Government Mandated Private Pensions: A Dependable and Equitable Foundation for Retirement Security? Rowena A. Pecchenino and Patricia S.

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1 WORKING PAPER SERIES Government Mandated Private Pensions: A Deendable and Equitable Foundation for Retirement Security? Rowena A. Pecchenino and Patricia S. Pollard Woring Paer 999-0B htt://research.stlouisfed.org/w/999/999-0.df Revised August 00 FEDERA RESERVE BANK OF ST. OUIS Research Division 4 ocust Street St. ouis, MO 630 The views exressed are those of the individual authors and do not necessarily reflect official ositions of the Federal Reserve Ban of St. ouis, the Federal Reserve System, or the Board of Governors. Federal Reserve Ban of St. ouis Woring Paers are reliminary materials circulated to stimulate discussion and critical comment. References in ublications to Federal Reserve Ban of St. ouis Woring Paers (other than an acnowledgment that the writer has had access to unublished material should be cleared with the author or authors. Photo courtesy of The Gateway Arch, St. ouis, MO.

2 Government Mandated Private Pensions: A Deendable and Equitable Foundation for Retirement Security? Rowena A. Pecchenino Michigan State University East ansing, Michigan 4884 hone: fax: rowena@ilot.msu.edu Patricia S. Pollard Federal Reserve Ban of St. ouis St. ouis, Missouri 630 hone: fax: ollard@stls.frb.org The views exressed in this aer are solely those of the authors and do not reflect the views of the Federal Reserve Ban of St. ouis, nor of the Federal Reserve System.

3 Government Mandated Private Pensions: A Deendable and Equitable Foundation for Retirement Security? Abstract We develo a model of an overlaing generations economy characterized by rivate ensions where ris averse agents face both longevity and investment riss. The government mitigates the effects of longevity ris by mandating that individuals urchase annuities. Investment ris arises since the returns on annuities deviate randomly from actuarial fairness as a result of differences in the costs of administering ension funds (or, equivalently, deviate randomly from the maret return as a result of differences in fund manager ortfolio choice. Thus, identical agents ensions may yield drastically different returns: the government s ension olicy is not horizontally equitable. We define olicies that achieve horizontal equity, and discuss heuristically the costs and benefits of imlementing these olicies.

4 I. Introduction Surred by demograhic changes many countries are considering relacing their ay-as-you-go ublic ension rograms with rivatized rograms. Privatization is something of a misnomer as ension investment, at least u to some ercentage of wages, would be government mandated. Generally, rivatization is imagined to tae the form it has in Chile and the United Kingdom where individuals can invest in any of a number of government aroved ension funds. The returns on these funds can differ because of differences in ortfolio choice as well as differences in costs. The individual investor bears the ris. While many have worried about ortfolio ris in regard to rivate ension funds, a more salient ris may be cost ris. Most countries that have established rivate systems have minimum income guarantees artly to address systemic or generational ris as well as to rotect low wage earners. To limit idiosyncratic ris countries such as Chile and Argentina enalize ension funds whose returns deviate too much from the average return. As a result, most funds hold nearly identical ortfolios. 3 Even where the ortfolio comositions are similar across funds returns to investors can differ as a result of differences in costs. The costs charged by the firm are to comensate it for collection, money management, record eeing and ayouts (Mitchell 999. In both Chile and the United Kingdom aggressive advertising by ension funds has added to the costs borne by the investor. In some countries, such as Chile, the cost structure is relatively simle with In Chile all worers below a certain age were required to articiate in the rivate system, in the UK, in contrast, worers have the otion of remaining in the ublic system or choosing the rivate system. While our analysis examines cost ris all our results also aly to ortfolio ris or any other ris that is intragenerational in nature. 3

5 only front-load fees allowed. In other countries, such as Mexico and Argentina, the comlexity of the fee structure maes it difficult to comare costs across ension firms. Moreover costs change over time maing it difficult for an investor to determine ex ante the cost of investing in one ension fund relative to another. In Chile, because fees are levied only at the time the investment is made any changes in the cost of managing these investments must be levied on new investments. iewise, since all rivatized systems are relatively young, the cost of maing ayments to retirees is hard to redict. Nor are these costs inconsequential. In many atin American countries costs are averaging -3 ercent of wages, substantially reducing investment returns no matter how well or oorly the ortfolio is chosen. 4 In the United Kingdom, based on current costs, an individual who wors for 40 years and contributes to a ension fund may have at retirement a ension balance that is 8 ercent lower than it would have been in the absence of investment costs (Orszag 999. In this aer we develo a model that allows us to examine an overlaing generations economy characterized by rivate ensions. In our model ris averse agents face two tyes of ris: longevity ris and investment ris. The government mitigates the effects of longevity ris by mandating that each individual lace a fraction of his after tax income when young in an annuity, thereby exosing all individuals to investment ris. The investment ris arises since the returns on all available annuities deviate randomly from actuarial fairness as a result of differences in the costs of administering the ension funds. 5 Thus, identical agents ensions may yield different returns: the government s ension olicy is not horizontally equitable. We examine whether olicies exist that can 3 4 For details see Shah (997 and U.S. Congressional Budget Office (999. See for examle, Mitchell (999, Queisser (999 and U.S. Congressional Budget Office (999. 4

6 achieve horizontal equity, and then discuss, heuristically, the costs and benefits of imlementing these olicies. Secifically, we find that if the dominant form of individually undiversifiable ris faced by ensioners is administrative cost ris, then the government can imrove uon the maret outcome, in both exected utility and horizontal equity terms: government mandated rivate ensions may be a deendable and equitable foundation for retirement security. II. The Model Consider a Diamond (965 style overlaing generations, infinite-horizon economy comrised of identical two-eriod lived agents, erfectly cometitive firms, annuity marets, and a government. A new generation is born at each date t. For simlicity we assume that there is no oulation growth, and that at each date N agents are born. Without loss of generality assume N is unity. Agents in this model, as in Ecstein, et al. (985, are not altruistic: the old do not care for the young and the young do not care for the old. Agents references are defined over consumtion alone. Agents in the first eriod of their lives, the young, are endowed with one unit of labor. They suly their labor inelastically to firms. They divide their wages between their own current consumtion, saving (comrised of an annuity, direct holdings of caital, or both for consumtion when old, and ayment of wage taxes, τ w 0, quoted as a roortion of their wages. Agents in the final eriod of their lives, the old, consume any old-age benefits they receive and their accumulated after tax savings. An agent dies at the onset of old age with robability (-( and lives throughout old age 5 Investment ris could arise instead as a result of differences in ortfolio comosition. 5

7 with robability (. If an agent dies at the onset of old age his unannuitized wealth is bequeathed to the young. 6 Agents may save for retirement by urchasing an annuity or by lacing funds directly in caital. By law, each agent must urchase an annuity of value of at least ϕ ercent of lifetime after tax wages. There is a fixed cost of er annuity contract or caital fund urchased. Agents, in their investment decision, face two forms of ris: life san and investment. Investment ris is modeled as follows. There are many ossible, observationally equivalent, ensions in which an agent can invest. The funds hold identical ortfolios, but there are unobservable differences in the costs of managing these funds/administering these accounts. A roortion ( ay the net return ( r(t /(, while the remainder ay r(t /( (, where [0,] and [0,], <, measure the deviation of the return on the annuity from actuarial fairness. Since at i =, the return on an annuity equals the return on directly held caital, no agent will choose to hold caital directly, and there will be no unintentional bequests. 7 The fixed cost is assumed to be large enough to reclude individuals from diversifying 6 This assumtion of unintentional rather than altruistic bequests is consistent with emirical findings by numerous researchers: see Hurd (990, and Auerbach et al. (99. Altonji et al. (99 find that arents and their adult children are not altruistically lined. But, other researchers find an oerative bequest motive (Hamermesh and Menchi, 987; Hurd, 995, at least among the wealthy. aitner and Juster (996 find suort for intergenerational altruism but note that it is not the major exlanation for saving. Since there is no consensus on this issue, we will maintain the assumtion of unintentional bequests. 7 We have modeled the ris faced by ensioners as arising from unobservable cost differences among the available ension funds. This leads ensions to deviate from actuarial fairness. We could, alternatively, have modeled ris as arising from ortfolio choice decisions made by fund managers. For this alternative formulation, suose that there is no aggregate ris but ortfolio managers who choose not to hold the maret earn returns that deviate from the maret return. This would generate high return and low return funds which would ay out actuarially fair returns on the underlying ortfolios. That is, assume that funds are observationally equivalent ex ante, and with robability an agent invests in a high return fund that ays the actuarially fair return (r / and with robability (- an agent invests in a low return fund that ays the actuarially fair return (r /. The return on the maret is (r (-(r. Analysis of this alternative model generates qualitative results identical to those in the administrative cost model. 6

8 away the investment ris on their own accounts. 8 Thus, the structure of our model gives us two grous of old agents: the rich old and the oor old. While we have ruled out adverse selection and moral hazard as reasons for deviations from actuarial fairness, we note that all ension firms that serve real world marets face the same adverse selection and moral hazard roblems, can all diversify their riss, and yet have different ex ost returns on their annuity contracts. Moreover, Finelstein and Poterba (999 show that adverse selection cannot exlain all of the deviation from actuarial fairness. In addition, their wor indicates that much of this adverse selection cost can be eliminated through comulsory rather than voluntary annuitization. et the reresentative member of generation t's references be reresented by H ( U ( = ln c ( ( [ ( ln c ( t ( ( ln c ( t ] t t t where c t ( is consumtion by a member of generation t when young, c H t ( t [ c ( t t t ] is consumtion by a member of generation t when old if he urchased a high-return (low charge [low-return (high charge] annuity, and ( is the robability that an agent born at date t will live throughout old age. The firms are erfectly cometitive rofit maximizers that roduce outut using the Cobb-Douglas roduction function Y( = A(K( N( -, [0,]. K( is the caital stoc at t, N( is labor at date t, and A( > 0 is a roductivity scalar. Caital dereciates fully in the roduction rocess. 8 Three emirical observations suort these assumtions: gross returns on government mandated rivate ension ortfolios do not vary greatly, if at all, across ension funds; agents do not all invest in the same ension fund (that is, thus, revealed to be the low cost fund; and, agents generally do not invest in multile funds (artly as a result of governmental restrictions. 7

9 The government in this economy may imose taxes on wages, τ w (, and/or taxes on the investment income of the old, τ (, and/or imose lum sum taxes on the old, (, to achieve its social welfare goals (secifically, horizontal equity. The government must maintain a balanced budget. The government alternatively can institute a olicy under which only a single ension lan exists, where that lan ays the average of the returns on the underlying ortfolios. III. Equilibrium A cometitive equilibrium for this economy is a sequence of rices {w(, R(t, a sequence of caital stocs, { ( }, ( > 0, r(} t= H allocations, {, (, ( } t t ct t ct t = = t, given, a sequence of c ( t, and a sequence of taxes { } w (, τ ( t, ( t t= τ, such that given these rices, allocations, and taxes agents maximize utility, firms maximize rofits, the government satisfies its budget constraint, and marets clear. The reresentative agent at time t taes as given the wage, w(, the return on saving when old, r(, the tax rate on wages, τ w (, the tax rate on investment income, τ (, the lum sum tax (, old age benefits, T H ( and T (, and the fixed cost of investment (, and chooses ension saving, s(, to maximize ( subject to ( c ( = w(( -τ ( s( ( t w H ( r( t H (3a ct ( t = s( ( ( ( ( τ t t T t ( ( r( t (3b ct ( t = s( ( T t ( 8

10 (4 s( ϕw( ( τ ( w Only the investment income of the well-off old meets the means test and so is taxed. Substituting constraints ( and (3a,b into the reresentative consumer s objective function (, forming the agrangian and maximizing yields the first-order condition (5 [ w(( -τ ( s( ( ] w ( ( ( ( r( t ( τ ( t ( r( t s( ( τ ( ( t t T ( H ( t ( ( ( ( ( r( t ( r( t s( T ( ( t µ = 0 where µ is the agrange multilier on the savings constraint. The individual firm taes wages and rental rates as given and hires labor and caital until their marginal roducts equal their factor rices (6 ( A ( ( = w( (7 A ( ( = R( where ( is the caital-labor hours ratio. Because of the assumtions of constant returns roduction technology and inelastic labor suly, (6 and (7 also define factor maret clearing. The government must maintain a balanced budget, thus, taxes are set so that revenues equal benefits. We will examine four olicies designed to achieve horizontal equity or to lessen the extent of horizontal inequity as well as the olicy of letting the maret decide, and a ay-as-you-go olicy regime. The first olicy achieves horizontal 9

11 equity by imosing a lum sum tax on those ensioners who invested in low charge funds and transferring the roceeds to those ensioners who invested in high charge funds ( r( t ( r( t (8 s( ( t = s( T ( t ( ( where ( ( t = ( ( T ( t and T H ( t = 0. The second olicy achieves horizontal equity by taxing the ension returns of those ensioners who invested in low charge funds and transferring the roceeds to those ensioners who invested in high charge funds: ( r( t ( r( t (9 s( ( τ ( t = s( T ( t ( ( where (-(T ( r( t (= ( s( ( t ( τ and T H (t = 0. The third olicy reduces, but does not eliminate, horizontal inequity by taxing the wages of the young and transferring the roceeds to those ensioners who invested in high charge funds. If the olicy is to decrease the inequity by ξ ercent, then, for T H (=0: (0 τ w ( t w( t = ( ( ( ξ ( r( t s( ( ( ( T ( t ( (. = The fourth olicy achieves horizontal equity as the government offers only a single ension fund that yields the average return of the underlying funds. In this case, all the tax and transfer arameters equal zero and the return on this single ension fund equals ( ( ( ( ( r ( t. ( ( 0

12 Under the fifth olicy the government maes no attemt to affect horizontal equity. It neither levies taxes nor maes transfers. Under the sixth olicy, T H ( = T ( = T( and the ay-as-you-go ublic ension ays a relacement rate, ζ, on wages. Thus ( τ ( t w( t = ( T ( t = ( ζ ( w( t. w The goods maret clears when the demand for goods equals the suly of goods. Thus, saving today determines the caital stoc tomorrow (3 s( = ( and the return on saving equals the return on caital (4 R( = ( r(. IV. Policy Analysis Solving for the steady-state interior equilibrium (the mandated ension is less than the desired ension under each of the olicies yields the following allocations. Policy : um Sum Taxes = [ A( ] c Y = [( A ] c H c = = A

13 Policy : Taxes on Pension Returns ] ( [ ( ( = A ] ( [ ( = A c Y A c c H = = Policy 3: Tax on Wages to Effect a ξ ercent Reduction in Horizontal Inequity = ξ ξ ξ ( ( ( ( ( A

14 3 = ξ ξ ( ( ( ( A c Y = A c H = ( ξ ξ A c Policy 4: Single Fund ] [( = A ] [( = A c Y A c c H = = Policy 5: No Taxes-No Transfers ] [( = A ] [( = A c Y = A c H = A c

15 4 Policy 6: Pay-as-you-go with Actuarially Unfair Annuities 0, ( > ] ( ( [ ( ( ζ ζ ζ ζ ζ = A ] ( ( [ ( ζ ζ ζ = A c Y ζ A c H = ( ζ A c = ( For each of these olicies the steady-state equilibrium exected utility of the reresentative agent can be comuted and the exected utility levels comared. Comarison of olicies and 4 reveals that the imosition of lum sum taxes or the single fund restriction yields identical equilibrium allocations. Further, olicies and 4 are both horizontally equitable as is olicy. However, since taxes on ension returns are distortionary, olicy will lead to lower exected utility than the either olicy or 4. Policy 5 results in the same steady state levels for the caital stoc and consumtion of the young as do olicies and 4, but is not horizontally equitable.

16 While it is ossible to solve analytically for exected utility, it is more straightforward to do so numerically. We assume that =.5, the ratio of Social Security beneficiaries to contributors in 000 (Board of Trustees, Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds, 00 and that ζ=.43, the relacement rate for those retiring in 000 who earned the average wage while woring (U.S. House of Reresentatives Committee on Ways and Means, 998 The values for the other arameters are: =.75, =.3, =.5, =.75, =., ξ=.50, and A=5. Under these arameter values an interior steady-state equilibrium exists for all olicy regimes. The raning of regimes by exected utility is found in Table. Table Raning of Policy Regimes and Horizontal Equity Policy Regime Caital Stoc Exected Utility Horizontal Equity - um-sum Taxes Single Fund No Tax - No Transfer Taxes on Pension Returns Taxes on Wages Paygo with Annuities This raning suggests that since the ris affects only the old, and thus there are no intergenerational riss to share, olicies that redistribute income among the old (olicies and dominate those that redistribute income inter-generationally (olicies 3 and 6. Moreover, as Table indicates, achieving horizontal equity (the ratio of consumtion when old with high returns to consumtion when old with low returns may not be a reasonable olicy goal if the only way of funding the redistribution is via distortionary 5

17 taxes since to achieve ex ost horizontal equity it is necessary to give u ex ante exected utility. On the face of it, it aears that either olicies or 4 will achieve the horizontal equity goal and imrove welfare over olicy 5. If the lum-sum tax olicy is infeasible (since it requires that the government comile a vast amount of information on individual ensioners to determine the erson secific lum sum tax, and so could be very costly to execute rather than costless as assumed in the analysis, a single fund may effect an imrovement on the no tax - no transfer regime even if there are costs to the government of administering the ensions accounts (though not the ension funds. This is because, to the extent that ension fund costs are driven by advertising and by administering small accounts, their costs would fall since there would be no reason to advertise and since the government would be administering the accounts. Thus, even if the government is less efficient in administering the small ension accounts, there is still the otential for cost reduction and consequently imrovements in individual welfare. The results are robust to changes in the arameters. For examle, decreasing the robability of investing in a low charge fund,, reduces the steady state exected utility under all olicy regimes without changing the raning given in Table. The raning also is not deendent on the secific values of the cost arameters, and, nor is it necessary that =. 9 Increasing both s while holding the ratio / constant results in greater horizontal inequity in olicies 3, 5 and 6. In contrast, raising the ratio / reduces horizontal inequity in these three olicies. 9 The inequality < is required to reserve the raning. 6

18 Decreasing the tax rate on wages, τ w, in olicies 3 and 6 increases exected utility. If the relacement rate, ζ, is very small it is ossible that (holding ξ fixed olicy 6 dominates olicy 3 in exected utility. 0 If ξ is reduced then olicy 3 dominates olicy in exected utility. The increase in exected utility that results from a decrease in τ w in olicy 3 or olicy 6, however, comes at the cost of greater horizontal inequity. Setting ξ and ζ =0 reduces olicies 3 and 6 to olicy 5 (no taxes or transfers. V. Conclusions In this aer we have develoed a model of rivatized, government mandated ensions. We have shown that if the dominant form of individually undiversifiable ris faced by ensioners is administrative cost ris (as a result of advertising, etc. that leads to ex ante identical ensioners earning different returns on their ex ante identical ensions, then the government can imrove uon the maret outcome, in both exected utility and horizontal equity terms, by restricting the choice of ensions to a single fund (which could/would be a comosite of many rivate sector funds. Further, should the government be more efficient than the rivate sector at managing small accounts, as Diamond (999 suggests, and should government account management reduce ension firms costs by removing the need to advertise to attract accounts, then average ortfolio returns would increase as well. Thus, our results, in ractice, would loo much lie 0 The critical value for ζ is using the arameters listed in the text. The critical value for ξ is.347. iewise for ζ less than.04686, olicy 6 dominates olicy in exected utility. If the undiversifiable ris is ortfolio ris, and if an individual ension fund fails, some ensioners would see their ension eliminated because of an unlucy investment choice. Such an outcome would be liely to call forth a ublic olicy resonse such as the use of general funds to subsidize the unlucy ensioners. However, if the government offers all agents a single fund comrised of many rivately managed ortfolios (which together constitute the mare, the failure of any one ortfolio would have a 7

19 Gramlich s Individual Accounts lan, as resented in the Reort of the Advisory Council on Social Security. This result generalizes to all other undiversifiable ortfolio riss that fall on the elderly alone. If, contrary to the assumtions of this model, most riss are intergenerational in nature, then government mandated rivate ensions do not and cannot overcome these riss. 3 Thus, whether government mandated rivate ensions can rovide a deendable and equitable foundation for retirement security deends in large art on the tyes of riss faced by the average ensioner. If most riss are intergenerational in nature, then the answer is a clear no. If most riss are intragenerational in nature, then the rosects are, in rincile, good. negligible effect on the system. 3 Rangel and Zechauser (999 establish that neither maret mechanisms nor the current ay-as-you-go social security system overcome intergenerational riss. Funded ensions fail on this count as well since they can, at best, effect intragenerational redistributions. 8

20 References Altonji, J. G., F. Hayashi, and. J. Kotlioff, 99, Is the extended family altruistically lined? Direct tests using micro data, American Economic Review 8, Auerbach, A. J.,. J. Kotlioff, and D. N. Weil, 99, The increasing annuitization of the elderly - estimates and imlications for intergenerational transfers, inequality, and national saving, NBER Woring Paer No. 48. Diamond, P. A., 965, National debt in a neoclassical growth model, American Economic Review 55, Diamond, P.A., 999, Administrative costs and equilibrium charges with individual accounts, NBER Woring Paer Ecstein, Z., M. Eichenbaum, and D. Peled, 985, Uncertain lifetimes and the welfare enhancing roerties of annuity marets and Social Security, Journal of Public Economics 6, Finelstein, A. and J. Poterba, 999, Selection Effects in the Maret for Individual Annuities: New Evidence from the United Kingdom, NBER Woring Paer No Hamermesh, D. S. and P.. Menchi, 987, Planned and Unlanned Bequests, Economic Inquiry 5, Hurd, M. D., 990, Research on the elderly: economic status, retirement and consumtion and saving, Journal of Economic iterature 8, Hurd, M. D., 995, Using subjective survival robabilities in life cycle models, mimeo, Deartment of Economics, SUNY Stony Broo. aitner, J. and F. T. Juster, 996, New Evidence on Altruism: A Study of TIAA-CREF Retirees, American Economic Review 86, Mitchell, Olivia, S., 999, Evaluating Administrative Costs in Mexico s AFORES Pension System, Pension Research Council, PRC WP 99-. Orszag, Peter, R., 999, Administrative Costs in Individual Accounts in the United Kingdom, Center for Budget and Policy Priorities, March. Queisser, Monia, 999, Pension Reform: essons from atin America, OECD Develoment Centre, Policy Brief No. 5. Rangel, A. and R. Zechauser, 999, Can Maret Institutions Generate Otimal Intergenerational Ris Sharing? in J. Cambell and M. Feldstein, eds., Ris 9

21 Asects of Investment Based Social Security Reform, Chicago: University of Chicago Press, forthcoming. Shah, Hemant, 997, Towards Better Regulation of Private Pension Funds, World Ban olicy Research Woring Paer # 79. Social Security Advisory Council, 996, Reort of the Advisory Council on Social Security, Volumes I and II, Washington, D.C.: Social Security Administration. U.S. Congressional Budget Office, 999, Social Security Privatization: Exeriences Abroad, Washington, D.C.: U.S. Congressional Budget Office. 0