پویایی پس انداز دوران بازنشستگی - تئوری و واقعیت

Pension problems and reforms are in the foreground of public interest and political action in many countries, yet economic theory offers inadequate support for finding viable solutions, because it is heavily loaded with simplifying concepts and unrealistic assumptions. These concepts and assumptions are briefly summarized in Chapter 1, while a generalized framework based on them is presented in Chapter 2. The basic stationary assumption is then relaxed in Chapter 3 what results in the conclusion that a profound, not just technical, but conceptual innovation is required. Chapter 4 outlines a few major issues and concepts for a more realistic pension economics. A summary is given in Chapter 5.

Adults are supposed to work, to earn income and from that to pay for their consumption. Yet in the first and (for the majority) in the last years of human life people do not earn while they must consume. The question is, how are these two, non-earning stages of life financed? The simplified answer is: from the excess income of the stage in-between, in other words, from savings over the earning span. Thereby the rather narrow ‘conceptual framework’ is complete: the trinity of income, consumption and saving explain all aspects of the problem. Maybe a fourth concept, wealth (expectancy, assets, stocks) should be added, although it is nothing but accumulated saving. The problem, by definition, is cross-sectional as well as longitudinal. In any given moment, the young (children), the earners and the elderly (pensioners) live together in human society. On the other hand, all cohorts (generations, surviving individuals) proceed through these three stages of life with the passing of time. It is extremely difficult, however, to handle cross-sectional and longitudinal aspects simultaneously. Theory needs a simplifying assumption: the ‘stationary population’ where all cohorts go through identical life-paths. Sometimes the assumption is quite crude: all individuals are supposed to work for N years and live M years thereafter. Sometimes the approach is more subtle, for example the probability of dying at age k is a given number mk. In some models life consists of two or three periods, in others many years of age are considered. Invariably, however, successive cohorts are identical. Consumption and/or earning depends on age but age-specific properties are constant over time. The most important implication of the stationary assumption is the ‘Golden Rule congruence’. Longitudinal relations are always affected by the growth rate and the interest rate, which make longitudinal concepts numerically different from their qualitatively corresponding, cross-sectional counterparts. If and when, however, these two rates are equal (the Golden Rule case) then longitudinal proportions (in some models even quantities) are identical with the cross-sectional ones. The stationary assumption makes room for the representative individual whose presence is required by orthodoxy, because his role is life-time ‘utility maximization’ under selected constraints. Utility is most often derived from consumption (or in some human capital models from work and/or leisure), while income (or consumption) is exogeneously given. Thus in most models optimization yields the ‘longitudinal allocation’ of consumption (or income) over the life-path. The optimal allocation is then considered viable for all individuals and cross-sectional, macroeconomic conclusions can be drawn. Without exception, optimization is subject to the longitudinal (alternatively referred to as individual, competitive, actuarial) budget constraint, to be called here unambiguously the ‘zero-bequest constraint’, which calls for equality of life-time consumption with life-time income. After this point, however, theory is branching off with respect to the cross-sectional environment. For the life-cycle theory of saving and in most human capital models non-zero aggregate saving is either explicitly required or implicitly presumed, as these theories are mainly concerned with wealth (positive or negative). To the contrary, over-lapping generations (OLG for brevity) are built on the dual-constraint principle: besides longitudinal zero bequest, the cross-sectional (or social, conservative, pay-as-you-go, feasibility, etc.) ‘zero-saving constraint’ is also imposed and situations when both constraints are simultaneously satisfied, are called ‘equilibria’. Technically, a certain clumsiness is characteristic of most studies. One reason is that the growth rate and the interest rate are separately denoted and treated, with the result that at least one of them must be constant over time (whether zero or not, does not really matter too much, except that zero is more convenient). The other reason — in OLG models — is the inconvenience inherent in dealing with two concepts (longitudinal bequest and cross-sectional saving), substituting from here to there, watching two constraints simultaneously.

The financing of the two consumption-dominated stages of life is more or less institutionalized in modern societies. Child-raising and education are supported through tax-exemptions, children's and maternity allowances, government-subsidized schools and universities, student loans — to an extent and in forms that vary from country to country. On the other hand, there exist various types of mandatory pension schemes in most countries and such schemes are largely or almost exclusively responsible for income in old age for the majority of the population. It would be highly desirable for economic theory to consider the two problems and two groups of institutions in their mutual interdependence — in other words, to develop the realistic counterpart of the theoretical three-period case. Arguments could even be raised for an arrangement — maybe somewhat futuristic — where the actual financing of the two consumption-dominated stages would be linked (Augusztinovics (1997)). In contemporary reality, however, several significant factors separate child-costs from retirement financing and this is well reflected in a split literature: one fraction about childhood and human capital, another about retirement. No wonder that the two-period cases of theory are still predominantly referred to, although the gap between a stationary theory and the non-stationary reality is usually ignored. The rest of this paper is devoted to issues, mostly unresolved, waiting for thorough inquiries by the economics of mandatory pension systems. (Voluntary retirement saving, although prudent and desirable, is an entirely different matter that will not solve the problem of old-age income security for the majority of people.) The argument will be built around a tentative, illustrative rather than complete outline of an accounting framework that should be equally relevant for public or private, PAYG (pay-as-you-go) or funded pension schemes. This is not to say that the type of governance and the mode of finance are irrelevant, but these are aspects amply covered in the ongoing pension debates in most countries. Here we shall focus on more basic issues, common for all types of pension schemes: first of all on demographic, economic and system-specific trends that determine cross-sectional and longitudinal balance or imbalance in a system. We begin with two descriptive identities, to reveal the factors that shape the revenues and expenditures of a pension scheme. For the cohort born in x, in calendar period (year) t: equation(14) View the MathML source equation(15) View the MathML source where Hx,t, number of persons in active age; Ax,t, number of contributors (employed); ax,t=Ax,t/Hx,t, employment intensity, vx,t=Vx,t/Ax,t, average wage; Lx,t, number of persons in pensionable age; Zx,t, number of beneficiaries (pensioners); zz,t=Zx,t/Lx,t, retirement intensity; px,t=Px,t/Zx,t, average pension. Both identities begin with the crucial demographic fact, the number of persons in the respective age-span. It should be noted, however, that these numbers are not purely demographic: pensionable age is determined by the statutory retirement age, which may be — often is — different for men and women, for various occupations. This is the first indication of demographic trends being important, but not predominantly responsible for pension problems. Secondly, not all active-age persons are contributors and not all pensionable-aged people are actually pensioners. Partly because early as well as delayed retirement is usually permitted (under certain conditions), and partly because the respective pension scheme may not cover the entire population, or some participants may not have acquired sufficient pension rights on their own. The resulting intensitiesax,t and zx,t thus reflect the coverage by the pension scheme on one hand and the crucial economic effect on the other hand. For historical reasons, most pension schemes are employment-based in the sense that actively employed (often including self-employed) persons are required to contribute, proportionally to their labour income (or a limited portion of it). Various pension systems relate in various ways to those who are not employed (unemployed, students, enlisted soldiers, housewives, disabled persons, etc.). The resulting complications are ignored in this stylized accounting framework — as they should not be in a veritable pension model. Employment and retirement intensity, ax,t and zx,t, respectively, of cohorts around the statutory retirement age tend to move in opposite directions, depending on economic cycles. Pension systems may stumble in times of severe and long-lasting recessions or crises, when output, employment and real wages shrink, when those who can, escape from unemployment into early retirement. For the more distant future of employment-based pensions, the spread of ‘atypical’ working arrangements on the labour market is likely to raise serious problems, as the traditional contribution base will probably be contracting to an extent far beyond the much-feared demographic effect. Relations with the income tax system (e.g. wages may be gross and pensions net of tax, etc.), possible exemptions from contribution and non-compliancy are also ignored in our stylized framework. What remains, therefore, is average wage vx,t and average pension px,t to be taken into account. Assuming that contributions are due — and paid — according by a rate mx,t out of the contribution base Vx,t, the revenues and expenditures of the pension system, and/or individual cohorts, can be accounted for by aggregation. Elegant theorems can be hardly proved but crucial empirical analysis is possible and desirable. For transparency, we define cross-sectional and longitudinal average rates, applying a constant ρ technical discount factor in the latter cases (more refined methods of averaging are of course possible). Henceforth bold characters indicate longitudinal concepts: View the MathML source Let us first consider the relation between expenditure and the contribution base cross-sectionally. If the mt contribution rate corresponded exactly to their ratio, the annual balance in t would obviously be zero. Hence the ratio may be called the ‘internal contribution rate’ of the system: equation(16) View the MathML source where View the MathML source, demographic dependency ratio; View the MathML source, intensity ratio; View the MathML source, ‘replacement’ rate; gt=dtit, system dependency ratio. System dependency gt — the product of demographic dependency dt and intensity ratio it — equals the ratio of beneficiaries over contributors. Prudent studies of pension issues discuss the concept, but it is often identified with the demographic ratio in simplified arguments for general public consumption. Empirical evidence, however, demonstrates that system dependency may seriously deteriorate for economic reasons, resulting from a sharp rise of the intensity ratio (declining employment and increasing retirement), even during demographically benign periods. Exactly this has happened, for example, during the 1990s in the Central-European transition countries (cf. Augusztinovics (1999)). Reversely, a favourable decrease of the intensity ratio (shrinking unemployment and delayed retirement) may well counter-balance, at least to a large extent, the effect of population aging in the next century. The ratio of average pension over average wage, rt is generally called replacement rate, but quotation marks are justified since present pensions do not replace present wages; replacement is per se a longitudinal concept. (Cf. Kruse (1997).) Anyway, as shown by the right-most segment of (Eq. (16)), the internal contribution rate finally boils down to the product of the system-dependency ratio and the replacement rate. Therefore, in principle the procedure is reversible, an ‘internal replacement’ rate can be defined as the ratio of the actual contribution rate over system-dependency: equation(17) View the MathML source The mutual interdependence of contribution and replacement rates is a crucial problem for pension system design. It is somewhat obscured by the distinction, fashionable in the pension literature, between ‘benefit defined’ and contribution defined pension systems. In pension politics, the interdependence is usually shielded from public debate. While in many countries there is a growing pressure to reduce contribution rates in the name of ‘competitiveness’, seldom is it made clear that in the long run the consequence may be mass poverty in old age. The cross-sectional ‘balance’ (contribution revenue minus pension expenditure) of the pension scheme can be expressed in terms of the difference between actual and internal rates: equation(18) View the MathML source The balance, however, depends naturally also on the absolute magnitude of the aggregate contribution base, e.g. on the size of pension scheme (fund) or of the country. Therefore, actual and internal contribution and replacement rates seem to be more convenient tools for comparative analysis. It is easy to percieve, even without formal description, that analogous concepts may be and should be defined longitudunally, combining the earning and retirement spans for each cohort. Either the longitudinal, internal contribution rate of the corresponding internal replacement rate would balance the cohort’s life-path with respect to the pension scheme. Obviously, internal (balancing) rates vary from cohort to cohort — as did the theoretical zero-bequest function Sx(u). Conclusion: either all relevant parameters of a pension scheme are cohort-specific and adjusted precisely from year to year — what seems to be practically impossible — or longitudinal balances could not be expected to be zero. Inter-cohort redistribution is inevitable in any pension system, quite apart and distinct from the usual, cross-sectional concept of ‘intergenerational transfers’ from the ‘young’ to the ‘old’. Fig. 2 demonstrates the results of simplified calculations in the case of Hungary. All parameters, except the demographic ones, were kept constant in time and ρ=1 was assumed. Hence pure demographic trends are revealed, based on official forecast until 2050 and simple projection after that. The sharply increasing line, denoted by CR, represents the cross-sectional internal contribution rate mt over two centuries. horizontal straight lines represent longitudinal internal rates mx over the earning span of cohorts born in the year indicated to the left of the line. It is evident that now, around 2000, applying the cross-sectional internal contribution rate would result in huge negative longitudinal balances for all cohorts presently in the labour force, but the situation would change around 2020. (The statutory contribution rate is much higher. The general picture is much less clear if economic parameters are also allowed to change.)It should be added that desaggregation of birth cohorts by social properties (e.g. gender, educational attainment, occupation, etc., and/or participation in a given pension fund) would be absolutely necessary within a similar accounting framework. This has not been formally demonstrated here for brevity. The reader is requested to visualize a third index attached to each concept, beyond x and t, say n that would indicate social group n, born in x, in calendar year t. Then Vx,t,n and Px,t,n would represent the group's contribution base and pension, respectively, mx,n and rx,n their longitudinal internal rates, Dx,n the life-time balance of their involvement with the pension system. Naturally, it would turn out that intra-cohort redistribution is inevitable as well. The concept in pension parlance that corresponds to the theoretical zero-bequest constraint, i.e. to longitudinal balance, is ‘actuarial fairness’. This concept is often identified with the lack of redistribution, implying that at the time of death the present value of life-time benefits equals that of life-time contributions. It is usually assumed that funded schemes are actuarially fair while PAYG schemes are ‘redistributive’. That is a fallacy: all veritable pension schemes are redistributive by nature. Firstly, because they are insurance pools against the mortality risk, redistributing among individuals according to longevity, from those who die early to those who live long. (Even in principle, full actuarial fairness at the individual level is possible only in so-called pension funds that permit cumulated personal contributions to be taken out in a lump sum on retiring, or transformed into a fixed-length annuity, or be inherited at any point of time in case of death of the insured person. Such funds are, however, just pseudo-pension schemes, particular savings devices substantially not much different from banks or investment funds.) Secondly, because they operate with parameters, at least a few of which are standardized, most often the statutory contribution rate. Hence they cannot really adjust to cohort- and group-specific parameters, — not to mention the uncertainty of future. Pension schemes are necessarily redistributing among birth cohorts and social groups. It is unfair to promote private pension funds by advertising the ‘your money remains yours’ slogan. Thirdly, an intentional redistribution from the rich to the poor works in most public schemes, but it is a counter-productive addition to the pension institution. Social assistance and pension insurance should rather be separated in order to make the pension system transparent and incentives to contribute viable. For there is something that ordinary people, who know little about actuarial fairness, expect from the pension system. Maybe it could be called ‘pension fairness’, meaning that benefits, — as long as they last, i.e. until death — should be secure and proportional to previous contributions. (For example, two persons with very similar contribution histories should not receive substantially different pensions because they belong to different occupations, or retired at different points of time, or had been subjected to different rules of indexation.) Such fairness is not incompatible with redistribution resulting from various reasons of differences in longevity. Denying the existence of redistribution, and/or fight endless controversies about privatization and the mode of finance does not seem to be a fruitful course for pension economics and pension reform proposals. Clear concepts and definitions of the various types of redistribution as well as generally accepted (acceptable) methods of measurement would be urgently needed. In lack of anything more refined, even the dispersion of cohort- and group-specific internal rates could provide quantitative, empirical evidence about the actual size and direction of redistribution in various pension schemes. Such evidence could then provide guidance for public debate and political decisions on three crucial points: (1) the scope of the pension system, best measured by the average internal rates; (2) how much redistribution is acceptable, tolerable or unbearable for the society as a whole; and (3) how to avoid unbearable redistribution. These are the real issues for pension reform design. Financial balance should, of course, be kept in mind but it must not be the number one priority