CAIRN-INT.INFO : International Edition

1The demographic factor is central to the debate on the necessary changes to old-age pension systems. In this article, Gustavo De Santis compares different theoretical Pay-As-You-Go pension systems, examines their respective merits and proposes a new system which has the potential to preserve the equitable character of the PAYG principle in a changing demographic context. Based on the relative standards of living of the different age groups, the system involves accumulating reserves when conditions are favourable and depleting them or going into debt in less favourable periods. The demographic structure evolves over time, and in the long run the reserves compensate the losses. The exposition is organized primarily around the demographic aspects of the different theoretical systems and is illustrated by simulations that clarify the demonstration. It offers a perspective detached from the discussions that inform the national debates in which as citizens we all have an interest.


“‘Would you tell me please which way I ought to go from here?’ Alice asked. ‘That depends a good deal on where you want to get to’ said the Cat. ‘I don’t care much where…’ said Alice. ‘Then it doesn’t matter which way you go’ said the Cat. ‘… so long as I get somewhere’ Alice added as an explanation.”
(Lewis Carroll, Alice’s Adventures in Wonderland)

3Forms of economic support for the elderly have always existed. In pre-industrial times, this was primarily a private matter. Under many forms, and frequently with limited success, caring for the aged was the responsibility of families and households (see Bengtsson and Fridlizius, 1994; Reher, 1998). With the industrial revolution and the urbanisation process that ensued, proximity and therefore also solidarity between family members declined, and alternative systems of a collective nature developed gradually for the economic protection of the elderly (Conrad, 1991; Ritter, 1991). These arrangements were originally fully funded but in most cases, at least in Europe, and for a variety of reasons [1], turned later to Pay-As-You-Go (or PAYG). The difference is that, with funding, individuals are forced to save when they are adults and working, and deplete their own capital progressively in their old age when their labour income shrinks or disappears; with PAYG, current pensions are paid out of current contributions taken from younger cohorts, and there is no accumulation of capital [2].

4In recent times, PAYG pension systems have experienced serious financial difficulties that most observers tend to impute to their basic intrinsic weakness: with no collateral (i.e. savings), there is no guarantee that sufficient resources will actually be available to pay the promised future pensions. The survival of the system depends on whether the relevant variables (labour force participation and productivity, number of retirees, etc.) will evolve at least as favourably as the designers of the system imagined. Unfortunately, system designers are policy makers. They tend to be short-sighted because they know they will not be in charge forever, and because they seek the support of voters who are possibly even more short-sighted than they are [3]. All this conspires to bias the system towards excessively generous promises that may prove impossible to keep, as the recent history of most PAYG systems and their frequent adjustments suggests [4]. The difficulty of foreseeing the future availability of resources, and the related tendency to promise too much, are among the reasons why several economists prefer funding to PAYG. Its role, according to some of them, should be sharply reduced, possibly to a mere safety net for those who are both elderly and poor (see Disney, 1996, 2000; Feldstein and Ranguelova, 2000). International financial institutions strongly support this view (World Bank, 1994, 1997) or, according to some observers, impose it on recalcitrant but economically weak countries (Müller, Ryll and Wagener, 1999).

5In these pages I will not discuss all the reasons that may motivate this preference for funding. They are basically economic, and involve, for instance, the stimulus to capital accumulation and, hence, economic growth, or the assumed optimal balance between the public and the private sphere in the annuity market. Instead, I will try to show that most of the alleged shortcomings (Ponzi scheme [5], intrinsic instability, extreme variability of internal rates of return, discouraging effects on the labour market, etc.) are not characteristic of PAYG per se, and, in particular, that they do not affect the ES version that I will present below.

I – Simplifications, assumptions and “philosophy”

6To simplify matters, I will keep this exposition at a very high level of abstraction, assuming that there is only one all-encompassing intergenerational transfer system, that all workers are subject to the same rules regardless of their sex, industry, birth cohort, etc. and that management costs are negligible. Other forms of social intervention (such as poverty eradication) are also disregarded here.

7I will concentrate in particular on the demographic mechanisms that may or may not drive a PAYG intergenerational transfer system out of equilibrium. The economic side of the story will be kept as simple as possible, assuming the absence of any variation: productivity is given, and so are activity rates, unemployment, prices (there is no inflation), etc. [6] Further, I will refer exclusively to average incomes (on the one hand: wages and salaries net of contributions; on the other: transfer benefits), and will avoid the issue of individual variability. For the latter aspect, see De Santis (1997 and 2002).

8Perhaps the simplest way of approaching the pension problem is to think that current production [7] is a sort of very large pie that must be apportioned between “participants” — traditionally employed individuals and retirees, but in my proposal, more extensively, the young, adults and the elderly. The basic question is: how? Several points are worth considering already at this stage. The first is that if one ignores how large the pie is or may become in the future, and still looks for a permanent solution to the pension problem, only relative (not absolute) incomes should be considered — an approach that is still far from accepted in public debate. Incidentally, this is also difficult to apply technically, if actuarial criteria are to be met, because each retiree, with his or her own history of contributions, wants a “fair deal” and claims at least as much pie (in the form of pension benefits) as he or she paid in the past in the form of contributions, plus interest.

9The second point is that (relative) “entitlements to the pie” may be allotted on a group basis or on an individual basis. Both these “direct” solutions present shortcomings, among other reasons because demographic structures vary. Imagine for instance that the rule is that 80% of the pie should go to the employed, and 20% to the retirees. This may be fair on average, but one year there may be 90 employed and 10 retirees (whose average pension income would therefore be exceptionally high: 2.25 times as high as the net labour income of each employed person); and another year a totally different situation may emerge — say, 50 employed and 50 retirees — with the opposite effect in terms of individual welfare: each retiree now receives merely 25% of what accrues to an employed person. The intergenerational transfer system performs better if one decides that each retiree should have, for instance, 60% of what each employed person is left with after paying his/her contributions. But, in the two extreme scenarios above, this translates into extremely varying contribution rates (6.25% and 37.5%, respectively) and this, too, is scarcely advisable. This example, however unrealistic its figures may be, serves to illustrate the tendencies that might emerge in the real world if demographic factors were disregarded in the design of the system. It also suggests that it might be a good idea to save part of the pie in years of plenty (90 employed, 10 retired) and use this reserve in years of scarcity (50 employed, 50 retired) to keep both contributions and relative incomes constant, or almost so. In other words, a reasonably flexible reserve capital may help in the management of an intergenerational transfer system, even if it is essentially based on the PAYG principle.

10Notice that changes in the pensioner/employed ratio may derive from two distinct causes: participation in the labour market (an economic variable), and age structure (a purely demographic variable). To my knowledge, no one has ever tried to disentangle these two elements. Below, I will try to show how important it is to separate them, so as to be able to use actual economic behaviour (participation in the labour market) coupled with an age structure of reference.

11Traditionally, adults are expected to work in the market and the elderly are not. But, who is old? Isn’t “old age” a dynamic concept that should somehow be linked to the mean length of life, e0? Do 50 years always mean the same, regardless of whether life expectancy at birth is 40 or 85? And, if the answer is no, what link should one establish between the increase in e0 and the evolution of the retirement age (called here β )?

12And, finally, at socially agreed age β, why should the elderly be forced to retire, either by law or by practical (e.g. fiscal) arrangements? There may be several reasons linked to the functioning of the labour market (for instance they may have become too expensive, or unfit for a particular occupation) but, from the point of view of the transfer system, this is senseless. Ceteris paribus, more workers, including more elderly workers, make a bigger pie and a bigger slice for all claimants, which is one of the objectives that intergenerational transfer systems should pursue.

II – Three theoretical types of PAYG pension systems, plus two

13Several different versions of PAYG pension systems have been proposed so far. They all share the common feature that, in each year, the mass of contributions must match the mass of benefits, or, stated as a formula:

15where R = retirees,bR = their average pension benefit, W = employed, wW= their average gross wage, and c = the payroll contribution rate. (Notice that the focus here is not on the whole of the pie — WwW — but on the part that goes from the employed to the retired).

16With populations that are perfectly stationary, both demographically and economically, it is easy to identify a set of values that satisfy condition [1] once and forever. But if there is some kind of variation — demographic, economic, or both — equation [1] will not always hold, unless at least one of its variables is left free to adapt, i.e. is used as dependent. Since the number of retirees R, the employed population W, and the average gross wage w (linked to labour productivity) are exogenous to the pension system, only two variables may act as dependent: the payroll contribution rate c, and the average pension benefit bR. Depending on which one is selected for this role, three main theoretical types of PAYG emerge (Table 1) [8].

Table 1

Classification of three theoretical types of PAYG

Table 1
Dependent Label Name Instrumental variable variable(s) DC Defined Contribution c bR DB Defined Benefit bR c RS Risk Sharing rRW =bR/ wW (1-c) c, b R

Classification of three theoretical types of PAYG

17The first type fixes the contribution rate c and lets pensions benefits bRvary accordingly, as in the first scenario of the preceding section, so that its basic equation reads

19The second type fixes the average pension benefit bRand lets the contribution rate c vary in consequence, so that its basic equation becomes

21Notice that this approach relies on real (absolute, not relative) pension incomes (bR), and is therefore (in my view) inadequate in a world where everything changes unpredictably all the time.

22The third type (Risk Sharing) fixes the ratio rRW between the retirees’ pension benefits bR and the employed’s net wages wW (1 – c), as in the second scenario introduced above. In this arrangement, both pension benefits

24and the contribution rate c

26depend on the value selected for r. Equations [4] and [5] introduce a principle of “risk sharing” between employed and workers and pensioned, because whatever happens (for instance, with labour productivity, inflation, or unemployment), their relative economic distance r will remain unaffected (see Musgrave, 1981; Hagemann and Nicoletti, 1990; or Gonnot, Keilman, and Prinz, 1995).

27Elsewhere (De Santis, 2002), I show that most actual PAYG pension systems, although very different from country to country, form a fourth, distinct group that works remarkably worse than the theoretical types just described. There are two main reasons for this: a) no variable is explicitly defined as dependent, and left free to vary, so as to make sure that inflows (contributions) match outflows (payments); b) individual pensions are calculated with complex and widely varying formulas that typically take into consideration several variables such as past contributions, industry, gender, age at retirement, inflation, or expected future growth of productivity. In every period, individual and therefore also average pensions constitute an independent and largely unpredictable variable that, together with several others (survival, age at retirement, employment status, productivity, etc.), makes the system hardly manageable, scarcely transparent, and potentially unviable in the long run.

28It is precisely this type of PAYG system that is currently in financial and theoretical difficulty. But the current debate on how to reform it, especially in Italy, often reminds me of Alice’s dilemma (see epigraph): patches are frequently proposed, and sometimes implemented, in order to face the most urgent crises, but a clear vision of the (indefinitely sustainable) pension model that should be set up seems to be missing. This article sets out to present one called ES, Equitable and Stable (the fifth, in my classification). First it discusses some of its theoretical properties, and later it shows that the model performs better in simulations than all available alternatives [9].

29In the discussion and simulations that follow, I will avoid the intricacies of the economic sphere as much as possible, not because I think the system is weak in this respect (see De Santis, 2002), but because understanding its demography is already complicated enough and because its most original distinctive feature (the reference age structure) is demographic. I will not discuss either the issue of how to go over from the current system to PAYG-ES or, for that matter, of what happens when any PAYG system is modified, or matures. In all cases I will present matters as if each of the PAYG systems under scrutiny were already in full maturity.

III – The rationale of PAYG-ES

30I think that the main weakness of any long-term financial arrangement is that conditions can vary unexpectedly, thereby deceiving the hopes of, and not keeping the promises made to, those who decided, or were forced, to participate. Within limits, this is acceptable, because everybody knows that the future is uncertain; beyond certain limits, however, expectations will be frustrated, the confidence of the general public will be shaken, and the whole system may crumble, with potentially dire consequences.

31PAYG-ES is basically a set of rules that is meant to guarantee that an intergenerational transfer system is viable, i.e. can exist forever with almost unchanging characteristics, independently of how the demographic and the economic situations evolve. It is always possible to introduce changes, obviously, but the important point is that, up to a limit, modifications will not prove necessary. In other words, the system can last forever, at least in principle. In addition to this, the system possesses a few other desirable features, in particular:

  1. almost perfect intergenerational, or actuarial, equity is assured [10]: generations pay in contributions as much as they receive in benefits;
  2. the contribution load can remain relatively constant over time;
  3. relative incomes (employed vs. retired; young vs. adults vs. elderly) can remain constant over time;
  4. everybody can keep on working for as long as he/she pleases: pension benefits will, in all cases, start to be paid exactly at the predefined age P (e.g. 60 or 65), regardless of the employment status of the elderly;
  5. dynamic threshold ages (for instance, a retirement age that grows over time as life expectancy increases, according to pre-defined criteria) can be introduced in a way that is consistent with the general framework;
  6. child benefits may be incorporated in the intergenerational transfer system, an extension over traditional pension systems that I find theoretically defensible and technically useful (cf. below).
PAYG-ES distinguishes between three sets of variables. Some are dependent, and come out as a consequence (for instance: the contribution rate, once everything else has been fixed). Some are exogenous (for instance, survival [11]) and must be accepted as such. Finally, some are instrumental, i.e. decided on the basis of a general social agreement. For instance, the threshold ages that define adulthood (α and β) may be high or low, and may or may not evolve with e0; pension benefits may be generous, but then contribution rates will be high too; the reserve capital may be large or small, etc. It is by acting on these policy variables that each society can shape the general constraints of PAYG-ES to make them conform to its own preferences, traditions, culture, etc.

32Let us now see how the proposed system works in practice. Already in equation [1] above, two main policy decisions emerge as crucial: on the normal age at retirement β, and on whether pensions payments should be more or less generous. Indeed, given wW(average wage, exogenous to the pensions system), a lower retirement age β increases the retired-to-employed ratio R/W; and a higher pension transfer bRtranslates into a higher equilibrium payroll contribution rate c.

33The picture is more complex than this, however. Let us consider an enlarged version of equation [1], that is


37where R = retirees; E = elderly, W = employed, A = adults: bE = bR(R/E) is therefore the average pension income of each elderly person; while wA = wW(W/A) is the average net labour income of each adult. The interest of using equation [7] instead of equation [1] is that it highlights that the two socio-economic categories customarily used in this case, W and R, i.e. employed and pensioned, derive from a compositional effect (how large the three basic demographic groups are: Y, A, and E), and from two behavioural effects: participation in the labour market, W/A, and in the pension system, R/E. Besides, with equation [7] the policy choice of setting ages α and β (beginning and end of adulthood) emerges explicitly as crucial.

38On average, each adult pays (c wA) in contributions. Equation [7] implies that all those who work pay contributions, regardless of their age [12]; on the other hand, only those who are in a convenient age bracket may receive an intergenerational transfer benefit b: each young person receives bY(that may be zero, and in this case the system reduces to a simple pension system), whereas each elderly receives on average bE. Elderly workers intervene in both kinds of transfers: they pay a contribution cwAout of their salary, but they also receive an average benefit bE.

39Currently, no existing pension system incorporates child benefits among its transfers (i.e. bY = 0). There are good historical reasons for this, but, in my opinion, including the young among the recipients of these benefits should not be excluded a priori, on several grounds. Theoretically speaking, if one accepts the principle that an intergenerational transfer system should protect those who are not of working age, children (below a conventionally defined age α, like 15 years, for instance) are as entitled as the elderly to such a transfer. Besides, pension systems may exert a depressing effect on fertility (see e.g. Harrod, 1950; Nugent, 1985; Cigno, 1991; Cigno and Rosati, 1992), which, in the long run, causes population aging and decline, and therefore undermines the basis of the system itself, so that a counteracting mechanism, like explicit child benefits, may well be needed.

40Finally, there is also a practical reason. As the simulations of Section IX show, including child benefits among the provisions of an intergenerational transfer system exerts a non-trivial stabilization effect, because, very frequently, the relative weights of the two age groups move in opposite directions, and this limits the variability of the total transfer needs within each period.

41But the main element of innovation in the PAYG-ES transfer system is the notion of reference age structure, which serves two main purposes. On the one hand, it constitutes a standard of reference for appreciating the peaks and troughs of the current age structure. In particular, I will speak of “favourable” demographic phases when there are relatively more adults in the current than in the reference age structure, and “unfavourable” demographic phases when the reverse is true (more young and/or elderly in the current than in the reference age structure). One important implication of the use of the reference (instead of the current) age structure is that, in periods when the current age structure is favourable, the PAYG-ES system tends to accumulate resources (or a reserve capital) that it depletes in periods when the age structure is unfavourable. The topic is discussed more in depth in Section IV.

42On the other hand, the reference age structure constitutes a point of attraction, or a pivotal line, around which, by definition, the current age structure oscillates. Figure 1, representing a case of favourable age structure (proportionally more adults in the actual than in the reference population), gives an idea of how the principle works [13].

Figure 1

Actual and reference age structure for Italy in 2001

Figure 1

Actual and reference age structure for Italy in 2001

43In Section V I will argue that, for all practical purposes, one can use as “reference” the age structure of the stationary population associated with the current life table, but, for the time being, let us just assume that this reference age structure is given. As Figure 1 shows, adding a policy decision on the threshold ages α and β (beginning and end of adulthood), produces Y, A and E, i.e. the proportions young, adult and elderly in the reference age structure. For instance, in the case of Figure 1 (e0 = 82; α = 15; β = 65), one finds that Y = 18.2%, A = 59.5%, and E = 22.3%.

44In this hypothetical population, equation [7] becomes

46and the average adult net [14] wage transforms into wA(1 – c). Now, let us apply a modified version of Risk Sharing, and let us assume that a general policy agreement has been reached, for the present and for the future, on the most convenient ratio r between average transfers b and adults’ average net wages, so that transfer benefits for the young and for the elderly, are

48For instance, excluding child benefits results in rY = 0 (and therefore also bY = 0); at the other extreme of the age scale, virtually every arrangement is possible, but, just to fix ideas, let us imagine that pension benefits should average 60% of (net average) wages, so that rE = 0.6. With equation [9] in mind, equation [8] can be re-written as

50After re-organisation, one obtains the equilibrium contribution rate

52For instance, with the assumptions set forth above (e0 = 82; α = 15; β = 65; rY = 0, rE = 0.6), the resulting equilibrium contribution rate is c= 18.4%.

53The basic idea behind PAYG-ES is simply the following:

In PAYG-ES, there are a few key instrumental (or policy) variables: the threshold ages α and β that, given e0, define the proportions Y, A and E (young, adult, and elderly) in the reference population; and the ratios rYand rEbetween average benefits (bYfor children and bEfor the elderly) and the adult net wage wA(1 – c). All of these policy variables must be defined in such a way as to guarantee that equation [11] — applied to the reference, not to the actual population — holds at any point in time.

54The details of PAYG-ES will be discussed shortly, but some of its merits should emerge already at this stage. By making use of a reference age structure, and of three demographic groups instead of two social categories, PAYG-ES never matures: all of its variables in eq. [11] must be defined as if the system were, and were to remain indefinitely, on an equilibrium path.

55No variable in PAYG-ES is, or needs to be, forecast or projected: accepting that the reference age structure is the age structure of the current stationary population (see Section V), everything (including the economic dimension, not discussed here) is based on observed (current or past) variables only. In other words, no forms of distortion can be introduced in the system through over-optimistic, or simply inaccurate, forecasts, although instrumental variables may obviously always be adapted if collective preferences (on the policy variables α, β, rY, or rE) change.

56This is of the greatest importance. Take survival conditions, for instance: changes in mortality are virtually sure to take place, but they are difficult to predict (see for example Wilmoth, 2001; Oeppen and Vaupel, 2002). On the other hand, they are precisely and timely measured in all the developed countries. With ES, it is possible to decide beforehand how to cope with variations in survival, for instance adapting the basic contribution rate c, or the threshold ages α and β : an example is given in the simulations of Section IX. What matters is that the necessary parametric adjustments in the system can be made automatically, and need not become discretionary, i.e. create discontinuities with the past, pass through public debates (parliamentary decisions, government bills), with the delays and social contrasts that this generates, and the generational inequities it introduces (Auerbach, Gokhale, and Kotlikoff, 1994).

57On the other hand, since everything revolves around the reference age structure, variations in fertility and migration play only a relatively minor role. In other words, the system is relatively protected from demographic shocks (but see next section and the simulations).

58We may note in passing that economic shocks also affect PAYG-ES much less than any other PAYG transfer system [15], although this point is not developed here (see De Santis, 2002). For instance, lower labour productivity (i.e. lower wW) and/or lower activity rates (i.e. lower W/A, for instance, because of unemployment, expanding underground economy, etc.) translate into a lower average adult gross wage wA, and this, given r and c, automatically lowers the value of the average transfer payment b. Changing signs, the same happens for higher labour productivity, or an increase in the employment ratio (the ratio W/A), or even inflation (causing an increase in the nominal, but not in the real value of wages and benefits). All of these events share two common features: they affect the standard of living of the three basic demographic classes of the community in the same way (this is guaranteed by the constant proportionality factor r), but they do not affect the transfer system itself, which keeps working as before.

IV – PAYG-ES in detail

59With PAYG-ES three sets of variables must be distinguished: instrumental (or policy); exogenous, and dependent.

60One of the policy variables is r in equation [9], i.e. the ratio between average pension transfers and average net wages. Everything else given, once r has been decided, the value of cfollows automatically from equation [11]. In other words, one cannot have both generous pension allocations relative to net wages (high r) and low payroll rates (c) — not even in phases with a favourable age structure, because here it is the reference and not the current age structure that counts.

61Two more policy variables are the threshold ages α and β that separate the young from the adults (α) and the adults from the elderly (β). It is the choice of these thresholds α and β that, together with exogenously imposed survival conditions, determine the shares Y, A, and E (i.e. the proportions of young, adult and elderly in the reference population). Note that α and β need not be constant over time: actually, as shown in Section IX, it is possible (and, to me at least, preferable) to adapt them to the evolution of mortality, for instance in such a way that Y, A, and E remain constant as mortality risks change.

62Another policy variable must be added to keep the reserve capital at an acceptable level that is close to its target level K, which may be zero or (preferably) greater than zero. In each year, actual contributions AwAc do not necessarily match actual transfer payments EbE + YbY. Contributions exceed payments when the demographic conditions are favourable, and fall short of them in the opposite case. On top of this the existing capital (or deficit) K yields (or must be financed at) a market rate of interest i, producing a flow iK[16]. The algebraic sum of all of these flows gives the yearly variation in the reserve capital ΔK

64Ideally, the system should be designed in such a way that K oscillates only moderately around its reference value K, so that imbalances ΔK are never large, alternate in sign, and no ad-hoc adjustment is ever necessary. However, in particular circumstances, and notably when the demographic structure is distorted, ΔK may remain constantly above or below zero for some years, and this may cause the actual reserve capital to deviate too much from its target value K. Several options are available to contain this drift. One of these is to add a variable component to the reference payroll contribution rate c, cv, for instance according to a (growing) function k

66so that the overall contribution rate becomes

68The policy variable is the function k in eq. [13], giving the reactivity of the payroll contribution rate to imbalances in the reserves of the system. Obviously, the steeper k is, the quicker the reserves of the system get back to equilibrium, but, on the other hand, the greater the deviation of the actual payroll contribution rate c is from its target value c, the less the advantage of having a reference age structure in attenuating the effects of the demographic fluctuations. The variability of c around its target value cis admittedly a disadvantage of the proposed system. However, this variability proves relatively moderate in computer simulations; it may be constrained within pre-defined limits by ad hoc measures, and, most importantly, it is compensated by the fact that it permits other relevant variables of the system to remain constant (see Sections VII to IX for an example) [17].

69So, to summarize, there are several policy (or instrumental) variables: r (ratio between transfers and net wages), α and β (threshold ages: these, together with e0 — exogenous — determine the proportions Y, A, and E), and k (effect on the payroll contribution rate of a gap between the optimal K and the actual K reserve level).

70At the same time, there are also several exogenous variables: survival conditions (determining the age structure of the reference population); other demographic variables (determining the age structure of the actual population); labour market conditions, and notably employment status and productivity (determining gross salaries w and, together with c, individual and average contributions C); and the market rate of interest i.

71Two sets of independent variables determine the dependent ones: the proportions Y, A, and E in the actual and Y, A, and E in the reference population; the various payroll contribution rates (c, cv, c), net wages w(1 – c), and net transfers b.

V – The reference age structure

72In this Section I will not be able to prove, but will try to show, that the current stationary population (i.e. the stationary population associated with the current life table, with Lx years lived at each age, and life expectancy e0 = ΣLx) can be used as a proxy for the reference age structure that PAYG-ES requires. This section relies heavily on the notion of long run — meaning possibly thousands of years. This does not imply that the proposed system reaches its equilibrium values only in the long run. On the contrary, PAYG-ES is constantly in, or very close to, equilibrium, thanks to the adjustment process of equations [13] and [14] or to similar mechanisms. But proving that the demographic structure converges towards the assumed reference curve guarantees that the adjustments of equations [13] and [14] will only be needed to fine-tune the system, not to fix structural imbalances, and will operate only for relatively short periods. “Short” in this context may mean 100 years or more, but once again, this barely affects the system. In the rather extreme simulations of Sections VIII and IX, for instance, the actual payroll contribution rate exceeds its reference value for over a century, but the difference (within 3 percentage points, in that case) always falls within the margins that, by assumption, had been collectively agreed upon in advance, while everything else functions normally.

73Let us initially assume that migration is absent, and mortality constant. In the very long run (thousands of years), the rate of demographic growth must be virtually identical to zero, otherwise the population would explode, or disappear [18]. With no migration and constant mortality, this can be achieved only through fluctuations in fertility, such that the long-run reproduction rate approaches unity. In this scenario, each cohort Nt of newborn in year t can be expressed as

75where N is the (unknown) average of Nt, while nt is its deviation from average, which I am assuming is distributed with average equal to 0, and a given, although possibly unknown variance. In any year t, the population age structure is given by

77and the expected value for this quantity is equation im19the stationary population.

78With changing mortality (and therefore also changing reference population structure) I cannot prove any convergence, but even with rather extreme variations in mortality, all the simulations I ever attempted gave excellent results when the reference population was based on the corresponding period life table. This probably depends on the fact that year-to-year variations in life expectancy are modest in relative terms (i.e. Δe0/e0), even when they are high by historical standards. Besides, their sole effect on PAYG-ES comes through a variation in the proportions of the three basic reference groups, Y, A, and E, and these proportions change only modestly, anyway.

79The same holds for migration: it affects the actual age structure, for sure, but should it also be included in the reference age structures, at least those cases when there is a consolidated tradition of in- or out-migration? My answer is negative: in my simulations I have invariably verified that using the “simple” reference age structure (i.e. that derived from the current life table) gives excellent results. This probably depends on several factors. In the first place, it is only age-specific net migration that matters, i.e. that may change the age structure of the actual with respect to the reference population. Secondly, net migration could in principle prove perfectly neutral if its age structure were identical to that of the reference population. In practice, this is never the case since migration takes place at relatively young ages but, and here comes the final reason, even when they are high by historical standards, age-specific migration flows tend to be relatively modest with respect to a reasonably large population, or at least short-lived, and therefore their long-term impact on the age structure proves modest, or even negligible.

VI – A theoretical comparison between forms of PAYG pension systems

80Table 2 presents a synthesis of the differences between the four types of PAYG pension systems I listed above.

Table 2

A synoptic view of four variants of PAYG

Table 2
">Characteristics Name (Label) Defined Contribution DC Defined Benefit DB Risk Sharing RS Equitable and Stable ES Theoretical/Empirical Theoretical Theoretical Theoretical Theoretical Status in literature Known Known Known New(a) Main relevant variables cbWRwW ? cbWRwW ? crRWWRwW ? EA??? c cve0r YAEYAEKwA Budget constraint C=B Yearly Yearly Yearly Over several years Age structure used Current Current Current Reference Do variations in any of the following affect (impair) the working of the pension system (regardless of other impacts they may have, e.g. on the standards of living)? Employment ratio Yes Yes Yes No Labour productivity No {Yes}(b) No No Inflation No {Yes}(c) No No Fertility and migration Yes Yes Yes {No} Main constant term(s) c B rRW rEA, c Main variable term(s) b c C c {, }(d) What if mortality decreases? b decreases C increases c increases; b decreases *c ; b   and  (a) But see De Santis (1995, 1997, 2002). (b) Unless the rate of growth of pension benefits equals the rate of growth of wages. (c) Unless the rate of growth of pension benefits incorporates inflation. (d) In three different variants: see next row. Legend c = payroll contribution rate r = ratio between pensions and taxable wages b = average pension amount C = total contributions of one year A = adults W = employed E = elderly R = retired B = total pensions of one year Y = young w = gross wages  = threshold age at which old age conventionally starts (retirement age)  = threshold age at which adulthood conventionally starts {} = approximately, or depending on circumstances

A synoptic view of four variants of PAYG

81The use of r (ratio between transfers and net wages) makes PAYG-Equitable and Stable similar to Risk Sharing. But ES constitutes an improvement over RS in several ways, because of its flexible budget constraint (K tends towards K, but does not need to coincide with it all the time) and its reserve capital (K can be greater than zero), because it uses a reference age structure, and because it refers to age classes (Y, A, E), and therefore incorporates changes in the employment ratio (W/A) through the variable wA = wW(W/A). Ceteris paribus, lower participation in the labour force or growing unemployment indicate lower per capita production, and this automatically lowers the average transfer benefits b in ES.

82Let us briefly consider the effects of a few possible exogenous shocks.

1 – Demographic changes: fertility and migration

83ES tends to absorb demographic shocks more easily than other forms of PAYG. Let us imagine, for instance, that age-specific employment ratios do not vary, but that the current age structure is distorted with respect to the reference age structure, and has a higher-than-normal share of adults, for instance because of the presence of cohorts of adult baby boomers, or because of immigration flows. In the traditional versions of PAYG this translates into a higher-than-normal wage mass, which permits higher pensions or lower contribution rates, or both. PAYG-ES, on the contrary, automatically recognizes this phase as transitory, and, since wAhas not changed, pension benefits and the contribution rate remain constant too. The extra contributions thus collected augment the reserve capital of the system, which will be used later, when this extra number of adults (and workers) will age and be transformed into an extra amount of elderly (and pensioners). At that time, once again, instead of the belt-tightening that traditional PAYG systems impose, a self-triggering depletion of the extra reserves will allow everything else to remain constant [19].

2 – Demographic shocks: mortality

84In the traditional versions of PAYG, longer life expectancy translates into relatively more retirees, thus forcing higher contributions or lower pension benefits, or both. As we shall see in Section IX, ES leaves these options open (EScb), but it also admits the alternative of adapting threshold ages, either just β (ESβ), or, better, both α and β (ESαβ). In the former of these two alternatives, there are progressively fewer young and more elderly in the population, but cand r may remain unchanged; in the latter, Y, A, and E (in the reference population) do not vary, and this guarantees invariance in everything else as well. Regardless of which version is adopted, the important innovation of ES is that adjustments to variations in the length of life may (or, better, must) be defined, and collectively agreed upon in advance, and take place automatically, thus always maintaining the system in equilibrium.

85Note that this is a major advantage of ES over most other versions of PAYG. Obviously, when life expectancy increases, all pension systems benefit from an increase in retirement age β (see Section IX), but the important point here is that only ES gives a criterion for identifying the necessary changes in α and β that is internally consistent, because it derives from the reference population.

3 – Labour productivity and inflation

86Variations in labour productivity are neutral in PAYG-ES, and in almost all traditional versions of PAYG, although with PAYG-Defined Benefit this happens only if pension benefits grow exactly as fast as wages do. The same goes for inflation.

87Although the issue is not discussed here, it is worth remarking in passing that this neutrality does not generally apply to most currently functioning versions of PAYG, where legacies from the past (which determine current pensions benefits) and other specific arrangements typically confer a great importance to labour productivity and inflation.

4 – Retirement decisions

88Several scholars contend that aggregate “demographic” approaches to the analysis of pension systems are insufficient, because they disregard “behaviour”, i.e. individual decisions on whether and when to retire from the labour force (e.g., Lee and Tuljapurkar, 1997; Gruber and Wise, 1999). For instance, everything else given, workers may decide to retire sooner if it is advantageous, and this may disrupt a pension system even if the age structure has not changed much, or at all, from a previous, less troubled period. Therefore, so the argument goes, what is needed is (complex) micro-simulation models that will allow researchers to detect and measure the advantages of early retirement, and therefore forewarn about the risks of a “retirement stampede”.

89While I share this point of view with regard to the analysis of existing pension systems, I do not think that it must necessarily apply to the design of new ones. Another possibility is to adopt a scheme that proves indifferent to retirement decisions, as in the case of PAYG-ES. Here, the use of wA, and r (the proportionality factor for transfer benefits) indicates that, ceteris paribus, if work participation diminishes, for instance because workers retire early, standards of living will diminish for everybody (employed and retired; adults and elderly), but this will not affect the pension system in any other respect, because all the other variables will remain unchanged: α, β, K, k, c, etc. On the other hand, PAYG-ES does not encourage any particular attitude towards the labour market: independently of one’s employment status, pension benefits will not be paid before age β, and will be paid after age β.

VII – Computer simulations: background

90In the preceding section, I tried to prove that ES is preferable to other forms of PAYG by referring to a few of its theoretical properties: independence of changes in the current age structure (and therefore, also, of fertility and migration), and independence of all kinds of economic variations, like inflation, activity, labour productivity, etc. In this section I will try to prove that it also performs better “empirically”, i.e. in simulations.

91As mentioned, in PAYG-ES some variables are given exogenously, some are chosen instrumentally, and finally, some result as consequences. The simulations of Sections VIII and IX, for instance, are based on the assumptions in Table 3.

Table 3

Scenario no. 1 – description

Table 3
3(a) – Exogenous variables Variable Symbol Value Total fertility rate TFR 2.11.6 Life expectancy at birth e0 77 years Average labour productivity ( = gross wage) w 1 Employment ratio (Employed/Adults) W/A 0.6 Retirees/Elderly ratio R/E 0.6 3(b) – Instrumental or policy variables Variable Symbol Value Lower limit for adulthood  15 years Upper limit for adulthood ( = “retirement" age)  65 years Relative(a) child benefit [ = bY / wA (1-c)] rY 0% Relativea pension benefit [ = bE / wA (1-c)] rE 75.4% Reference level of reserve capital K 1 year of pension benefits Sensitivity of cv k cv = 3% (K –K)/BYBE(b) (a) Relative to an adult’s average net labour earnings. (b) But subject to the condition that |cv| 3%. 3(c) – Resulting values for the dependent variables Variable Symbol Comes from Value Reference payroll contribution rate c eq. [11] 18.7% Variable payroll contribution rate cv eq. [13] –3% < cv <3% Overall payroll contribution rate ( = c+cv) c eq. [14] 15.7% <c <21.7% Share of the young in the reference population Y (e0; 19.2% Share of adults in the reference population A (e0;;) 61.9% Share of the elderly in the reference population E (e0;) 18.9% Adults’ gross labour earnings wA eq. [6]–[7] 0.600 Adults’ net labour earnings wA(1–c) eq. [9] 0.488 Average pension benefit for the elderly bE eq. [9] 0.368 Average pension benefit for retirees bR eq. [4] 0.613

Scenario no. 1 – description

92Starting from these assumptions, let us consider two different demographic evolutions that may represent the case of the majority of the developed countries [20]:

  • in scenario No. 1, everything else being equal, fertility declines at first (the TFR, total fertility rate, or number of children per woman, reaches 1.6) and resumes its equilibrium value (2.1) later;
  • in scenario No. 2, the mean length of life (or life expectancy at birth e0) increases from 77 to 85 in a hundred years, and then stabilizes at the new, higher level, while the TFR adapts, so that, eventually, the population returns to stationarity.
In both cases I start, and end 300 hundred years later, with a stationary population. This has the sole purpose of making sure that everything gets back to equilibrium, and facilitates the calculation of the measures of performance that I will introduce shortly, but stationarity is not a necessary condition for PAYG-ES to function. Note also that in scenario No. 1, the reference age structure never changes (e0 = 77), while in scenario No. 2, the reference age structure gradually evolves from one where e0 = 77 to one where e0 = 85.

93In scenario No. 1, only 4 types of PAYG will be compared: Defined Contribution, Defined Benefit, Risk Sharing, Equitable and Stable. In the second scenario, on the contrary, since e0 increases, we will need to distinguish between three sub-variants for each of them (2, 2’, and 2”), depending on what varies. In scenario 2, threshold ages do not move: it is the payroll contribution rate c that adapts (except for DC, where it is pension benefits b that decrease, c being fixed by definition).

94In scenario 2’, age at pension β increases in such a way that all economic variables remain fixed in the ES system (c, r, …): in practice, as e0increases from 77 to 85, β changes from 65 to about 69.

95Finally, in scenario 2”, adult threshold ages a and β increase in such a way that the proportions Y, A, and Ein the reference populations do not vary, and this constancy extends therefore also to all other variables in the ES system (c r, …). In practice, with e0increasing from 77 to 85, α reaches 16.5 (up from 15), and β 70 (up from 65).

96The criteria for comparing the performances of the various forms of transfer systems are, needless to say, a crucial issue. It is perhaps worth remembering that one of the reasons of dissatisfaction with PAYG pension systems is that they are unpredictable. Current rules may not be valid tomorrow, depending on how circumstances evolve. Hence, my criteria for excellence will be based on constancy: the less a key variable is forced to change, the better. With this in mind, let us consider four different dimensions:

  • Variability over time of the yearly contribution rate ct(ideally approaching 0). Some PAYG transfer schemes cause c to deviate from its original level: this implies that some generations are taxed differently from others, with possible undesirable economic consequences (e.g. increase in labour costs, etc.). The ideal is a scheme that leaves the contribution rate c constant at the socially preferred level.
  • Variability over time of rt(ideally approaching 0). Some PAYG transfer schemes cause variations in the yearly ratios r between pension benefits b and net wages w(1-c), thus making the young and the aged richer or poorer relatively to the adults. Since this is typically an unwanted consequence of unforeseen demographic (or — not discussed here — economic) dynamics, a solution that leaves the ratio r unaffected is preferable.
  • Actuarial (inter-generational, or simply generational) equity implies that each generation pays in contributions C just as much as it receives in benefits B. A possible measure of generational equity is therefore the difference Dg = Bg - Cg, to be calculated (in real terms [21]) for each generation g. The ideal is a scheme that guarantees perfect generational equity (Dg = 0), or at least that deviates from this objective as little as possible. Absence of equity, however, can be revealed by two slightly different measures:
  • average of Dgover time (ideally approaching 0). If μ(Dg) differs from zero, the system proves sensitive to demographic variations (increase or decrease of population) that tend to cause generational gains or losses in the transfer system;
  • variance of Dgover time (ideally approaching 0). If var(Dg) differs from zero, the system proves sensitive to demographic variations (increase or decrease of population) and tends to distribute the resulting gains and losses inequitably across the generations considered in the simulation (with some earning or losing more than others).

VIII – Computer simulations: scenario No. 1

97In scenario No. 1, mortality does not vary (e0 is constant at 77 years), but fertility falls to 1.6 and then gets back to reproduction level (Figure 2b). This causes the population to eventually lose about a third of its members (Figure 2c). Since the system is displacing resources towards the elderly, population reduction implies a sort of capital loss (Lee, 1994; 2000a), which will have to be redistributed somehow among the participating cohorts.

Figure 2

Computer simulation of population, scenario No. 1

Figure 2

Computer simulation of population, scenario No. 1

Sources : Author’s computations.

98In this example, with constant e0, the reference age structure does not change: however, the actual age structure will be disturbed in the course of time. For instance, the proportion of the young falls from 19% to 15% before getting back to 19%; the adults (aged 15-64) expand to 64%, then shrink to 59%, and eventually resume their reference share of 62%; the elderly, finally, peak at 24%, but then fall back to 19% (Figure 2d–2f). Note, however, that Figure 2e illustrates one of the basic mechanisms behind PAYG-ES: favourable ( A > A) and unfavourable (A < A) periods alternate, and are roughly of the same order of magnitude if one chooses a proper standard of reference.

99Indeed, depending on the kind of PAYG system in force, the impact of this scenario on the payroll contribution rate may prove sizeable. From its initial level of 18.7%, the payroll rate generally rises (although not in Defined Contribution, by definition), to more than 24% in the case of Defined Benefits, to 23% with Risk Sharing, and to less than 22% with the Equitable and Stable solution (Figure 3).

Figure 3

Payroll contribution rate c under scenario No. 1 (%)

Figure 3

Payroll contribution rate c under scenario No. 1 (%)

Sources : Author’s computations.

100In two variants of PAYG, namely Risk Sharing and Equitable and Stable, the ratio r between the elderly’s pension benefits bEand the adults’ net labour earnings w(1 – c) remains unaffected at 75.4%, but in the remaining two variants this ratio oscillates significantly, sometimes dropping to 58% (Defined Contribution) [22], and sometimes climbing to 81% (Defined Benefit) (Figure 4).

Figure 4

Cross-sectional “equity” under scenario No. 1 (ratio between pension benefits and net adult earnings)

Figure 4

Cross-sectional “equity” under scenario No. 1 (ratio between pension benefits and net adult earnings)

Sources :Author’s computations.

101Finally, a look at intergenerational equity [23] in Figure 5 shows that all the PAYG systems considered here suffer when population declines (precisely because they transfer resources forward). They react differently, however, either in terms of the absolute amount of the loss (graphically represented by the area comprised between the x axis and each curve), or in terms of how they distribute the loss among the generations. Sometimes they concentrate it in relatively few cohorts, and sometimes they spread it upon several of them.

Figure 5

Intergenerational equity under scenario No. 1: difference between the overall amount of pension benefits and the total contributions paid over life, relative to the annual adults’ net labour earnings, per cohort (in %)

Figure 5

Intergenerational equity under scenario No. 1: difference between the overall amount of pension benefits and the total contributions paid over life, relative to the annual adults’ net labour earnings, per cohort (in %)

Sources : Author’s computations.

102Table 4 provides a summary of these results. Although the variables refer to different, non-comparable dimensions (variability of contribution rate; variability of relative standard of living of elderly and adults; intergenerational equity), there seems to be little doubt that Defined Contribution displays the worst performance, because it introduces unacceptably high variability in transfer benefits [24]. In this simulation, for example, around year 150, the elderly become extremely poor relative to the adults (see Figure 4). Defined Benefit is systematically worse than both Risk Sharing and Equitable and Stable; these two perform similarly, but the latter proves slightly preferable in all respects.

Table 4

Synthetic results of scenario No. 1

Table 4
Type Characteristic Variance (x 10,000) Average c(a) r(b) D(c) D(d) DC c=constant 0.00 298.21 7.54 –0.73% DB b= constant 28.50 27.64 9.33 – 0.87% RS r= constant 17.19 0.00 6.86 – 0.84% ES RS+reference age structure 14.61 0.00 5.84 – 0.85% Note: For all indicators zero is the best possible outcome. (a) Equilibrium payroll contribution rate (variance over 300 years  10,000). (b) Ratio between pensions and wages (variance over 300 years  10,000). (c) Difference between benefits and contributions, relative to 1 year of pay (variance over 200 cohorts  10,000). (d) Difference between benefits and contributions, relative to 1 year of pay (average over 200 cohorts).

Synthetic results of scenario No. 1

IX – Scenario No. 2, and the introduction of child benefits

103Figure 6 presents the demography of scenario No. 2, with increasing life expectancy (from 77 to 85), slightly lower fertility (so as to ensure long term stationarity), and a population that grows by about 10% (thanks to longer life). With fixed threshold ages, the population becomes considerably older: those over 65, for instance, increase from 19% to 24.5% of the total population, while the young (0-14) shrink to 17.5% and the adults to about 58%. With moving threshold ages, however, aging becomes much less important. In Figure 7, we present the proportion of the elderly under the three subscenarios (2, 2’ and 2’’) described earlier. This offers a reminder that the definitions of youth, adulthood and old age depend very much on conventions, which need not remain fixed as survival conditions change.

Figure 6

Computer simulation of population, scenario No. 2, (fixed threshold ages)

Figure 6

Computer simulation of population, scenario No. 2, (fixed threshold ages)

Sources : Author’s computations.
Figure 7

Proportion E of the elderly in the population under scenario No. 2, with different values of threshold age β (scenarios 2, 2’ and 2")

Figure 7

Proportion E of the elderly in the population under scenario No. 2, with different values of threshold age β (scenarios 2, 2’ and 2")

Sources : Author’s computations.

104Let us further complicate the picture by considering two alternative transfer systems in all four scenarios (1, 2, 2’ and 2"), one with and one without child benefits, but in all cases, such that the initial equilibrium payroll rate is 18.7%. We therefore obtain 8 cases: for each of them, the performance of the four PAYG systems is presented in Table 5.

Table 5

Synthetic results of various scenarios, with and without child benefits

Table 5
Type Characteristic Variance (×10,000) Average Variance (×10,000) Average c(a) r(b) D(c) D(d) c(a) r(b) D(c) D(d) Without child benefits(e) With child benefits(f) No. 1: fluctuations in fertility DC c=constant 0.00 298.21 7.54 –0.73% 0.00 53.27 1.16 –0.31% DB b=constant 28.50 27.64 9.33 –0.87% 9.53 3.84 3.11 –0.35% RS r=constant 17.19 0.00 6.86 –0.84% 5.99 0.00 2.22 –0.34% ES RS+reference age structure 14.61 0.00 5.84 –0.85% 5.90 0.00 2.18 –0.33% No. 2: life expectancy increases, threshold ages (αβ) do not vary DC c=constant 0.00 891.77 0.17 0.14% 0.00 199.62 0.70 0.36% DB b=constant 106.33 110.67 6.15 0.97% 43.85 18.70 2.63 0.63% RS r=constant 60.96 0.00 3.91 0.77% 26.41 0.00 2.07 0.57% ES RS+reference age structure 60.09 0.00 3.60 0.75% 26.06 0.00 1.92 0.56% No. 2’: life expectancy increases, age at pension (β) adapts DC c=constant 0.00 32.95 0.90 0.32% 0.00 2.58 0.30 0.233% DB b=constant 2.18 1.91 0.99 0.42% 0.35 0.13 0.30 0.232% RS r=constant 1.42 0.00 0.93 0.40% 0.23 0.00 0.29 0.232% ES RS+reference age structure 1.28 0.00 0.84 0.39% 0.21 0.00 0.26 0.226% No. 2’’: life expectancy increases, both threshold ages (αβ) adapt DC c=constant 0.00 15.26 0.88 0.268% 0.00 2.50 0.13 0.07% DB b=constant 0.88 0.74 0.39 0.261% 0.34 0.13 0.05 0.07% RS r=constant 0.59 0.00 0.43 0.263% 0.22 0.00 0.06 0.07% ES RS+reference age structure 0.55 0.00 0.38 0.257% 0.20 0.00 0.05 0.06% Note: for all indicators zero is the best possible outcome. (a) Equilibrium payroll contribution rate (variance over 300 years, ×10,000). (b) Ratio between pensions and wages (variance over 300 years, ×10,000). (c) Difference between benefits and contributions, relative to 1 year of pay (variance over 200 cohorts, ×10,000). (d) Difference between benefits and contributions, relative to 1 year of pay (average over 200 cohorts). (e) Pensions start at about 75% of salaries. (f) Pensions start at about 50% of salaries; child benefits at 25%.

Synthetic results of various scenarios, with and without child benefits

105The main results may be summarized in relatively few words:

  • In all the scenarios presented here (and indeed, in all the scenarios I ever tried) the inclusion of child benefits improves the performance of every PAYG transfer system in all possible respects. Every PAYG transfer system with child benefits is characterized by lower variability in payroll rates c, in the relative incomes of the three age classes r, and in generational equity D.
  • The inclusion of child benefits, however, has only a limited impact on the ranking of the systems.
  • In all cases, Defined Contribution seems to introduce too much variability in the relative income of the elderly and the young relative to that of the adults, especially with fixed threshold ages (scenario No. 2), and without child benefits. This leaves Equitable and Stable as the undisputedly preferable PAYG transfer system in all demographic scenarios and in all possible respects.
  • All systems perform better if threshold ages vary, especially when the variation regards both α and β, but the ES version is constantly the best (and, incidentally, it is the only one for which the variation of α and β is internally consistent, because it derives from the use of the reference population).
  • One shortcoming of the Equitable and Stable version, though, is that it requires flexibility in the reserve capital. Let us consider scenario No. 1: there is almost a century of below-replacement fertility, with no compensating immigration; the population eventually declines to about two thirds of its original size; and there are generous pension transfers, but no child benefits. During the period when the actual reserve level is lower than the reference level (equivalent to one year of pension benefits), the difference between the two drops to – 280% of the annual pension benefits in the worst year; the actual reserve K then corresponds to – 180% of the yearly pension benefits, which represents the overall debt of the transfer system — something that may be in the neighbourhood of (–)27% of the GDP of the time (Figure 8). This, in my opinion, is not unacceptable, because the scenario is extreme. Even in the worst year, contributions cover at least 93% of transfer benefits [25] and, most importantly, the situation is by definition temporary. The intrinsic characteristics of the system ensure that imbalances will compensate (and debts will be repaid) in the long run, which cannot be said of most existing PAYG transfer systems. However, if such a debt is judged excessive, several measures can be taken to limit it: for instance, lower pension/wage ratios; the inclusion of child benefits; the predefinition of an accepted range of variation for the reserve capital (for instance: it shall never become negative), although, in this case, the equilibrium contribution rate c will have to increase more than indicated in these simulations, thereby reducing the advantage of ES over RS.

Figure 8

Under scenario No. 1, difference between the actual and the reference level of: (a) the reserve capital (in % of one year of pension benefits) and (b) the payroll contribution rate (in percentage points)

Figure 8

Under scenario No. 1, difference between the actual and the reference level of: (a) the reserve capital (in % of one year of pension benefits) and (b) the payroll contribution rate (in percentage points)

Sources : Author’s computations.


106Aging is probably a predicament (MacKellar, 2000), but pension systems are a problem, and one that aging aggravates. The problem is complex, especially in those very frequent instances where specific arrangements exist for different industries; where expectations have been created and rights conferred on faulty bases; and where changes in the rate of economic growth, or in the pace of demographic change, have been unexpectedly rapid.

107In this article I show that the theoretical versions of PAYG proposed so far in the literature, despite their high level of abstraction (leading in fact to practical inapplicability), when confronted with a series of possible changes in the economic or the demographic sphere, cannot keep their most basic parameters constant: contribution rate, intergenerational equity, and relative income of the young, the adults and the elderly. However, I also contend that the basic principles of PAYG may be preserved and revived in a new version, called PAYG-ES, Equitable and Stable. The proposed system uses the idea of Risk Sharing, where a constant ratio r is in all cases maintained between the incomes of pensioners and workers, so that economic shocks are evenly spread over all segments of the population. It expands it, however, in that it also tends to spread the effects of demographic shocks evenly over the various cohorts. In order to do so, it must introduce some elasticity in its accounts. Contributions and benefits must balance only in the long run, so that the reserves of the system oscillate around their long-run equilibrium value, which may or may not be equal to zero.

108On a higher level of abstraction, one could say that what is really difficult is to keep some parameters constant over time when everything else is subject to change. Without this element of stability, however, the very rationale for the existence of a pension system vanishes, and so do popular confidence and support. PAYG-ES solves the problem by keeping relative indicators constant, both on the economic side (the ratio r between average transfers and average net labour incomes) and on the demographic side (and this is the novelty of the present proposal). In the latter case, one could push the argument further and tend to fix, over time, the span of life an average individual spends in the three basic demographic phases: youth, adulthood, and old age. This ideal can be approached by letting conventional threshold ages move. This alone, together with a constant r (ratio between benefits and net wages) guarantees that everything else in the PAYG transfer system will remain practically constant.

109ES solves the technical problems posed for PAYG transfer arrangements by varying economic and demographic circumstances. But this is only a small step. Convincing the general public that only relative measures can be kept constant over time, that each worker’s pension income in t years will be a fraction of the salaries that will prevail by then, and that pension benefits will start at an age β that keeps moving from year to year (depending on survival conditions) is probably going to take a long, long time.


Financial support from the Italian Ministry of University and Scientific Research and from the 5th European Research Programme (FELICIE – Future Elderly Living Conditions In Europe, No. QLRT-2001-02310, http:// www. felicie. org) is gratefully acknowledged. My thanks also to Massimo Livi Bacci, Nico Keilman and two anonymous referees for their helpful comments on an earlier version of this paper.


  • [*]
    Department of Economics and Statistics, University of Messina, Italy.
  • [1]
    In Europe, financial failures were basically caused by rampant inflation following World War II. Policy considerations also played their part: see for Italy, INPS (1993); for France, Kessler (1992).
  • [2]
    Mixed systems also exist, and the PAYG-ES that I will present below shares with them the characteristic of a reserve capital, although with a different function. Note that with funding each generation uses “its own” accumulated capital to pay its own pension benefits, whereas with PAYG there is a transfer of resources from one generation (working adults) to the preceding one (retired elderly). Even in this case, however, people reason as if workers had saved some money in the course of their working lives and were to derive their own pension benefits from this. This line of reasoning, often implicit, is formalized in the so-called “notional-defined contribution system” (Disney, 2000) which characterizes the recent pension reforms of Italy, Sweden, Latvia and Poland.
  • [3]
    One of the reasons why compulsory pension systems exist is that it is assumed that in dividuals, left to their own devices, would consume most of what they earn during their adulthood and save too little for their old age (see e.g. MacKellar, 2000, p. 386). In PAYG, there is often only a loose link between today’s forced savings (favouring the previous cohorts, now old) and tomorrow’s consumption (that will be provided by a new cohort of workers). It allows generous promises to be made easily at the expense of future contribution payers, thus re-introducing a slightly different kind of myopia.
  • [4]
    See, for example, European Economy, 1996, No. 3; Baldacci and Peracchi (2000); Takayama (2003). For a debate on the pension system in the US, see, among others, Diamond (1996) and Gramlich (1996).
  • [5]
    A “Ponzi scheme of financing” may be defined as the repayment of debt with the issuance of new debt, and owes its name to Carlo Ponzi (1882-1949), an Italian migrant to America who accumulated a fortune through a chain-letters system but was eventually discovered and arrested. With no production of goods or services, such a system can work only as long as new lenders come in, and these can be lured into the system only through very generous but financially unsustainable promises. Latecomers (in our case, the latest cohorts of workers) are sure to lose their money.
  • (6)
    Removing these assumptions does not affect the proposed system, whereas it affects, sometimes heavily, the functioning of most other versions of PAYG.
  • [7]
    More precisely, the labour’s share of this production, because contributions are levied on wages and salaries.
  • [8]
    Other cases, not discussed here, can be found in Keyfitz (1985; 1988).
  • [9]
    Among these, I will not consider empirical versions of PAYG, but only the three theoretical types just discussed, which, however, perform better than all the actual implementations I know (not shown here: see De Santis, 2002).
  • [10]
    Elsewhere (De Santis, 2002) I show that PAYG-ES can guarantee actuarial equity also at the individual, not just at the cohort, level. On the other hand it can also be implemented in a version that produces pension benefits that are the same for every elderly person (complete redistribution), or strikes any balance in between.
  • [11]
    As a measure of survival I will use the latest available period life table, and in particular the Lxseries of years lived at each age that form the age structure of the stationary population associated with the current survival (or mortality) conditions. For the sake of brevity, I will some times refer to this age structure using simply the summary measure e0 = ΣLx(life expectancy at birth, or mean length of life).
  • [12]
    That is, the employed W can be of any age, not only adults, but also young or old. On the other hand, not all adults need to be employed: the fewer the employed, the lower the factor (W/A) that determines the average wage of the adults.
  • [13]
    The notion of reference age structure is sometimes vaguely referred to in the literature or implicit in practical applications. As for the former, see, for instance, Livi Bacci (1995), or the notion of “demographic bonus” or “window of demographic opportunities” that the UN has frequently used in recent publications (e.g. UNFPA, 2002); as for the latter, see, for instance, the current US public pension system, which, since the reform of 1983, has started to accumulate extra reserves to face the bulk of pension payments foreseen around the year 2020, when most of the baby boomers are likely to retire (Bosworth, 1996; Lee, 2000b). To the best of my knowledge, nobody ever tried to define it formally.
  • [14]
    Net of payroll contributions: other forms of taxation, or government spending, are excluded from this analysis.
  • [15]
    I mean that such shocks do not force any change in the basic parameters of the system, but, obviously, they do affect the standard of living of the population. For instance, ceteris paribus, with higher unemployment, the average adult earns less (because the rate W/Ais lower), and, given r, the average transfer benefit b becomes smaller too. The principle is the same as in Risk Sharing, but covers the whole population (everybody is either young, adult or old) and therefore incorporates unemployment, for instance (through the ratio W/A), whereas in RS the focus is on workers and pensioners only.
  • [16]
    For the sake of simplicity, I am assuming that the same ‘i’ applies both to assets and liabilities.
  • [17]
    The variability of K(actual capital) around its target value Kmay create problems of management, similar to those currently experienced in the US (Diamond, 1996; and Gramlich, 1996), or Sweden (Palmer, 2003). I will not discuss this issue in these pages, but let me just note that this variability can be limited through equation [13] which, in practice, makes ESmore and more similar to an enlarged version of Risk Sharing as Kdeviates from K. (“Enlarged” because ESrefers to the relative incomes of all three population segments — young, adults and old — not just to two socio-economic categories, workers and pensioners. See equation [7]).
  • [18]
    The latter is indeed not an impossible outcome: however, it seems safer to rule this scenario out in designing a viable, potentially ever-lasting pension system. Should it become true, admittedly, the PAYG-ESpension system proposed here would collapse, but so would any other arrangement of intergenerational transfers.
  • [19]
    Complete neutrality is not possible, unfortunately. If A > A (actual versus reference share of adults), K will exceed K (actual versus reference reserve capital), and this will bring the variable component of the contribution payroll rate cv below zero, thus pushing c below c. If this effect is kept within reasonable limits, however, the process described in the text, although somewhat attenuated, will not altogether disappear.
  • [20]
    Although in some developed countries fertility is lower than 1.6 and may never get back to 2.1, the age structure there may benefit from migration inflows that may partly compensate for low fertility. Besides, it remains to be seen whether fertility will be that low for a hundred years in a row, as assumed in simulation 1. PAYG-ESworks well also with longer periods of low (but not extremely low) fertility.
    Several other simulations, not presented here, lead to the same conclusions that emerge from these two. On the other hand, variations in the economic sphere, not discussed in these pages, prove much less troubling, because (thanks to its use of relative incomes) PAYG-ESis almost neutral to economic changes.
  • [21]
    In these pages, I am simplifying this passage by assuming constancy in the economic sphere, and therefore a direct comparability of all monetary values (discount factor = 1). On a more formal plane, I am assuming that π (the rate of growth of labour productivity, here set to 0 for the sake of simplicity) coincides with the “natural” rate of growth of the system g. This is coherent with the condition that is normally set in the literature (e.g. in Aaron, 1966; Barro and Sala-I-Martin, 1995), that g=π + i, under the assumption that the rate of population growth i cannot deviate from 0 in the long run. In practice this means that in case of “short-term” demographic growth, the temporary extra inflow of contributions (when the actual proportion of adults exceeds its reference equivalent) should not be used to inflate pension payments. It should be saved as an extra reserve capital instead, and used about 40 years later when the proportion of the elderly starts to grow (the same holds mutatis mutandis with low fertility and population decrease).
  • [22]
    This happens because the payroll contribution rates remains fixed at 18.7%, but, as the number of employed adults declines, the elderly (whose number declines much later) have fewer resources available, and become comparatively poorer.
  • [23]
    Defined as the balance between lifetime contributions and benefits (current values of all payments). This measure is computed only for the 200 cohorts for which we have a complete history.
  • [24]
    Variability here is measured with the variance: use of different indicators leads to the same conclusions (not shown here).
  • [25]
    In several countries the situation is currently much worse: in Italy, for instance, contributions cover less than 90% of pension outlays. The rest is financed through general fiscal revenues, and the cumulated imbalance is not presented as such, even though it contributes substantially to an overall public debt that is about 100% of the GDP.


PAYG (Pay-As-You-Go) transfer schemes may take different forms. In this article I classify those proposed in the literature in three main classes. I present a new variant, labelled ES, or “Equitable and Stable”, and discuss some of its distinctive features, with special regards to its demographic rationale. There are two main innovations in the proposed system: 1) its use of a reference, instead of the current, age structure, with the implication that, in each period, the system may incur deficits, or accumulate assets, that even out in the long run; 2) its use of average incomes of age groups (the young, adults, and the elderly) instead of average incomes of social groups (workers and pensioners). These novelties, combined with the use of relative (as opposed to absolute) incomes, create an original mechanism. Theoretical arguments and computer simulations indicate that ES differs from, and compares favourably with, other versions of PAYG.



Les systèmes de retraite par répartition peuvent revêtir des formes différentes. Dans cet article, je classe en trois grandes catégories ceux qui sont décrits dans la littérature. Je présente une nouvelle variante, baptisée ES (Équitable et stable), et j’en détaille certaines caractéristiques, en accordant une attention particulière à sa logique démographique. Le système que je propose comporte deux innovations principales : 1) il utilise une structure par âge de référence au lieu de la structure du moment, ce qui implique que, de période en période, le système peut subir des pertes ou engranger des excédents qui s’équilibrent dans le long terme ; 2) il utilise les revenus relatifs des groupes d’âges (les jeunes, les adultes et les personnes âgées) au lieu de ceux des catégories sociales (les actifs et les retraités). Ces innovations, combinées avec le recours aux revenus relatifs (et non absolus), engendrent un mécanisme original. Arguments théoriques et simulations empiriques montrent que le système ES se démarque des autres types de système de répartition, et que la comparaison est en sa faveur.



Los sistemas de pensiones por repartición se basan en diferentes modelos. En este artículo clasifico los sistemas que se describen en la literatura en tres grandes categorías. Tam-bién presento una nueva variante, que denomino ES (equitativa y estable) y describo sus características, en particular su lógica demográfica. El sistema que propongo presenta dos in-novaciones importantes: 1) se basa en una estructura por edad de referencia en lugar de apo-yarse en la estructura del momento, lo cual implica que, de un periodo a otro, el sistema puede sufrir pérdidas o acumular excedentes que se equilibran a largo plazo; 2) utiliza los ingresos relativos por grupo de edad (jóvenes, adultos y personas mayores) en lugar de basarse en los ingresos por categoría social (activos y jubilados). Estas innovaciones, junto con el recurso a los ingresos relativos, en lugar de absolutos, dan lugar a un mecanismo original. Los argumen-tos teóricos y las simulaciones empíricas muestran que el sistema ES se diferencia de los otros sistemas por repartición, y que se puede comparar ventajosamente con ellos.


  • OnlineAaron Henry, 1966, “The social insurance paradox”, Canadian Journal of Economics and Political Science, August, pp. 371-374.
  • OnlineAuerbach Alan J., Gokhale Jagadesh, Kotlikoff Laurence J., 1994, “Generational accounting: a meaningful way to evaluate fiscal policy”, Journal of Economic Perspectives, Vol. 8, No. 1, pp. 73-94.
  • Baldacci Emanuele, Peracchi Franco (eds.), 2000, Reforming the Social Security System. An International Perspective, Rome, ISTAT.
  • Barro Robert J., Sala-I-Martin Xavier, 1995, Economic Growth, New York/etc., McGraw-Hill.
  • Bengtsson Tommy, Fridlizius Gunnar, 1994, “Public intergenerational transfers as an old-age pension system: A historical interlude?”, in John Ermisch, Osamu Saito (eds.), The Family, the Market and the State, Oxford, Oxford University Press, pp. 198-215.
  • Bosworth Barry, 1996, “Possible effects of ageing on the equilibrium of public finances in the United States of America”, European Economy, ‘Reports and Studies’, No. 3, (Ageing and pension expenditure prospects in the western world), pp. 127-154.
  • Cigno Alessandro, 1991, Economics of the Family, Oxford, Clarendon Press.
  • Cigno Alessandro, Rosati Furio C., 1992, “The effects of financial markets and social security on saving and fertility in Italy”, Journal of Population Economics, Vol. 5, No. 3, pp. 319-41.
  • Conrad Christoph, 1991, “The emergence of modern retirement: Germany in an international comparison (1850-1960)”, Population: An English Selection, 3, pp. 171-200.
  • OnlineDeSantis Gustavo, 1995, “Pay-as-you-go transfer schemes: a new perspective”, in EAPS-IUSSP-IRP, Contributions of the Italian Scholars to the 1995 European Population Conference (Milan, 4-8 September), Rome, IRP.
  • OnlineDeSantis Gustavo, 1997, “Welfare and ageing: how to achieve equity between and within the generations”, Proceedings of the 23rd General Conference of the IUSSP (International Union for the Scientific Study of the Population), Beijing, 11-17 Oct., Vol. 1, pp. 185-201.
  • DeSantis Gustavo, 2002, Trasferimenti intergenerazionali: una modesta proposta [Intergenerational Transfer Systems: a Modest Proposal], Rome, IRP.
  • Diamond Peter A., 1996, “Proposals to restructure social security”, Journal of Economic Perspectives, Vol. 10, No. 3, pp. 67-88.
  • Disney Richard, 1996, Can we Afford to Grow Older?, Cambridge (Mass.)/London, The MIT Press.
  • OnlineDisney Richard, 2000, “Crises in public pension programmes in OECD: what are the reform options?”, The Economic Journal, Vol. 110, No. 461, pp. F1-F23.
  • European Economy,1996, Ageing and Pension Expenditure Prospects in the Western World (Reports and Studies, No. 3).
  • OnlineFeldstein Martin, Ranguelova Elena, 2000, Accumulated Pension Collars: a Market Approach to Reducing the Risk of Investment-based Social Security Reform, NBER Working Paper, No. W7861, August.
  • Gonnot Jean-Pierre, Keilman Nico, Prinz Christopher, 1995, Social Security, Household and Family Dynamics in Ageing Societies, Dordrecht/Boston/London, Kluwer Academic Publishers.
  • OnlineGramlich Edward M.,1996, “Different approaches for dealing with social security”, Journal of Economic Perspectives, Vol. 10, No. 3, pp. 55-66.
  • Gruber Jonathan, Wise David A., 1999, Social Security and Retirement Around the World, New York/Chicago, NBER.
  • Hagemann Robert P., Nicoletti Giuseppe, 1990, “Le financement des retraites publiques face à la transition démographique dans quatre pays de l’OCDE”, Économie et statistique (L’avenir des retraites), No. 223, pp. 39-51.
  • OnlineHarrod Roy, 1950, Papers of the Royal Commission on Population, London, His Majesty’s Stationary Office [Extract published in Population and Development Review, 2001, Vol. 27, No. 4, pp. 781-789].
  • Inps, 1993, Le pensioni domani [Pension Benefits Tomorrow], Bologna, Il Mulino, 442 p.
  • OnlineKessler Denis, 1992, “Histoire et avenir du système de retraite”, in Georges Tapinos (ed.), La France dans deux générations, Paris, Fayard, pp. 187-221.
  • Keyfitz Nathan, 1985, “The demographics of unfunded pensions”, European Journal of Population, Vol. 1, pp. 5-30 [also in AAVV (1993) Readings in Population Research Methodology, UNPF, Vol. 8: “Environment and economy”, Chapter 27: “Economics and population research”, pp. 27.30-27.42].
  • Keyfitz Nathan, 1988, “Some demographic properties of transfer schemes: how to achieve equity between the generations”, in Ronald D. Lee, W. Brian Arthur, Gerry Rodgers, Economics of Changing Age Distribution in Developed Countries, Oxford, Clarendon Press, pp. 92-105.
  • Lee Ronald D., 1994, “Fertility, mortality and intergenerational transfers. Comparisons across steady states”, in John Ermish, Naohiro Ogawa (eds.), The Family, the Market and the State in Ageing Societies, Oxford, Clarendon Press, pp. 135-157.
  • OnlineLee Ronald D., 2000a, “Intergenerational transfers and the economic life cycle. A cross-cultural perspective”, in Andrew Mason, George Tapinos (eds.), Sharing the Wealth: Demographic Change and Economic Transfers Between Generations, Oxford, Oxford University Press, pp. 17-56.
  • Lee Ronald D., 2000b, “Long-term population projections and the US social security system”, Population and Development Review, Vol. 26, No. 1, pp. 137-143.
  • Lee Ronald D., Tuljapurkar Shripad, 1997, “Death and taxes: longer life, consumption and social security”, Demography, Vol. 34, No. 1, pp. 67-81.
  • Livi Bacci Massimo, 1995, “Popolazione, trasferimenti e generazioni” [“Population, Transfers and Cohorts”], in Onorato Castellino (ed.), Le pensioni difficili [Difficulties with pensions], Bologna, Il Mulino, pp. 19-38.
  • OnlineMacKellar Landis, 2000, “The predicament of population ageing. A review essay”, Population and Development Review, Vol. 26, No. 2, pp. 365-397.
  • OnlineMüller Katharina, Ryll Andreas, Wagener Hans-Jürgen, 1999, Transformation of Social Security: Pensions in Central-Eastern Europe, Heidelberg/New York, Physica Verlag, 305 p.
  • Musgrave Richard A., 1981, “A reappraisal of financing social security”, in F. Skidmore (ed.), Social Security Financing, Cambridge (Mass.), MIT Press.
  • OnlineNugent Jeffrey B., 1985, “The old-age security motive for fertility”, Population and Development Review, Vol. 11, No. 1, pp. 75-97.
  • Oeppen Jim, Vaupel James W., 2002, “Broken limits to life expectancy”, Science, Vol. 296, No. 5570, pp. 1029-1031.
  • Palmer Edward, 2003, “Pension reform in Sweden”, in Takayama Noriyuki (ed.), Taste of Pie: Searching for Better Pension Provisions in Developed Countries, Tokyo, Maruzen, pp. 245-270.
  • OnlineReher David S., 1998, “Family ties in western Europe: persistent contrasts”, Population and Development Review, Vol. 24, No. 2, pp. 203-234.
  • OnlineRitter Gerhard A., 1991, Der Sozialstaat. Enstehung und Entwicklung im Internationalen Ver-gleich [The Welfare State. Characteristics and Developments in International Comparisons] Munich, Oldenbourg Verlag, 252 p. (1st ed. 1989).
  • Takayama Noriyuki (ed.), 2003, Taste of Pie: Searching for Better Pension Provisions in Developed Countries, Tokyo, Maruzen.
  • OnlineUnfpa, 2002, The State of World Population 2002. People, Poverty and Possibilities, New York.
  • Wilmoth John, 2001, “How long can we live? A review essay”, Population and Development Review, Vol. 27, No. 4, pp. 791-800.
  • World Bank, 1994, Averting the Old-Age Crisis, New York/Oxford, Oxford University Press.
  • OnlineWorld Bank, 1997, World Development Report, New York/Oxford, Oxford University Press.
Gustavo De Santis [*]
Gustavo De Santis, Deparment of Economics and Statistics, University of Messina, Italy
  • [*]
    Department of Economics and Statistics, University of Messina, Italy.
Uploaded on on 03/03/2014
Distribution électronique pour I.N.E.D © I.N.E.D. Tous droits réservés pour tous pays. Il est interdit, sauf accord préalable et écrit de l’éditeur, de reproduire (notamment par photocopie) partiellement ou totalement le présent article, de le stocker dans une banque de données ou de le communiquer au public sous quelque forme et de quelque manière que ce soit.
Loading... Please wait