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The UK savings gap.

We set out a framework for measuring the adequacy of saving in the United Kingdom by assessing the absolute level of savings based on individual preferences of different ages. We examine this relationship between age and savings using data from the Expenditure and Food Survey 2004-5. We show that, while the level of national saving is about 8.4 percentage points of net national income lower than is required if one assumes that each cohort pays its own way, wealth holdings are considerably higher than are required on the same basis. Looking at household, rather than national saving, the current pattern of benefits on public sector pensions removes the need to save for old age. While perhaps 4000m [pounds sterling] of household wealth holding can be accounted for by bequest and other transfer motives, our results suggest excess wealth holding of around 1600m [pounds sterling] in 2004.

Keywords: Savings gap; household and national saving; capital accumulation; bequests and transfer inter vivos

JEL classifications: D10; D31; D91; E01; E21

Introduction

In recent years there has been considerable discussion of a number of questions associated with the general issue of saving. On the one hand there have been concerns about pensions, leading to the report by the Pensions Commission (2005) and the subsequent proposals for the reform of the state pension system (Department of Work and Pensions, 2006) and for the introduction of the new low-cost National Pensions Savings Scheme. On the other hand there have been fears about levels of indebtedness, partly as a concern over the risks faced by people with large debts but also because, in rather general terms, high levels of debt could be indicative of a failure to make adequate provision for the future. Household savings rates have declined in recent years and this adds to the general sense that saving might be low.

Nevertheless, these observations lack a firm reference point. It is not possible to know whether current savings patterns should be an object of concern without defining an appropriate level of saving. A decline in saving on its own does not distinguish a move from excess saving to adequate saving from a fall from adequate to inadequate savings rates. In this article we answer the question, obviously subject to the range of assumptions needed to define the problem, what should the savings rate be?

Earlier work has looked at this from a macroeconomic perspective (Pomerantz and Weale, 2005). The macroeconomic approach is very straightforward. Given an existing holding of wealth, how much saving is needed for the stock of wealth to grow in line with income--thus sustaining the economy as it is at present. However this approach faces a number of objections stemming largely from the fact that it does not identify what motivates saving. If saving is intended to fund retirement, then a measure of savings adequacy needs to reflect the age structure of the population. If the existing level of wealth is inappropriate then so too will be the measure of required saving delivered by the calculation set out above. In this paper we therefore set out a framework for assessing savings adequacy based on the decisions of representative individuals of different ages.

Our work is closely related to the studies of savings behaviour by Gokhale, Kotlikoff and Sabelhaus (1996) and Kirsanova and Sefton (2006). However both of these authors attempt to explain differences in savings rates, over time in the case of the first paper and between countries in the second paper. We limit ourselves to assessing the absolute level of savings and wealth holding.

Household saving and national saving

In any analysis of savings rates it is important to make the distinction between household saving and national saving. National saving is the sum of the saving of the different institutional sectors in the economy, the household sector, the corporate sector and the government sector. In any study of saving adequacy, national rather than personal saving is the appropriate focus. There are a number of reasons for this.

A low level of government saving (e.g. a large deficit on the current budget) implies that taxes are going to rise in the future to service the accumulating debt. If households are going to have an increased tax bill in the future then they need higher savings to finance their retirement than would be the case if taxes were not set to rise. Adding together household and government saving provides a short-cut means of taking account of this effect. Even though the Government does not belong to the household sector, households have to address the financial implications of government behaviour and it therefore makes sense to assess household savings needs in the light of this. Much the same argument applies to the corporate sector. Accumulation of wealth by companies implies that corporate dividends will rise in the future. Thus if companies are saving, the need for households to save to finance their retirement is reduced.

Essentially the argument is that, one way or another, households have command over the whole of national resources in order to finance whatever future needs they may have. In turn this means that the question whether any particular household needs can be met is answered not by looking at the wealth and saving of the household sector directly but by looking at the resources available to the whole economy; this means looking at national wealth and national saving.

There are, nevertheless, good reasons for looking at the behaviour of households and the taxes and transfers that they face; it is quite possible that households make their spending and saving decisions taking the structure of these as fixed, with the obvious implication that tax and transfer arrangements are an important determinant of actual savings behaviour (Feldstein, 1974; Disney, 2006) even though they themselves represent no more than the transfer of resources from one sector in the economy to another. We therefore also make a comparison between the saving and wealth needed by the household sector in the presence of the tax/transfer system with that which would be needed in its absence. The difference between the two indicates the extent to which the tax/transfer system may affect savings and wealth. In our analysis of household behaviour we focus on the decisions of individual adults who make up households.

The modelling framework

The question whether saving is adequate can be addressed only in the context of a model which provides a need for saving and therefore allows a normative analysis of saving. The reference model we use is the life-cycle model in the absence of risk. We assume that each cohort intends to pay its own way, calculating the saving level associated with this aim. In essence, therefore, saving is calculated from the application of the lifetime budget constraint given a lifetime consumption profile and information on the value of lifetime income. We assume initially that there is no bequest motive and that all saving is fully annuitised, with the implication that the assets of people who die are shared among the survivors of the same cohort (Yaari, 1965).

Adequacy of national saving

We denote [y.sup.L.sub.it] as the labour income gross of all taxes and deductions of a representative member of cohort i at age t and [c.sup.c.sub.it] it as its comprehensive consumption. Comprehensive consumption is related to individual consumption, [c.sup.H.sub.it] in the following way:

[c.sup.c.sub.it] = [c.sup.H.sub.it] + [c.sup.G.sub.it] - [[tau].sup.c.sub.it]

where [c.sup.G.sub.it] is consumption provided by the Government and [[tau].sup.c.sub.it] is indirect taxes net of subsidies collected on consumption goods. Thus [c.sup.c.sub.it] is the total consumption by the cohort measured at basic prices rather than market prices. If the current calendar year is [t.sup.*], each cohort is indexed by the calendar year in which it becomes economically active, and we assume it is aged 20 when this happens, then the current consumption of each cohort is given by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where [T.sub.max] is maximum age, with [t.sup.*] [T.max] < = i < = [t.sup.*]. We denote the series of cross section observations of consumption in period [t.sup.*] by the vector [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with a similar notation used for other variables. In our empirical analysis we distinguish men and women. In order to simplify our notation we omit the relevant superscripts except where essential.

We make the assumption that each cohort holds the wealth it needs to finance future consumption given future income but does not plan to make any bequests or transfer any income to other cohorts. Given this basic model the wealth per capita held by cohort i at the start of the year in which it is t years old is, with [s.sub.it] being the number (or proportion) of cohort members alive when aged t and r the constant rate of return gross of tax but net of depreciation

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

This analysis identifies with the assumption of full annuitisation, the relationship between composite consumption and labour income which has to hold if each cohort does pay its own way. But, there is no reason why the current wealth holding of each cohort, its labour income expectation and its consumption plan should be consistent with the budget constraint; the constraint depends in any case on how we choose to model future labour income and consumption plans. If we assume, as we do, that everyone plans ahead, then the budget constraint is represented by the restriction that the initial value of wealth, for the cohort currently aged 20, is zero. The observed consumption profile may not satisfy this.

With our assumption that income and consumption grow at rate g, we relate the per capita consumption of cohort [t.sup.*] - t when it reaches the age of [tau] + 20 to that of the cohort aged [tau] + 20 observed in year [t.sup.*] as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

with similar relationships holding for income variables.

With this means of projection of future consumption and labour income, we then scale the consumption profile derived from the data to impose the budget constraint. If consumption satisfying the budget constraint is denoted [[??].sup.c.sub.it] = [lambda][c.sup.c.sub.it] where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

can be calculated from the observed profile and assumptions about the growth rate and the interest rate.

In turn required cross-section wealth holding per capita is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

From these variables we can now calculate net national income, total wealth and total consumption. We assume that at time v the number of people in the cohort born in year j, and therefore of age v-j is [n.sub.j,v-j]. Total labour income, wealth and consumption are given as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

From these variables we calculate required national saving as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Even, of course if [lambda] = 1, so that the intertemporal budget constraint can be balanced with consumption taking its unscaled value, there is no guarantee that past saving has been adequate. Thus [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] does not on its own guarantee that the consumption profile can be afforded; one also needs to compare actual aggregate wealth, [[??].sub.v] with the value of aggregate wealth generated by the life-cycle model, [W.sub.v] The exercise is slightly complicated by the fact that we make the calculations separately for men and women, to reflect the fact that we observe different income profiles and survival rates for the different sexes.

Adequacy of household saving

We can use a similar approach to explore the adequacy of household saving. There are two important differences from the assessment of national saving. First of all we are concerned with the ability of individuals to pay for individual consumption at market prices instead of the nation's ability to pay for composite consumption at basic prices. This means that we focus our attention on [c.sup.H.sub.it] instead of [c.sup.c.sub.it] Secondly, instead of looking at labour income gross of taxes and other deductions, we look at individual non-property income net of taxes and transfer payments denoted [y.sup.H.sub.it]. We define [y.sup.H.sub.it] = [y.sup.L.sub.it] - [[tau].sup.H.sub.it] where [[tau].sup.H.sub.it] represents direct taxes and transfers paid by households to the Government less social security benefits and other transfers received from the Government. If [r.sup.I] is the rate of return received by individuals, and [c.sup.H.sub.it] is the actual plan for individual consumption, then we follow the earlier approach to define

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Aggregating individual variables provides of course the totals for the household sector apart from the problem of non-profit institutions which we ignore. Using obvious notation, we define required household saving as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Once again we add across all cohorts currently alive to compare both required saving and required wealth holding with actual saving [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and actual wealth holding, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. We again make these calculations separately for men and women.

Income, consumption and tax profiles

It is clear from the previous sections that the profiles for labour income, net transfers and consumption form the core data required for our analysis. Such profiles, in so far as they relate to household or individual activities, are derived from the results of household income and expenditure surveys. There are, in broad terms, two possible approaches to the construction of these profiles. The simpler one is to use the cross-section provided by an annual survey. This in essence constructs a snapshot view of the income, taxation or consumption of people of different ages in any particular year and uses this cross-section to construct an estimate of the expected income/ taxation or planned consumption of younger people. In a general environment in which incomes and consumption rise over time it would be unreasonable to assume that the consumption of a 70 year-old today is a good forecast of the consumption plan of a current 30 year old in 40 years time. But if we make an assumption that underlying growth is superimposed on this cross-section profile, then the idea that expectations about future incomes or consumption plans can be derived using the cross-section profiles is much more reasonable. This is the approach of equation (1).

This approach has the great advantage that the tax data, the income data and the individual consumption data can all be drawn from a consistent data set such as the Expenditure and Food Survey. It is, nevertheless, open to the objection that it confuses time effects, age effects and cohort effects.

Deaton (1997) suggests that, from a succession of cross-section surveys and with appropriate identifying restrictions, it is possible to separate these out by regressing the variables of interest on appropriate dummy variables. While, when the underlying framework is stable, the approach has obvious attractions, there are nevertheless a number of disadvantages. First of all, the profile showing consumption, income or transfers as a function of age is best interpreted as an average for the estimation period. This means, in particular, the pattern of transfers linking gross and net income is not that associated with any particular year or any clearly-defined tax/benefit regime. In our exercise the model plainly shows saving as being influenced by expected taxes and benefits; the assumption that these are related to the regime currently in place is much more satisfactory than the assumption that they are related to some sort of average over the past 30 years or so. Results based on an average would be of interest in the current environment only if one were sure that the pattern had not changed much over time. It is clear, however, that this is not the case; there have been substantial reforms to benefit arrangements since 1997 when Labour came to power. If taxes/transfers are to be based on recent observations rather than a long-run average, it is very difficult not to do the same for all other variables. Otherwise there will be an inherent inconsistency between income before and after transfers and also between individual income and individual consumption.

A second difficulty arises from the fact that it is recommended to set up the dummy regression so as to explain log values of the variable of interest; the method is theoretically more coherent when applied to the consumption profile. This means that the resulting profiles will describe geometric rather than arithmetic means and will therefore be downward biased. The downward bias will increase with the dispersion of the underlying data. Since both income and consumption dispersion tend to increase with age--at least during working life, this bias will not be a constant proportion of the resulting estimates but will increase over time. The downward bias to income will almost certainly be larger than that to consumption because the data are more dispersed. Thus saving late in working life will be understated if one uses Deaton's dummy variable method. This bias cannot be corrected by scaling alone since it also tilts the profile.

The second problem can be avoided by the use of a linear rather than a log-linear regression despite the loss of theoretical coherence. But the first point provides, in our context, a powerful case for using a growth-augmented cross-section to estimate the profiles, and we use the Expenditure and Food Survey 2004-5 with variable definitions in Appendix 1.

This, nevertheless, does not provide all the information that we require. It allows us to identify labour income, net non-property income and household consumption (although this is aggregated to households). Observed government consumption, [[??].sub.G.sub.it] and indirect taxes [[tau].sub.c.sub.it] are taken from updated profiles (1) used in the construction of generational accounts (Cardarelli, Sefton and Kotlikoff, 2000). These profiles again provide cross-section values and are growth-adjusted before use.

Households and individuals

A separate issue arises as a result of the distinction between households and individuals. The Expenditure and Food Survey and indeed most surveys which collect consumption information are constructed around the concept of the household. The reason for this is obvious. Some components of consumption (such as food) may not be consumed by the individual responsible for procurement; other types of consumption such as costs related to housing are collective rather than individual in nature. In either case an arbitrary allocation is needed to attribute consumption to individuals. The income information is, however, set out in terms of individuals; in the case of benefits calculated in the light of family circumstances this means that the income is assumed to accrue to the person legally entitled to receive the benefit.

Some households comprise more than two adults and these are inherently difficult to unravel. We exclude these from the consumption data, so that all households in the sample used to calculate the profiles consist of one or two adults. There are in fact three types of family unit (2) to consider; single men, single women and couples. All three types of family unit may have dependent children present.

We allocate reported household consumption between men and women by making the assumption that, at each age, the consumption of women is proportional to that of men with the ratio of the two being given the ratios of the present discounted values of net non-property income for women and men evaluated at the age of 20. (3) This provides the required profiles for individual consumption by sex. The General Household Survey 2004-5 allows us to identify the proportion of men and women of each age who live as couples rather than singly; we denote these proportions [[psi].sup.M.sub.j] and [[psi].sup.W.sub.j] and make the simplifying assumption that in any couple both partners are of the same age. We extend our earlier notation so that the total number of family units is given as [n.sup.F.sub.v-j,j] with family consumption [c.sup.F.sub.v-j,j] for units born in year j and observed in year v. With [n.sup.M.sub.v-j,j] representing the number of men and [n.sup.W.sub.v-j,j] the number of women (provided by the mid-year population estimates), then [n.sup.F.sub.j,v-j][c.sup.F.sub.j.v-j] = [n.sup.M.sub.j,v-j][c.sup.M.sub.j,v-j] + [n.sup.W.sub.j,v-j] [c.sup.W.sub.j,v-j] as a matter of identity. We also calculate the number of family units as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

With the ratio of men's to women's consumption given by [phi] = [c.sup.M.sub.j,v-j]/[c.sup.W.sub.j,v-j] the three equations can be used to calculate [c.sup.M.sub.j,v-j] and [c.sup.W.sub.j,v-j] from the observed consumption per household unit. The calculations provide us with profiles which take account of the fact that the ratio of single to married people changes with age, and also of the fact that the balance of single men to single women changes considerably with age; single old people are predominantly female. At ages where most people live in couples, the consumption of men and women is well below that of the average family unit, while in old age when there are many more single people, and women predominate, the consumption of men given by the above approach rises above that of the average family unit.

This approach carries with it the implication that consumption by adults supporting their children is treated on the same basis as consumption by adults. It offers a simple framework in which to work, albeit with the disadvantage that changes in family size over time are not reflected in changes to the consumption profile.

The profiles for government spending and also for indirect taxes net of subsidies provided to us were constructed per capita with resources as well as taxes being allocated to children as well as to adults; separate profiles exist for men and women. To put them on the same basis as the profiles for individual consumption, we construct, from the General Household Survey, matrices showing the total number of children of each sex classified by the age of the head of the family unit. (4) For male children we then multiply by the estimate of the overall number of family units estimated above and divide by the number of men in each age. This gives an array which allocates the boys across the male adult population by age of each and is used to allocate the public consumption and net indirect taxes in the same way. Consumption and taxes attributed to girls in the generational accounting profiles are allocated to women in the same way. These consumption profiles neglect the consumption of the services provided by owner-occupied housing. We assess the implications of this subsequently.

[FIGURES 1-2 OMITTED]

Survival rates

Separating out household consumption into consumption of men and women allows us to use survival rates appropriate to individuals and avoids the complication of trying to convert these into household or family survival rates. These survival rates are not published by the Government Actuary; however the Government Actuary does publish tables of cohort life expectancy by age up to 2054 at ages with intervals of five years. We use a cubic spline to interpolate life expectancy to individual years and then calculate the ratios of adjacent survival rates as

[s.sub.i, t+1]/[s.sub.it] = [e.sub.it] - 1/[e.sub.i, t+1].

In order to provide life expectancies beyond 2054 we assume that the trend increase in life expectancy after 2054 is half of that between 2029 and 2054 in order to derive the required survival rates. Separate calculations are carried out for men and women.

The combination of interpolation and the fact that the numbers from the Government Actuary (5) are rounded means that at young ages survival rate ratios very slightly above one can be generated. These ratios are set to one.

National income and consumption

Using the framework set out above we calculate the required savings rate conditional on different assumptions about the growth rate and the real rate of interest. We present results for the savings rate and the ratio of wealth to labour income in tables 1 and 2.

These compare with a figure of 4.8 per cent for the savings rate and 8.40 for the ratio of wealth to labour income (end year) in 2004. Except with the assumption of a very low growth rate and a high rate of return, the actual savings rate is well below what is required with the implication that cohorts currently working will have to choose between i) accepting lower consumption paths than those assumed, ii) working longer to deliver more labour income or iii) financing their consumption by means of imposing burdens on or at the expense of wealth transfers to their descendents.

The picture for national wealth-holding appears to be more satisfactory. We noted that, with a per capita growth rate of 1.5 per cent per annum, the required ratio of wealth to labour income was 4.05 as compared to an actual ratio of 8.40. However actual national wealth comprises two forms of assets, produced wealth which has been acquired by saving, and land and other non-produced assets. A rising price of land increases national wealth but, instead of being the outcome of saving it is simply a transfer from future purchasers of land to current owners, i.e. from the unborn and young to older people. This burden is offset if owners of land give it to those who do not yet own it, either on death or through inter vivos transfers. Thus if one wants to look at the adequacy of national wealth to finance retirement on a basis which does not involve intergenerational transfers, it is more relevant to look at produced wealth (including net foreign assets) only.

The national balance sheets show that 41.4 per cent of national wealth at the end of 2004 was produced wealth, with the remainder being accounted for by land and a small number of other non-produced assets such as the spectrum, giving a ratio of produced wealth to labour income of 3.48. Thus, if non-produced wealth is treated as something which cannot fairly be used to fund retirement, then the amount of wealth held is 86 per cent of what is required--a shortfall which is probably not of great concern given the inherent inaccuracies surrounding the calculation. However the fact that saving is inadequate means that this shortfall is likely to increase.

The values of [lambda] for men and women depend on the interest rate and growth rate. We find that with a growth rate of 1.5 per cent per annum and a real interest rate of 4 per cent per annum the value for men is 0.989 while that for women is 0.738. The difference between the two reflects the relatively arbitrary way in which we have allocated consumption across men and women; the key point is that for each cohort to pay its own way consumption levels need to be substantially lower than they are.

In practice, wealth is considerably higher than is required by the life-cycle model; the property income resulting from this means that extra consumption can be afforded. But the values of [lambda] are nevertheless counterparts to the observation that the required savings rate is sharply higher than the actual savings rate.

In looking at these figures one has to remember that our reference value of consumption excluded the consumption value of the benefit conferred by owner occupation of housing. There are two possible interpretations of this. One is that the required mark-down on a comprehensive measure of consumption is all the greater. The alternative, consistent with the observation that the value of produced capital is not far from the required holding, is to assume that, for one reason or another, people treat land as something to hold in trust rather than as part of life-cycle saving. Thus this component of consumption is more or less financed out of land holdings rather than being associated with saving for retirement. We consider this issue further when we explore individual income and consumption.

These calculations are performed by adding across cohorts, with the size of each cohort given by the 2005 population figures. However, one might reasonably be interested in identifying the effects of the baby boom on savings needs. The baby boom peaked in 1965 and has resulted in bias towards a youthful population. If the population had a steady-state structure instead of that resulting from the mid-century surge in birth rates there would be more retired people and relatively fewer people saving up for retirement. We can explore the implications of this by constructing a new population structure based on the mortality rates for 2004. The balanced population is one which declines with age, with the declination being the mortality rates. Using a balanced population we find that with an interest rate of 4 per cent per annum and a growth rate of 1.5 per cent per annum, the required savings rate falls from 13.2 per cent to 8.7 per cent; wealth holding is increased slightly from 4.05 to 4.15. Thus the baby boom has the effect of raising the required national savings rate by 4.5 percentage points.

Individual income and consumption

The exercise can be repeated by looking at individual income and consumption rather than national income and consumption and aggregating to provide figures for the household sector. This delivers very different results because the Government taxes people when they are of working age so as to be able to afford to pay benefits to them after they have retired. Inevitably this means that, if people do not want to leave legacies or to transfer money to their descendents inter vivos the need to save for old age is lower than it would be if the only non-property income they received was derived from work.

We look at the implications for savings and wealth using the same growth rates as before. However we reduce the assumed rate of return from 4 per cent per annum to 3 per cent per annum or 6 per cent per annum to 4.5 per cent per annum to allow for a notional 25 per cent tax rate on income from capital. This is at best an approximation; the rate of corporation tax is higher but some forms of capital asset and most notably housing are tax-favoured with both income and capital gains accruing tax free.

With a growth rate of 1.5 per cent per annum and an after-tax real interest rate of 3 per cent per annum, we find [lambda] = 0.98 for men and 0.95 for women. Thus the mark-down is much smaller than was the case when national income and consumption were considered.

Tables 3 and 4 show that the lifetime household consumption profile can be met with very slight negative wealth holding and therefore, in an expanding economy, very slight negative saving. The reason for this is that recorded household consumption is lower than recorded non-property income even in old age, with the implication that people do not need to save for their retirement. (6)

Comparing these figures with the data, we see that actual household saving net of depreciation in 2004 was in fact -1 per cent, largely in line with our model. Instead of the negative wealth which would be associated with negative saving, the data show very substantial household wealth holdings of 8.8 times net non-property income (mid-2004 value).

The magnitude of the wealth puzzle can be put as follows. With total household wealth at end-2004 of 5632 billion [pounds sterling] and an adult population of 45.5 million people, the average adult in the country owns wealth worth 124,000 [pounds sterling]. Young people cannot have accrued this sort of wealth out of their average earnings and therefore, unless they receive large transfers or bequests from old people, probably own much less wealth. This in turn carries the implication that old people must own much more wealth. The effect is accentuated if very old people are assumed to reduce their wealth level so as to exhaust their wealth holdings at death. There are a number of possible reasons for the high wealth holdings and we review them in turn.

1. Household wealth was acquired historically and households are now in the process of running down their wealth holdings.

2. Households hold wealth for the purpose of making bequest and transfers inter vivos.

3. Households have future consumption plans and/or income expectations very different from those represented by the profiles.

4. There are substantial measurement errors in the data, and with the true data an estimate of aggregate wealth holding much closer to that observed would be generated.

We consider these issues in turn.

Historical capital accumulation

It is possible that the high level of wealth is a consequence of unanticipated capital gains and in that sense unplanned. One might imagine that if capital values appreciate over a sustained period, then excess wealth will build up. Obviously the excess can be corrected by spending, but people may not want to spend all of their excess wealth at once, so sharp capital gains are likely to lead to high wealth holdings at least for a while.

A historical perspective (7) of this is provided by figure 3, which shows household wealth as a multiple of two measures of household income: gross labour income and gross disposable income. While neither of these corresponds with net non-property income, the two measures have the advantage that they can be identified for a long period and it is clear that the broad picture does not depend crucially on which is discussed.

[FIGURE 3 OMITTED]

The ratio of wealth to income fell in the years after the Second World War as government liabilities (which are household assets) declined relative to GDP. This was a consequence of a move to budget balance combined with rising levels of GDP rather than debt retirement. House prices also declined in this period as controls on building and purchase of new houses were lifted. From 1960 to the early 1980s the ratio was reasonably stable, although the effects of the stock market and housing boom of the early 1970s are visible. Since the mid-1980s, asset holdings have risen sharply relative to income despite the setbacks caused by the housing crash of the late 1980s and early 1990s and the effects of the stock market weakness in the early part of the present decade.

Increases in wealth arise either from increases in saving or capital gains and transfers. Since 1987, the average value of saving net of depreciation as a proportion of disposable income was 3 per cent. On the other hand, the average increase in wealth as a proportion of disposable income was 52 per cent. Thus it is clear that saving by households has played little role in the accumulation of household wealth. There is no reason to think that the picture was very different earlier in the 1980s or that it would be changed substantially if one also took account of saving by companies.

There have been three main sources of capital gains since 1985 which we see as the start of the shift in wealth-income ratios above their range of the previous 35 years.

i) House prices have risen by 6.17 per cent per annum compared with a rise of 3.06 per cent per annum in gross disposable income after adjusting both for inflation.

ii) Nominal and real long-term interest rates have fallen. On 20-year gilts the zero-coupon yield net of the current inflation rate has dropped from 3.67 per cent per annum to 1.38 per cent per annum.

iii) Share prices as measured by the FTSE index have risen by 4.71 per cent per annum in real terms.

We discuss their implications subsequently.

Bequests and transfers inter vivos

Our analysis ignores the effects of transfers between cohorts. Old people hold wealth partly with the aim of bequeathing it to young people when they die. The legatees hold onto the bequests they receive in order to leave them to their descendents. In a steady state these bequests should be expected to increase at the rate of growth. If the real rate of interest is higher than the rate of growth, then the interim holder of the legacy nevertheless receives an income from it which can be spent on consumption.

In 2003-4 the total value of legacies in the UK was 48 [pounds sterling] billion. Of this 16 billion [pounds sterling] was left by people who were married and the bulk of this can be presumed to be left to their surviving spouses rather than to much younger people. Nevertheless something over 30 billion [pounds sterling] (3 1/2 per cent of net national income or net household income) was probably transferred from old people to young people by means of legacies. The average size of an estate on which probate is granted is 161,000 [pounds sterling] for women and 187,000 [pounds sterling] for men with about half of all deaths being associated with grants of probate. There is not a great deal of variation in the average age of the estate with the age of the deceased although estates left by people aged under 45 are plainly smaller than the others. (8)

The implications of this for wealth holding can be seen from simple calculations. If half of all men aged 45 or older held an average of 187,000 [pounds sterling] to leave it to a successor and half of all women held an average 161,000 [pounds sterling] for the same reason then 2000 billion [pounds sterling] would be accounted for. If half the population aged 30 or over held these sums for bequest purposes, the total amount of wealth would still be only 3000 billion [pounds sterling]. This is, however, an overstatement of the amount of wealth held for bequest purposes since, as we have noted above, the surviving spouse may inherit the means to leave a bequest from the dying spouse. A more reasonable estimate of the wealth held for bequest purposes and recorded in the probate statistics is probably around 2000 billion [pounds sterling]. This is consistent with the estimates provided by Blinder (1988) and Davies and Shorrocks (1999) that bequests account for 35-45 per cent of total wealth.

If one accepts the consumption and income profiles as correct, the only other behavioural explanation of the high level of wealth is that, in addition to the bequests which can be observed from probate statistics, people hold wealth in order to make transfers inter vivos (9) and those through mechanisms such as trusts on which probate is not required. We do not observe these but we can infer that they would have to be roughly twice as large as legacies in order to account jointly for the wealth held by the household sector. Such a figure is larger than that found by Gale and Scholz (1994) for the United States of America from the Survey of Consumer Finances carried out there. They identify 33 per cent of household net worth as being held for transfer purposes with bequest wealth being slightly smaller. Klevmarken (2004) finds, however, that in Sweden inter vivos transfers are much smaller--possibly reflecting a greater role of the state in Sweden than in the United States.

On the whole, while it is important to mention that there is widespread agreement that intergenerational transfers account for a significant fraction of household wealth, quantitative estimates vary widely. To some extent, the dispute is definitional (Kotlikoff, 1989). On balance, however, the evidence from other countries suggests that it is unlikely that inter vivos transfers could account for much more than 2000 billion [pounds sterling] of household wealth. This points to excess wealth of 1600 billion [pounds sterling] in 2004.

Future consumption and income plans

It is, of course, possible that people currently saving do not expect to receive as much income in the future as our profiles show. Reasons for this might include that they do not expect state benefits to grow at the trend real growth rate implicit in the figures reported in tables 3 and 4. There is, of course, some justification for such a belief. In the recent discussion about UK pension arrangements, it is plain that there is substantial political resistance to the idea that the pension credit should grow in line with wages. Employees may also be concerned that their future employment income is going to be reduced as businesses cut back on contributions to pension schemes. People may also wish to consume at a higher level than our consumption profiles show or be saving up because they are concerned about the risks of high costs for care expenditure in extreme old age.

There is plainly one form of consumption need which is omitted from household-based surveys. The costs of residential care of elderly people are excluded from these surveys because those living in residential care are not living in households. This has the effect of raising the consumption of older and very old people. Saving before retirement and in retirement may in part be motivated by a desire to be able to afford the costs of long-term care. If people die without actually incurring these costs, then their savings will be translated into unanticipated bequests received, for the most part, by their descendents. To the extent that these savings are not actually needed to finance consumption, they are therefore presumably identified in the bequest data discussed above.

Measurement errors

There is the obvious possibility that the data are mis-recorded. Our profiles imply substantial saving by very old people--a phenomenon which has been widely observed. There is the possibility that they are under-recording their consumption because they fail to account for it all. We also have a concern that the estimated consumption of young people is biased upwards. We avoid some of the problems of allocating household consumption by looking at data only for households with no more than two adults present. But the consumption of young people is therefore only recorded from those who have set up their own households. These are likely to have higher incomes and therefore higher consumption than the average person in this age group. Thus the consumption profile of the young may be biased upwards.

It is also important to mention that the aggregate wealth figures include some wealth owned by non-profit making institutions such as the Church, the universities and charities. The national balance sheet puts the net value of produced capital owned by these bodies at 58 billion [pounds sterling] at the end of 2004. While they almost certainly own substantial amounts of land and financial claims it seems unlikely that they can account for very much of total household wealth.

Adjusted profiles

We carried out some experiments adjusting the consumption and income profiles using the least squares method set out in Appendix 2 so as to ensure that aggregate non-property income, consumption and wealth data were met and that people of each age held just enough wealth to finance their remaining consumption, given expectations of future income. There are in fact five constraints--the three given by the macroeconomic variables and two more--that the income and consumption profiles are consistent with zero initial wealth for both men and women. However, using a growth rate of 1.5 per cent per annum and a real rate of return of 3 per cent per annum did not result in age profiles of income, consumption or wealth which were plausible. This difficulty in accommodating the macroeconomic facts might be seen as reinforcing the view that household and therefore national wealth holdings are unusually high as a result of unanticipated capital gains rather than deliberately high as a part of the life-cycle process enhanced by bequest and transfer motives.

Implications

Our results show something of a paradox. We are unable to account for household wealth holding except with the assumption that large amounts of wealth are held for transfer or bequest purposes. Even this suggests a substantial excess holding. The alternative is that at least a part of the wealth holding has been acquired unexpectedly. If the second is the case it must be quite likely that people will respond to their wealth holdings by spending them, although there must be reasonable grounds for uncertainty as to how long this process would be expected to last. In extremis if people respond to unanticipated gains of this sort by increasing both life-time spending and bequests in proportion the impact will be more sustained but shorter in any particular period than if they decide to enjoy a splurge and then revert to something close to their previous consumption paths.

Of the three factors identified above as causes of increased wealth since 1985, (i) and (ii) do not in any sense represent real increases in wealth. They simply bring resources forward from the future to the present and are, in that sense, a transfer from future generations and those who do not yet own wealth, to current wealth holders. The main component of house prices is land prices and it is obvious that, except when land prices change as a result of changes in ways of using land, an increase in land prices cannot represent an increase in the resources available to the country. In the same way a reduction in real interest rates results in future income streams being valued more highly but does not itself lead to higher future income. The increase in share prices may be a consequence of increased opportunities for profit, but a component of it is also due to shares being re-rated and this again does not create any extra income. The amount of wealth needed to finance a given consumption profile does, of course, depend on the real rate of interest and, looking at the national savings figures of table 1, it is clear that wealth needs have risen as real rates have fallen although not by enough to account for actual holdings of wealth. However, looking at household wealth needs, the effect is small and of the opposite sign because, with our profiles, households do not need to own wealth to finance their consumption paths. (10)

Sustained but perhaps unanticipated increases in wealth like those identified above have an immediate effect on legacies. The value of any money left on death reflects the market value of assets at the time of death. To the extent that consumption and inter vivos transfers adjust only slowly after capital gains, bequests will increase more than in proportion since the wealth holdings of those dying will be temporarily high. Thus the current bequest figures, coming after a sustained period of rising wealth driven by capital gains, might be more likely to overstate than to understate steady-state holdings for bequest purposes. On the other hand it is also possible that bequest and transfer motives may themselves be functions of asset prices. If parents are concerned about their children's ability to buy housing, they may decide to leave them larger bequests or to make larger inter vivos transfers to them as house prices rise. Depending on the sensitivity of transfers and legacies to asset prices it is, of course, possible for their planned values to rise faster than have asset prices. Thus, even if wealth holders have not fully adjusted to the increase in asset prices it is possible for bequests to be sustained at or perhaps above current levels. But in the absence of major measurement errors in our profiles it also implies either i) that inter vivos transfers on a scale similar to or larger than bequests take place or ii) that consumption of wealth holders will rise above the levels shown in the profiles. Even though we do not have independent observation of the level of inter vivos transfers it seems likely that the under pinning provided by high asset prices to consumption levels in the British economy is almost certainly very substantial.

Conclusions

The United Kingdom's level of national saving is lower than is required if one assumes that each cohort should pay its own way and that expected future levels of income and consumption are related to current observed cross-sections. Wealth holdings are considerably higher than are required on the same basis but if one looks only at produced wealth the amount is not far short of what is needed. Such an outcome seems to be purely fortuitous. If one looks at household saving and household wealth instead of national saving and national wealth, the pattern of government transfers implies that on average households have no need to save for old age, with reported consumption falling short of non-property income after retirement. Thus a reasonable conclusion is that government policy, as represented by the system of taxes and transfers in place, removes the need to save for retirement.

Considerable research effort has gone into understanding the nature of precautionary responses to risk and uncertainty when households make consumption and saving decisions. (11) It would be desirable to learn more about motives for holding wealth and how these have changed over the years; certainly no more than about half, and probably less than that, of household wealth holdings can be explained by bequest motives.

Labour's achievement in reducing pensioner poverty clearly has brought with it unprecedented new challenges. The introduction of the minimum income guarantee, and its successor, the pension credit, have certainly acted as a disincentive to save. This may account for the sharp fall in household saving seen since 1997.

In policy terms it is undesirable that households should address excess holdings of wealth by spending them. The accrual of wealth that has been achieved since the mid-1980s has taken place largely through mechanisms which bring future resources to the present and therefore as a result of imposing burdens on future generations. In turn this means that a government concerned with intergenerational equity should consider policies to reverse this transfer. Methods of doing this include policies designed to depress asset prices--such as the tax on housing which the National Institute has advocated in the past--and also for the Government to run a fiscal surplus, building up holdings of assets which can be used to supply resources to future generations.

Appendix 1. Data

The variables from the Expenditure and Food Survey which we used are: From File 2004-05_dvhh_ukanon.sav

p560tpTotal Expenditure (National Accounts)

b038p Council Tax--Last Payment weekly amount (Great Britain only)

b030 Domestic Rates--last payment (N. Ireland only)

p396 Age of Household Reference Person

a062 Composition of Household (< 18 indicates 1 or 2 adults)

weightaAnnual weight

From File 2004-05_dvper_ukanon.sav and 2004-05_rawper_ukanon.sav

a004 Sex

dvage Age

p008 Normal gross wage, salary (13 week rule)

p011 Gross wage--last time paid--(13 week rule sub) subsidiary employment

p029 NI contributions paid by non- employees

p031 Social security benefits included in income calcs

p037 Income from subsidiary self-employment

p047 Income from self-employment (main)

p049 Income from pensions, annuities

p050 Income from other sources

p051 Total personal gross income (normal)

p075 NI employees contribution--current

p079 Income tax payments less refunds

The weights used are those from the household file--with each person being identified by the case number to which it belongs. The variable dvage is available on

2004-05_rawper_ukanon.sav but can be matched to the records in

2004-05_dvper_ukanon.sav in order to identify actual ages: the age variable in

2004-05_dvper_ukanon.sav has all ages over 80 set to 80.

Income from pensions and annuities comes in two forms. Civil Service pensions are unfunded and therefore a burden on current taxpayers of the same type as social security payments. The survey does not distinguish funded from unfunded pensions; we therefore split them in the same proportion as is shown in the national accounts. This results in one third of pensions being included as non-property income.

Gross labour income (12) is defined as p008+p011+(p031+p037)*2/3+employers' national insurance and pension contributions with the ratio of employers' contributions to wages and salaries derived from the national accounts for 2004.

Net non-property income is p008+p011+(p031+p037)*2/3+employers' pension contributions+p031+[gamma]p049-p075-p079-p029 with y being the share of unfunded pensions in the total and employers' contributions again being imputed from the data in the national accounts.

In the assessment of national spending and saving we use p560tp as the reference variable and deduct consumption taxes as allocated in the generational accounts. For looking at household spending and saving we add on to consumption at market prices council tax and domestic rates (b038p+b030).

All the variables are scaled so that the survey totals are consistent with the national accounts aggregates.

Appendix 2. Adjusted income/expenditure profiles

There are a number of ways in which we can construct coherent income/expenditure profiles from the data that we have--with each being appropriate to answering a different question. Here our aim is to measure the savings gap and we define this as the difference between actual saving and the amount that would be saved if each cohort were to pay its own way. Paying its own way itself has two meanings as we discussed above. One can look either at so doing on a national basis or on a household basis; in the former case if each cohort provides for itself the only resource available to it is labour income while in the latter case we need also to take account of transfers from other cohorts arising as a result of the tax and benefit system.

Some sort of adjustment to either the income or the expenditure profiles is going to be needed to ensure that each cohort pays its own way since it is very unlikely that the data themselves will satisfy the requirements of lifetime accounting balance. We put the balance of the adjustment on income. As we have noted, individual wealth is much bigger than would be the case if people wished to finance the consumption path as derived from the cross-section data with the individual income profile identified in the same way. The very low wealth holdings we have identified mean that the assumption that people expect to do no more than pay for their own consumption path, and that all wealth is annuitised in order to avoid leaving bequests, fails to account for the data.

There are two other motives for holding wealth, beyond financing consumption. One is to make transfers inter vivos to one's descendents and the other is to leave legacies. Both of these in essence are holding wealth in order to make transfers since the legacy can be thought of as a transfer paid at the end of life. We aim to identify a transfer profile which shows the amount paid or received as a function of age needed so as to ensure that the macroeconomic relationship between wealth and consumption is delivered, subject of course to the constraint that the value of transfer paid equals the value of transfers received in any year. This is most simply done making the assumption, as before, that wealth held for consumption purposes is annuitised. With any other assumption--such as that bequests are accidental--it would be necessary to establish the mean size of the transfer arising at death and to add remaining transfers to this.

With one criterion to satisfy there is obviously a large number of possible transfer profiles that would achieve this. We use a least-squares criterion to define our transfer profile. We identify, for men and women separately, the transfer profile as [[theta].sup.F.sub.it] and [[theta].sup.M.sub.it] as the transfers paid by women and men. These transfers satisfy the accounting constraint (13)

[summation][n.sup.W.sub.v-j,j][[theta].sup.W.sub.v-j,j] + [n.sup.M.sub.v-j,j][[theta].sup.M.sub.v-j,j] = 0

We also have to satisfy the accounting identities for consumption and income

[T.summation over (v=20)][n.sup.W.sub.v][c.sup.W,I.sub.v] = [n.sup.M.sub.v][c.sup.M,I.sub.v] = [C.sup.I]

[T.summation over (v=20)][n.sup.W.sub.v][y.sup.W,I.sub.v] = [n.sup.M.sub.v][y.sup.M,I.sub.v] = [Y.sup.I]

The identity representing the cumulation of wealth can be helpfully written in matrix form. The model we use is one in which terminal wealth is zero and, given the values of consumption and income, we can then work backwards to find the value of wealth held at any age.

The matrix RW shows for women the combination of survival, discount and growth factors applied to the current crosssection income/expenditure profile so as to indicate the present discounted value of that income/expenditure, making the assumption that both income and expenditure grow at the rate g. Here [s.sup.W.sub.i,j] is the probability that a woman currently of age i is alive at age j.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

with a similar matrix [R.sub.M] for men.

From these matrices, and with given cross-section income and expenditure profiles, we can calculate the amount of wealth that needs to be held as a function of age in order to finance future expenditure plans after taking account of both growth relative to the current cross-section and survival prospects. The resulting cross-section wealth profiles are then given by

[w.sup.W] = [R.sup.W]([c.sup.W] - [y.sup.F])

[w.sup.M] = [R.sup.M]([c.sup.M] - [y.sup.F])

The accounting constraint aggregate wealth should match its observed value and can be written in vector form as

[n.sup.M]' [w.sup.M] + [n.sup.w]' [w.sup.W] = W A.3

while the constraint that the initial value of wealth is zero is given by

[w.sup.M](1) = 0; A.4

[w.sup.W](1) = 0; A.5

where x(1) indicates the first row of column vector x.

Thus we have to choose new values for the consumption and income profiles subject to three accounting constraints for consumption, income and wealth (A.1-A.3) and also the additional two constraints that initial wealth is zero for both men and women (A.4 and A.5).

We set z' = [[y.sup.W]'[y.sup.M'][c.sup.W]'[c.sup.M]']' and denote by [z.sup.*] the adjusted vector of income and consumption which satisfies the five accounting constraints. We find this as the solution to the least squares problem

Min ([z.sup.*]' -z')[V.sup.-1]([z.sup.*] -z) - 1'([Az.sup.*] -c)

where V is a weighting matrix, [lambda] is a vector of Lagrange multipliers, A is the constraint matrix representing the five linear constraints A.1-A.5 and c is the vector of constraint values given by aggregate consumption, income and wealth for the year in question plus the two zeros representing initial wealth holdings of men and women.

The solution is given as

[z.sup.*] = z - VA'[(AVA').sup.-1] (Az - f)

The results are going to be sensitive to three choices, the values of g and r and the choice of the variance matrix V. The experiments we conducted assumed that the variance of the income elements was three times that of the consumption elements of z and also that there was a correlation of 0.9 between adjacent adjustments to the income and expenditure elements. The adjustments to income were assumed to be uncorrelated to those to expenditure.

REFERENCES

Blinder, A.S. (1988), 'Comments on Chapter 1 and Chapter 2', in Kessler, D. and Masson, A. (eds), Modelling the Accumulation and Distribution of Wealth, Oxford, Clarendon Press.

Browning, M. and Lusardi, A. (1996), 'Household saving: micro theories and micro facts', Journal of Economic literature, 34, pp. 1797-855.

Cardarelli, R. Sefton, J. and Kotlikoff, L.J. (2000), 'Generational accounting in the UK', Economic Journal, 110, 467, pp 547-74.

Davies, J.B. and Shorrocks, A.F. (1999), 'The distribution of wealth', in Atkinson, A.B. and Bourguignon, F. (eds), Handbook of Income Distribution Vol 1, Amsterdam, Elsevier-North Holland.

Deaton, A. (1997), The Analysis of Household Surveys. A Micro-economic Approach to Development Policy, Johns Hopkins University Press.

Department of Work and Pensions (2006), 'Security in retirement: towards a new pensions system', http://www.dwp.gov.uk/ pensionsreform/pdfs/white_papercomplete.pdf

Disney, R. (2006), 'Household saving rates and the design of public pension programmes: cross-country evidence', National Institute Economic Review, 198, October.

Feldstein, M. (1974), 'Social security, induced retirement and aggregate capital accumulation', Journal of Political Economy, 82, pp. 905-26.

Gale, W.G. and Scholz, J.K. (1994), 'Intergenerational transfers and the accumulation of wealth', Journal of Economic Perspectives, 8, pp. 145-60.

Gokhale, J., Kotlikoff, L.J. and Sabelhaus, J. (1996), 'Understanding the postwar decline in US saving: a cohort analysis', Brookings Papers On Economic Activity, 1, Washington D.C., pp. 315-90.

Kirsanova, T. and Sefton, J.A. (2006), 'A comparison of national savings rates in the UK, US and Italy', European Economic Review (forthcoming).

Kotlikoff, L.J. (1989), 'Intergenerational transfers and savings', Journal of Economic Perspectives, 2, 2, pp. 41-58.

Klevemarken, N.A. (2004), 'On the wealth dynamics of Swedish families: 1984-1998', Review of Income and Wealth, Series 50, pp. 469-92.

Pensions Commission (2005), Implementing an Integrated Package of Pension Reforms, http://www.pensionscommission.org.uk/ publications/2006/final-report/final_report.pdf

Pomerantz, O. and Weale, M.R. (2005), 'Are we saving enough? The macroeconomics of the savings gap', National Institute Economic Review, 191, January, pp. 79-93.

Sefton, J.A. and Weale, M.R. (1995), Reconciliation of National Income and Expenditure, Cambridge, Cambridge University Press.

Solomou, S. and Weale, M.R. (1997), 'Personal sector wealth in the United Kingdom', Review of Income and Wealth, Series 43, pp. 297-318.

Weil, P. (1993), 'Precautionary saving and the permanent income hypothesis', Review of Economic Studies, 60, 2, pp. 367-83.

Yaari, M.E. (1965), 'Uncertain lifetime, life insurance and the theory of the consumer', Review of Economic Studies, 32, 2, pp. 137-50.

NOTES

(1) We are grateful to James Sefton for providing these profiles.

(2) Family units were formerly referred to as benefit units.

(3) Using the same interest and growth rates as in the subsequent savings calculations.

(4) The General Household Survey is able to distinguish family units from households because, unlike the Expenditure and Food Survey, it does not attempt to measure consumption.

(5) http://www.gad.gov.uk/Life_Tables/eoltable.htm

(6) An important factor behind this result is that income from social security benefits identified in the national accounts is nearly 40 per cent higher than that reported in the Expenditure and Food Survey. We have scaled all variables to be consistent with national accounting totals.

(7) The data are taken from Sefton and Weale (1995), Solomou and Weale (1997) and the 1987 Blue Book as well as the current National Accounts data base.

(8) See http://www.hmrc.gov.uk/stats/inheritance_tax/menu.htm

(9) We are grateful to James Sefton for stressing to us the importance of this.

(10) This also has the implication that changes in life expectancy have little impact on required household wealth holding.

(11) See Browning and Lusardi (1996) for a comprehensive survey of the theory and facts concerning saving. Weil (1993) provides an important earlier exposition of the precautionary motive.

(12) We have included 2/3 of self-employment income, assuming that the remaining 1/3 accounts for deprecation and the net return to capital.

(13) It should be noted that this constraint is specific to the age structure of the population in our reference year, j. With different population structures either the profile of payments or the profile of receipts has to change. Thus this profile cannot be completely stable over time. We do not explore the implications of the movement in the profile which is necessary to maintain the accounting constraint over time.

Ehsan Khoman and Martin Weale*

* National Institute of Economic and Social Research. e-mail: e.khoman@niesr.ac.uk or m.weale@niesr.ac.uk.
Table 1. The required national savings rate (net saving/
net national income)

 Per capita growth rate

Real interest rate 0.5% p.a. 1% p.a. 1.5% p.a. 2% p.a.

4% p.a. 8.60% 10.70% 13.20% 16.00%
6% p.a. 6.50% 8.00% 9.60% 11.50%

Table 2. The ratio of wealth to labour income

 Per capita growth rate

Real interest rate 0.5% p.a. 1% p.a. 1.5% p.a. 2% p.a.

4% p.a. 3.42 3.73 4.05 4.39
6% p.a. 2.33 2.75 2.83 3.10

Table 3. The required household savings rate (net
household saving/net private sector income)

 Per capita growth rate

Real interest rate 0.5% p.a. 1% p.a. 1.5% p.a. 2% p.a.

3% p.a. -0.06% -0.10% -0.13% -0.13%
4.5% p.a. -0.09% -0.15% -0.20% -0.23%

Table 4. The ratio of household wealth to household
non-property income

 Per capita growth rate

Real interest rate 0.5% p.a. 1% p.a. 1.5% p.a. 2% p.a.

3% p.a. -0.14 -0.12 -0.1 -0.08
4.5% p.a. -0.2 -0.18 -0.16 -0.15
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Date:Oct 1, 2006
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