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The implications of switching from unfunded to funded pension systems.

I. Introduction

In principle the distinction between unfunded and funded pension systems is simple: in unfunded schemes pensions paid to those currently retired are financed by contributions from current workers and firms; in funded schemes a stock of assets is accumulated from contributions which is used to finance pensions. In practice unfunded schemes tend to be run by the state - for the very good reason that private agents would find it hard to enforce the intergenerational contract implicit in unfunded schemes; in many cases unfunded, state schemes also redistribute income to the less well off because the level of contributions paid by workers (either directly or on their behalf) bears a closer relation to their lifetime income than does the pension they subsequently receive. For example, in the UK all those with a full entitlement to a basic state pension receive the same pension; and a full entitlement is not dependent on the value of contributions paid over the working life but rather upon the number of years in the workforce (either employed or unemployed). In practice most funded schemes are run by the private sector (either occupational pensions or private pensions where contributions are only made by the individual); and while there is often redistribution implicit in these schemes it is not generally from the better off to the less well off. In the UK, occupational pensions redistribution has more normally been from those who move jobs relatively frequently to those who stay put; personal pensions are invariably defined contribution schemes where pensions are dependent on the value of the fund at retirement and there is no redistribution between pensioners.

Because of these institutional facts much of the discussion of the relative merits of funded and unfunded schemes is as much about the relative efficiency of public against private sector provision, and the desirability of redistribution to the less well off, as it is about funding per se. In this paper I will try to be clear about what is intrinsic to funded and unfunded schemes and what is not; my aim is to consider the advantages and disadvantages of reducing reliance on unfunded pensions and moving to a (more) fully funded system. I will assume that unfunded schemes are state run systems because only the state can enforce contracts with future generations. But funded systems can be run by the public or private sector. I will argue that what matters for funded systems is the degree of linkage between contributions and subsequent pension payments and the portfolio composition of funds rather than whether they are run by the public or private sector. High linkage is where pension payments are (given rates of return on funds and after accounting for administrative costs) close to being of equal present value to that of (net of costs) contributions - this is approximately true with defined contribution, personal pensions in the UK. Low linkage would allow for significant redistribution - for example by having pension payments out of funds accumulated by a person's lifetime contributions having a fixed element and rising less than proportionately with fund value.

[TABULAR DATA FOR TABLE 1 OMITTED]

Most state pension schemes in developed countries are unfunded (pay-as-you-go) systems. Table 1 presents information on state pension systems in some of the major economies; it shows total spending, contribution rates, retirement ages and the degree of indexation of benefits. There is substantial variability across countries; Continental European state pension schemes tend to be much more generous that the UK and US systems both in terms of replacement rates (the ratio of typical pensions to current average labour income) and in the rate at which entitlements to pensions accrue. As a result aggregate pension payments and typical contribution rates are also much higher. Few schemes have any significant assets - the US scheme is an exception, though even here forecasts suggest that on current policies the fund will be exhausted within about thirty years (Feldstein 1997).

A combination of rising life expectancy and declining fertility rates will, in the absence of dramatic shocks (wars, new fatal diseases) or of a sharp rise in inflows of relatively young immigrants, cause the proportion of the population aged over 65 to rise sharply over the next forty years in nearly all developed countries. With an unfunded scheme if the proportion of the population of working age falls relative to the number over the current typical retirement age at least one of the following must happen: contribution rates will rise; the average level of pensions relative to wages will fall; the age of eligibility for receipt of pensions will rise; or the system will move into deficit (assuming it started in balance).

The implications of ageing populations for the structure and financing of unfunded state pension schemes have been the main factor behind the recent upsurge in analysis of, proposals for and (in some cases) implementation of switches from unfunded to funded schemes. One indication of the scale of likely shifts in population structure is given by Chart 1 which shows United Nations projections of the demographic structure of Europe to 2050. The total population of Europe is projected to change little over the period, but the age structure changes a great deal. Chart 2 shows OECD estimates of the scale of deficits that these demographic shifts could cause to unfunded pension schemes in various countries (see Roseveare et al (1996)). The chart shows the OECD estimate of the present value of the future gaps between contributions to state schemes (at 1996 contribution rates) and likely pension payments (assuming a constant ratio of pensions to average incomes and that retirement ages are unchanged)(1)). The figures are on a per capita equivalent expressed in sterling and at 1990 prices. The chart reveals huge potential deficits in many European countries - in present value terms over [pounds]20,000 for every person in Italy, Germany and France alive today; in Sweden, Belgium and Denmark the figures are even higher.

In the UK and the US proposals for phasing out unfunded (or pay-as-you-go (PAYG)) pensions have focused on replacing them with personal funds where contributions go directly into an individual's own account. It is perceived to be a merit of these accounts that they are seen as an individual's property and that greater contributions going into an account will (for a given path of future rates of return) mean proportionately higher future pensions. The implication of this is that funding will imply high linkage and will make pensions sensitive to realised rates of return on assets. This raises serious issues about the risk and redistributive characteristics of such funded schemes. These issues are addressed in Section V of this paper.

In the first part of the paper I abstract from the risk and distribution issues and consider the average level of pensions that could be paid in funded and unfunded systems and how those average benefits might evolve (and create winners and losers from different generations) in the transition from one system to another. In Section II I focus on the long run, looking at the implications for average incomes, pensions, the capital stock and real rates of return of having an unfunded system or of having moved (at some point) to a funded system. The reason for looking at the long run is simple: if it turns out that having established a fully funded system there were no gains in terms of average outcomes then there would be no point in making the costly transition from an unfunded scheme. The existence of long run benefits is a necessary condition for embarking on a costly transition; but it is certainly not sufficient because along the way funds have to be accumulated. That could (but does not necessarily) mean that consumption has to be lower for some generations as the funds are accumulated. So there may have to be losers on a transition path and their losses may be large enough and widespread enough that a transition is undesirable and/or unfeasible. These transitional issues are considered in detail in Section III. The implications for governments and for people of different generations of a switch are very sensitive to the initial generosity of unfunded (PAYG) pensions, to the pace of demographic change and to the rates of returns on assets. I will analyse the transition issues for the UK, Germany and for Europe as a whole. In Section IV I consider whether deficit financing can smooth the path of consumption for different generations through a transition so that there are no losers. Deficit financing can, under certain circumstances, help the transition process; but whether this is so depends upon the cost of debt to the government relative to the rate of return on funds accumulated in pension funds and also upon the scope governments have to run much larger deficits.

One thing is very clear when we look at transition paths; there is no simple "solution" to the problem that many European countries find themselves in where future pension liabilities of unfunded state systems are massively in excess of the value of future contributions at current rates (at least under the current pension arrangements and given likely demographic developments). Indeed one of the messages to come out from Section III is that the most difficult time to embark on a transition to a funded system is when demographic change is about to start putting greater strains on unfunded schemes.

In the final section I draw some conclusions from the analysis focusing on the differences between the UK and other major European countries (in particular Germany).

II. Long Run Implications of Alternative Pension Arrangements

While it is the scale of the potential burden that ageing brings to the financing of unfunded state pensions that has generated the interest in switching to funded schemes the economic case for a switch is most forcefully made by focusing on the long run when, by definition, demographic structure is unchanging. Samuelson (1958) pointed out long ago that in a steady state - where population structure is assumed constant, as is the contribution rate into a balanced PAYG pension scheme - the effective return on contributions made to an unfunded pension scheme is equal to the growth of the aggregate wage bill (which is the sum of growth in real wages per person and of the number of workers). It may seem strange to talk about a return on contributions to an unfunded scheme when contributions are immediately paid out; what we mean here is the real value of the pensions paid to a person relative to the value of the contributions they made while at work. If the share of wages in GDP is roughly constant over time this return on payments to a PAYG scheme will, on average, be close to real GDP growth. The return on contributions to a (defined contribution) funded scheme is the average, net rate of return on the assets in the portfolio (averaged over time and across asset classes and net of administrative costs and of any tax payable). Abstracting from risk considerations, it follows that in the long run a funded scheme will provide better pensions for given contributions than an unfunded scheme if the rate of return on assets exceeds GDP growth(2).
Table 2. Real Rates of Return: Equity & Debt

 (percentage)

 Average Annual Real Return(1) Average
 Annual
 GDP Growth
 1962-94 1970-82 1983-94 1961-94

US 4.31 -0.29 9.2 2.99
Japan 4.67 2.01 7.41 5.80
UK 4.39 -0.14 9.27 2.32
Germany 4.06 0.51 8.60 3.05
France 3.60 -1.05 11.07 3.40
Italy 1.89 -6.32 13.20 3.52
Netherlands 3.92 -0.41 9.72 3.14
Belgium 3.31 -0.63 8.96 3.12
Ireland 4.76 -2.37 11.28 4.27
Denmark 6.42 6.39 8.53 2.83
Spain 3.13 -6.59 11.55 4.21
Portugal(2) 3.82 - 3.82 4.31
Austria 5.43 0.06 11.51 3.31
Norway 4.95 -0.09 15.24 3.74
Sweden 5.34 0.5 11.48 2.46

Mean 4.23 -0.66 10.06 3.48

(1) Real Rate of Return = 0.5R + 0.5 (% change S + d)
R = Real long term interest rate; nominal long term bond yield minus
consumer price inflation.
S = Real share price index.
d = Equity dividend yield.
(2) Data refers to 1983-94.


Table 2 shows the average annual rate of growth in GDP in major developed economies over the past thirty years. The table also shows the real rate of return that would have been earned over roughly the same period on a portfolio invested equally in domestic government bonds and in domestic equities. The table shows that in most cases the average annual real return on the portfolio exceeded the rate of growth of GDP; but in most cases the difference is quite small and in several cases (Japan, Italy) GDP growth exceeded the return on assets. The picture would, however, be very different if we had considered a portfolio only of domestic equities. For much of the 1970s inflation in many countries was very much higher than had been anticipated and ex-post real returns on fixed income assets were unusually low; equities proved a much better hedge against inflation. A pure equity portfolio would have generated returns in excess of GDP growth in every country; but it would also have had different risk characteristics from the bond/equity portfolios.

This observation illustrates the obvious point that a comparison between funded and unfunded pension schemes depends crucially on the portfolio of assets that is acquired with contributions. We return to the important issue of the relative risk of funded and unfunded schemes below.

Demographic change is likely to have a major impact on GDP growth and the rate of growth of the aggregate real wage bill; and population shifts and other changes in the macroeconomic environment mean that expected real rates of return on assets over the next forty years may not be equal to average real returns over the past few decades. So the numbers in Table 2 should be interpreted with care. Alternative guides to the relative magnitude of future long run returns on assets and growth in aggregate wages are yields on long dated indexed linked bonds and estimates of long run productivity growth and shifts in population structure. The longest-dated, inflation-proof UK government bonds have had yields over the past five years that have averaged about 3 1/2 per cent. Over the post war period UK GDP has increased by just over 2 per cent a year while growth in GDP in the other major European economies has been somewhat higher. But over that post war period the population of working age in most developed economies has increased substantially whereas over the next fifty years it will not; so a figure of between 2 per cent and 2.5 per cent likely to be an overestimate of the average future growth in aggregate real wages. And a yield of 3 1/2 per cent is likely to be an underestimate of the average return on a portfolio with assets such as equities, property and nominal bonds that are risky and could be expected, over the long term, to outperform sovereign debt with a guaranteed real return.

So it seems highly likely that the rate of return exceeds GDP growth. But that in itself does not show that switching to a funded scheme will increase welfare; it merely shows that once a switch had been made, and capital accumulated, the new long run average level of consumption could be higher for everyone. A comparison of rates of returns says nothing about the costs of switching from an unfunded to a funded scheme. Furthermore, the Samuelson analysis is based on a comparison of returns in two steady states where population structures are unchanging. At the same time a comparison of rates of return may actually understate the long-run benefits of a switch from unfunded to a funded scheme because it ignores any impact on labour supply decisions of any associated switches in the linkage of pensions to contributions. In the UK national insurance contributions for those who have opted out of the state earnings related pension scheme - and who will only receive the basic pension - are not closely related to the state pension that will eventually be paid. This lack of linkage between the major part of payments into the state scheme and pensions received means that the contributions act largely as a tax on labour - with associated distortions - rather than as forced savings. The scale of the induced distortions depends on the sensitivity of labour supply to after tax wages and on the level of other labour taxes to which pension contributions are added. Contributions to a personal fund - the value of which determines future pensions - are, in contrast, a form of saving; if the contributions were to be mandatory, part of the saving might be involuntary (and might simply reduce other saving) but the distortion to labour supply would still be lower than with contributions to an unfunded scheme with no linkage between payments and pensions.(3)

All this means that if we are to analyse the overall, macroeconomic effects of having unfunded pension systems, and the long run implications of a switch to funding, we need some way of working out how private sector labour supply and saving decisions are influenced by a PAYG system and how the aggregate effects of individual behaviour (on the capital stock, rates of return and tax revenue) feed back on individual behaviour. In the next section I describe a model designed to do this and use it first to look at how aggregate outcomes in the UK and in Europe as a whole might eventually look with and without an unfunded state pension scheme. I then use the model to analyse one (very simple) way of moving away from an unfunded state scheme - that is simply announcing that the value of the state pension will be set on a declining path from some point in the future. An alternative proposal for switching is also analysed before we move on to consider debt financed transitions.

III. Analysing Long Run and Transitional Issues With Calibrated Models

A useful - perhaps the only - way to gauge the overall impact of alternative pension arrangements on labour supply, private sector saving, interest rates, the capital stock and GDP is with a model that explicitly analyses the interaction of people of different ages over time. Since the path breaking work of Auerbach and Kotlikoff ten years ago (see Auerbach and Kotlikoff (1987)) there have been several studies using calibrated, overlapping generations models of the economy to analyse shifts in taxes, alterations in pension arrangements and movements in population structure. What I do in this section and in the next section is to summarise what such a model suggests would have happened in the past, and will happen in the future, under three different scenarios: 1. if an unfunded pension scheme of the type that currently exists had always been in place and continues into the future; 2. if there had never been a state pension system and rational, forward-looking agents had made their own provision for retirement and 3. if there is a transition from the first regime to the second. In each case the calibrated model uses the actual demographic profiles of the UK and Europe from the past and United Nations projections of the population structure for the future.

Any model of aggregate outcomes is reliable only to the extent that the behaviour of the individuals underlying its structure is a decent approximation to actual behaviour. The model whose properties I want to describe here is based on the assumption that individuals are forward-looking and plan their working lives, consumption behaviour and savings in the light of their expectations of economic conditions over the course of their lives. More specifically, the model assumes that individuals aim to smooth their consumption over life in an environment where income from work is highly variable over time. In this model it is assumed that people begin work at 20 years of age and that their productivity in work increases gradually up to their mid-40s; after that labour productivity tails off, ultimately at quite a rapid rate. Given how wages evolve over time, and given individual labour productivity, individuals decide how much labour to supply at different points in time. At some points in their lives individuals will save while at others (most obviously in retirement) individuals may run down assets as labour income tails off. How much people save and how many hours they work depend on public pensions and on labour taxes. In versions of the model where there is an unfunded state pension I set the tax rate on labour income at a proportional rate so that the overall revenue generated in each period equals the total payment of state pensions. This rate moves over time. State pensions are paid 43 periods after individuals start work (corresponding to an age of 63 if we have the typical worker begin work at 20) Individuals plan their saving, spending and labour supply decisions in an optimal way in the light of current and future tax rates and state pensions.

In solving the model we work out the interest rate which makes the supply of capital (ie the demand for wealth) equal to the demand for capital from firms. The supply of capital (demand for wealth) arises because people want to smooth consumption in the face of volatile labour income; for simplicity I assume no bequest motive (which in the real world is important). The demand for capital depends upon the structure of production; we assume that firms aim for that level of capital which makes the marginal return from extra investment exactly equal to the real interest rate. The supply of capital comes from domestic saving; obviously this is an abstraction and some part of domestic investment is financed from overseas. But an assumption that the real rate of interest is an exogenous variable fixed in a world market and invariant to population changes in the UK or Europe is not very useful since ageing will affect all developed countries. (A detailed account of the model and its properties is given in Miles (1997a)).

To perform simulations with this model we need to describe key aspects of behaviour with several parameters which determine the degree of substitutability between leisure and consumption, the extent to which people can trade off consumption today against consumption tomorrow and the value individuals place upon leisure. Parameters are chosen in such a way that with the demographic structure of the UK and of Western Europe as it is in 1995 the model generates aggregate outcomes which broadly match those that actually arose.

Long Run Issues

The first question I ask is whether real rates of return would exceed GDP growth if there were no unfunded pensions. The model was first used to project how savings, capital stocks, real interest rates and GDP might evolve with a state-run, PAYG pension scheme where neither the generosity of pensions (ie replacement rates) nor retirement ages change. The replacement rate is set to be flat and as the demographic structure shifts the contribution rate levied on labour income changes to match revenues against payments. For the UK simulations I set the replacement rate at 20 per cent; in 1996 the basic state pension for a couple was worth close to [pounds]5,000 while average earnings for a full time male worker were just under [pounds]20,000. If a typical couple of working age have one person working full time and another half time the ratio of basic pension for a retired couple to the average earnings of a typical couple of working age is [pounds]5000/[pounds]30000 = 16.7 per cent. I set the replacement rate a bit above this level because it is likely that someone working part time receives a per hour rate below that of a full time male worker. For the simulation where we look at Europe as a whole the replacement rate needs to be set at a much higher level. In France, Germany and Italy state pension replacement rates in excess of 50 per cent have been common, though are now set to fall (see Chand and Jaeger 1997). For the European projections we use a 40 per cent replacement rate. It is important to note that the results of these experiments are not forecasts; it is unlikely that state pensions will remain constant relative to average earnings in most European countries. These simulations show what might happen if state pensions in different countries continued to be as important a source of resources for those in retirement as they are now.

Chart 3 shows the projected UK rate of growth of GDP based on the model. On the same graph we show what the marginal rate of return on extra investment would be where individuals save for their own retirement and there is no pension scheme. This marginal rate of return is consistently above the growth of total real wages (which equals GDP growth) suggesting that a switch to a funded scheme in the UK would, in equilibrium, generate higher returns; over the 100 year simulation period (1960-2060) aggregate wages are predicted to grow at an average rate of 1.6 per cent with a PAYG state pension while the rate of return where individuals rely entirely on their own saving for retirement consumption averages 4.1 per cent.

It is important to be clear about what this result means. With no state pension scheme saving, and the capital stock, would be higher. This does not guarantee that once capital has been accumulated it generates higher average levels of consumption. The capital stock could rise beyond the so-called Golden Rule level. What the simulations suggest is that the extra saving that would result in the UK if there were no state pension scheme would not take the capital stock to that level and would allow higher average consumption in the long run. The European simulations (Chart 4) imply the same is true on the Continent: throughout the 100 year simulation the projected growth of aggregate real wages (which equals GDP growth), assuming unfunded state pensions are paid, is substantially below the real return on capital that we estimate would be generated with no state pensions; the former averages 1.74 per cent and the latter 4.4 per cent.

The welfare and policy implications of these results have to be considered carefully. Because the rate of return on assets exceeds the growth of aggregate real wages there is the potential for average pensions to be higher for most generations with no state pensions. But this is very different from saying there are clear gains from phasing out such a system once it has been set up. There are three important points here. First, even if we just compare two versions of history - one where a pension scheme has always been in place and one where an unfunded scheme never existed - there are generations better off with the unfunded scheme because big demographic shifts work in their favour.

The second reason why policy comparisons based solely on average steady state lifetime resources of generations under alternative pension arrangements are inadequate is that such comparisons abstract from risk; intergenerational risk sharing and insurance aspects of state pension schemes are lost if a switch is made to a defined contribution, fully-funded scheme where pensions paid to each person depend only upon their contributions and the rate of return on funds accumulated on their behalf. We return to this important subject in Section V.

The third reason why comparisons of average outcomes in steady states is in itself inadequate as a basis for a policy decision on switching from unfunded to funded schemes is that they say nothing about the transition costs to specific generations of switching from one regime to another. Those costs are not difficult to understand. If an unfunded system is phased out - so that ultimately what were contributions from workers to be paid out immediately to pensioners are instead accumulated on their behalf in a fund - resources still need to be found to pay pensions for those in or near retirement. Just as one set of generations benefit when an unfunded scheme is first established, one set of generations may have to "pay twice" when such a scheme is run down. Whether there have to be losers, who they are and how great their losses might be are the critical issues to which we will now turn.

Transition Issues

There are an infinite number of ways in which an unfunded state pension scheme can be run down. Perhaps the simplest strategy is for the government to announce that from some point in the future the value of the state pension will start to decline (either absolutely or relative to average earnings) and continue falling gradually over some transitional period until it is worthless. Provided that the policy is credible, and that individuals plan ahead, private sector saving should rise as people adjust in anticipation of lower state pensions. (In practice saving for retirement may need to be mandatory because of myopia and moral hazard; we return to this point below). There is an obvious argument that any such announcement should be made many years before the value of pensions starts to fall so that workers can begin to prepare by accumulating more in private pensions or other forms of wealth. But unless the start of the transition is postponed for fifty or more years there will inevitably be some people (younger workers at the time of an unanticipated announcement) who will have already made saving and work decisions in the expectation of future pensions that exceed what they will ultimately receive.
Table 3. Gainers and Losers from a Transition that Begins to be
Implemented in 2020

 UK Europe

cohort age in 1997

[greater than]57 I >> 0 I >> 0
50 - 57 L -0.09% L -0.6%
40 - 50 L -1.1% L -2.3%
30 - 40 L -3.0% L -5.7%
20 - 30 L -3.8% L -7.2%
10 - 20 L -2.2% L -4.2%
0 - 10 G +0.7% G +1.7%
-10 - 0 G +3.95% G +9.2%
-20 - -10 G +6.5% G +15.7%
-30 - -20 G +7.4% G +18.7%
-40 and others not born G +7.2% G +18.9%
(ie all future generations)

G = gain; L = lose; I = indifferent (lifetime utility virtually
unchanged).


This problem is obviously much worse if the announcement is only made at the time that state pensions begin to be scaled back or, worse, if no explicit announcements are made but policies are adopted that, if pursued, will inevitably cause the replacement rate to fall. Arguably the decision of the Thatcher government in the early 1980s to upgrade the basic UK state pension in line with prices rather than earnings is an example of the latter. If basic state pensions in the UK continue to be fixed in real terms the replacement rate will gradually decline. At an average rate of growth of real wages of 2 per cent a year a basic state pension that was worth 20 per cent of average earnings to a retired couple in 1997 would be worth only about 8 per cent of average earnings by 2040 and worth less than 6 per cent of earnings by 2060. In fact it is unclear that UK policy quite fits this description. First, future governments may decide to increase pensions by more than consumer price inflation. Second, and perhaps more important, although the relative value of basic state pensions in the UK will fall substantially if price (rather than earnings) indexation continues, other welfare payments to pensioners may rise more rapidly as a result. Indeed those who focus just on the scale of future contribution rates to balance the UK pension system and argue that the UK faces no demographic "problem" because those rates need not rise are almost certainly taking too narrow a view of the impact of ageing on the public finances. Already around 1.5 million of the 10 million pensioners in the UK are dependent on Income Support (which is available at higher levels than the basic state pension). Invalidity Benefit (payable to long-term sick individuals) was paid to 25 per cent of males aged between 60 and 64 in 1994/95 and to 17 per cent of those aged between 65 and 69. The numbers claiming these benefits has grown sharply since the value of basic state pensions in the UK began to fall relative to average earnings in the mid 1980s (See Blundell and Johnson, (1997)).

Even if current UK policy should not be thought of as a gradual phasing out of the unfunded pension it is instructive to consider the implications of such a policy. I used the simulation model described above to analyse the impact of reducing the replacement rate of the state pension from current levels to zero in a gradual process beginning in 2020. The delay allows agents to respond to future lower pensions but it certainly does not ensure that no generations lose. We can use the model to be explicit about which generations would win and which lose from such a strategy. We do so by calculating a measure of the lifetime utility of the representative agent of each cohort (from those who are aged 20 in 1950 to those who are aged 20 in 2050). We compare how each cohort does in the base case where the state pension stays constant (relative to average earnings) with how they do when the ratio of the state pension to average earnings starts to fall from 2020 and reaches zero by 2040. In the base case and on the transition path the contribution rate paid by workers in each year varies; in the base case it rises as the support ratio falls and in the transitional case it eventually falls to zero (by 2040) as the value of pensions is reduced. Because in this simple model people are forward-looking and do smooth consumption over life by saving during working years there is no reason for extra saving to be made mandatory when the state pension is phased out. (In this model unless the mandatory level was set very high compulsion would have no effect since people would just adjust other saving; in practice to get the "right" level of saving compulsion might be necessary).

The table shows how people of different ages in 1997 gain or lose, relative to the base case, as a result of the phasing out of the pension. Column 1 and 2 show the results for the UK (where the phasing out is from a 20 per cent replacement rate) and column 3 and 4 shows the results for Europe as a whole (where we have taken a 40 per cent replacement rate and phased it out over the same 2020-2040 period). The first column for each country shows whether those in the relevant age cohort gain or lose. The second column is an estimate of the scale of the gain or loss; it is the percentage by which wages in the base case simulation would need to have been higher or lower over the whole working life to generate the same level of welfare as is given by the transition path. So for people in the UK aged between 30 and 40 at the time of an announced change in 1997 (that begins to be phased in 2020) the average decline in utility generated is the equivalent of a cut in wages in every period of their working life of about 3.0 per cent.

In both cases those aged 57 or more in 1997 (23 years before the state pension begins to decline) are roughly indifferent. These are people who will be dead before pensions start to fall (since we assume an adult life of 60 years and take 20 years as the age adulthood begins and people start work). The reason these people are roughly indifferent, rather than strictly indifferent, is that the capital stock and real rates of return are slightly different over their remaining lives as a result of the announced future transition and this does affect welfare, but the impact is very small. Everyone aged between 7 and 57 in 1997 is worse off because the state pension is phased out. Everyone aged under 7 and every future generation, none of whom now have a vote, is better off. This result is the same for the UK and for Europe as a whole; but the scale of the gains and losses is very different. In the UK in the long run people are better off by an amount roughly equivalent to a productivity rise of just over 7 per cent; for Europe as a whole the gain is more than twice as high (18.9 per cent). But the losers are also worse off in Europe; those aged 30-40 at the time of the announced change lose the utility equivalent of 5.7 per cent off lifetime productivity.

The result that the great majority alive now would be worse off if the unfunded state scheme is phased out - even though every future generation (none of whom have a vote) is better off - illustrates the nature of the transition problem rather clearly. Democratically elected governments facing voters who focus on the direct implications for them (and not for all future generations) of changes to state pension systems would find it hard to get support for this kind of transition plan.

Alternative Transitions

The obvious drawback with the transition path analysed above is that unless the start of the phasing out of unfunded pensions is delayed for several decades it involves scaling back the value of state pensions paid in the future to those who have limited time to respond. An alternative strategy is to design a path for contribution rates that both leads to full funding (where ultimately all contributions are invested) but also ensures that pensions are never lower for any generation. Feldstein and Samwick (1997) describe how such a scheme might work and simulate its effects on a very simple model of the US pension system. The system works like this. First we calculate the equilibrium contribution rate such that if all payments were invested it would generate a flow of pension payments equal to pensions under the existing PAYG (unfunded) system. If the rate of return exceeds the growth of the aggregate wage bill this contribution rate (which we call the fully funded contribution rate) will be below the PAYG contribution rate.

At the initiation of the transition all workers, whatever their age, pay this funded rate and these contributions go into their own personal fund. An extra contribution is also paid to finance pensions for those in retirement which are not covered by their own accumulated personal funds. Clearly at the initiation of the transition no funds exist so the overall deduction from wages is the sum of the fully funded rate and the old PAYG contribution rate. In the second year of the transition there are a group of newly retired people who have made one year's worth of contributions to their own funds and who, as a consequence, require slightly less of their overall pension to come from the PAYG system; the PAYG contribution rate (assuming other things equal) is now slightly lower. As time passes each new cohort moving into retirement has a slightly larger fund accumulated from their payment of the fully funded rate over a longer period. As a result the contributions needed to finance the unfunded part of aggregate pensions declines.

If a working life lasts 40 years then exactly 40 years after the transition is initiated the first worker who needs only rely on his or her own funds for a retirement pension retires. But the residual PAYG contribution rate would not yet be zero since all people older than this newly retired worker would be depending on PAYG transfers for a part of their income. If retirement lasts 15 years it would not be until 55 years after the transition was initiated that the PAYG tax would be zero; only then would the system be fully funded. But the overall contribution rate of workers (the sum of the fully funded rate and the declining PAYG rate) would have fallen below the PAYG rate some years before. At what point the overall contribution rate of workers drops below the old PAYG rate depends in a very sensitive way upon the rate of return, working lives, demographic structures and how fast real wages grow. And it is the path over time of the overall contribution rate relative to the old PAYG rate that determines which generations win and lose and the scale of their gains or losses.

In order to assess the impact of such a transition scheme in Europe Andreas Iben and I have developed a very simple simulation model which we apply to the UK and to Germany. The key features of this stylised model are:

* It assumes that the relative numbers of people of different ages alive at each point from now until 2060 match United Nations projections.

* Working lives are assumed to last 41 years and retirement lasts 20 years (the weighted average of the life expectancy for males and females who reach adulthood in Europe is already around 80 years and set to rise in future); our model could be thought to apply to someone who starts work at 20, retires on their 61st birthday and dies just before their 81st birthday.

* It assumes that wages for each person rise over time due to two factors: first, there is general productivity growth which means that real wages for all workers are g per cent higher each year; second there is age-related productivity so that as people become more experienced they earn more. How each agents' real wages grow from one year to the next depends on the sum of these two sources of growth. For simplicity we assume the two growth rates are equal.

* As a base case we assume a given replacement rate and then calculate how the overall contributions of workers have to evolve either under the continuation of a PAYG system or on a transition to a fully funded scheme. Because the demographic structure is changing the contribution rate is not constant even if the PAYG system is left unchanged.

* We assume that the pension paid to the retired at [TABULAR DATA FOR TABLE 3 OMITTED] any time is a certain proportion of the wages of someone who is then half way through their working life; given our simple assumption that the age-wage relation is upward sloping the person half way through their working life is the median earner and the wages of the median earner grow at g per cent each year. Thus pensions are indexed to the growth of aggregate productivity and the replacement rate (for the PAYG, unfunded system and for the funded system) is defined in terms of median earnings.

Tables 3a to 3e summarise the results at various parameter values for the model calibrated to UK demographics and using a 20 per cent replacement rate; Charts 5 and 6 show the paths of the PAYG rate (assuming no transition) and the contribution rate that converges on the fully funded system (by 2060) for different real rates of return and at a rate of growth of wages (g) of 2.4 per cent a year.

The figures reveal some points clearly. First, the contribution rate to which the fully funded system converges to give the same pension level as the PAYG system is highly sensitive to the assumed rate of return. With r = 3 per cent it is just under 8 per cent; with r = 7 per cent, it is about 2.5 per cent (if the replacement rate was 40 per cent instead of 20 per cent both figures would be twice as high and the ratio is unchanged). Second, the pure PAYG contribution rate (the curve that starts as the lower of the two on each graph) is rising in every case because the support ratio declines steadily over the next fifty years. Third, the time when the curves cross (so that the overall contribution rate on the transition falls below the contribution rate on a continuation of a fully unfunded system) depends on the rate of return.

The first panel in the table (3a) shows the crossover time given that the transition starts in 2001. The crossover time for the UK is just over 20 years with a 9 per cent real rate of return. It is 36 years with a 3 per cent rate of return and with 2.4 per cent aggregate labour productivity growth. If the growth of wages exceeds the rate of return there is no crossover. Panel 3b shows the highest combined tax rate reached on the transition path. Usually this is at the outset of the transition (2001) but for some combinations of parameters it is later because of demographic shifts. Table 3c shows why this can happen; here we show when the PAYG rate would peak if there were no transition; that panel also shows the rate the contribution would need to rise to. Note that this differs substantially from actual projections of the UK national insurance contribution rate because that rate reflects less than full indexing against wage rises and it is a rate levied only on part of wages; the rate we show in the simulations is the proportional rate that would be charged on all wage income to balance the hypothetical PAYG scheme with a constant replacement rate.

Finally Table 3e shows a measure of the net gain over the remainder of their lives to people of different ages at the transition date. The figure shows the net present value of the money gain or loss over each person's remaining life as a proportion of the present value of remaining wage income - ie the amount by which real wages would have to be higher or lower to keep the real present value of lifetime resources the same as if the PAYG system was continued. Once again these figures are highly sensitive to rates of return and assumed real wage growth. The table shows that if the real rate of return was 5 per cent and the rate of growth of aggregate real wages was 2.4 per cent someone aged 40 at the start of the transition would lose the equivalent of 3.8 per cent of their rest of life wage income. But someone born in 2000, who would not start work until 2020, gains the equivalent of 2.5 per cent of lifetime wages. The person not born until 2040 (age-40 at the start of the transition) gains the most since they do not start work for 60 years and only ever pay the fully funded rate; this is worth the equivalent of a 6.6 per cent increase in lifetime income.

It is clear from Table 3e that even with the most favourable combination of parameters (low wage growth and high rate of return) there are a substantial number of losers from the transition. Even with wage growth at only 1 per cent a year and a real rate of return that is consistently 9 per cent, all workers (20 year olds to 60 year olds) at the time of transition lose - though only by very small amounts (less than 1 per cent of income); at these parameter values the long run gain is worth over 10 per cent of income.

But with less favourable parameter combinations there are more losers and each loses a good deal more. With wage growth at 2.4 per cent and the rate of return at 3 per cent everyone aged between 30 and 60 at the transition is, in present value terms, worse off - a 40 year old suffers the equivalent of a drop of 6.8 per cent in rest of life income.

Tables 4a to 4e and Charts 7-8 show the same calculations for Germany but with a much higher replacement rate of 55 per cent (that roughly equals the current German replacement rate (Chand and Jaeger (1997)). German demographic developments are less favourable to an unfunded [TABULAR DATA FOR TABLE 4 OMITTED] scheme, and to a transition from one, than in the UK and this, in conjunction with a much higher replacement rate, generates much bigger gains and losses for different generations. The charts show that the initial joint contribution rate on the transition path can be very high - over 33 per cent if the real rate of return is 5 per cent and with 2.4 per cent aggregate productivity growth. The crossover points are generally further ahead than in the UK case (panel 4a) and now the date at which the combined contribution rate peaks is invariably later than the start of the transition (which is where it would peak with a static population).

The big differences from the UK case are seen in Table 4e where we show the net present values of the gains and losses for different generations. If the rate of return is 5 per cent and the rate of wage growth is 2.4 per cent workers aged 40 or more at the transition lose the equivalent of over 10 per cent of rest of life income. But in the long run workers would experience the equivalent of a permanent 25 per cent increase in wages.

The key result from these transition simulations is that at the time a transition starts a majority of workers are worse off in the sense that the present value of their own rest of life resources falls - often substantially. But long-run benefits are substantial. This prompts an obvious question: could debt financing be used to distribute some of the gains of future generations to those who live through the transition?

IV. Deficit Financing

The post war record suggests that the real rate of return on the kind of assets that private pension funds in the UK typically hold has been significantly in excess of real GDP growth and of the increase in aggregate real wages. International evidence (Table 1 above and Abel et al (1989)) suggests that this is true for most developed countries. And the simulation model described above generates an equilibrium path for the future real rate of return that is substantially in excess of both GDP and wage bill growth over all horizons. The implication of this - if we abstract from issues of risk aversion and income distribution - is that once a transition from an unfunded to a funded scheme is complete welfare for all subsequent generations will be higher. The previous sections have shown that without relying on deficit financing the transition will cause certain generations to be worse off, and those generations could form a majority of voters thus permanently blocking any change. But since the value of the future benefits are permanent while the costs of the transition are transitory it might seem that a temporary increase in fiscal deficits to compensate what would have been the losers would solve the problem.

In general this is false, as a simple example shows. Suppose the population is constant and there is no productivity growth so that at a steady contribution rate the value of unfunded state pensions that a person will receive in retirement equals the contribution they paid while working. The rate of return (or the real rate of interest) is positive so that a switch to a funded scheme will mean that for the same contribution rate pensions would be 1+r times as great, where r is the rate of interest over the period from when contributions are made to when payments are made in retirement. (In reality, of course, contributions are made over a lengthy working life and pensions paid at an even rate in retirement but nothing is lost by considering a simple case where people work for one period and are retired for one period.) To make the transition a government could allow all workers to accumulate their contributions into a fund earning r and issue debt with the same value as those contributions to pay pensions to the current retired. In the next period the new generation of retired find that the value of their pensions is higher by the interest rate, r, times the value of the contributions. But assuming that the government has to pay the same rate of return on the debt it has issued it needs to raise taxes by an exactly equal amount to prevent the stock of debt rising further. The extra taxes exactly offset the extra income to pensioners and mean that average post tax resources in the economy are exactly where they were with the PAYG scheme. The inescapable logic of this argument has been spelled out formally and in a much more general setting by Breyer (1989). It should not come as a surprise that issuing bonds - which merely makes an implicit government liability to pay future pensions an explicit liability represented by a stock of debt with a current market value - in itself can solve nothing.

But debt financing most certainly can help in a transition if the funding cost of government debt is below the return on funds accumulated from pension contributions. And in practice it might seem as if that condition holds. Over the last fifteen years the UK government has been able to issue long-dated, index-linked debt at a real yield that has averaged around 3 1/2 per cent. Over the post war period the average annual yield on UK equities has been around 7 per cent. But it is far from clear that on a risk adjusted basis the yield on equities (or on any portfolio of risky assets) exceeds the yield on government debt; indeed asset pricing theories (eg the capital asset pricing theory) make it almost definitional that in equilibrium this would not be the case.

Of course equilibrium asset pricing theories may be a poor guide to the real world; the so-called equity premium puzzle (that equities yield too much, relative to safe assets, given their risk) is testament to this. But the point remains that even if assets in a fund on average earned twice the cost of government debt that might only just be enough to compensate for risk. And in fact it is unlikely that equities will in future earn twice the yield on indexed government bonds. The rate of return on corporate capital is likely to fall if the ratio of capital to workers rises; demographic trends will see the proportion of the population of working age fall over the next forty years and the simulation results above suggest that a steady rise in the capital labour ratio, and gradual decline in the marginal productivity of capital, will follow. So the yield on claims on corporate capital may be below twice the index-linked bond yield even before we make a deduction from equity returns for the administrative costs of managing funds.

Ultimately, even if the yield differential between government debt and the return on other assets meant that a debt financed transition from unfunded pensions was feasible governments might reject it. Most European countries (the UK is an exception) are struggling to bring the stock of debt down towards 60 per cent of GDP to satisfy the Maastricht criterion. And the Growth and Stability pact specifies that once a monetary union is established member countries will be fined if their deficits exceed 3 per cent of GDP. There are exemptions from fines in exceptional circumstances; financing the transition from an unfunded state pension scheme is not one of them.

V. Risk and Incomplete Markets

In the simple case of a static model the strategy of issuing government debt to cover existing pension obligations that can no longer be financed through a PAYG pension scheme is self-defeating if the return that needs to be offered on that debt is equal to the return on assets that are built up by current workers. In that case future tax increases to pay off the debt will wipe out the benefit of the existence of a fund of assets whose return exceeds GDP growth. So even if the rate of return is substantially higher than the growth of GDP, there will be no benefit from switching from a pay-as-you-go scheme to a funded scheme. Of course so long as the funds of the pension schemes are substantially invested in equity and if the equity premium (the excess return on equity over bonds) is significant, there is the scope to go through the transition period with no losers and long term gainers. This raises several issues. If individuals are given choice over the composition of portfolios of funds accumulated from their (potentially mandatory) contributions will they opt for safe assets yielding (after costs) a return little different from the yield on index linked bonds? And if portfolios are heavily invested in equities do they generate a risk-adjusted return which exceeds the cost of debt? In both cases the answers depend on the actual and perceived risk and return characteristics of assets and on individual attitudes toward (and understanding of) risk.

Risk comparisons between funded and unfunded schemes also depend upon the volatility of unfunded pensions. And whether returns on a fund are more volatile than returns paid out of taxes on workers is very hard to gauge. This is because how one should calculate probabilities of governments falling short of, or exceeding, expectations of pension payments is unclear. Given recent history, it is at least plausible that the returns from PAYG schemes are as risky as the returns on a diversified portfolio - one needs only to look at the unanticipated changes to the SERPS system in the UK to see the scope for huge and hard to predict changes in the rate of return earned on contributions to unfunded schemes. More generally, whole generations of workers in Europe may face a rate of return on their contributions to PAYG state schemes which, by the middle of the next century, will have turned out to be dramatically lower than its history would have lead them to expect.

But in the context of risk more interesting welfare issues with funded and PAYG pension systems arise from the likelihood that financial markets do not allow people to insure against certain kinds of uncertainty. Market incompleteness means that many important risks cannot easily be hedged by individuals. Unfunded state pensions which have a significant element of redistribution may lessen the cost of such market incompleteness. If so a switch to a funded scheme where pensions paid are closely linked to the value of past contributions made may exacerbate the impact of missing markets. It is not a switch to funding per se that is the real issue but an increase in the linkage between the value of contributions and the value of pensions. In practice nearly all proposals for switching to funding would imply a high degree of linkage.

It is important to distinguish two different types of risk here, neither of which is easy to insure against in financial markets. First there is individual (or idiosyncratic) income risk. A pension system which distributes resources between pensioners of the same generation in an egalitarian way does provide a hedge against this type of risk.

Second, there is income risk which affects a whole generation (wars, technology shifts which benefit current workers but not the current retired, shift in the burden of taxation between labour and capital). Unfunded pension schemes represent a form of insurance against such risks because the value of pensions paid to the current retired depends upon the labour income of another generation.

Merton (1987) has made the central point about missing markets and unfunded pensions in a typically insightful way. In a world with a complete set of financial markets - that is one where all forms of wealth can be traded in well functioning markets - one would expect that the equilibrium portfolio of a representative agent would simply be the market portfolio. That is, the optimal portfolio of wealth for any agent would be a portfolio with asset shares equal to the aggregate shares of different components of wealth in total national worth. Merton's own work suggests that this proposition is true in a surprisingly large class of models (and not just in the highly restrictive case where the standard capital asset pricing model holds). The overall stock of assets in any economy comprises physical assets - houses, factories, machines - but also includes the stock of human capital, the current and future value of the labour that can be supplied by people in the economy. The value of human capital is likely to substantially exceed the value of other types of assets. In most economies wages and salaries make up well in excess of 50 per cent (and often nearer 80 per cent) of GDP. Thus factor payments going to human capital may be three or four times as large in a typical developed economy as payments going to other factors of production (dividend and bond payments to holders of corporate equity and debt). Human capital in real economies is not readily tradable; I cannot now sell claims on my future labour income. The implications of this obvious point are rather profound. In a world where the most important single class of asset is not traded the portfolio decisions of private agents are seriously restricted.

Let us suppose there is no tradable asset that has close to the same characteristics as a claim upon human capital. Then in a world where people begin their life with no assets other than human capital, spend a period out of the labour force, work for a substantial proportion of their lives but are then retired for a significant proportion of their lives, their portfolios of assets will be significantly different from the portfolio that would be chosen if all assets were tradable. Specifically, in the early and working periods of life far too much of the portfolio of overall wealth will be in the form of human capital (and non-diversified human capital at that) which cannot be traded (only current hours of work can be sold). In retirement, when human capital is zero, the portfolio of assets will be far too heavily weighed in favour of marketable assets. Merton has shown that on efficient risk sharing grounds this is sub-optimal. The key point about all this is that tax financed, state retirement pensions may well represent as close as one can get to a human capital type asset. In the absence of a market in human capital a system whereby the government levies a tax upon current workers and uses the proceeds to finance retirement pensions may help correct the market failure. Such a scheme gives the old a means of acquiring a claim upon human capital whose returns are uncertain and hard to predict - whilst also effectively reducing the exposure of the working and young to current shocks to real wages. Dismantling a pay-as-you-go state pension scheme would exacerbate the problem of incomplete markets.

It is important to be clear about the implication of this observation. It is not that pay-as-you-go, state run pension schemes are superior on risk grounds to funded schemes. Rather it is that there is some role for state financed schemes which re-distribute money from current workers to the current retired. Merton is very clear on this point. The fact that there are inter-generational, risk-sharing benefits to tax financed retirement benefits most definitely does not imply that a PAYG scheme should provide all (or even most) of retirement income. But it does suggest that a complete switch to funded schemes with high linkage between contributions and subsequent pensions is undesirable.

Conclusions

It is plausible that in the long run people would be better off if pensions were funded. But in the transition to such a scheme funds need to be accumulated and that requires national saving to be higher. While deficit financing can, under certain circumstances, help spread the burden of the transition across generations the scale of extra debt that might be needed in many European countries is problematic in the context of Monetary Union. Ultimately, it is likely to prove hard to make significant headway towards greater funding of pensions without some people being worse off. The problems that the Italian and Austrian governments have had recently in scaling back the generosity of state pension schemes is testimony to the difficulty of making the transition. In short, the transition to a funded scheme is hard to manage in a way that would get widespread support. The task is harder the more generous are existing state pensions, the more rapid is the ageing of the population and the more constrained is the government in using deficit financing. Given all this the UK is in a relatively good position (visa vis rest of Europe) to complete a transition which, arguably, began almost twenty years ago. Things are much tougher on the Continent.

But there are more than transitional issues. Unfunded pension schemes can help people insure against shocks that affect particular generations and because such schemes often involve intra-generational redistribution (because linkage is often quite low), as well as inter-generational transfers, they can help compensate for missing insurance markets. A key question for those who advocate a complete move to funded schemes is how the redistributive and insurance roles that are played, to varying extents, by state-run, unfunded pension schemes could be achieved by other means. Governments can, of course, use a wide variety of tax and benefit policies to redistribute resources and insure losers; they can compensate people for misfortunes through means other than the pension system. And targeted benefits to the least well off among the elderly are very different from universal, state-run, unfunded schemes which provide the great part of retirement resources for the majority of people.

If switching completely to funded schemes is problematic because of transitional costs, and potentially undesirable because of missing markets and concerns about distribution, then where are we left with the problems facing unfunded schemes stemming form generous pensions and ageing populations? One central message of this paper is that there is no simple way out of the problem that many European governments find themselves in. A switch to funding imposes costs while sticking with generous unfunded pensions will generate big rises in contribution rates and in associated labour market distortions. Gradual increases in (state) retirement ages are planned in several countries (including the UK, Germany, Italy and the USA) and these increases help to reduce annual contribution rates to either funded or unfunded schemes (for a given level of pensions). In the light of the sharp rises in life expectancy over the past fifty years, and the decline in the amount of physically demanding labour, a phased in rise in retirement ages is surely appropriate. In 1945 life expectancy at birth for a male was about 65 years in the UK. In 1995 the figure was about 75; World Bank projections are that life expectancy by 2050 will be about five years greater again. Regardless of the merits of funded and unfunded schemes gradual rises in retirement ages over tune are likely.

NOTES

(1) Unless governments have already announced a phased in change in male or female retirement ages when such plans are taken into account.

(2) This is related to the so called Golden Rule condition from growth theory which is that equality of the rate of return and growth of output maximises sustainable consumption.

(3) Feldstein (1996, 1997) has argued that in the US the scale of the distortions to labour supply generated by contributions to PAYG pension systems is large and the benefits of switching to a system where contributions are paid to a personal fund are correspondingly great. But the fund could still be notional rather than real. In fact it is likely that the greatest distortions to labour supply stem from the disincentives they often generate to working beyond the normal retirement age.

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