تقسیم خطر بین نسلی در طرح تأمین اجتماعی

Pay-as-you-go (PAYG) schemes entail beneficial risk sharing and diversification features in multi-pillar pension systems. Depending on the pension formula these features vary, however, significantly for different types of PAYG schemes. We derive individually most-preferred PAYG rules, represented by a risk-sharing parameter, for young and old members of a society. Preferences depend on the correlation between the risks of the PAYG scheme and the return risk of a funded scheme and on expectations about the durability of the pension rule. We find that the generations' interests with respect to the optimal PAYG rule typically do not fully clash, in particular if future economic conditions are expected to be similar to today's. We discuss the implications of these findings for the political economy of pension systems, offering an explanation why one typically observes “mixed” PAYG rules in reality.

It is now widely acknowledged that pay-as-you-go (PAYG) social security schemes may exhibit beneficial effects in reallocating risks inter- and intragenerationally. Such effects include risk sharing (see Merton, 1983, Enders and Lapan, 1993 and Richter, 1993) and diversification features (cf. Hauenschild, 1999 and Dutta et al., 2000). Both types of effects may provide a rationale for including PAYG schemes into the pension mix although such schemes yield lower expected rates of return than funded forms of old-age provisions (Gale, 1991). It is also well-known that various forms of PAYG schemes differ considerably in their risk allocation features; the “pension formula” is of crucial importance here Bohn, 1999, Lindbeck, 2002 and Thøgersen, 1998. This feature is most easily visible from the defining property of a PAYG scheme that, in every period, current pension payments are financed out of current contributions. Assuming that the economy and its pension scheme are subject to stochastic shocks there are, in principle, two ways to keep the budget balance of the PAYG scheme intact: by adjusting benefits or by adjusting contributions. • If it is the policy of the PAYG scheme to keep the contribution rate constant (fixed contribution [FC] scheme), then pensions will depend on the future development of the economy. Future economic risks thus have to a considerable extent to be borne by pensioners. Investing in the “PAYG asset” is a risky activity as the relationship between contributions (during the working period) and pension benefits (during retirement) is stochastic. An FC scheme may contribute to a diversification in the risks of old-age consumption as a whole (when other stochastic sources of old-age income are available). • On the other extreme, a fixed-replacement [FR] scheme follows the policy to keep benefits constant, measured by the ratio between pensions and pre-retirement income (both calculated in real terms). Contributions to an FR scheme create a risk-free entitlement to a pension of a certain size, implying a deterministic nexus between contributions and pensions. The non-stochastic FR pension might provide insurance against other old-age consumption risks but means, on the other hand, that the risks of adverse changes in the economic environment stay with the contributors (i.e., the younger generation). Pure FC and FR schemes have been discussed by Thøgersen (1998) and Wagener (2002) and, in a more policy-oriented way, by Lindbeck (2002). In this paper, we extend the analysis to allow for convex combinations of FR and FC schemes. We will represent such mixtures by a policy parameter α∈[0,1], which measures the degree of intergenerational risk sharing inherent in the PAYG pension policy. As one could expect from previous analyses of “pure” schemes (α∈{0,1}), “intermediate” policies 0<α<1 assemble a rather complex mix of risk sharing and diversification features. Our motivation to investigate a continuum of mixed PAYG pension policies is threefold: • First, mixed schemes are the empirically dominant form of pension schemes. Pure FC or FR PAYG schemes do not exist in reality where pension formulae and policies typically combine elements of both schemes, often in a way difficult to disentangle. A piece of evidence is given in Fig. 1, which depicts contribution and replacement rates1 for the German statutory PAYG scheme, the Gesetzliche Rentenversicherung (GRV), over the last decades.With an FR scheme, the upper curves should be constant in Fig. 1; whereas, for an FC scheme, the lower curve should be flat. In Germany, obviously both pensioners and contributors face variations in the pension parameters that affect them.2 • Furthermore, many aspects of the recent policy debate on averting the old-age crisis in PAYG pension schemes can also be thought of in terms of FC/FR mixtures. For example, one of the guidelines for the recent German pension reform is to keep contribution rates stable. This signals to the general public that pensions might become more correlated to the future ups and downs of the economy and thus become more risky. At least partly, the distinction whether a PAYG scheme is more of the FC or the FR type is determined by the provisions for adjusting pensions to changes in the environment. In a number of countries, PAYG pensions adjust according to the price index, while in others they are linked to changes in current (net) wages. Not few countries adopt mixtures of these procedures. From an ex ante perspective and in real terms, price index related adjustment rules come close to an FR scheme: with the entry into retirement the pension is fixed in real terms, and retirees will not share fluctuations in the business cycle. This is different when pensions are—as it de facto happens in an FC scheme—indexed to current wages and, thus, are stochastic in real terms. The widely applied blending of price and wage indexation can (in our stylized framework) be depicted by intermediate values of α. • A second motivation for considering mixtures of FC and FR schemes comes from the interpretation of a PAYG scheme as an asset: At the price of contributions during working life, returns in the form of pensions can be earned. Pure FR and FC schemes then constitute two specific payment streams with different risk/return patterns. As an implication of the basic diversification theorems from finance theory individuals will often prefer a mixed portfolio of (PAYG) assets to a strategy of “keeping all their eggs in one basket”, i.e., they prefer intermediate values of α to the polar cases. One might call this intra-PAYG diversification—as contrasted to the usual diversification of multi-pillared pension schemes into funded and non-funded pillars. One of our aims is to elucidate the circumstances so that such intra-PAYG diversification is warranted. •Third, one might wish to explain the fluctuations observed in Fig. 1 and similar graphs for other countries. Why is none of the curves in such graphs flat? From a normative, Paretian perspective, pure FR and FC PAYG schemes are ex ante non-comparable; neither is Pareto superior to the other (Wagener, 2002)—and neither generally supports a Pareto optimal allocation. 3 By contrast, a positive, political economy perspective would view graphs as Fig. 1 and its kindred as emerging from political decision processes that are not generally guided by Paretian welfare considerations, but which use preferences of the members of society as one (major) ingredient of a public choice mechanism. (For example, majority voting implements the policy option which gets the largest number of votes, where a vote is a specific transformation of an individual's preferences.) Knowledge of the preferences of individuals of different types for intergenerational risk sharing is necessary, or at least helpful, for both designing and explaining PAYG politics. As it turns out, in a great variety of settings in our model individuals prefer an intermediate to any of the pure (FC or FR) schemes—which might provide an explanation why, in the real world, one indeed observes intermediate schemes more often than the pure ones. The primary interest of this paper is, thus, in the preferences of individuals over the continuum of PAYG pension mixes (formally: the shape of expected indirect utility as a function of α). We demonstrate how preferences vary with the position in the life cycle and with the economic situation at the point in time when preferences are solicited. A main finding is that, for a rather wide range of economic environments, the most preferred value of α for both older and younger individuals lies in the interior—and not at the extremes—of the unit interval: Everybody prefers some mixed PAYG scheme to a pure FC or FR scheme. It is particularly interesting to observe how individual preferences towards risk sharing within the PAYG scheme vary with the stochastic properties of the returns on savings. The correlation between PAYG payments and the returns on private saving can also be interpreted as that between a PAYG scheme and a second, funded pillar of a diversified pension system, given that funded schemes are a one-by-one substitute for saving. Roughly, if the returns to the two pillars are positively [negatively] correlated, individuals wish to have a PAYG mix with an intermediate value of α whenever their expectations on the future wage rate are optimistic [pessimistic]. Preferences for intergenerational risk sharing of the younger generation are also affected by their expectations on the “durability” of the scheme, i.e., on whether today's pension formula is expected to be also applied when today's young are old. Given that individuals would quite often opt for intermediate PAYG schemes, volatile curves as in Fig. 1 can indeed be explained as the outcome of politically aggregating these preferences. Moreover, our results indicate that the class of political mechanisms that potentially give rise to intermediate PAYG schemes with α∉{0,1} is very rich, including majority voting as well as representative democracies. In so far, our findings likely explain, or are at least consistent with, the empirical observation that real-world pension schemes are mostly of a mixed, and not of a pure type. This paper is organized as follows: Section 2 presents the framework of our analysis. 3 and 4 derive the individual preferences over different PAYG mixes. Section 5 discusses the implications of our findings for the political economy of intergenerational risk sharing in PAYG schemes. Section 6 concludes.

We started from the observation that in real-world PAYG pension schemes neither the contribution nor the replacement rate are constant over time. One possible interpretation for this is that PAYG policies involve some positive, but variable degree of intergenerational risk sharing. The aim of the paper then was to elucidate the preferences which risk-averse individuals in different positions of their life cycles and under various initial conditions (represented by the “historical” wage rate) develop for risk sharing through the pension scheme. We did so in a two-pillar pension scheme where individuals have access to private old-age savings. Note, however, that this two-pillar pension model in fact includes three assets: the one to which private savings go, a riskless PAYG asset and a risky PAYG asset. The parameter α determines the blend of the two PAYG assets within the first pillar. Individual preferences for PAYG mixtures are influenced by the return risk in the second pillar (savings) —which should not come as a surprise if one views old-age provisions as a portfolio problem. Correlations (and not only return differentials) play an essential role if one wishes to assess PAYG schemes correctly. We assumed the parameter β>0 to be exogenous and invariable. This, chiefly means that we do not question the existence of the PAYG scheme itself. Advocates of radical changes in social security sometimes argue that PAYG schemes should be entirely abolished (β=0) due to their low returns. However, since saving in our model earns stochastic returns, there is indeed scope for PAYG social security here, even for schemes with relatively low expected rates of return Gale, 1991 and Hauenschild, 1999: rational individuals will wish to include PAYG schemes in their old-age income mix for the motives of diversification and insurance. Assuming that β is constant presupposes a constant scale of intergenerational transfers (at least in expected terms) and, given that saving and (FC) funded pensions are perfect substitutes, implicitly also invariant shares of funded and PAYG components in the two-pillar pension mix. Our focus here was on the type of the PAYG scheme, represented by the risk-sharing parameter α. With regular voting on social security, the size of the pension scheme or the blending of PAYG and funded pensions certainly figure more prominently than α on many a policy agenda. Recent reforms, e.g., in Germany (2001; see Bonin, 2001), Sweden (1997; see Wadensjö, 2000), and Italy (Dini reform 1995; see Antichi and Pizzuti, 2000), which deliberately shifted pension policies towards an FC regime, indicate, however, that α might indeed be regarded as a policy variable in itself. For future research, it might be interesting to combine voting on both the transfer and the risk-sharing components of PAYG schemes—although, given the multi-dimensionality of that problem, a collective choice analysis will presumably become more problematic. Our main question was to analyze individual preferences over the risk-sharing parameter α. An important finding was that under slightly optimistic expectations for the future insurance and diversification motives are important from all individuals' points of view. Aggregating these individual preferences in the political process then might explain PAYG pension formulae that have both the contribution and the replacement rate fluctuating. While different political mechanisms will, for sure, induce different outcomes with respect to intergenerational risk sharing (i.e., generate different numerical values for α), the polar outcomes of pure FC or pure FR schemes will emerge from very few mechanisms only. Even mechanisms that allocate all political powers to one generation will generate mixed PAYG pension schemes, provided that expectations for the future are at least slightly optimistic. As moderate optimism seems to have been the dominant expectation with respect to future economic growth over the past decades after World War II, this might explain why most real-world PAYG schemes indeed are of an intermediate type.