Abstract
While the basic idea of generational accounting has remained unchallenged, current practice shows a growing diversity of approaches. Methodological differentiation, which reflects the novelty of the general concept, concerns the construction of the generational accounts for future generations and the measurement of intergenerational imbalance.
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If not indicated otherwise, immigration in this text refers to net immigration, i.e. the balance of gross immigration and emigration. Furthermore, it is taken for granted that immigration is positive. We do not refer to (net) emigration explicitly, as it is empirically irrelevant in most OECD countries. With emigration, all statements considering immigration need to be reversed.
To derive tt k, generational accountants proceed parallel to equations (2.6) to (2.8), benchmarking a relative age-specific profile of government purchases against net government purchases in the base year.
In the opposite case, if maintaining base year fiscal policy allows to unburden future generations, equal treatment of all prospective newborns yields a lower bound of the tax cut.
The working life span of two successive generations overlaps completely except for one year. Assuming that age-specific labor supply and the employment profile do not vary, life cycle wage income of the later born cohort exceeds income of the preceding cohort by exactly the productivity gain in this single year.
The average lifespan of present and future generations could differ by a small degree, if the projections account for declining mortality. However, changes in generational accounts due to mortality changes between subsequent generations are generally negligible.
This argument abstracts from macroeconomic repercussions of course, which could work in the opposite direction.
The original formula, which replaces the nominator of equation (4.10) by GAt,t+1,unfortunately, reached textbook level, like in Raffelhüschen and Walliser (1996). Even some fairly recent contributions to the literature, for example Jagob and Scholz (1998), keep to this error.
If discounting were possible, the economic `lifetime’ of base year and future generations would differ by one year. One would have to abandon the discounting of future payments for that year, in order to arrive at a meaningful base of comparison, tracing base year and future newborns over an identical number of years.
The easy proof is given in the Appendix A.2.
This is worth mentioning, as introductions to generational accounting often seem to suggest that distinction between men and women is fundamental to the method. The sustainability results of generational accounting studies that do not consider gender differentials due to data deficiencies [Feist et al. (1999), Bovenberg and ter Rele (1999b)] are fully comparable to studies that do.
If, for example, base year newborns of group m bear twice the net lifetime tax burden of a member of group n, each future m-type individual counts for two members of the reference cohort. Obviously, if the ratio of subgroup-specific accounts equals unity, equation (4.16) simplifies to equation (4.9). Disaggregation into separate population groups is trivial, unless they exhibit distinct fiscal characteristics when considering the entire life cycle.
This impression seems to guide Havemann (1994), where he criticizes the assumption of generational accountants that `the set of future generations ... must ... pay off the existing national debt ...’ (p. 97), suggesting that the present living ought share part of this burden.
Here and in the following, the superscript S is used to indicate a sustainable life cycle tax burden.
To give an example, in the unsustainable fiscal policy scenario, the generational account for the youngest generation is calculated as GA t , t = 10+0, 5*20+0, 2*5.
For example, according to the sustainability indicator 9r, intertemporal redistribution through fiscal policy in Argentina and Norway appears very similar [Kotlikoff and Leibfritz ( 1999, Table 4.2)]. However, the fiscal imbalance of about 60 percent observed in the two countries is reached at considerably different tax burdens (22,700 versus 106,300 US-dollar for the base year newborn) and in a markedly distinct demographic environment. It would be careless to conclude that the long-term economic impacts of fiscal policy in the two countries are comparable, despite similar relative generational imbalance.
Net tax payment of immigrants born prior to the base period enter the budget residual via equation (4.3).
Recall equation (4.12), p. 58. While this relation is true for the absolute change of future generational accounts, it does not hold for the relative variation of tax burdens.
The argument in this section is strongly influenced by Raffelhüschen (1996).
To see this, substitute equations (4.1) and (4.2) into (4.9), and differentiate the resulting expression for GAt+1,t+i with respect to GAt,t•
In this unlikely but conceivable case (compare scenario (b) in Table 4.1), appli-cation of l’Hôpital’s rule yields lim 7r = aGA t+11+9 /acA I,I , which is finite.
Provided that government purchases are regarded as personal transfers, present newborn agents are life cycle net transfer recipients in all member states of the European Union except Italy [Raffelhüschen (1999c, Table 5)]
Note that ß = a + (1 — a)(GAt, t /GAt,t) Obviously, /3 1 for a 1, and /3 1 for a 1, provided that GAt,t O.
The respective policy parameters are constructed parallel to equation (4.21). Supposed all transfers are adjusted, the sustainable generational account is given by GAt t = GAt t + aGAt t = ßGA t ,t,where ß = 1 + (a —1) (GAt,t /GAt,t ). Note that the sustainable net tax payment differs from that with adaptation of taxes. Adjusting government purchases, the sustainable generational account equals that under current tax and transfer parameters: GAt t = GAt t + GAt,t
Cf. Kotlikoff and Raffelhüschen (1999) in particular. The international survey by Kotlikoff and Leibfritz (1999) focuses less on this approach.
The analytical results supporting the following argument are derived in the Appendix A.3.
Note the analogy to the membership problem of a public club [Cornes and Sandler (1996, p. 359)). However, as generational accounting rules out externalities of absolute population size on both public revenue and expenditure, an optimal future cohort size does not exist.
In the special case where GAt+1,t+1(0,Pk°,k) and GAt+1,t+1(/3,N,k) meet on the 45°-line, the policy indicator indicates that the demographic change has no impact on fiscal sustainability at all.
As the sustainability approach has turned popular only recently, unanimous terminology is not reached yet. In the literature, the sustainability gap is also addressed as the generation balance gap [Cardarelli et al. (2000)] and as intertemporal public liabilities [Raffelhüschen (1999a)].
The literature on this topic, which deals with long-term net liabilities of public pension schemes in particular, is extensive. Cf. Van den Noord and Herd (1993) for an example with a European perspective. Franco (1995) provides a critical assessment of this approach, which stands somewhere between annual deficit accounting and the sustainability approach to generational accounting.
We pass over the proof, which requires some lengthy but easy manipulations of the different components of the sustainability gap, noting that age-specific per capita government purchases and transfer benefits vary by the same amount in absolute terms if one changes the definition of net taxes.
For example, the European cross-country comparison of the intertemporal state of public finances by Bonin and Raffelhüschen (1999) is exclusively based on this concept.
One may put forward the same argument against the debt-to-GDP indicator. However, it seems more relevant within the intertemporal context of generational accounting.
Alternatively, the policy revision could start from year t
This stylized procedure does not conflict with the central idea of the sustain-ability approach to model long-term trends in fiscal and demographic trends, in order to capture fiscal capability of future generations. Generation-specific differences in fiscal potential are not ironed out by a proportional adjustment of per capita taxes or transfers.
The tax-adjusted generational accounts of migrants can be written as GAy k = v y ,kGAy k for all y t and y k max{t + 1, y — D}. Even if the share of tax payments in the generational account does not differ between future resident birth cohorts, it certainly changes with migrant age when taking residency. Hence, one does not observe a uniform proportional variation of migrants’ generational accounts. A similar argument can be made, if the analysis distinguishes between resident subpopulations.
Maturation of the recently introduced pay-as-you-go pension scheme in the United Kingdom and the transition to a resettled pension system in Italy provide examples for long-term status quo developments, unfolding over half a century, that have been analyzed in a generational accounting framework. Cf. Cardarelli et al. (2000) and Franco and Sartor(1999), respectively.
This requires to replace the set of tax accounts in equation (4.25) with an analogous set of transfer accounts.
For a sketch of the proof, suppose government wealth and net government purchases are zero to limit notation. Furthermore, suppose no migration. Then, if fiscal policy balances the intertemporal public budget constraint by adaptation of fiscal parameters for future generations, it must hold that Er Pk, kGAt, k = Ek-t-D Pt, kGAt, k Supposed net tax burdens do not vary across future cohorts, it is also true that Pk,kGAt,k = GAt,t+1 E+1) In serting this condition into o the intertemporal public budget constraint and re-arrangement yields GAt,t+i = L= t_D Pt, kGAt, k/ Er t+i Pk,k(1 + g)k—(t+1) Thus, under the given conditions, the representative future generational account is unique, as the terms on the RHS are determined by initial fiscal policy parameters and exogenous demographics. As a corollary, the sustainability and the residual method yield identical future accounts.
This is the approach taken by the generational accounting studies collected by the European Commission (1999) where 7r is inapplicable due to application of a broad concept of personal transfers.
This aspect gains particular relevance comparing fiscal sustainability between developing and more advanced countries. But even within Western Europe, the current variation of life expectancy reaches almost four years, comparing Ireland [McCarthy and Bonin (1999)] and Sweden [Lundvik et al. (1999)].
This requirement actually comprises a set of necessary conditions, as one has to distinguish between resident and migrant cohorts. This set of conditions represents a generalization of the condition for a normal reaction under the residual approach. It can be derived parallel to Appendix A.3, writing the policy adjustment factor p first as a function of residents’ and migrants’ cohort size: p(Pk,k,My,k) = SG t (P k ,k, M y ,k)/ f (Pk,k, M y ,k),where f(-) represents the denominator of equation (4.25). Differentiating p(•) with respect to Pk,k for all k t,and furthermore with respect to M y ,k for all y t and y k max(t + 1, y — D) yields the set of necessary conditions. Even if fiscal policy does not discriminate between future birth cohorts, one is left with a set of D necessary conditions, D — 1 of which apply to immigrants, depending on their age when taking residency.
It is not always meaningful to define the baseline of cross-country analysis around a uniform growth and interest rate. For example, in order to design the specific economic conditions of what is still a developing country in many ways, the special baseline for Argentina [Villela Malvar (1999)] deviates significantly from the standards set for the world-wide generational accounting studies collected by Auerbach et al. (1999).
To conduct, for example, a tax experiment, one has to add equation (4.3), restricted to the tax accounts of living generations, to the nominator of equation (4.25).
They are, under the very special conditions that render the sustainability and the residual approach interchangeable.
If the lump sum amount is assigned to living and future generations, an analogous formula applies, where the outer summation begins in year t,while the inner summation always starts from the birth year of the oldest agent, y — D
This is evident from equation (4.26), as a â Idsct=o O. The overall impact of an interest rate increase is indefinite, as the sustainability gap is also a negative function of the interest factor.
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© 2001 Springer-Verlag Berlin Heidelberg
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Bonin, H. (2001). Assessing Fiscal Imbalance. In: Generational Accounting. Population Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04595-4_4
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DOI: https://doi.org/10.1007/978-3-662-04595-4_4
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