Pensions in a shrinking economy
- 230 Downloads
- 1 Citations
Abstract
An aging society with an absolutely or relatively declining labour force can – with constant capital intensity – experience a reduction in the national capital stock thereby in the short-term disengaging resources, which can be transferred to the elderly for consumption purposes. Hence, net savings are negative: dissavings of the pensioners exceed savings of the working-age population. An aging society can indeed survive by ‘eating up part of its capital stock’ for some time.
Keywords
shrinking population pensions economy savings and investmentsINTRODUCTION
Both developed and underdeveloped countries are undergoing in the twenty-first century a major secular demographic transition. The transitional process consists of a continuing fall in fertility and expansion of life expectation and it determines a progressive aging of most of the world population. In developed countries, the two persistent determining factors have been at work for many decades. In these countries, the fertility rate fell from 2.8 in 1950–1955 to 1.5 in 2000–2005, far below the replacement level of 2.1 children per woman. 1 Furthermore, in the first three or four decades of the twenty-first century the developed countries will face the retirement of their baby-boom generations. A number of developed countries, particularly those that recently started economic take-off and practised further development are also undergoing the demographic transition from higher fertility rates towards below-replacement rates leading to a continuing shrinking of the total population. In the developing countries, thus, aging will become apparent in the second half of the twenty-first century.
It is generally agreed upon that in an aging and shrinking population the forthcoming labour force scarcity – particularly in Southern and Eastern European countries, where between 2010 and 2050 the working-age population is likely to decline by about one-third – will increasingly place economies under strain, thereby jeopardizing the sustainability of old-age pension systems. After years of concern about the high growth rates of the world population nowadays in many developed countries the aging and the shrinking of the population is increasingly felt as a major problem. 2
Population aging has potentially substantial implications for the performance of the economy. There is a widespread fear that an increasing proportion of the elderly combined with a decline in the work force will deteriorate economic development, leading to a lower level of GNP and per capita GNP, hence lower net income for the workers and the pensioners. In particular an unstable age structure, for example a low proportion of working-age persons in the total population means that production likely will decrease relative to consumption and impede economic growth. On the other hand, a relatively smaller number of workers may lead to a higher retirement age and longer working days resulting in increased labour force participation. The crucial question western countries are confronted with therefore remains whether, and if so, how population aging with corresponding declining working-age population will affect the economic well-being of their citizens? Or, in other words, can sustainable prosperity be ensured in an aging and shrinking society?
The present article deals with this important question and concludes that an aging and shrinking society can maintain welfare for some time by not replacing part of its capital stock and transfer the resources becoming free for provision of additional income to the retirees. Our analysis begins with describing the adjustment of the production factor capital in a shrinking economy (Section ‘Capital in a shrinking economy’). Section ‘The model’ (with Appendix) describes in a highly stylized framework the working of a mature pension scheme based on funding as a process of transfer of income between generations regulated by the market transaction of capital assets that workers buy when active and sell when they retire. Section ‘Shrinking population and pension scheme financed by funding’ and ‘Secular decline of the population and pension scheme under funding’ consider the effects of a one-off and of a secular demographic decline, respectively, in an economy with an embedded pension system (financed by funding) on the main economic variables, size of capital stock, capital intensity, national income, national savings, wage rate, interest rate, per capita consumption of workers and of pensioners. Section ‘Concluding remarks’ draws conclusions.
CAPITAL IN A SHRINKING ECONOMY
It is generally argued that Western welfare states can neutralize the detrimental effects of population aging and subsequent population decline on productive capacity up to a certain extent by an increase of the retirement age, longer working days and/or a further increase of participating of the working-age population – in particular those groups which now suffer from low employment – in the labour force.3, 4 But above all labour force productivity growth is of crucial importance. Immigration can be beneficial to the economy only if the integration of the migrants into the workforce and into the society as a whole is successful. 5 The productive capacity of countries is declining with the size of the labour force but increases with the productivity rate of the smaller labour force. If smaller cohorts of workers have higher levels of human capital – because the preceding generation has invested more in each child – standards of living may rise further despite aging and a higher amount of transfers to the elderly. 6
It can be shown that even a modest rate of technological progress is (necessary and) sufficient to offset the adverse consequences of population aging and a declining labour force on welfare and the consumption level.7, 8 Note that in those analyses the capital effect in a shrinking economy is ignored.
An aging society (opposed to a younger society) can hold and probably will hold most of the time a larger capital stock; hence a higher capital intensity (or capital–labour ratio), a declining capital productivity and a rising labour productivity and higher real wages. Therefore, an enhanced capacity is created to finance old-age pensions. In an aging society with an absolutely or relatively declining labour force, new relative scarcities of factors also arise. Labour is now scarcer opposed to capital, leading to higher levels of wages and lower interest rates.
- a
No reduction in net per capita investment, leading to a further increase in the capital intensity of production. Consequently, today less consumption goods can be produced. On the other hand, the higher capital intensity gives rise to a larger labour productivity and a larger future resource base. High flexibility of the economy, viz. a high elasticity of substitution between capital and labour and a high elasticity of savings to the interest rate, makes that a larger part of the capital stock – becoming redundant as a result of the declining labour force – can be absorbed by an increase in the capital intensity, resulting in a higher per capita level of output, hence of workers’ income and even of pension benefits.
- b
A reduction in net investments occurs but they remain positive – the capital stock and the capital intensity are still increasing – thereby augmenting in the medium term, the volume of consumption for the whole population. In this case, savings of the younger population still exceeds dissavings of the elderly, but to a diminishing extent. Eventually, net investments and net savings become zero: the copper rule zero growth path arises. 9 Note that the case of zero net savings is only consistent with zero population growth and constant capital–labour ratio or consistent with a declining population with higher capital–labour ratio. Note also that the scale of the benefits of a lower investment level and a lower required savings rate would likely to be less than the figures might suggest. Only new capital investments are in most cases incorporating new technologies of production, which are of crucial importance for further productivity growth. Relying on the old capital stock alone means a productivity loss. Capital accumulation combined with good institutions, policies and technological progress will without diminishing marginal capital returns result in continued economic growth.
- c
A reduction in the stock of capital – with constant capital intensity – thereby (in the short term) disengaging resources that can be transferred to the aged. In this case, net investments are negative or, in other words, dissavings of the elderly exceed savings of the working population. An aging society can indeed ‘live on its capital’ for some time. Part of the capital stock is not reproduced and consumption goods are produced instead of replacing worn-out capital goods. 10
- d
As far as the allowable rate of capital stock reduction does not exceed capital depreciation, redundant capital can be disengaged rather easily by diminishing or halting gross investments and, hence, can be easily ‘turned back into consumption’. The fastest feasible decline is given by the rate of deplacement. On the other hand, when allowable disinvestment exceeds capital depreciation practical problems arise in respect of the (physical) feasibility of consuming part of the existing capital stock. When allowable disinvestment equals capital depreciation, – that means a steady-state contraction of the capital stock – the economy with a decreasing labour force moves along the equilibrium negative growth or decline path. We may speak of the iron rule decline path. 9 As a consequence, there is no need for new pension savings apart from the case of compensating dissavings elsewhere. 11
- e
Ultimately, capital equipment invested abroad (running surpluses on the current account) can be sold, thereby acquiring foreign currency by which consumer goods can be bought (implying sustained current account deficits). 12
In the 1960s (when Aaron wrote his famous article), there were no limits to growth (or we were not aware of it) of the world economies. The first report of the Club of Rome (1971) warned humanity for depletion of resources of energy and of other raw materials. They were largely ignored. At the beginning of the twenty-first century scarcity of energy, many other exhaustible resources and food products are resulting in substantial price increases that may impediment further economic development.
In conclusion, in an aging society it is far from sure that the golden rule growth path will continue forever. By reducing the capital stock in relative or even in absolute terms per capita welfare, nonetheless, can be maintained for some time. In a later stage, growth rates of national product can become zero or even negative. Unluckily we might notice a quite new trend, viz. that many economies after some point of time in the twenty-first century will be moving from a golden rule growth path via copper rule zero growth to an iron rule decline path.
PENSIONS IN A SHRINKING ECONOMY
In the present paragraph, we consider some illustrative numerical examples that show how an economy with an incorporated pension scheme based on funding evolves and adjusts to a shrinking of the population. We utilize the basic neo-classical model where the capital is owned by the elderly via pension funds.
The model
We consider a stationary neo-classical economy with two identical overlapping generations. The three conditions of equilibrium are full capacity, full employment and equality of savings and investments. Thers is no technological progress or productivity growth. In the stationary state net savings are zero. There are two equal-length life periods: each person works in period 1 and is retired in period 2. The elderly lends the total amount of savings accumulated during their working years at the beginning of each period to the pension institutions, which in turn invest them in productive activities. At the beginning of each period, the firms that borrowed the financial capital from the pension funds hire the labour force. At the end of each period, net per capita national product is composed of the wage rate and the return to capital. The workers use their wages for consumption and buying assets from the old generation. The old generation consumes all its income (their original capital plus interest earned on it) and dies.
The demography thus is characterized by a stationary or zero growth population with two overlapping generations – groups of workers and retired non-workers – of size N equal to 100 individuals each. In the next Sections ‘Shrinking population and pension scheme financed by funding’ and ‘Secular decline of the population and pension scheme under funding’ owing to a fall in fertility the working population in period 1 – note that the length of a period is roughly 30 years – shrinks from 100 to 90. In period 2, demographic equilibrium is restored resulting into 90 individuals in both groups of workers and retirees. In Section ‘Higher longevity’ population decline continues until in period 15, the size of the groups of workers and retirees stabilizes at 50 individuals each. Furthermore, in a stationary population the economy with zero net savings is stationary also. Workers and retirees consume according to their preferences equal amounts of goods and services. Dissavings of the elderly are precisely matched by savings of the working population. The pension funds system functions as an intermediary between the overlapping generations.
To better show the working of pension finance systems in a Cobb–Douglas framework, we make use of the so-called transition equation, as employed, for example, by Auerbach and Kotlikoff (see in more detail in the Appendix section). 13
Shrinking population and pension scheme financed by funding
Old steady state
Population decline in period 1 in a neo-classical economy; pensions financed by funding
| Period | Working population | Retired population | Capital stock | Per worker capital | National income | National savings | Wage rate | Interest | Per capita workers | Consumption pensioners |
|---|---|---|---|---|---|---|---|---|---|---|
| (N w ) | (N r ) | (K) | (K/N w ) | (Y) | (S) | (w) | (r) | (c w ) | (c r ) | |
| Old steady state | 100 | 100 | 268.89 | 2.69 | 1345.5 | 0.00 | 9.42 | 1.50 | 6.73 | 6.73 |
| 1 | 90 | 100 | 268.89 | 2.99 | 1249.8 | −19.12 | 9.72 | 1.39 | 6.95 | 6.44 |
| 2 | 90 | 90 | 249.77 | 2.78 | 1222.5 | −5.47 | 9.51 | 1.47 | 6.79 | 6.85 |
| 3 | 90 | 90 | 244.31 | 2.71 | 1214.4 | −1.62 | 9.45 | 1.49 | 6.74 | 6.76 |
| 4 | 90 | 90 | 242.69 | 2.70 | 1212.0 | −0.48 | 9.43 | 1.50 | 6.73 | 6.73 |
| 5 | 90 | 90 | 242.21 | 2.69 | 1211.2 | −0.14 | 9.42 | 1.50 | 6.73 | 6.73 |
| 6 | 90 | 90 | 242.06 | 2.69 | 1211.0 | −0.04 | 9.42 | 1.50 | 6.73 | 6.73 |
| — | — | — | — | — | — | — | — | — | — | |
| — | — | — | — | — | — | — | — | — | — | |
| New steady state | 90 | 90 | 242.00 | 2.69 | 1210.9 | 0.00 | 9.42 | 1.50 | 6.73 | 6.73 |
| Total consumption 1210.9 | ||||||||||
The retirees own the capital stock, 268.9 units of account that via the pension fund system has been lent to the firms. The firms pay the workers wages equal to the marginal product of labour. A paternalistic imperative says that consumption opportunities for workers and elderly are equal. The contribution rate of the pension scheme appears to be 0.2855. National product is 1345.5. The per capita consumption is 6.73 units. For a retired individual, the 6.73 units are equal to the value of the per capita capital stock (2.69 units) plus the interest on it of 1.50. 14
One-off decline of the labour force; transition to a new steady state
We will next consider how a neo-classical stationary economy adjusts to a decline in fertility. Assume a baby bust, leading to a lower number of workers. In the example shown in Table 1 (: transition to a new steady state), we assume that in period 1 a decline in fertility level reduces the working population from 100 to 90. Labour is becoming more scarce. As a result the wage rate tends to increase and – given the labour supply of 90 workers and the unaffected capital supply of 268.9 units – becomes equal to 9.72 units. The new capital–labour ratio is higher than before, 2.99 opposed to 2.69, leading to a lower interest rate, 1.39 opposed to 1.50 and a higher wage rate, 9.72 against the pre-baby bust value of 9.42 and a higher level of consumption of the workers of 6.95 (in period 0: 6.73). This phenomenon is referred to as the demographic dividend. Owing to the fall in the interest rate per capita consumption of the elderly decreases from 6.73 to 6.44 units. 15
Total wages in period 1 amount to 874.8 (that is, 9.72 × 90) and workers’ savings are accumulated to 249.8 (that is, 874.8 × 0.2855), which are lower than before 268.9 (: 942 × 0.2855) because the number of workers is lower. The capital stock at the beginning of period 2 is 19.1 units less than the capital stock at the beginning of period 1. Or, in other words, the dissavings of the retired elderly are not completely matched by the savings of the working population. Aggregate net savings are −19.1. Part of the capital stock has not been replaced but instead consumption goods are produced, which are consumed by the pensioners (0.19 unit per head). 16 Remember that the retirees have the ownership of the capital stock and, thus, are exclusively entitled to income supplements from dissavings. Total consumption in period 1 is 1268.9, which is higher than national product (that is 1249.8). The difference is again 19.1, that is the decline in the capital stock which is eaten up.
In the second period, the lower savings of the smaller working population lead to a rise in the interest rate and consequently to a lower capital intensity of national production. In this period and in following periods also the savings supply of the workers is insufficient to uphold the capital stock, which continues to decline from 268.9 to 242.
The new steady state is restored at a position of lower aggregate activity (Y=1210.9), but with the same capital intensity of production, at the same wage rate (w=9.42) and identical interest rate (r=1.50). Per capita levels of consumption (both c w and c ret 6.73 units) are equal to those in the old steady state. The number of both workers and retirees is 90, opposed to 100 earlier. In the new steady state, the fertility rate is back on its replacement level.
Age structure
We may observe that age structure is ignored in the model used. Age structure directly determines the relative size of the working-age population given that labour force participation rates vary by age. A decline in fertility rates reduces the number of children and raises the share of the working-age population and labour supply in the short run. Persistently low-fertility levels (below replacement value) imply a relatively large size of the elderly and a smaller size of the young working generation compared with the stationary (zero-growth) population. In period 1, birth rates are assumed to return to their replacement level of 2.05.
Finally, note the crucial assumption made that the adjustment of the economy, viz the capital stock to the fertility shock always will take place smoothly. In period 1, the capital supply is relatively abundant, interest rate falls and the capita-labour ratio increases. Actually dissavings take place. Later, the production factor capital becomes relatively scarcer again and the interest and the capital–labour ratio restore to the old steady-state level. Such an adaptibility highly likely does not exist in the real world. The model leaves practically no scope for distortions.
Summarizing, the potentially adverse effects of a one-off decline of the labour force for welfare and consumption can easily be absorbed by not replacing part of the capital stock (or dissavings), keeping per capita consumption of both workers and pensioners, per worker capital and the contribution level constant from one steady state to the other.
Secular decline of the population and pension scheme under funding
Proportional shrinking population in a neo-classical economy; pensions financed by funding
| Period | Working population | Retired population | Capital stock | Per worker capital | National income | National savings | Wage rate | Interest | Per capita workers | Consumption pensioners |
|---|---|---|---|---|---|---|---|---|---|---|
| (N w ) | (N r ) | (K) | (K/N w ) | (Y) | (S) | (w) | (r) | (c w ) | (c r ) | |
| Old steady state | 100 | 100 | 268.89 | 2.69 | 1345.5 | 0.00 | 9.42 | 1.50 | 6.73 | 6.73 |
| 1 | 95 | 100 | 268.89 | 2.83 | 1298.0 | −9.44 | 9.56 | 1.45 | 6.83 | 6.58 |
| 2 | 90.3 | 95 | 259.41 | 2.87 | 1238.8 | −11.83 | 9.61 | 1.43 | 6.87 | 6.64 |
| 3 | 85.7 | 90.3 | 247.58 | 2.89 | 1178.5 | −12.05 | 9.62 | 1.43 | 6.88 | 6.66 |
| 4 | 81.5 | 85.7 | 235.53 | 2.89 | 1120.1 | −11.68 | 9.63 | 1.43 | 6.88 | 6.67 |
| 5 | 77.4 | 81.5 | 223.84 | 2.89 | 1064.2 | −11.16 | 9.63 | 1.43 | 6.88 | 6.67 |
| 6 | 73.5 | 77.4 | 212.68 | 2.89 | 1011.0 | −10.63 | 9.63 | 1.43 | 6.88 | 6.67 |
| — | — | — | — | — | — | — | — | — | — | |
| — | — | — | — | — | — | — | — | — | — | |
| 14 | 50 | 51.3 | 140.70 | 2.81 | 682.1 | −5.24 | 9.55 | 1.45 | 6.82 | 6.74 |
| — | — | — | — | — | — | — | — | — | — | |
| — | — | — | — | — | — | — | — | — | — | |
| New steady state | 50 | 50 | 134.45 | 2.69 | 672.7 | 0.00 | 9.42 | 1.50 | 6.73 | 6.73 |
| Total consumption 672.7 | ||||||||||
In the new steady state, both the working population and retired population are 50, half of the population size in the old steady state. 18 Also national income is reduced by 50 per cent to 672.7. All per capita economic variables are at their original level. After a very long period of relatively low-fertility rates it finally is restored at its replacement level around 2.05.
Conversely, if we imaginarily face continued low-fertility rates assuming no net immigration and constant longevity population size declines persistently. The economy is shrinking proportionally and ultimately comes to a complete standstill approaching zero level. That can be considered as a sustainable, but highly likely not as a desired equilibrium.
Higher longevity
Shrinking population and living longer in a neo-classical economy; pensions financed by funding
| Period | Working population | Retired population | Capital stock | Per worker capital | National income | National savings | Wage rate | Interest | Per capita workers | Consumption pensioners |
|---|---|---|---|---|---|---|---|---|---|---|
| (N w ) | (N r ) | (K) | (K/N w ) | (Y) | (S) | (w) | (r) | (c w ) | (c r ) | |
| Old steady state | 100 | 100 | 268.89 | 2.69 | 1345.5 | 0.00 | 9.42 | 1.50 | 6.73 | 6.73 |
| 1 | 95 | 120 | 330.11 | 3.47 | 1380.4 | 8.57 | 10.17 | 1.25 | 6.61 | 6.20 |
| 2 | 90.3 | 114 | 338.69 | 3.75 | 1342.0 | −9.42 | 10.41 | 1.19 | 6.76 | 6.50 |
| 3 | 85.7 | 108.3 | 329.26 | 3.84 | 1283.8 | −14.29 | 10.48 | 1.17 | 6.81 | 6.60 |
| 4 | 81.5 | 102.9 | 314.97 | 3.87 | 1222.2 | −15.31 | 10.51 | 1.16 | 6.83 | 6.62 |
| 5 | 77.4 | 97.7 | 299.85 | 3.88 | 1161.7 | −14.81 | 10.51 | 1.16 | 6.83 | 6.63 |
| 6 | 73.5 | 92.9 | 285.03 | 3.88 | 1103.9 | −14.20 | 10.51 | 1.16 | 6.83 | 6.64 |
| — | — | — | — | — | — | — | — | — | — | |
| — | — | — | — | — | — | — | — | — | — | |
| 14 | 50 | 61.6 | 188.72 | 3.77 | 744.8 | −6.92 | 10.43 | 1.18 | 6.77 | 6.71 |
| — | — | — | — | — | — | — | — | — | — | |
| — | — | — | — | — | — | — | — | — | — | |
| New steady state | 50 | 60 | 180.22 | 3.60 | 734.6 | 0.00 | 10.28 | 1.22 | 6.68 | 6.68 |
| Total consumption 734.6 | ||||||||||
In the new steady state, the capital–labour ratio is 3.60 vis-à-vis 2.69 before. As a result, labour productivity rises from 13.45 to 14.69. Hence, despite considerable aging the per capita consumption is only slightly less than in the old steady state, 6.68 against 6.73.
Summarizing, it appears that the potentially adverse result of a relative or even absolute decline in the labour force on the economic well-being (consumption level) of the population can at least partially, but virtually always fully be offset by dissavings (or the effect of non-replacing part of the capital stock). In addition, owing to a higher capital intensity of the economy during the transitional period a higher level of consumption of the workers can be realized. The pensioners’ consumption at that time is slightly less.
CONCLUDING REMARKS
In the present article, we examined the effects of a one-off and a secular decline in population on the main economic variables using a basic neo-classical framework and a Cobb–Douglas production function with unitary elasticity of factor substitution. Stylized numerical examples are utilized as an illustration.
We may conclude that the economy adapts to a demographic decline in the first place through a rise in the capital intensity leading to a lower interest rate and a higher wage rate, enabling higher consumption for the workers, but not so for the retired. By not replacing part of the capital stock additional resources become available for the elderly for maintaining at least in part their level of consumption. A highly flexible economy makes it more likely that some part of the capital made redundant by a decline in the labour force will be absorbed by an increase in the capital–labour ratio and another part will become free for supplementing the consumption of the pensioners. Up to the present time this so-called Solow effect has not been a major factor, but it can be an important one in the coming decades in aging countries.
The economic effects of population decline will be more in line with the aforementioned findings when the country is larger, while for a smaller country like the Netherlands the economic effects of a shrinking population may be either amplified or reduced owing to specific economic characteristics of the smaller country, for example, the interest rate is a exogenous variable, hence independent of a changing capital–labour ratio. In addition, there are differences among member states in their preferences for leisure and consumption over time and pension arrangements vary considerably in scale and scope.
Finally, it is (too) easy to forget how rapidly real incomes have grown over the twentieth century, viz. about a sevenfold increase. At current trend growth rates GDP will double in real terms roughly every 30–35 years. It can be concluded that without doubt we can afford to grow older. We in the European countries (and elsewhere in the more developed world as well) are rich enough to sustain an old-age pension for a more numerous older population. A fortiori, it can be said that we are approaching saturation in the consumption of material goods, not only of necessities but of luxury goods as well, which were only science fiction or dreams during the first half of the twentieth century. 20
As individuals and nations grow more affluent they tend to increase the share of total spending devoted to some commodities and reduce the share devoted to others. Food is a clear example of the first category. Outlays for health, education and provision for incomes in retirement, sickness/disability and unemployment will all increase their share as per capita national income rise. As individuals and nations continue to grow more affluent it seems likely that they will wish to spend – and can afford to do so – more on pension income and health care. Hence, the share of expenditures for pension provisions and health care facilities in national income will grow further and as a result is not anything to be concerned about.
REFERENCES AND NOTES
- UN Population Division. (2009) World Population Prospects: The 2008 Revision. New York: UN Population Division.Google Scholar
- It is impressing that the hypothetical continuation of the current fertility rates would lead to a population from 6.1 billion in 2000 to 12.8 billion in 2050, 43.6 billion in 2100, 244 billion in 2150 and 134 000 billion in 2300. Attention to a declining population was already given by Keynes, J.M. ((1937) Some economic consequences of a declining population. In: D. Moggridge (ed.) The Collected Writings of John Maynard Keynes. London: Macmillan).Google Scholar
- Policy measures may include a higher retirement age, reducing older workers’ wage gains – so that older workers are no longer such more expensive than younger workers – and eliminating basic held views about the employment of older people. Recommended are policies directed at increasing employment opportunities for older workers by recontracting them in less prominent jobs with lower wage rates..Google Scholar
- Jensen, S.E. and Jorgensen, O.H. (2009) Low fertility, labour supply and retirement in Europe. Sankt Gallen: University of St. Gallen. WDA−HSG discussion paper 2008/3) argue that in European countries a higher retirement age tends to decrease labour supply. This is exactly the opposite of what policy measures intend to make happen.Google Scholar
- Note that, for example, immigration from Eastern European countries apart from brain drain is making the aging of the population in those countries even more serious.Google Scholar
- Despite higher participation rates the working population in Western countries ultimately will decline. As long as productivity growth is exceeding population decline GNP continues to grow. Only a stagnating productivity growth in a more distant future will be unable to offset the decline in the employed working-age population.Google Scholar
- See, for example, Kuné, J.B. (2003) On Global Aging; Old−age Income Systems in the EU and Other Major Parts of the World. Heidelberg, Germany: Springer-Verlag.Google Scholar
- Kuné, J.B. (2009) Population aging and welfare: The case of the Netherlands. Pensions: An International Journal 14 (4): 231–241.CrossRefGoogle Scholar
- Opposed to the golden rule growth path, well known from economic growth theory.Google Scholar
- This effect is also called the Solow effect: Society can permit to consume more whereas it is able to invest less and still maintain the per worker production level. Again, innovative technology cannot or only to a minor extent be introduced, as they are often incorporated in reproduced capital goods. The situation can get worse if the baby boom generation in the coming decades want to sell their assets to the smaller younger cohorts resulting in an ‘asset market meltdown’.Google Scholar
- As a consequence the elderly also lack the ownership of the pension capital stock that can be considered as a more secure basis for retirement income than the willingness and ability of the current labour force for paying pension contributions under a pay-as-you-go system.Google Scholar
- Increased investment abroad may alleviate the aging problem in the ‘western’ developed countries. Note, however, that virtually all the major (and smaller) developed countries will have the same problem in nearly the same time period ahead. The aging ‘western’ world as a whole has only a rather small foreign sector. Or, in other words, not all societies can play the same game at the same time. Japan, for instance, has during the last few decades invested its current account surpluses abroad, to a large extent however in countries which also face an aging problem. Realizing overseas assets Japan – on a macro-level – may probably solve at least in part its aging problem but at the expense of making the problem of those other countries worse.Google Scholar
- The Auerbach−Kotlikoff (A–K) framework (see Note 19) – applied by themselves for presenting the transition path following an epidemic – can be employed in answering the question whether pension schemes can be helpful in the face of labour force decline and whether part of the capital stock can be transformed smoothly into consumption for the retired. The A−K framework is used by S. Cesaratto (Pension Reform and Economic Theory; A Non-Orthodox Analysis. Cheltenham, UK: Edward Elgar) to criticize the neo-classical approach in pension reform measures. Evidently, integrated analyses are preferential to investigate the effects of a demographic transition on the economy. Noteworthy are the INGENUE − studies of CEPII; for example, M. Aglietta, ((2001) Macro-economic Consequences of Pension Reform in Europe: An Investigation with the INGENUE World Model, Paris: CEPII. Working Paper 17).Google Scholar
- The interest rate r is not an annual interest rate. The length of a period in the model of Section ‘The model’ is roughly 30 years. The corresponding annual interest rate is 3.1 per cent.Google Scholar
- Note that the effects of a demographic change on human capital is ignored. If parents invest more in child quality, when there are less children, a declining labour force is accompanied by more human capital per worker leading to a higher level of production and welfare.Google Scholar
- Only part of the capital stock that wears out is replaced. In Table 1, the replacement rate in period 1 is 7.1 per cent (19.12 divided by 268.89). Since we consider periods of about 30 years this percentage is very low. Depreciation generally will be much higher.Google Scholar
- Note that in the converse situation of a persistently growing population the capital intensity is lower. Also per capita consumption during the transition to a new steady state is lower than in equilibrium owing to positive net savings.Google Scholar
- The recovery of countries with rather low-fertility levels (less than 1.5) to a new steady state of population size on replacement level appears to be increasingly difficult (Lutz, L. (ed.)) (2006) The low fertility trap hypothesis: Forces that may lead to further postponement and fewer births in Europe. Vienna Yearbook of Population Research 2006. Vienna, Austria: Austrian Academy of Sciences).Google Scholar
- For simplicity it is assumed that 100 retired people living (1+x) periods can be approximated by 100 ×(1+x) retired people living one period.Google Scholar
- In most western countries, nowadays, the poverty line is at a level of real income that was attained by only those in the highest 10 per cent of the income distribution about 1900.Google Scholar
- As in Auerbach and Kotlikoff ((1995) Macroeconomics; An Integrated Approach. Cincinnati, OH: South−Western College Publishing).Google Scholar
- A slightly different approach is followed by L. Seidman (1999) Funding Social Security; A Strategic Alternative. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar