GENERATIONAL ACCOUNTS AND GENERATIONAL BALANCE

GENERATIONAL ACCOUNTS AND GENERATIONAL BALANCE: AN ASSESSMENT PETER DIAMOND *

Abstract - Generational accounting is accounting as part of normative presented by Auerbach, Gokhale, and consideration of government activity. A Kotlikoff for normative consideration of second strand is the use of generational government and positive analysis of accounting in a positive theory of individuals. Generational balance is individual behavior. A third strand is the presented as a normative criterion and a presentation of generational balance as useful target for political economy. This both a normative criterion and a useful assessment distinguishes cost and utility target for political economy. Relative to bases for such calculations and concludes all of these is also an attack on the that the cost basis is interesting and conventional deficit (in its standard more useful—easier to get straight variations) as a useful tool for economic conceptually and consistent with a analysis. In this assessment, I draw on residual calculation of the impact on the previous reviews by Baker (1995), future . Generational Cutler (1993) and Haveman (1994). balance as currently calculated does not seem good by itself for identifying either equitable policies or good ones. THREE PARALLELS It is useful to start with calculations that bear some partial resemblance to gener- ational accounts and that have some familiarity. The three to be discussed are INTRODUCTION the projections for Old-Age, Survivors, The development of generational and Disability Insurance (OASDI) and accounting in the joint and separate Medicare, the calculations of the writings of Auerbach, Gokhale, and incidence of taxes, and the calculations Kotlikoff (for example, 1991, 1994, of federal government impact by state. 1995; AGK, hereafter) has three strands. One strand is the role of generational Each year projections are prepared for OASDI and Medicare. Since I am more

*Department of , Massachusetts Institute of familiar with the former, I will concen- Technology, Cambridge, MA 02139. trate on that one (Board of Trustees,

597 NATIONAL TAX JOURNAL VOL. XLIX NO. 4

1995). Three projections are prepared, a budget. This is done by identifying central “best” projection and two that groups (for example, by state) and straddle it to represent some measure of allocating both expenditures and taxes a range of alternative projections. The to the different groups (Forsythe and projection extends 75 years into the Friar, 1993). future. The focus of the projection is the state of the trust funds. The basis of the In allocating expenditures, there are two projection is existing legislation, ignoring ways that such a calculation could be a non-negativity constraint on the trust done, based on costs or utilities. One funds. Being a projection, the calcula- way would be to take the cost of tion describes what would happen to different expenditures and allocate the the trust funds if the assumptions cost to different people who are behind the projection came to be identified as benefiting from the realized. The central idea is to identify expenditures. This necessarily involves a with considerable lead time when the somewhat arbitrary allocation of current legislation is likely to be inconsis- common costs. It has the adding-up tent, to need changes in benefits and/or property that the total allocated is equal revenues in order to have a path on to the aggregate of government which Social Security can continue. In expenditures. This approach is based on addition to projecting current legisla- measuring from the government’s tion, the same methods are used to perspective who the money is spent on. calculate the implications of alternative A different approach would be to legislated changes that might restore calculate a utility-to-individuals for the actuarial balance. There are a variety of different expenditures. Thus, the short- and long-run concerns that the marginal rate of substitution between projections are meant to flag as reasons the government program and income for concern about the future of the forms the basis of the valuation, rather program. than a fraction of the cost of providing the program. In this case, one would be Since the late 1940s, there have been trying to value the net utility impact of repeated calculations of how the U.S. the combination of taxes paid, transfers tax system affects different groups in received, and benefits received as a the economy (Musgrave et al., 1951; result of the expenditures. Note that if Pechman, 1985). The focus of the there are insurance components to the analysis is to identify groups by income government-provided transfers, then an level and to allocate the tax revenue ex ante utility-based approach to taxes collected in a year to the different net of cash transfers needs to assess the groups, recognizing the incidence of the premium people are willing to pay for taxes, not just the legal liability to pay. In the insurance. When everyone is trading addition to the allocation of the entire the equivalent of all of the government tax revenue, the methodology is used taxes, transfers, and expenditures at the for differential incidence—the examina- same prices, then everyone will have the tion of the distributional impact of same marginal rates of substitution proposed tax changes. between their net receipts of dollars or benefits from different programs. In the While the tax analysis considers only tax more realistic case that there are not collection (possibly net of cash trans- complete and perfect markets, marginal fers), another approach is to consider rates of substitution will differ across the impact of the entire government people.

598 GENERATIONAL ACCOUNTS AND GENERATIONAL BALANCE

Depending on how people valued the countries, educational expenditures), an expenditures, the sum of utilities from anomaly related to the definitions in the the expenditures might be larger or National Income and Product Accounts smaller than the aggregate level of (NIPA). The current calculation is a mix expenditures. This difference between of cost-based calculations and utility- the cost and utility approaches in the based calculations, which again is presence of an adding-up condition is anomalous. In terms of the grouping of relevant for the ability to allocate a the population, all the not-yet-born are residual aggregate cost to some group combined using a residual calculation, rather than estimating directly. That is, not separate generational calculations. with a cost-based approach, having The lack of a consistent cost-based allocated some of the cost to some calculation seems to make the use of a groups, the cost relevant for the remainder residual calculation for future genera- of the population is the difference be- tions inappropriate. tween the total and what has been allocated. The same residual approach cannot be used with a utility-based GENERATIONAL ACCOUNTING— approach. In addition, restriction to a RETROSPECTIVE 2 single year makes the treatment of invest- It seems to me that we are interested in ments somewhat awkward, since these comparing the impacts of alternative are meant, in part, to affect people government policies on people born at (somewhat the same people, somewhat different2 times. Thus, we want some different people) in future years. generational accounting, although we also continue to want calculations based In all three of these examples, the on other groupings. The issue in this response of equilibrium in the economy section is what generational accounting to the programs is not part of the can hope to measure and how it has calculation. That is, there is a partial been and could be done. equilibrium nature of the calculation, rather than general equilibrium determi- To delay some issues about projection, I nation of the full set of changes in the begin by discussing historical account- economy. ing. Assume that one had a full history of government actions. Year-by-year and From1 the perspective of these examples, person-by-person, assume that we had generational accounts are prospective a complete description of the impact of and cover many years, like the Social government actions. (For some people Security projections. Like the other two in some settings, even the year may be calculations,1 generational accounts are too long an accounting period—for concerned with an allocation among example, the utility of poverty alleviation groups (identified by date of birth and measures will depend on the frequency gender) not in the total budget or public and timing of payments.) For any debt. The current version of genera- individual, we would see the set of tax tional accounts is neither a calculation payments to the government. Given an based solely on taxes (or taxes net of incidence theory, one would also have cash transfers) nor a calculation allocat- year-by-year estimates of taxes “really” ing the full government budget. Rather, paid. Similarly, one would have a series it is the somewhat anomalous combina- of year-by-year estimates of cash tion of taxes, cash transfers, Medicare, transfers received. One also wants to and Medicaid (and, in some other value the benefits received other than in

599 NATIONAL TAX JOURNAL VOL. XLIX NO. 4

cash. (In a world with military drafts, precisely displaced identical private there are also costs-in-kind as well as insurance, having no real effects benefits-in-kind.) This would include whatsoever. Assume the government goods received free (highway use, for program is identical to the displaced example) and goods sold at less than private insurance, including the costs of what they would have cost without the running the program. Then, examina- government action (access to national tion3 of the cash flows would find that parks, for example). One might want to individuals are losing from the program recognize individual uncertainty and to the extent of the administrative costs, calculate as of some date the distribu- even though real allocations are tion of transfers that might have been unaffected. In practice, Social Security received at some later date, given the provides insurance that is different from rules in force when that later date that in the private market and has happens—as with annuitized retirement administrative costs that are lower than benefits. Indeed, evaluation of insurance those of private insurance markets. programs on an individual ex post basis would be peculiar. The next step, assuming one wanted to take it, is to determine how to convert this array of annual estimates into a It is worth noting that similar to the scalar. While this is simple in a world contrast between evaluating goods and with complete markets that are available services on a cost or utility basis is the to all at the same prices, the issue is a contrast between evaluating cash mess when different people face payments that contain an insurance different interest rates, and incomplete- component on a cost or utility basis. ness of markets implies that people are Since people pay markups when they making personal expenditure decisions purchase insurance privately, any utility- under uncertainty about future transac- based evaluation of the government tion opportunities and future resources provision of insurance should involve and needs. such a markup. For example, the real annuities provided by Social Security While tempting, it is inadequate to should be worth considerably more collapse this issue into a choice of (relative to expected cost) than the interest rate. The inadequacy parallels nominal annuities in the market, which the same issue in benefit-cost analysis, themselves show substantial markups. where the determination of shadow Thus, a cost-based calculation of Social prices for government expenditure Security uses the amounts actually paid decisions is not adequately discussed as (possibly marked up by the small a debate over the right discount rate. administrative costs). With a utility- (For a discussion of tax incidence in the based calculation, the benefits received presence of liquidity constraints, see would be considerably marked up, Hubbard and Judd, 1986.) It is the multiplied by a factor possibly reaching interest rates on that 1.5. This is a nontrivial issue. By making tie together the histories of tax revenue, no markup, current generational expenditures, and debt in a single accounting is using a cost or, more budget constraint. Assuming the tax accurately, a cash-received basis. receipts from the taxation of interest income are separately recognized as This issue can also be seen by consider- part of taxation, it is gross-of-tax ing a government program that interest rates paid that become the right

600 GENERATIONAL ACCOUNTS AND GENERATIONAL BALANCE

measure for evaluating the net cost-to- risk characteristics approximating those government of dealing with people in of government taxes and spending. This different years. On the other hand, the is a focus on lifetime utilities, not the cost interest rates relevant for evaluating the of government. This is not the interest impact on individuals are generally rate which satisfies their present dis- different interest rates (apart from the counted value government budget people who are holding such debt constraint. Since many people hold little throughout their lives, assuming that or no assets, this is an approach that the interest was not taxed and that makes some sense for the well-off, not these rates represent marginal deci- for the population in general. Nor does it sions). And the choice of interest rate is correct for taxes on interest earnings different for different portions of the which would be appropriate for a utility- population. This is particularly an issue based approach. Perhaps, consistent with with Social Security. If you think that a this logic, different interest rates should major justification of Social Security is be used for different government paternalism—to force people to save programs, with much higher interest rates more than they would if left to them- used in part. But then, we know that it is selves—then it would be potentially not generally true that the correct misleading to value Social Security using adjustment for risk is simply a different the interest rates inherent in the interest rate, that then gets compounded preferences of the people subject to its repeatedly into the future. They do report mandates. On the other hand, this can calculations with different interest rates, be viewed as a cost of paternalism so one can see the effect of different where a mandate is deemed inappropri- choices. Using an interest rate above the ate. However, one cannot “get off” that government rate and calculating Social easily if the interest rates relevant for Security benefits on a cash-received basis combining cash flows in two different is combining a utility-based calculation years are different when perceived at with a cost-based calculation. alternative earlier dates. That is, at age 21, I might make a decision that affects Of the assumptions used by AGK, I have relative incomes at ages 50 and 60 in a a few comments on the treatment of way that reveals an implicit interest rate. capital income taxation. They capitalize At age 40, I might make a decision that the inframarginal fraction of part of the shows a different implicit interest rate. income, and all of the corporation and There is no obvious answer to what the estate taxes, but do not capitalize any of historian should do in making this the taxation of residential capital. While calculation. This problem arises from some benefits of local government also incomplete markets. The same problem get capitalized, suggesting some netting arises if preferences for the future out, a more detailed treatment seems change over time. In this case, it is hard, warranted. In determining the fraction and possibly impossible, to develop the of the personal income tax to multiply normative basis for a single lifetime by the fraction inframarginal in order to utility-based calculation. know how much to capitalize, they take the fraction of capital income in Net For a single interest rate, the same for National Product (NNP). This seems odd all members of a , AGK since capital income is so heavilyreceived choose a rate meant to reflect what by high-income people, while much of they estimate to be the return equal to labor income goes to peoplenot subject the rate required to hold an asset with to income taxation.

601 NATIONAL TAX JOURNAL VOL. XLIX NO. 4

GENERATIONAL ACCOUNTING— assume that Social Security will receive PROJECTION new legislation that restores actuarial balance. One way to allow for the need Contrasting the future with the past, for such an adjustment would be to there are two further issues. One is to leave Social Security out of the genera- project the economic environment for tional accounts. This is different from the government. For example, how the situation in which one considers the much will government-provided medical impact of all government programs. A services cost and how much will defense similar issue arises with the integration cost. Second is to describe what should of federal, state, and local accounts. be used as the course of government This involves an implicit political action. That is, what projections should assumption, when one is using the be made about future legislation, either accounts to identify future federal to extend the current way of doing revenue issues. things into the future or to recognize that some ways of doing things are For projection purposes looking for likely to be changed. This is a major inconsistency, describing a scenario that issue since many projections of current might happen, the evolving budget practices lead to politically unlikely or constraint that will affect future taxes even inconsistent outcomes. For depends on the realized real interest example, both the Medicare and OASDI rates. Ex ante combinations of different trust funds are projected to go negative stochastic future cash values are not if existing legislation on taxes and part of such a projection of a scenario. benefits is projected into the future. That is, for some purposes, one might What projection should be used in a want a projection of what will happen if setting like this? The answer depends a particular set of economic and on the purpose for the accounts. If one government behavior assumptions is wants to show the inconsistency of met. For other purposes, one might current Social Security legislation, one want an expected utility calculation of wants to project current legislation. If how the entire future is perceived. The one wants to show the detailed latter involves, explicitly or implicitly, a generational impact of that inconsis- behavior of government as a function of tency, one would need to select an how the economy evolves. For example, alternative source of revenue to one would evaluate Social Security maintain the promised benefits or an differently depending on whether one adjustment of the benefits. (Conceptu- viewed future legislation as zero-sum ally simpler is the comparison on a political risk or as a device for generational basis of alternative intergenerational risk spreading in the methods for restoring actuarial balance.) presence of incompleteness in the Alternatively, for positive analysis of “contract” covering the relationship short-run private behavior, the projec- between Social Security and the tion should be based on the beliefs of evolution of the economy. the private agents. In considering how generational accounts for the entire After 2004, the 1994 Office of Manage- budget should reflect Social Security, ment and Budget (OMB) projection there is a similar dichotomy. If the assumes that expenditures per person in purpose is to identify the concerns with three broad age groups will increase general revenue and general revenue with productivity. Thus, the projections financed programs, then one might assume that changes in the relative sizes

602 GENERATIONAL ACCOUNTS AND GENERATIONAL BALANCE

of the groups result in no changes in per activities, including the annuitization capita expenditures. This might overesti- provided by Social Security and Medi- mate the effects of population change care. on spending since expenditures per capita such as education might adjust to Another issue arises with the role of the size of the receiving population, actual legislation. The AGK calculation is with a larger group receiving less per based on a projection of government person. This assumption is important in policies meant to reflect continuation of the comparison of how generational current policies. Insofar as the behavior accounts vary with the rate of productiv- of individuals is based on projections of ity increase. However the projection is government policies, it will be based on done, the variation of outcomes with the projections by the individuals of the rate of productivity growth is what they think might actually happen. sensitive to the relationship between the These two approaches to projection projection of expenditures and the differ in a central way. Insofar as assumed rate of productivity growth. generational accounting is meant to highlight the unsustainability of continu- ing current policies, it is not a good POSITIVE GENERATIONAL ACCOUNTING instrument for estimating individual Starting with a life-cycle model of responses. Individuals will focus on what individual savings, the authors view the they think will happen, not what would calculation of changes in a lifetime happen if current unsustainable policies budget constraint as a good basis for were unchanged. For example, when predicting the private market response the government projects the inconsis- to new legislation. Liquidity constraints tency of current Medicare and OASDI make this highly questionable as an legislation, we would expect individuals approach to short-run behavior. For to recognize the possibility of change in example, consider the government making their savings decisions. Thus, introduction of mandatory loans to the both the 1977 and 1983 Social Security government (that are not tradable and changes had massive decreases in not usable as collateral), paying the projected future benefits. However, market interest rate. Since liquidity current consumption behavior did not constrained individuals cannot offset reflect a massive drop in lifetime income this reduction in their access to purchas- when the legislation passed, since the ing power, this has an impact on short- nonviability of existing legislation was run demand. Having had an effect on clear. short-run behavior, this policy then has an effect on the later long-run behavior GENERATIONAL ACCOUNTING— of the same people; as a consequence TELESCOPED of any short-run impacts, people reach older ages with different wealth than AGK allocate net taxes (or taxes and they would otherwise have had. This expenditures) to current generations. can affect their choice of planned While one could use the same methods bequests and so their lifetime marginal to make allocations to future genera- propensity to consume. It is clear that tions one at a time, AGK do not do this. the lifetime marginal propensity to Rather, they use the government budget consume scalar used in Gokhale, constraint and the assumption that each Kotlikoff, and Sabelhaus (1994) is not a future generation bears the same net sufficient statistic for many government cost relative to income in order to

603 NATIONAL TAX JOURNAL VOL. XLIX NO. 4

calculate a single net (per generation) of the Social Security actuarial imbal- cost for all . This is ance relative to taxable earnings. Yet different from projecting the current such a calculation based on the income policies indefinitely into the future. tax ignores possible changes in FICA Instead, it is a residual calculation of a taxes that might happen to restore net amount available across the birth actuarial balance in Social Security. dates of these different generations.

GENERATIONAL BALANCE—NORMATIVE Among the questions raised by this procedure is the role of the interest rate In addition to generational accounting, in collapsing these future net costs into calculating the lifetime economic impact the present. Insofar as one is taking a of government actions, AGK consider cost basis, then the government interest generational balance. Generational rate is the appropriate one to use and balance is defined as equality between there seems little ambiguity (for a the growth-adjusted lifetime accounts projection, as opposed to recognizing of current newborns and future explicitly the uncertainty about the generations. For current newborns, the future). However, if one takes a utility- calculation is done using the projections based approach, then one uses marginal of government polices; for future rates of substitution in order to infer the generations, the calculation is done as a appropriate interest rate. But for any residual. Calculating the ratio of net given generation, these are only taxes to projected income, constant for inferable over the period that the all future generations, that will balance generation is alive; it is not a basis for the government’s infinite horizon selecting interest rates for the time budget. As argued above, this calcula- before their birth. In addition, the tion only represents a constraint on the government budget constraint holds for government if the calculations are done government cash flows, not for the on a cost basis, including the interest utilities associated with those cash rate faced by the government. Thus, a flows. Thus, I think that one cannot utility-based calculation, which might be telescope as AGK do with a utility basis, seen as the most interesting from a but only with a cost basis. In the social welfare function perspective, is vocabulary used above, there is no not consistent with this residual adding-up constraint on a utility basis calculation, which has a cost basis. that makes the sum of utilities equal to any constant. One cannot then infer the There are three questions to ask about net cost to future generations as a generational balance. First, assuming residual. the calculations are done fully, is balance in a utility-based approach a This telescoping is part of the procedure social welfare optimum. Second, if the AGK follow on the way to examining calculation is done on a cost basis, does generational balance. One has no need the level of normative value extend to for telescoping for some interesting this calculation. (I do not ask about the calculations, such as what size (perma- mixed calculation with only some nent) increase in the income tax would expenditures included.) Third, does yield government present-discounted- calculating what it would take to restore value budget balance given a projection balance have a valuable political role, of current expenditure patterns. This is even if there is not a social welfare basis analogous to the calculation of the size for choosing this outcome precisely; that

604 GENERATIONAL ACCOUNTS AND GENERATIONAL BALANCE

is, the distinction between generational deficit. One example is the sale of balance as a normative criterion and as assets. a political tool. Exclusive attention to generational It is clear that an optimum overlapping- balance would also have its limitations. generations (OLG) growth calculation One example would be the impact on will not generally have generational balance of policies far into the future balance on either a cost or utility basis. which might be legislated relatively Redistributing across generations will be painlessly since they would have no part of such an optimization with visible effects in the near term. This probability one. Second, one would reflects the tension between short want to look at a full calculation of the horizon measures which encourage impact of the government, not a partial substitution across the time limit in the one. That is, one would not draw overall measure and long horizon measures normative conclusions from consider- which allow announcement of deferred ation of part of government activity. To policies, which might be better imple- indicate an example of the problems run mented sooner and also might not into with a mixed calculation, the happen. Appendix contains a model where the economy is in a steady state, but a In addition, since generational balance is calculation would show imbalance. a comparison of newborns with the future, there are policies that are clear changes in generational distribution that GENERATIONAL BALANCE—POLITICAL would not show up as a change in I conclude that the role of generational generational balance. For example, a balance is in the political economy program of increased taxes used for realm, not that of normative economics. education would affect newborns and From this perspective, the question is future generations the same and so the utility of going beyond the use of would not contribute to generational generational accounting to assess the balance even though current older differential incidence of alternative generations are paying higher taxes for government policies and calling for the benefit of future generations. generational balance. Two questions arise with any such political calcula- To see an example of a problem with tion—the extent to which a call for generational balance considering only generational balance would help to taxes net of cash transfers, consider the pressure government to have a wider role of assets that provide services that perspective of the effect of policies are given away, such as the interstate than would otherwise occur and the highway system. AGK value government extent to which unfortunate policies wealth by capitalizing fee income would be pursued because they make received by the government at an a summary statistic look better, with- interest rate. As they point out, a out having the same effect on the complete adjustment in this framework underlying reality. Focus on the would include the value of physical conventional deficit encourages assets deducted from the public debt government actions that look good in and the future services provided by this light, even if they are not necessarily these assets added to the government helpful with capital accumulation, which expenditures to be financed. Since the is a major part of the concern with the framework does not value the services,

605 NATIONAL TAX JOURNAL VOL. XLIX NO. 4

but only recognizes the cost of provid- have been laboring without as much ing them, this is an inadequate picture feedback from the rest of the profession of intergenerational fiscal relations and as they deserve. I think that current would have a perverse political incentive focus on the cost basis for projection is from a drive for generational balance. likely to be more useful than current The perversity comes from the equal focus on the utility basis. This approach contribution to generational balance is easier to get straight conceptually and from cutting expenditures on current is consistent with the use of a residual public consumption and cutting to calculate the impact on future expenditures on current public invest- generations. I do not think that genera- ments that do not generate revenue. tional balance calculated as it is cur- rently is a good basis by itself for Including some but not all government identifying either equitable policies or programs raises problems wherever good ones. Of course, neither is an the line is drawn between what are exclusive focus on conventional budget identified as transfers (and included) balance a good basis for identifying and what are not. Consider a pro- either equitable policies or good ones. gram to give vouchers for school lunches as opposed to giving grants to ENDNOTE schools to provide lunches. These are economically very similar in their I am grateful to Alan Auerbach and Larry Kotlikoff for helpful comments. generational distributional conse- quences. Yet would one count the former in taxes net of transfers but not REFERENCES the latter? Auerbach, Alan J., Jagadeesh Gokhale, and Laurence J. Kotlikoff. “Generational Accounts: A Meaningful Alternative to Deficit Accounting.” Conclusions Tax Policy and the Economy 5 (1991): 55– I conclude that generational accounting 110. is interesting. It is interesting whether Auerbach, Alan J., Jagadeesh Gokhale, and Laurence J. Kotlikoff. “Generational one looks at future taxes or future taxes Accounting: A Meaningful Way to Evaluate net of future expenditures, and it is .” Journal of Economic Perspectives 8 interesting whether one looks at future No. 1 (Winter, 1994): 73–94. generations and the trajectory of the Auerbach, Alan J., Jagadeesh Gokhale, and public debt separately or telescopes Laurence J. Kotlikoff. “Restoring Generational them through the government budget Balance in U.S. Fiscal Policy: What Will It Take?” constraint. At a minimum, I think it Federal Reserve Bank of Cleveland Economic Review 31 No. 1 (1st Quarter, 1995): 2–12. would be beneficial to have official projections well out into the future, Baker, Dean. Robbing the Cradle? Washing- ton, D.C.: Economic Policy Institute, 1995. paralleling those of the Social Security Trustees. This might lessen the political Board of Trustees, Federal Old-Age and Survivors Insurance and Disability Insurance tendency to overfocus on a particular Trust Funds. 1995 Annual Report of the Board period, such as the year 2002, leading of Trustees of the Federal Old-Age and Survivors to misleading statements about some Insurance and Disability Insurance Trust Funds. policies. Also, I think it would be Washington, D.C.: Government Printing Office, 1995. beneficial to devote more research resources to examining how to do Cutler, David M. “Review of Generational Accounting: Knowing Who Pays, and When, for generational accounting better and to What We Spend by Laurence J. Kotlikoff.” Na- report alternative calculations—AGK tional Tax Journal 46 No. 1 (March, 1993): 61–7.

606 GENERATIONAL ACCOUNTS AND GENERATIONAL BALANCE

Forsythe, Dall, and Monica Friar. “The The current generation pays taxes equal to rB. For consist- Federal Budget and the States: The Flow of ency, we assume that these are paid at the end of the period Funds Between the Federal Government and the and need to be discounted back to today to be comparable States: A Ten-Year Review.” Taubman Center to government wealth, which is –B, equal to government for State and Local Government, John F. debt. Thus, its generational burden is rB/(1 + r’), where r’ is Kennedy School of Government, Harvard University Working Paper. Cambridge, MA: the discount rate used in the calculation of generational Harvard University, 1993. balance. Gokhale, Jagadeesh, Laurence J. Kotlikoff, and John Sabelhaus. “Understanding the Next, we calculate the burden on future generations, denoted Postwar Decline in United States Saving: A N. AGK state that, discounted back to the present, the burden Cohort Analysis.” NBER Working Paper No. on each future generation is the same, apart from growth, 5571. Cambridge, MA: National Bureau of which is assumed to be zero here. This is not precisely what Economic Research, 1996. they mean—for the infinite sum in equation 10 in their 1991 Haveman, Robert. “Should Generational paper would imply a zero value of N. They must mean that Accounts Replace Public Budgets and Deficits?” each generation has the same tax discounted back to its birth, Journal of Economic Perspectives 8 No. 1 adjusted for growth. In this case, we sum N/(1 + r’) exp (t) from (Winter, 1994): 95–111. t = 1 to infinity. This is equal to N/r’. Hubbard, R. Glenn, and Kenneth L. Judd. “Liquidity Constraints, Fiscal Policy, and Thus, the formula for the burden on future generations is Consumption.” Brookings Papers on Economic Activity 1 (1986): 1–61. Musgrave, Richard, J. J. Carroll, L. D. Cook, 1 and L. Frane. “Distribution of Tax Payments by Income Groups: A Case Study for 1948.” National Tax Journal 4 No. 1 (March, 1951): 1– N/r’ = B – PDV(T) = B – rB/(1 + r’). 53. Pechman, Joseph. Who Paid the Taxes, 1966– 85. Washington, D.C.: The Brookings Thus, the generational balance expression is Institution, 1985. U.S. Office of Management and Budget. “Generational Accounting.” In Budget of the 2 United States Government: Analytical Perspec- tives, Fiscal Year 1995, Chapter 3. Washington, N – rB/(1 + r’) = B(r’ – r). D.C.: Government Printing Office, 1994.

Thus, there is not generational balance even though we are in APPENDIX: A MODEL a steady state with every generation paying the same tax. To see the consequences of selecting a higher rate for Clearly, this is an unsatisfactory solution. AGK might (and did) discounting the future than is paid on government debt, argue that, with certainty in this model, r’ should be set equal consider a simple model where each generation (all of the to r. However, if we introduce the agency costs associated same size) lasts one period, so there are no complications from with private loans that are a major contributor to the spread overlapping generations or from differently timed payments for of interest rates in the economy, then we will have this a generation. Assume that in the past the government has problem back without any aggregate uncertainty. (Formal borrowed B in order to finance a durable asset that gives each modeling would need extended lives in order to have loans.) generation a flow of services or to finance a war. Assume that The same point can be made in another way. With a debt of B each generation pays taxes, T, equal to rB, to cover the interest and an interest rate of r, the government debt can be financed cost on the debt. It would appear that each generation was in by annual payments equal to rB. If these are discounted back exactly the same position and there would be intergenerational to the present at a different interest rate, r’, equal to the rate budget balance. However, if a higher interest rate than the used for discounting the taxes of future generations, then the government rate is used in the calculation, there is not present discounted value of government interest payments is balance. The imbalance comes from the fact that taxes are rB/r’, not B. The thrust of AGK’s argument appears to be that, calculated for the current generation, and these are since the future is uncertain, the current generation should determined by the government interest rate. But a residual pay more in taxes than the expected utility of taxes on future calculation using a different rate would result in imbalance. generations. This seems unsatisfactory.

607