retirement decisions, using time-series data for the 1951–82 period. The saving replacement effect dominates the retirement effect, leading to a strong negative overall impact on saving from the introduction of the social security system.

Challenges to the Life-Cycle Model

Other studies have cast doubt on the applicability of the life-cycle model for both Japan and other countries, on the basis of the observed saving behavior of the elderly in household data. In particular, these studies suggest that the saving rates of elderly households are not significantly lower than those of working-age households; that the elderly do not decumulate assets; and that elderly house-holds leave substantial bequests. Hayashi, Ando, and Ferris (1988), for instance, found only limited support for the life-cycle model in the behavior of elderly single-member households in Japan. For the elderly more generally, they attributed the apparent lack of wealth decumulation to the importance of intergenerational bequests. Bos-worth, Burtless, and Sabelhaus (1991) attempted to infer the effect of demographic changes on Japan’s aggregate saving rate by examining differences in age-specific saving rates. In particular, they held the saving rate of each age group constant and changed the population shares of each group to obtain alternative aggregate saving rates.5 The size of the effect on the aggregate saving rate depended on how different the age-specific saving rates were; these authors concluded that the differences in saving rates were not large enough to affect the aggregate saving rate (Bosworth, Burtless, and Sabelhaus (1991, pp. 220–21)).

The (apparent) high saving rate of the elderly has sometimes been explained in terms of a dynastic model of household behavior, in which the current generation cares about the welfare of the next generation (see Barro (1974)). Such intergenerational altruism can motivate intentional bequests, explaining why the propensity of elderly households to consume out of wealth might be lower than that predicted by the life-cycle model. However, although the dynastic model can explain intentional bequests, it is less clear that it can explain why the saving rates of elderly households would be similar to those of working-age households.6 In particular, in both the dynastic and life-cycle models, households will smooth consumption over time. If income is not similarly smooth, then the household saving rate will vary systematically with income in either framework. Continued saving by the elderly, then, must imply that their incomes do not decline with age.7 This is not a prediction of either the life-cycle or dynastic model per se, but rather must reflect either continued high labor supply by elderly households, or the replacement of labor income by other sources of income as households age. These issues are examined in the next part of this section.

Measurement of Saving in Household Data

There are two difficulties with studies of household saving that show continued saving by the elderly. The first is that income and wealth are often defined inappropriately, in that no distinction is made between earned income and other sources of income. The second is that household saving is often not observed directly; rather, saving is inferred from hypothetically constructed wealth profiles of the elderly, and these profiles may be subject to considerable mismeasurement.

As regards the definitions of income and wealth, it is important to distinguish between earned income and income from other sources such as social security benefits and private pension plans. The former yields a flow of goods and services to the economy as a whole, while the latter represents either a transfer from other households or the running down of assets that are not included in household balance sheets. Income from fully funded private pension plans is an example of retirement income that largely represents asset decumulation.8 Benefits from a pay-as-you-go social security program represent transfers from working-age to retired households—consumption out of this income will lower the saving rate for the economy as a whole, unless consumption by workingage households falls by an equivalent amount. This will not, in general, be the case when households are forward looking. As illustrated in Appendix 4-1, working-age households will spread the effect of a change in social security taxes over both current and future consumption. A rise in transfers from the young to the elderly then reduces the consumption of the young by less than it increases that of the elderly, causing the aggregate saving rate to fall.

The second difficulty with some household studies is that they must infer, only on the basis of observations for a single period of the wealth of households of different ages, how the wealth of households will change over time.9 There are several reasons why this is problematic, especially in the case of Japan. One is that the elderly poor tend to get absorbed in the families of their children and thus drop out of the sample of households. Looking, in a given year, at the profile of household wealth by age of the household head then tends to overrepresent relatively rich elderly households. Bias also arises because the elderly who have been hospitalized on a long-term basis are not included in survey data. Their saving rates are typically very negative, especially when the public health care component of their consumption is included. Furthermore, adjustments must be made because households of different ages have different lifetime incomes and, thus, asset wealth owing to productivity growth and other factors. Although researchers typically attempt to control for these “cohort” effects, the techniques are often arbitrary. In general, the power of the results is weakened by the need to impute key information.10 Finally, the translation of wealth profiles into saving rates is complicated by unanticipated capital gains and losses on existing wealth, as well as inter vivos transfers.

The problems of adjusting for unearned income and imputing wealth profiles can be avoided by using direct information on the consumption and income by source of elderly households. This permits the distinction between earned and unearned income and obviates the need to construct artificial age-wealth profiles. Such data were compiled in Japan for both retired and working elderly households in the 1990 Annual Report on the Family Income and Expenditure Survey (FIES; Japan (1990)), as shown in Table 4-2.

Table 4-2.

Income, Consumption, and Saving of Retired Households1

(Monthly average in thousands of yen)

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Source: Japan, Management and Coordination Agency (1990, Table 18, p. 114).

Defined as households whose head is jobless and over age 60.

The surge in 1990 is due to a reduction in the payment interval for annuity benefits from three to two months.

Defined as disposable income less living expenditures as a share of disposable income.

Saving rate out of disposable income, excluding social security benefits.

Elderly retired households in Japan account for11½ percent of the total households covered in the survey, whereas elderly working households account for 5 percent.11 For retired households, living expenditures exceed disposable income by a significant margin: on average, these households dissave at an annual rate of 21 percent, even before adjusting for unearned income. In the event, unearned income in the form of social security benefits accounts for by far the largest component of income for retired households, averaging over 70 percent of total income.12 For elderly households whose head is still working (whose average age is significantly lower than that for retired households), the situation is quite different: the saving rate remains positive at17½ percent—income is almost double that of retired households, while expenditures are only 30 percent higher. These data suggest that, after retirement, household income drops off more sharply than consumption, resulting in dissaving for retired households.13 The drop in earned income, however, is partially buffered by a rise in transfer payments, and this moderates the change in the saving rate that would otherwise be observed.

The aggregate saving rate of both retired and working elderly households is minus 3½ percent, compared with the 25 percent saving rate of working-age households computed from the 1990 FIES. Assuming that the saving rates of these two groups remain unchanged, it is possible to calculate the effect of a shift in the demographic structure toward a higher proportion of elderly. Specifically, a rise in the elderly dependency ratio of 1 percentage point would lower the aggregate saving rate by 0.2 percentage point, holding the saving rate of elderly and workingage households constant.14 While significant in light of the size of the projected rise in the elderly dependency ratio, this response is substantially lower than the average estimated effect obtained using aggregate data shown in Table 4-1. The difference is examined in more detail in the next part of this section.

Simulation Using a Life-Cycle Model

It was shown above that there are significant differences in the saving rates of elderly and working-age households in Japan. Nevertheless, holding the saving rate of each group constant, the impact of a demographic shift on the aggregate saving rate is smaller than that suggested by some econometric studies. A more sophisticated estimate of the effect of demographic shifts on aggregate saving is presented below. Specifically, a life-cycle model for Japan is simulated using projected changes in the age composition of the population. The results indicate an effect on saving exceeding that suggested by differences in household saving rates, but lower than the average estimate obtained using aggregate data.

The life-cycle model is described in detail in Appendix 4-2. It follows in the tradition of Tobin (1967) and White (1978), in that the focus is on the behavior of individual households, with variables such as the real interest rate and the real growth rate held to be exogenous. The representative household is forward looking and maximizes lifetime utility subject to a budget constraint. Household income consists of after-tax labor income, interest income on accumulated assets, social security benefits, and inherited wealth. The consumption path is affected by factors such as the rate of time preference, the real interest rate, and the intertemporal elasticity of substitution. Uncertainty about the time of death causes households to plan to consume less toward the end of their life span, reflecting a lower probability that they will be alive to benefit from this consumption.15 Uncertainty about death also generates a precautionary demand for saving. Because wealth cannot become negative even if the household lives beyond the average life expectancy, households plan to finance consumption over a longer life span than they expect, on average, to live. This implies that households typically die with positive wealth and leave bequests to the next generation, even though they derive no utility from bequests per se.

Initial values for certain variables were chosen to be consistent with observed data for Japan during the 1970–90 period: in particular, the risk-free real interest rate averaged 3 percent;16 labor-augmented productivity growth averaged PA percent; and population growth averaged 1 percent. Parameters determining consumption profiles were similar to those used in other studies of household behavior.17 Simulating the model with these assumptions yielded a household saving rate of 16.7 percent and a ratio of household assets to income (that is, accumulated wealth) of 5.5, compared with observed data (1970–90 average) of 18.0 percent and 5.5, respectively.

The predictions of the model are very similar to the actual data, both for the saving rate and the level of accumulated assets. The appropriateness of the life-cycle model was also tested by comparing its predictions for the behavior of elderly households with the observed data. The household survey data obtained from the 1990 FIES were first corrected for imputed rent on owner-occupied housing by multiplying the estimated value of owner-occupied housing by the rate of return on other assets in the model. This imputed rent was added to both the observed income and consumption of elderly households, and the saving rate was recalculated on a consistent basis. For elderly households in 1990, the model’s prediction for the saving rate was—2 percent compared with an adjusted observed saving rate of –2½ percent. Predictions for the share in income of earned income, social security benefits, and other income were 31, 34, and 35 percent, respectively, compared with adjusted survey data of 30, 32, and 38 percent. Again, the predicted and actual series correspond closely. The consistency of the predictions with the observed data is reassuring evidence that the life-cycle model can provide a realistic characterization of household saving behavior.18

The model was then simulated to track projected demographic changes over the period 1990–2030. The elderly dependency ratio is projected to rise from 17.7 in 1990 to 46.2 in 2030. The model results for the projected household saving rate were: 1990, 21.3 percent; 2000, 18.7 percent; 2010, 14.7 percent; 2020, 12.0 percent; 2030, 10.4 percent—implying a total change during the 1990–2030 period of –10.9 percent. Of course, this simulation indicates only the change in the household saving rate attributable to demographic considerations; the actual change in the saving rate will depend on other factors. For instance, the decline in saving would tend to be moderated by a rise in the real interest rate if lower saving otherwise would cause a shortage of saving relative to investment.19

The ratio of the simulated change in the household saving rate to the change in the elderly dependency ratio over the 1990–2030 period is about 0.4. This lies between the estimates discussed above: specifically, the ratio of 0.2 obtained by changing population shares while holding the saving rates of the elderly and the working-age populations constant; and the average estimated impact of 0.86 derived from aggregate data.

The difference between the simulation results and the impact when household saving rates are held unchanged is due primarily to the induced effect on the saving rates of changes in social security taxes. In particular, social security tax rates are currently low relative to those that will be needed to support a higher ratio of elderly to working-age households in the future (see Section V of this volume). As illustrated in Appendix 4-1, the increase in the tax rate will be reflected partly in lower consumption of working-age households, and partly in a reduction in their saving rate. This induced effect on the saving rate of working households reinforces that of the shift in weights toward elderly households with a lower saving rate.

It is more difficult to reconcile the predictions of the life-cycle model with the estimation results obtained using aggregate data. One possibility is that the household data on which the life-cycle model is based may underrepresent some elderly households that have high rates of dissaving, such as those in which the head of the house-hold is hospitalized. In this case, the picture provided by the aggregate data would be more accurate. However, estimation using aggregate data has yielded a considerable range of estimates. The lack of consensus reflects, in part, that differences in the population structure across time periods and countries tend to be correlated with other macroeconomic variables. The comovement in these variables makes the estimation results sensitive to the exact specification of the equations and can lead to “overfitting” the data.20 In any event, it is interesting that the effect predicted by the life-cycle model is quite close to that obtained in the only study based exclusively on aggregate Japanese data since the mid-1960s (Shibuya (1987)).

Conclusions

This paper has analyzed the probable effect on the household saving rate of a shift in Japan’s demographic structure toward a more elderly population. Although many econometric studies using aggregate data have predicted a very large effect on the saving rate, some studies using household data suggest that the impact may be small.

By using more recent and detailed information on the income and consumption of retired households, the analysis has shown that the saving rates for the elderly calculated in some household-level studies may be misleading. It appears that the elderly do dissave, and that the rate of dissaving is very similar to that predicted by a life-cycle model of household behavior. In addition, a large share of the income of the retired elderly in Japan consists of social security benefits, which represent transfer payments from the working generation as opposed to a net flow of resources to the economy. The existence of social security benefits and taxes implies that the effect on the aggregate saving rate of changes in population shares cannot be assessed by holding the saving rates of elderly and working-age households constant.

Simulations of a life-cycle model indicate that the household saving rate is likely to decline steadily in coming decades as a result of the shift toward a more elderly population. Although the effect of this demographic shift is significant, it is smaller than that suggested by some studies using aggregate data, which have suggested that the household saving rate may become negative over the long run. The effect is larger, however, than the change implied when the saving rates of the elderly and working-age populations are held constant, because of the role played by social security benefits and taxes.

Appendix 4-1. Effects of Demographic Change on Saving With and Without Social Security

In simple versions of the life-cycle model, the saving rate of each generation is independent and unaffected by the demographic structure of the population. The effect of a demographic transition on the aggregate saving rate then equals the change in the share of each generation in total income multiplied by its saving rate:

Δ(S/Y)=ΣΔwisi,(A41)

where Δwi is the change in the share of generation i in aggregate income, and si is its saving rate. Demographic shifts alter wi and thus the aggregate saving rate when si differs across generations. This decomposition is not useful, however, when the income of some generation is zero because si is undefined. An alternative approach that avoids this problem defines saving as a share of consumption:

Δ(S/C)=ΣΔwisi,(A42)

where Δwi and si refer, respectively, to the share of each generation in aggregate consumption and its savingto-consumption ratio.

A simple example of the effect of a demographic transition without social security is shown in the upper panel of Table 4-3. Each household divides its consumption equally between two periods; household income equals 1 in the first period and 0 in the second; the interest rate is 0. In the initial equilibrium—period 1—it is assumed that there are one “young” household and one “elderly” household. The aggregate wealth of the economy is½, representing the saving of the young to finance consumption in retirement. The saving rate of the young in relation to consumption is 1, while that of the elderly is—1. The aggregate saving rate is 0, since each generation has an equal share in total consumption.

Table 4-3.

Effect of a Demographic Transition on Aggregate Saving

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In period 2, the demographic structure shifts as the number of young households rises to two while the number of elderly households remains at one. Wealth rises, and the economy-wide saving rate becomes positive. The change in the latter can be inferred from equation (A4-2), since the share of the young in total consumption rises to2/3In period 3, the number of young households returns to one, while there are now two elderly house-holds. Economy-wide saving is negative because the wealth accumulated in period 2 is consumed by the elderly households. In period 4, the demographic transition is complete: saving and wealth have returned to their initial levels. An important aspect of this example is that, in each period, the saving-to-consumption ratio of the two generations is unchanged at 1 for the young and—1 for the elderly. This allows the effect on the aggregate saving rate of demographic shifts to be calculated using the above decomposition combined with unchanged saving rates.

Calculating the effect of a demographic transition is more complex in the presence of an unfunded social security program. In this case, the tax burden on young households depends on the number of elderly households that must be supported. Changes in the tax burden affect the saving decision of young households, leading to an interdependence between their saving rate and the demographic structure. This is illustrated in the lower panel of Table 4-3. The demographic transition is the same as in the first example; now, however, a social security program transfers income of ½ to each elderly household. These transfers are financed on a pay-as-you-go basis by taxes on young households. The initial equilibrium in period 1 is the same as that described above, except that young households do not save because consumption during retirement is financed by social security benefits. This lowers aggregate wealth to 0. In period 2, the social security tax rate on young households falls because the ratio of young to elderly households rises. Young households save a part of this tax cut to finance consumption during retirement; thus, their saving rate becomes positive, and economy-wide saving also becomes positive.

In period 3, the tax rate on the young households rises sharply to finance social security benefits for elderly households. The saving rates of both generations become negative because the elderly consume wealth accumulated in period 2, while the young finance a part of their social security taxes by going into debt. In period 4, the demographic structure returns to the initial equilibrium, but the saving rate is raised because of previous demographic changes. This “echo” effect occurs because the elderly household must save out of social security benefits to repay debt incurred in period 3. Period 5 (not shown in the table) is identical to period 1—both wealth and saving are 0.

Although this example is very stylized, it indicates some important aspects of the effect of demographic change on saving in the presence of an unfunded social security program. The first is that the saving rates of the young and elderly vary over time in response to demographic shifts. This means that the approach of weighting fixed saving rates by changing population shares is invalid. For instance, in period 1, the saving rates of both generations are zero. Varying the weights applied to these saving rates would imply—incorrectly—an unchanged aggregate saving rate in the face of a demographic shift. The second point is that there is no general tendency for the saving rate of the young to exceed that of the elderly. Indeed, in periods 3 and 4, the saving rate of elderly households exceeds that of young households. Nevertheless, the shift toward a more elderly population in period 3 reduces the aggregate saving rate by the same amount as in the example in which there is no social security and the saving rate of the elderly is always below that of the young.

Appendix 4-2. A Life-Cycle Model of Household Behavior for Japan

The life-cycle model used in this section is similar to that described by Tobin (1967) for the United States. The principal differences are that the model used here takes into account social security benefits and contributions, and also allows for precautionary saving, since the risk of death is not insured through private annuity contracts. In addition, the model used here is solved numerically rather than analytically, allowing more general specification of some relationships. The economy consists of overlapping generations of households, each of whose behavior follows life-cycle principles. A period in the model is one year in length. Households are assumed to become economically active at age 20, and the oldest possible age is 100. Each life-cycle then consists of 81 periods, and there are 81 distinct ages of households living at any time.

The time of death is uncertain; the probability of dying at a given age is based on 1990 mortality tables for Japan. Households maximize expected lifetime utility subject to the constraint that they cannot die with negative wealth even if they live to the oldest possible age. Thus the present value of planned consumption to age 100 cannot exceed that of lifetime wealth. Households that die before age 100 typically die with positive assets and leave a bequest; the after-tax value of bequests is divided among households aged 20 (the effective tax rate on bequests is assumed to be 25 percent).

Household wealth at age 20 consists of human wealth, social security wealth, and bequests. Human wealth is the discounted value of labor income, based on a cross-section profile of household labor income from the 1990 FIES. The profile of labor income shifts up over time, on the basis of assumed productivity growth of 1.7 percent a year. Growth in the earnings of a specific household then reflects both movements up the age-earnings profile as well as the upward trend in the profile itself. Households pay social security taxes on labor income and receive benefits beginning at age 60, on the basis of an average replacement rate of 40 percent. The tax rate on workers is adjusted to finance benefits on a pay-as-you-go basis. Labor supply is exogenous; thus, labor income is not affected by changes in the social security tax rate or benefits.

The consumption path of each household is determined by maximizing lifetime utility, where the latter is defined as the utility of “discretionary” consumption in each period discounted by a rate of time preference (p); the rate of time preference was set to equal 0 in the simulations, following Tobin (1967). The utility derived from discretionary consumption is proportional to the number of “adult-equivalent” members of the household at a given time; for this purpose, each child under the age of 20 represents ½ of an adult. The utility function for each period exhibits constant relative risk aversion; assuming a degree of risk aversion of unity implies that utility is simply the natural logarithm of consumption. Discretionary consumption at age t is measured as total consumption, Ct, less a minimum (“subsistence”) level of consumption, C:¯

U(Ct)=log(CtC¯).

The subsistence level of consumption was set to equal about ⅓ of the total consumption of working-age house-holds. The optimal growth rate of discretionary consumption at age t is then

(CtC¯)/(Ct1C¯)={(1+r)/[(1+ρ)(1+αt)]},

where r is the real interest rate (assumed to remain constant at 3 percent a year), and αt is the mortality hazard at age t. Household saving in each period equals the difference between income and consumption, where income includes the return on accumulated assets.

The equilibrium household saving rate and assets-to-income ratio for an assumed population growth rate of 1 percent a year were shown in the main text. The effect on the results of changing the population and productivity growth rates, and other parameters, was also examined. Compared with the baseline saving rate of 16.7 percent and asset-to-income ratio of 5.5, when the population growth rate is raised to 2 percent a year, the saving rate rises to 17.2 percent, but the asset-income ratio falls to 4.3. If productivity growth is raised to 2.7 percent a year, the saving rate drops to 12.2 percent, and the asset-income ratio falls to 3.0. When the real interest rate is increased to 4 percent a year, the saving rate jumps to 20.1 percent, and the asset-income ratio rises to 6.7 compared with the baseline. Increasing the social security replacement rate by 10 percent, to 50 percent, makes the saving rate fall to 13.9 percent, and the asset-income ratio drops to 4.6.

The most notable aspect of these results is that the saving rate declines in response to higher productivity growth. In contrast, some proponents of the life-cycle model have maintained that the saving rate should depend positively on productivity growth because a faster growth rate would shift income to the working generation—who have high saving rates—thus raising the aggregate saving rate. Such a result, however, depends on the assumption that working-age households are not forward looking. When they are forward looking, faster productivity growth raises lifetime resources relative to current income, lowering the saving rate. This offsets the shift in income to working-age households: the net impact on savings is ambiguous a priori. In the model considered here, the rise in consumption by the young more than offsets the shift in income shares, causing the aggregate saving rate to fall.

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1

A comparison of the outlook for the major industrial countries is presented in Masson and Tryon (1990).

2

For one of the early expositions of the life-cycle model, see Ando and Modigliani (1963).

3

When pension benefits are lump sum and the expected return on contributions equals the market interest rate, the offset will be one for one. When benefits are earnings-tested, or the rate of return exceeds the market interest rate, social security may induce households to retire earlier. Higher private saving for a longer retirement period (the “retirement” effect) would then tend to offset, at least partially, the saving “replacement” effect (see Feldstein (1974)).

4

Horioka (1991) has presented calculations that yield even larger effects, implying that the household saving rate would become significantly negative as early as 2010.

5

Appendix 4-1 provides an example of why holding the saving rates of different age groups constant is inappropriate in the presence of a social security program that is not fully funded.

6

See Auerbach, Cai, and Kotlikoff (1990) for a dynastic model that generates significant changes in saving rates as a result of demographic transitions.

7

Imperfections in capital markets could limit the ability of house-holds to smooth consumption by borrowing against future earnings. To the extent that such constraints are relevant in the life-cycle model, consumption would tend to be lower in the early stages of life and higher in the retirement period. This would tend to magnify the gap between the saving rates of working-age and elderly households.

8

Interest income on the remaining principal is small relative to the rate at which the principal is being run down.

9

This is especially true for the United States, where insufficient data have been available on household consumption to observe household saving rates directly.

10

Campbell (1991), for instance, has questioned the approach taken by Hayashi and others (1988).

11

Elderly households are defined as having a household head aged 60 years or over.

12

Takayama (1992) observes a similarly high ratio of social security benefits to household income in the 1984 National Survey of Family Income and Expenditures.

13

These data are only suggestive because of possible differences in the characteristics of working and retired households.

14

The initial elderly dependency ratio is 19 percent, and the ratio of the disposable income of working-age to elderly households is 1.8.

15

See Hurd (1990) for a discussion of the effect of mortality hazard on consumption profiles.

16

As measured by the ex post yield on government bonds, adjusted for increases in the GNP deflator.

17

The parameterization of the model is discussed in more detail in Appendix 4-2.

18

This evidence supports the original findings of Tobin (1967) for the United States and contradicts those of White (1978) and other authors who have suggested that the life-cycle model is not capable of explaining observed household saving behavior.

19

The saving rate would also be affected by the stance of fiscal policy. These simulations assume that the pension system is operated on a pay-as-you-go basis, implying a future rise in contribution rates to balance increasing benefits. Section V of this volume discusses alternative long-run simulations in more detail.

20

The collinearity of the explanatory variables implies that t- statistics may be low, even though the parameters are large in absolute magnitude. The choice of a specification that yields statistically significant parameters may imply parameter values that lie on the high end of the range of values that would be supported by the data.