Redistribution between generations

I ought to start a series on common macroeconomic misunderstandings. (I do not watch zombie films.) One would be that the central bank’s balance sheet normally matters, although this nice comment on my last post does the job pretty well. Here is one that crops up fairly regularly - that government debt does not involve redistribution between generations. The misunderstanding here is obvious once you see that generations overlap.

Take a really simple example. Suppose the amount of goods produced each period in the economy is always 100. Now if each period was the life of a generation, and generations did not overlap, then obviously each generation gets 100, and there can be no redistribution between them. But in real life generations do overlap.

So instead let each period involve two generations: the old and young. Suppose each produced 50 goods. But in one period, call it period T, the government decides that the young should pay 10 goods into a pension scheme, and the old should get that pension at T, even though they contributed nothing when young. In other words, the young pay the old. A fanciful idea? No, it is called an unfunded pension scheme, and it is how the state pension works in the UK. As a result of the scheme, the old at T get 60 goods, and the young only 40, of the 100 produced in period T. The old at T are clear winners. Who loses? Not the young at T if the scheme continues, because they get 60 when old (and assume for simplicity that people do not care when they get goods). The losers are the generation who are old in the period the scheme stops. Say that is period T+10, when the young get to keep their 50, but the old who only got 40 when young only get 50 when old. So we have a clear redistribution from the old in period T+10 to the old in period T. Yet output in period T and T+10 is unchanged at 100.

That example did not involve any debt, but I started with it because it shows so clearly how you can have redistribution between generations even if output is unchanged. To bring in debt, suppose government taxes both the old and young by 10 each period, and transforms this 20 into public goods. So each generation has a lifetime consumption of 80 of private goods.

Now in period T the government says that the young need pay no taxes, but will instead give 10 goods in exchange for a paper asset - government debt - that can be redeemed next period for 10 goods. In period T nothing changes, except that the young now have this asset. In period T+1 this allows them (the now old) to consume 50 private goods rather than 40: the 40 it produces less tax and the 10 it now gets from the government by selling the debt. Their total consumption of private goods has increased from 80 to 90. How does the government obtain these 10 to give the now old? It says to the young: either you pay 20 rather than 10 in taxes, or you can buy this government debt for 10. As people only care about their total consumption, the young obviously buy the debt. They now consume 30 in private goods in T+1, but 50 in T+2 when they sell their debt, which gets us back to the original 80 in total lifetime consumption.

This process continues until period T+10, say, when the government refuses to give the young the choice of buying debt, and just raises an extra 10 in taxes on the young. So the debt disappears, but the young are worse off, as they only have 30 of private goods to consume this period. Their total lifetime consumption of private goods is 70. We have a clear redistribution of 10 from the young in period T+10 to the young in period T enacted by the government issuing debt in period T.

If you are thinking that these redistributions need not occur if the debt is never repaid or the pension scheme never wound up, then we need to get a bit more realistic and bring in interest rates and growth (and the famous r<>g relationship), which these posts of mine (and these at least as good posts from Nick Rowe) discuss. But the idea with this post is to get across in a very simple way how redistribution between generations can work because generations overlap.

Unfunded pension schemes and intergenerational equity

Government debt and the burden on future generations

The Burden of Government Debt

Nick Rowe

How time travel is possible,

The burden of the (bad monetary policy) on future generations

Annuities and inheritance

Following the end to compulsory annuitisation in the budget, is everyone who can afford it going to take their pension pot and become a landlord? The argument that they will, which you will find on plenty of websites offering financial advice, goes as follows. First, you get a good return in the form of rental income relative to annuity rates. Second, you get to pass on the property to your children, rather than losing all your capital.

There is one important point we need to get out of the way first. Comparing rates of return from being a landlord to annuity rates is misleading, because the risk characteristics are different. A much more sensible comparison is to compare returns from being a landlord to investing in the equity market, or to compare annuity rates to rates of return on safe assets. And if you think that  house prices are bound to trend upwards and so carry no real risk, read this from Tim Harford.

The more interesting issue, however, is what happens to the insurance value of an annuity if an individual (lets call them George) can afford to live off the income from their capital and plans to pass on the capital to their children. Recall that for those who are not lucky enough to be as rich as George, an annuity is useful because it insures against the risk that they will live longer than their age group and might otherwise run out of money. However, if George has enough capital to live off the income from it, what point is there buying an annuity?

The answer is that it insures George’s children. Compare two plans. In the first (plan A), George invests all his pension in some form of asset, and lives off the income. In the second (plan B), George uses part of his capital to buy an annuity that gives George the same retirement income. As long as we stick to safe assets, annuity returns are bound to be higher than interest returns, because you never get the capital value of the annuity back. So under plan B George, having bought his annuity, will have some capital left. Plan B involves giving the capital left over to George’s children, now.

Both plans are designed to give George the same retirement income, however long George lives. Does plan B mean George’s children get less inheritance? No, because under plan A they only get the inheritance when George dies, but under plan B they get it now. So they can immediately invest George’s gift, and let the interest on it accumulate (rather than have George spending the interest). By the time George passes on, the value of their inheritance could well have grown to equal the value of the inheritance under plan A. [Under various assumptions it will. Which turns out to be better in practice depends also on the particular relationship between gift taxes and inheritance taxes that apply in the country George lives.]

The other important point is this. Under plan A, the date on which George’s children can access George’s inheritance is uncertain - it depends on how long George lives. Under the second it is not - they can access it at any time. So what an annuity does in this case is insure George’s children against the risk that George will live for a long time, meaning that it will be a long time before they get their inheritance. The insurance value of the annuity is not lost, but transferred from George to his children.

One final point. The idea that George’s inheritance would be equal the full value of George’s pension sounds as if George is being very generous indeed. (I’m assuming here that George has no other wealth - what made you think otherwise?) Put it this way. George’s pension is a result of his saving part of his hard earned money. If he gives it to his children, and they happen to retire just when George dies, they too can live off the interest - which means that they do not need to save for a pension of their own. So they seem to be a lot better off than George thanks to George’s generosity.

Now of course what I’m doing here is being a typical economist, which is trying to answer a question by asking what rational people would do in a world without imperfections, where arbitrage across assets holds etc. And, also being an economist, I found my analysis interesting in its own right. But as to what people in the UK are going to do with their new found freedom, in a situation where investors are supposedly buying up flats in London and not even bothering to rent them out, who knows.

Pensions and neoliberal fantasies

As those in the UK will know, one of the major changes announced in the recent budget was to ‘free up’ defined contribution pension schemes so that recipients were no longer forced to buy an annuity with their pension, but could instead take the cash sum and spend or save it how they liked. This has been generally praised by our predominantly neoliberal press. The government’s line that this was a budget for savers and pensioners has been accepted uncritically. Giving people the choice of what to do with their money - what could be wrong with that? After the budget the UK press were full of stories of new pensioners trying to cancel their annuity contracts.

So if I suggest that those who are due to receive a defined contribution pension in the next few years and who want to invest their money prudently are likely to be worse off as a result of this budget, that might come as a bit of a surprise. The reason is because of three things economists (who are not automatically neoliberal) worry about: adverse selection, moral hazard and myopia. I will translate these in turn, in ascending order of importance. But before I do a very simple point. Annuities are a good idea, because they insure against uncertain lifetimes. So unless you know your date of death with be earlier than for your age group, you should invest a large part of your pension in some form of annuity.

Moral hazard. Pensioners can now take the risk that they will not live for long and blow their pension on expensive holidays, knowing that if they are wrong and live longer they can always fall back on the welfare state. A reasonable state pension should avoid this (because those receiving it do not qualify for welfare payments), but the IFS believe (pdf) this will only be partially true in the UK.

Myopia. As Tony Yates points out “there is abundant evidence from the experimental and other empirical literature in behavioural economics and finance that we are i) terrible at paying proper attention to the wants of our future selves [usually neglecting them] and ii) terrible at responding rationally to risk.” We know (IFS again) that people underestimate the life expectancy of their age group.

Adverse selection. If everyone has to take out an annuity, annuity providers can make a reasonable guess at how long people on average will live. If instead people can choose, annuity providers face an additional uncertainty: are those not choosing to take out an annuity doing so because they believe they will not live as long as the average for their age group? If that is true - which it almost certainly is - then annuity rates will fall, because those still taking out annuities will live on average for longer. A greater concern is that this additional uncertainty will reduce annuity rates still further, as annuity providers require an additional margin to compensate them for the extra risk they face. In theory, the market could collapse completely.

I do not mean to imply that any of these, or even all three combined, are sufficient to justify compulsory annuitisation. What they do show is that the naive ‘choice must be good’ line may be neoliberal, but it is not economics. What does seem pretty clear is that the budget will lead to a reduction in annuity rates, so a perfectly reasonable headline after the budget would have been “Chancellor cuts incomes for new prudent pensioners”. If you do not remember that headline in your newspaper, perhaps you should change newspaper.

There is another neoliberal fantasy, and that is that private provision must be better than public provision. Yet pensions illustrate one area where this can be the opposite of the truth. Defined contribution pension schemes suffer from intergenerational risk. Suppose that those arguing real interest rates will stay low for a long time are right (secular stagnation). That means that the generation receiving their pension during this period will end up with a lower pension income that those that go before or after them. Indeed it is just this effect which has made annuities unpopular and which the government is playing to. People would like to insure against this kind of risk, but the problem in this case is that we need an insurer who in effect lives forever, so they can smooth out these good and bad times. There is just one economic actor that could do this, and that is the state. The state could do this in many ways, ranging from some form of unfunded government pension scheme to providing insurance to annuity providers.

As Tony Yates notes, you can see additional government borrowing during severe (liquidity trap) recessions as just this kind of intergenerational risk sharing. He also points out that there are time inconsistency issues when the state performs this role, although I would add that if the old continue to vote more than the young these may not be critical. If Roger Farmer is right (pdf), these issues involving uncertainty over generations may have consequences far beyond pension provision, and again the state may have a key role to play. Unless, of course, you are a neoliberal who will not countenance such things.

This post was inspired by this from Tony Yates, and also drew heavily on this post-budget briefing by IFS economist Carl Emmerson. For a much more detailed analysis (based on the government’s earlier proposals but also of relevance now) see this study (pdf) by David Blake, Edmund Cannon and Ian Tonks. 

Unfunded pension schemes and intergenerational equity

                In two earlier posts (here and here) I looked at issues involving debt and intergenerational equity. The second attracted a lot of interesting comments. Some had difficulty with the idea of debt as a burden, and I think one way to help here is to look at pension schemes. (I hope to return to other comments later.)

                When I talk about intergenerational equity to students, I go through all the ways that the current generation is exploiting future generations, like climate change, rising house prices, and rising government debt. I also say that of course the older generation could just get the younger generation to pay them directly. I then reveal, to the surprise of some, that that is exactly what happens in many countries because these countries run unfunded pension schemes.

                An unfunded scheme is where the working generation pays social security contributions, and that money goes straight into paying the pensions of the old, rather than buying some kind of asset (hence unfunded). When the scheme starts, the current old receive a windfall: a pension without having contributed anything. The young pay contributions, but then receive a pension when they get old from the new younger generation. So the older generation when the scheme starts are clearly winners, but are there any losers? The answer depends on two things.

                The first is whether the scheme ever stops. If it stops, the young in the period beforehand are clear losers. They paid contributions (which went straight to the then old), but get nothing when they get old. Obviously the scheme is a huge burden on this ‘final generation’. However if the scheme goes on forever, there is no last generation, so there is no loser on that account.

The second issue is whether those who are forced to save by contributing to the pension lose out because they could have done better saving for themselves. That in turn depends on whether the rate of interest (r) is greater than the rate of growth (g). Those who contribute to the pension scheme get back more than they put in because of economic growth. The income of the young as a whole will be higher either because of technical progress which raises income per head (assuming contributions are a fixed proportion of income), or because there are more of them which raises the number of heads. In either case the current young generation contributes more than the old did when they were young, so the old benefit from that extra money. However if they had saved themselves their return would be the rate of interest. So if r>g, each generation of young lose out a bit by being forced to save in a way that produces a return equal to g rather than r.

All that is happening here is that money is passing from one group to another, with the government acting as an intermediary. Society is ‘paying itself’. But this statement says nothing about intergenerational equity. Suppose the scheme only lasted one period. Money passes from the young to the old, but it would be absurd to say that this implied that the young were not losing out.

Those who read this earlier post will see the parallel with the case of government debt. With pensions the young get an implicit promise that they will receive their money back with a return equal to g, whereas those that buy debt get an explicit note saying they will get their money back with some rate of interest r. The implicit/explicit thing is not crucial here – after all the government can default! The key difference is that, if people are to buy the debt voluntarily, they get a return equal to the return on other forms of saving (=r). If r>g, taxes have to rise to make up the difference between the two when debt is issued.

An unfunded pension scheme has the same macroeconomic costs that I discussed before in relation to government debt. In particular, if the young save at least part of their pension this way, they will save less in productive capital, and if the amount of capital in the economy as a whole is less than the optimal level, this will be an important cost. In addition, to the extent that the contributions act like an income tax, it can distort work effort.

Does this mean that an unfunded pension scheme is a bad idea? You can see why it might be introduced even if it was a bad idea – its introduction is great for the current old, so they will always vote for it. There are two potentially important benefits, if the alternative is funded private schemes. First, it takes away a lot of the uncertainty in funded schemes. If you buy your private pension when the stock market is high, and retire when it is low, you could lose out in a big way. You might also want insurance against labour income risk. (See, for example, this paper by David Miles.) Second, it provides a safety net for those who were misguided enough not to contribute to a private pension. (For a useful reference on pension issues, see Oxford Review of Economic Policy Vol 22, No1, Spring 2006.)

                I think this nicely illustrates why intergenerational equity can never be the overriding concern when it comes to issues involving government debt or unfunded pension schemes. There are many other factors to consider that may be more important. If it was decided that the costs of unfunded pension schemes exceeded the benefits (or, more realistically, that the balance should move to funded schemes), then the generations involved in any transition would almost certainly lose out. They would become like the final generation in my discussion above. That issue of intergenerational equity should be important in any decision, but it should never be the only consideration.